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Journal of Nonlinear Optical Physics & MaterialsVol. 9, No. 3 (2000) 365–411c©World Scientific Publishing Company
NONLINEAR OPTICAL RESPONSE OF CYANOBIPHENYL
LIQUID CRYSTALS TO HIGH-POWER,
NANOSECOND LASER RADIATION
SVETLANA G. LUKISHOVA
Liquid Crystal Institute, Kent State University, Kent, OH, 44242, USAAlso Institute of Radioengineering and Electronics of the Russian Academy of Sciences,
11 Mokhovaya, 103907, Moscow, RussiaPresent address: IRE-SL, 172 Works Rd., Honeoye Falls, NY 14472, USA
Received 7 June 2000
Results from investigations are summarized into: (1) transient refractive and absorptive(two-photon) nonlinearities at 0.532 µm by the Z-scan method, and (2) reflective non-linearity in the near-IR, of linearly nonabsorbing cyanobiphenyl liquid crystals undernanosecond laser irradiation.(1) For isotropic liquid crystals at the several-nanosecond time scale and severaltens-micrometers beam-waist-diameter, transient molecular-reorientation and ther-mal/density refractive nonlinearities compete in changing the sign of the total transientrefractive nonlinearity. For the different, given pulse durations, the influence of cou-pled thermal and density effects on nonlinear refraction depends, through buildup time,on the beam-waist diameter. Nonlinear absorption coefficients depend on the incidentintensity. For planar nematic layers, cumulative effects in heating (and in refractivenonlinearity) were observed even at low, 2–10 Hz pulse repetition rate. These results areuseful for optical power limiting applications, and for intensity and beam-quality sensorsof pulsed, high-power lasers.(2) Reflective nonlinearity of chiral-nematic (cholesteric) mirrors near selective reflec-tion conditions for circular polarized light at λ = 1.064 µm was studied both under freespace irradiation and inside a laser resonator. Specially chosen experimental irradiation
conditions make it possible to attribute the observed changing of reflectivity to athermalhelix unwinding by the optical field. The results can find applications in laser-resonatormirrors, Q-switches and soft apertures for beam-profile formation, and also in showingthe limits of use cholesteric optical elements in high-power laser beams.
1. Introduction
Liquid crystals (LC)1,2 have become essential in display technology.3 Much less
well known is the use of LCs in, and the potential for improvement of, coherent
optical devices, such as lasers. For example, linear optical and electrooptical laser
elements4–8 made of LCs (mirrors, filters, retardation plates, modulators (light
valves)) are successfully used for more than 20 years. Discovery in 1980 of a giant
refractive optical nonlinearity 9,10 in LCs and its athermal, ten- to hundredfold
365
366 S. G. Lukishova
enhancement by dissolving a small amount (∼ 0.1%) of dye (chromophore) in the
LC-fluid,11 prompted further studies of the nonlinear optical response in these
materials, see, e.g. Refs. 4, 10 and 12–20. It is safe to say that, to date, no nonlinear
optical LC devices, in particular of χ(3) type, have progressed past the prototype
stage. In no small measure, this is caused by the uncertainties in values, i.e. lack of
reliable values, of nonlinear hyperpolarizabilities found in the literature.
The key characteristics of liquid crystals as a fluid material are the long-range
correlation between anisotropic molecules and the cooperative nature of their inter-
action with different, external fields.1–3 Figure 1 shows schematically the molecular
order of the so-called nematic (a) and isotropic (b) phases of LCs made of “rod-
like” molecules. The nematic phase with largely unidirectionally aligned molecules,
director (see arrows in Fig. 1), exists only within a restricted temperature interval
below the nematic/isotropic-liquid phase transition. While in this phase, the long
axis of the LC molecules can be uniformly aligned both perpendicular (homeotropic)
and/or parallel (planar, see Fig. 1(c)) to the fluid container’s walls, by special sur-
face treatment. Alignment is readily achieved in thin (less than∼ 200 µm thickness)
fluid layers.
(a) (b) (c)
Fig. 1. Nematic LC (a); isotropic LC (b); planar-aligned layer of nematic LC (c).
The attractiveness of LCs as a material includes their relatively low cost, ease
of use, including the possibility of filling various volumes (e.g. optical fibers21 and
porous glasses22), their very low absorption over a wide spectral interval including
the visible and IR,13 high damage threshold to laser radiation,4,5 and large electro-
optical and thermooptical coefficients.12,13 Molecular design provides wide latitude
in modifying structure/propertie relations. At least 80 000 LCs are now synthe-
sized. The present paper considers only simple model systems, cyanobiphenyl LCs3
(widely used in display technology), with a stable room-temperature nematic phase.
In addition to nematic phases, there exists the possibility to create spatially peri-
odic structures (chiral nematic, smectic phases).1–3 Furthermore LCs may serve as
solvent for different chromophores11 and/or dispersed as micrometer-size particles
in a polymeric matrix,23 adding to the variability of properties of possible liquid
crystalline devices.
The purpose of this paper is to update the reader on reliable values for LCs
nonlinear-optical materials parameters for several-nanosecond pulse duration. This
is a timely issue as comparing reported values is fraught by a multitude of potential
pitfalls that were not considered yet in the literature (to my knowledge). For in-
stance, the irradiation geometry and various time constants play a momentous role
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 367
in what value, and even sign, the transient nonlinear parameters may take. The
consideration of these problems will be useful for constructing liquid-crystalline
nonlinear optical devices, e.g. optical power limiters8 (using both pure and chro-
mophore-doped LCs12,13) and/or intensity and laser beam quality meters,24 for very
often used commercial green-irradiation Nd:YAG lasers, with several nanosecond
pulse duration and 2–10-Hz pulse repetition rate. As to the switching application,
an athermal reflective nonlinearity in chiral nematic mirrors will be considered in
connection with spatial and temporal profile formation of laser radiation.
The structure of this paper is as follows. In the present section, Sec. 1 (Intro-
duction), a short review of two principal mechanisms of refractive nonlinearities
in nematic LCs (orientational (Sec. 1.1) and/or thermal and density (Sec. 1.2))
is presented next for both the oriented-nematic and isotropic case. In Sec. 1.1,
the electronic refractive nonlinearity will be introduced, characterized much smaller
value for these materials. Mechanisms of nonlinear absorption will be reviewed in
Sec. 1.3. Reflective nonlinearity of chiral nematic mixtures based on helix unwind-
ing will be reported in Sec. 1.4. Section 1.5 contains short preview of problems
considered in present paper. Section 2 describes characterization of materials and
LC-cell fabrication (Sec. 2.1 — nematic and isotropic cells, Sec. 2.2 — chiral ne-
matic (cholesteric) mirrors). Section 3 presents two frequently used experimental
set ups (Z-scan (Sec. 3.1) and for measurements of reflective nonlinearity (Sec. 3.2)).
Section 3.1.1 describes determining the absorptive and refractive nonlinearities from
Z-scan data. The experimental results of author’s Z-scan measurements of transient
nonlinear refraction and nonlinear absorption of cyanobiphenyl LCs under several
nanosecond, 0.532-µm laser irradiation will be considered in Sec. 4 for isotropic LC
layers and in Sec. 5 for planar nematic layers. In Sec. 6, various transverse effects
in laser beam will be presented including cumulative spatial self-phase modulation
elliptical ring formation (Sec. 6.1), “dark” spot formation, asymmetric scattering
and cross-structure formation (Sec. 6.2). Numerical modeling of heat diffusion will
be discussed in Sec. 7. Section 8 contains experimental results on athermal reflective
nonlinearity of cholesteric liquid crystal mirrors under selective-reflection conditions
for free space irradiation (Sec. 8.1) and inside laser resonator (Sec. 8.2). Section 9
concludes the paper and provides an outlook for further possible experiments.
1.1. Orientational Refractive Nonlinearity
This section deals with the difference between molecular orientation in an optical
field (and its contribution to the nonlinear refraction) of LCs,25,26 and of ordinary
organic liquids with dipole molecules which also possess strong orientational non-
linearity, e.g. CS2.
As in ordinary organic liquids, individual (or pseudoindividual) molecular re-
sponse (nuclear reorientation) in LCs has been detected in the picosecond range.27,28
The peculiarity of a liquid crystalline material is the collective and correlated molec-
ular reorientation in the optical field (the so-called optically induced Freedericksz
368 S. G. Lukishova
transition). It is much slower than individual molecular response but contributes
enormously stronger to the nonlinear susceptibility χ(3)(−ω, ω, ω,−ω) and nonlinear
refractive index n2 (see Sec. 3.1.1) than optically driven reorientation by individual
molecules. The giant optical nonlinearity9,10 observed in nematic layers for CW-
laser-operation has nine orders of magnitude higher χ(3)(−ω, ω, ω,−ω) and n2 than
CS2 (n2(CS2) = 1.2.10−11 esu29), but its response time is slow (submilliseconds to
seconds).17
1.1.1. Nematic Layers
Once experimental progress permitted, it was realized that for intense fields,
fast collective and correlated orientational response of nematic molecules is
possible16,17,30,31 even for nanosecond irradiation. The buildup time and the mag-
nitude of the refractive nonlinearity are determined by the incident intensity.30 For
instance, for 6-ns excitation, the orientational-relaxation time of aligned nematic
5CB was observed to be of the order ≤ 1–100-µs.30 In a separate work,31 20-ns
pulses were shown to trigger formation of elliptical diffraction rings (similar to the
CW-optical-Freedericksz-transition9,10,32,33) as the result of orientational spatial
self-phase modulation.
For picosecond irradiation of oriented nematics the collective orientational effects
are weaker. Z-scan measurements for 0.532-µm, 33-ps pulse duration, yield values
for 5CB LC34 of n2par = 0.87n2(CS2) and n2perp = 0.58n2(CS2).
At high laser intensities the nonlinear response to picosecond and nanosecond
laser irradiation can be accompanied by intense hydrodynamic flow which cou-
ples to the reorientational process, the so-called flow-reorientational (alignment)
effects.35,36 This effect is not driven by density or temperature modulations but by
photoelastic stresses.
1.1.2. Isotropic LCs
Isotropic LCs are very attractive because of their excellent transparency even for
beam paths as long as tens of cm, opening an opportunity for use as nonlinear
materials in fibers.21 (Nematic LCs do not scatter light and are transparent only
in oriented layers). First experiments on short-pulse laser irradiation of isotropic
LCs have been reported in the early 1970–80s in connection with the optical Kerr-
effect and steady-state and transient self-focusing studies in organic liquids.37–42
The peculiarity of isotropic LCs (in difference with ordinary organic liquids) is
that its response time can be varied by temperature over a wide range, because its
temperature dependence scales as (T − Tc)−1, where Tc is the nematic/isotropic
phase transition temperature.18,37–44
For isotropic LCs, the value of steady-state n2 was measured to be more than
∼ 100 times in excess of CS2 with a dependence on the temperature buildup time
tbup of the order of several tens to hundreds of nanoseconds.18,37–44 For 6–9-ns pulse
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 369
duration, the orientational nonlinear refraction of isotropic LCs is transient41 and
transient n2 is expected to have a smaller value than the steady-state n2.18,37–44 It is
very important to note that the value of steady-state n2 depends on the temperature
as (T − Tc)−1 as does the response time, but the transient value of n2 is nearly
independent of the temperature.41 As an example, the transient values for MBBA
were reported to be of one order of magnitude larger than that of CS2.38,39
For picosecond irradiation of isotropic LCs, values of n2 range from 0.05 to
0.13 n2(CS2) for 1.064-µm, 30-ps pulse duration, for both Schiff base and ester
compounds.45
1.1.3. Electronic Nonlinearity
By comparison with the above mentioned orientational effects, electronic contribu-
tions to n2 that are fast (10−15s) for well-known LCs can be considered negligible.
Experimental value of electronic χ(3) (CARS) were found to be only ∼ 5 times
higher than that for glass (χ(3)(glass) ∼ 10−2 χ(3)(CS2)), for MBBA LC (both in
the nematic and isotropic state).46,47 Measurements of electronic contribution of
naphthyl core compounds6,48 both in the ordered and isotropic state (nearly degen-
erate four-wave mixing) at 1.053 µm showed values of χ(3) ∼ (0.1− 0.8) χ(3) (CS2).
These small electronic contributions are not straightforward to explain, especially as
similar conjugated structures of some polymers49 have thousand times higher value
of electronic n2. There is an opinion,50 that molecules with high hyperpolarizabil-
ities do not possess LC phases or have LC-phase in very narrow and unpractical
temperature region.
1.2. Thermal and Density Refractive Nonlinearity
As in any absorbing medium, thermal mechanism causes refractive nonlinearity
in nematic and isotropic LCs. Thermal nonlinearity coupled with density
changes12,13,21,36 competes with the orientational nonlinearity in changing the sign
of the total refractive nonlinearity. Another mechanism of density changes,
electrostriction,51 with buildup time in the nanosecond range, is comparable with
thermal/density contributions if the medium’s absorption coefficients are low. As
will be seen later (Sec. 1.3), at 0.532 µm a strong heating mechanism exists for the
LC model compounds considered here. That is why electrostriction is neglected
from now on.
Refractive index changes by heating are the sum of two contributions:
∆n = (∂n/∂ρ)T∆ρ+ (∂n/∂T )ρ∆T , (1)
where ρ is the density, T is the temperature. It is very important in the current
context that each term in (1) has its own characteristic turn-on time, and will
contribute differently under transient and steady-state regimes.52,53
370 S. G. Lukishova
1.2.1. Thermal-Density Nonlinearity
For several nanosecond pulse duration and several tens of micrometers beam waist,
the buildup time tac of the thermal-density-nonlinearity (∆n = (∂n/∂ρ)T∆ρ) can
be close to the laser pulse duration to.
tac = ro/Vs , (2)
where ro is the beam radius and Vs is the velocity of sound (Vs (LCs) ∼ 1500 m/s).
For tac > to the thermal-density-nonlinearity will not develop during the pulse.
Experimental values of n2 for this transient regime were reported in Ref. 52 for
absorbing organic liquid. It was found experimentally, that the transient absolute
value of n2 for to = 5 ns diminishes with ro increasing from 9 to 32-µm.
Acoustic-grating generation in LCs have been intensively studied both under
subpico-, pico- and nanosecond excitations.12,13,17,27,54
1.2.2. Thermooptical Effects
The thermooptic coefficient dn/dT in nematics is extraordinarily large, ranking
among the largest of all known materials.16 Not unexpected for these highly aniso-
tropic molecules, it depends on the orientation of the molecules. E.g., dnpar/dT ∼−2.5 · 10−3grad−1 for 5CB in the temperature interval 26–31◦C for incident polar-
ization parallel to the molecular orientation direction.55 For “perpendicular” po-
larization, dnperp/dT is of opposite sign and equals ∼ −1/2dnpar/dT .16 In the
proximity of the phase transition to the isotropic state, the slope of both dnpar/dT
and dnperp/dT steepens.55
For nematic LCs it was well-known that the thermooptical effect experiences
a lengthening of its buildup time (tens–hundreds of nanoseconds), rendering it in-
significant on a several-nanosecond time scale.12,13,36,56 Similar buildup times are
reported in Ref. 52 for absorbing organic fluid. Thermooptical effects for ro = 32 µm
were found to be more significant for pulses longer than ∼ 100 ns.52
Because of the slow buildup time, thermooptical (thermal-lens) spatial self-
phase-modulation rings in beam cross-section were observed only for CW laser
radiation.57–59 LC heating was in this case due to absorbing coatings on cell glass-
substrates, dissolving absorbing dyes in LCs and/or irradiation by high-average
power (∼ 1 W for 100-µm spot-size57) beams.
For pulsed lasers there exist, to my knowledge, no reports on thermal spatial self-
phase modulation rings, even at repetition rate regimes, although in Ref. 60 cumu-
lative effects (thermal memory) at repetition rate higher than 5 Hz for nanosecond
irradiation of planar-aligned nematic LC layers are mentioned.
Also important for the current paper is the thermal diffusion-relaxation time14
τdif ∼ D−1(1/r2o + π2/L2
o)−1 , (3)
where D is the thermal diffusion coefficient, Lo is the thickness of the cell. Coeffi-
cient D of nematic LCs is anisotropic. Typical τdif ∼ 10−2 − 10−6s14 for nematics
layers.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 371
1.3. Nonlinear Absorption Mechanisms and
Laser-induced Damage
Heating of cyanobiphenyl LCs by short-pulse laser radiation in the visible range
that drives photoacoustical and thermooptical effects, is caused by two-photon
absorption,27,61 concurrent or subsequent excited-state absorption,17,27,54 and
the efficient decay of the excited states through radiationless-recombination
channels.17,27 Strong nonlinear absorption was observed in optical power limiting
studies of LCs12,13,20,45,62–65 and Z-scan measurements.34,66–70
Linear absorption coefficients α of cyanobiphenyl LCs are incapable, however,
to produce heating effects at low incident average powers. Table 1 lists data13,71
for linear absorption coefficients α for 5CB and E7 (see Sec. 2).
Table 1. Linear absorption coefficients (α) of 5CB and E7.
Liquid crystal λ = 0.532 µm λ = 1.064 µm
5CB α ∼ 0.02 cm−1,13 α ∼ 0.04 cm−1 71 α ∼ 0.08 cm−1 13,71
E7 α ∼ 0.05 cm−1 13 —
1.3.1. Nonlinear Absorption Coefficients of Nematic and Isotropic LCs
For the nematic phase, the two-photon absorption coefficient has a several-times-
higher value for incident polarization parallel to the molecular dipole direction than
for perpendicular polarization.61 Already first experiments on optical power lim-
iting, acoustic grating generation and Z-scan measurements in LCs provided the
experimental evidence for two-photon absorption dichroism.34,54,63
Absolute values of nonlinear absorption coefficient β at several nanosecond pulse
duration are found to be one–two orders of magnitude higher than under several
tens of picosecond irradiation (see Table 2).17,20,34,54,65–70,72,73 In explanation of
such a difference, there is some speculation in the literature about excited state
absorption that strongly contributes to nonlinear absorption under nanosecond ir-
radiation, and especially long-living-triplet-state absorption that can be significant
over nanosecond time spans. The correct answer is not clear yet, in my view. Spec-
troscopic investigations of diluted solutions of cyanobiphenyl LCs74–76 show that
at 0.532-µm triplet absorption is much weaker than singlet observed, though, for
several-tens of picoseconds excitation.
1.3.2. Laser-induced Damage of LCs
Laser-damage issues are brought up here for two reasons, one obvious and one
potentially biasing measurements discussed so far. Laser damage obviously limits
LC devices’ useful power range and useful life. More important, in liquid crys-
tals it may start out as a transient effect prior to becoming a permanent material
372 S. G. Lukishova
Table 2. Nonlinear absorption coefficients (β) of liquid crystals at λ = 0.532 µm.
LC material Layer Layer β Pulse I Refer.
geometry thickness cm/GW duration GW/cm2
Nanosecondresults
5CB Planar, paral. 25 µm 180–650 7 ns 0.45–1.1 34
5CB Planar, paral. 25 µm 182 6.1 ns 1.17 69
5CB Planar, perp. 25, 120 µm 36 6.5–7 ns — 34, 67
5CB Isotropic 25, 120 µm 114 7 ns — 34
CB15 Isotropic 25, 120 µm 38 7 ns — 34
5CB Isotropic 1–2 mm 7–20 7 ns 0.3–0.9 present
5CB Isotropic 105 µm 89 7 ns 0.8 present
5CB Planar, paral. 105 µm 126 7 ns 0.36 present
CB15 Isotropic 1–2 mm 4.5–30 7 ns 0.2–0.9 139, pres.
CB15 Isotropic 25 µm 138 7 ns 0.75 present
ILC (mixture
of ester Isotropic 5 mm 60 20 ns 0.07–0.7 73
LCs)
Picosecond
results
5CB Planar, paral. 40 µm 0.3+0.5 I 28 ps 4–15 68
5CB Planar, paral. 120 µm 2.26 33 ps 8.33 34, 67
5CB Planar, perp. 120 µm 0.78 33 ps 23.3 34, 67
Schiff base
and ester Isotropic 5 mm 0.6 30–67 ps 1–25 45, 62
LCs
Cyanobi- Isotropic 2 mm 0.2–0.23 1.5 ps, 33 65
phenyl LCs 0.587 µm
ILC Isotropic 5 mm 2.3 66 ps 4–80 72, 73
modification. In this transient form, i.e. as a microscopic bubble77,78 that within
fractions of a second may redissolve back into the bulk, it may constitute one possi-
ble reason for the high nonlinear absorption coefficients measured under nanosecond
irradiation. In such experiments higher fluences (J/cm2) per pulse were used than
under picosecond irradiation. Bubbles scatter incident light77 and disappear on a
much longer time scale than nanoseconds. In Ref. 78 the importance was shown of
purifying “as received” LCs through filtration to remove condensation centers for
bubble formation on the surface of the LC cell under the irradiation by power laser
radiation even in the picosecond time span.
It should be pointed out that high-power laser applications of LCs are not the
principal sector among all LC applications. Commercial vendors of LCs are there-
fore unlikely to provide materials optimized for high-power-laser use. That is why
two types of possible contributors to laser damage of LC materials must be avoided.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 373
They are undissolved extrinsic impurities79 that can be removed using particle
filters and intrinsic impurities (dissolved gaseous components that can be removed
by degassing as well as synthesis byproducts or catalyst traces that can be removed
by chromatography).
Although laser-induced damage in LCs was intensively studied in connection
with optical elements for high-power, thermonuclear-scale lasers,4,5 there exist few
attempts to characterize the damage in the presence of two-photon absorption. I
will describe here the main results of laser damage studies in LCs that seem useful
in the current context.
In Refs. 4 and 5 it was shown that after purification of the “as received” LC
samples the laser-damage threshold for massive material modification (visible burst
of stable bubbles and glass chips in the cell surface and/or a web of scatter lines)
improved sharply. For purified (using 0.2-µm particle filter) and degassed, isotropic
5CB, thresholds for permanent photolysis of ∼ 9.6 J/cm2 and ∼ 4.4 J/cm2 were ob-
served under single and multiple shots respectively (1 ns pulse duration, 1-mm beam
diameter, λ = 1.053 µm). Under similar conditions, transient-bubble “damage” ob-
servable only under 110× darkfield magnification in “as received” LCs occurred
at ∼ 0.76 J/cm2 for isotropic 5CB and ∼ 0.89 J/cm2 for isotropic E7 (single shot
threshold).80
In the presence of two-photon absorption (λ = 0.532 µm) laser-induced damage
for isotropic, “as received” LC was studied at much longer, 20-ns pulse duration.12,13
Damage was characterized as appearance of visible bubbles. The “so-called” damage
threshold strongly increased from ∼ 5 J/cm2 to 80 J/cm2 with diminishing beam
diameter from ∼ 200 µm to 28 µm, a typical indicator for the presence of extrinsic,
localized factors in the material.
More detailed studies of other liquids (mostly water) were reported, e.g. in
Refs. 81–83. For organic liquids79 it was shown that under high-temperature py-
rolysis, caused by the optical breakdown and the following recombination of its
products, free carbon in soot form83,84 can be generated. UV-laser photolysis of
liquid aromatic compounds for production of graphite and polymeric carbon was
reported.85 In the case of LCs, carbon particles can also be created by the spikes
in energy that sporadically take place in short-pulse commercial lasers. These car-
bon particles may accumulate in the LC fluid over many shots and cause damage
to it.
1.4. Nonlinear Reflection of Thin Layers of Chiral Nematics
Near Selective Reflection Conditions
This section will deal with nonlinear optical properties of planar nematic LC layers
with chiral additive in the nematic fluid that posses the so-called selective reflec-
tion. The phenomenon will be discussed of nonlinear changing of reflectivity of
such chiral LC-mirrors by light-field only, both theoretical prediction and some ex-
periments including its application in self-adaptive switching laser-resonator-device.
374 S. G. Lukishova
The experiments were carried out at λ = 1.064 µm with no linear and nonlinear
absorption of the liquid crystalline material.
1.4.1. Helicoidal Structure of Chiral Nematic (Cholesteric) LCs and
Selective Reflection of Light
One of the most important properties of LCs containing chiral molecules (molecules
having structures such that mirror images are not superposable, like right and left
human hands) is a tendency to develop helicoidal structures.86 This chiral nematic
(cholesteric) LC helical structure leads to the important optical property of selective
(Bragg-like) reflection1,87,88 in wavelength and circular polarization. One full 360◦
rotation of the molecular layers is defined as one pitch length, Po, see Fig. 2. The
selective reflection wavelength λo = Ponav,1,87 where the average refractive index
of cholesteric LC, nav = (npar +nperp)/2. Pitch length can be adjusted for selective
reflection in visible and IR region using the proper concentration of chiral additive
in a nematic mixture. For a given mixture composition, it may be also controlled
by temperature or an external fields. Cholesteric mirrors with planar-aligned LC
layer (Fig. 2) were used in lasers since 1978.89–93 Their conventional operational
mechanism as other cholesteric-liquid-crystal optical elements (e.g. circular polariz-
ers, notch filters, soft (apodized) apertures) is based on linear propagation of light
through the medium.4,5,7,8,94,95
Half of pitch
Circular polarized laser radiation
Glass substrates
LC
Spacers
Fig. 2. Schematics of cholesteric LC mirror.
1.4.2. Nonlinear Selective Reflection
The effect of helix-pitch changes induced by an elliptically polarized, intense light
wave was predicted theoretically in 1982.96,97 In Ref. 96, it was calculated in detail
how this effect would manifest itself. At a threshold intensity of ∼ 106 W/cm2,
a drop in selective reflection coefficient would set in, leading to bistability in the
reflected beam. Such a bistability and helix-pitch dilation are different from ther-
mal effects caused by dye-photoabsorption in the cholesteric-LC-solvent. Thermal
nonlinearities in dye-doped cholesteric LC-layers have been investigated by many
authors, e.g. Refs. 98–101, but are of no interest here.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 375
1.4.3. Experimental Results on Athermal Changing the Cholesteric Pitch
by the Light Field only
The challenge in observing helix pitch dilation and its unwinding by optical fields
arises from the larger than E ∼ 104 V/cm electric-field strength requirement on the
optical wave that needs to act on the cholesteric LC for time periods commensurate
with the characteristic unwinding time of the helix th ∼ several milliseconds. There-
fore, neither short-pulse intensities exceeding by nearly an order of magnitude those
estimated needed102 nor rather lower intensities applied CW in Refs. 103–106, suc-
ceeded in triggering nonlinear changes in the reflection coefficient of nonabsorbing
cholesteric LCs.
The first successful experiments revealing small pitch dilation (without signifi-
cant drop in cholesteric LC reflectivity) were carried out in 1990. The pitch change
revealed itself in the form of retro-self-focusing and pinholing (soft aperture) of cir-
cularly polarized, CW, Gaussian beams reflected by the cholesteric LC output cou-
pler of a Nd:YAG laser.103–106 Change in coupler “curvature” allowed the resonator
to operate stably in TEM00 mode without intracavity aperture. The authors ex-
plained their results with an intensity-dependent helix pitch dilation in a spatially
non-uniform Gaussian beam, that caused phase shifts in the reflection along the
beam radius.106
The first athermal drop in cholesteric LC reflectivity in response to strong, circu-
larly polarized laser radiation was simultaneously observed by my group107–111 and
authors of Refs. 112–113. In my group, this effect was ascertained in four cholesteric
LC mirrors with different substrate-surface-treatment methods for planar-alignment
of LC-molecules. A special laser operational mode was used that assured several
short pulses (∼ 100 ns) with E ∼ 2.2–7 times threshold value to act on the medium
over the time interval th (∼ms). A 4.5 kHz pulse repetition rate laser mode was
used to accumulate pitch changes from pulse to pulse up to and including helix
unwinding. Pitch-dilation-induced reflectivity drop was detected both under free-
space-propagation conditions of the driving field as well as inside resonators in which
the cholesteric LC acted as end mirror. Inside the laser resonator, the reflectivity
drop of the cholesteric LC terminated lasing action in pulsed mode. Lasing recov-
ered again when the laser mode was switched to CW-operation (low peak power
density). The observed effect was independent of the average power density and,
in the presumed absence of two-photon absorption (λ = 1.064 µm), this made it
possible to attribute it to an athermal increase in the cholesteric LC pitch in the
optical wave field. Further details of these experiments will be considered in Secs. 2
and 8.
The authors of Refs. 112 and 113 used the property of nematic LCs to achieve
faster orientational response time to high-intensity beams (see Sec. 1.1). At incident,
single-pulse (in difference with my experiments with high-repetition rate pulses)
intensities of ∼ 100 MW/cm2, the cholesteric-LC-mirror reflectivity dropped from
90 to 25% even for single, nanosecond pulses. A cholesteric LC mirror has been
376 S. G. Lukishova
further used in an electrooptically Q-switched laser in place of the conventionally
used combination of dielectric mirror plus polarizer. Pulses of 10-ns duration with
peak intensities up to 1 GW/cm2 have been obtained. It was also shown that the
light-induced reflectivity drop leads to passive cavity-dumping and an improved
transverse beam profile.
1.5. Preview of Present Paper
The results of several sets of measurements of nonlinear refraction, absorption, and
reflection of cyanobiphenyl LCs with different cell thickness and various orienta-
tional order (isotropic, nematic, chiral nematic) will be considered in this paper.
1.5.1. Nonlinear Refraction Measurements at λ = 0.532 µm
• Several-nanosecond time-scale, the Z-scan measurements of transient value of
n2 of isotropic 5CB and CB15 LCs with beam-waist diameter 35–50 µm show
positive value of n2, 2.5–3.7 times in excess of n2(CS2), in difference with
7-µm-diameter measurements of Refs. 34 and 66 where negative-sign values were
reported for isotropic 5CB. This difference is explained by dependence of the value
of transient thermal-density nonlinearity with negative sign on beam-waist diam-
eter (see Sec. 1.2). For 7-µm diameter, tac is less than pulse duration time and
nonlinear refraction as a result of density changes prevails under the positive-sign,
transient, orientational nonlinearity.
• It will be shown that cumulative effects in thermal refractive nonlinearity are
important for planar-aligned nematic LCs even for low, 2–10-Hz pulse-repetition-
rate irradiation which is commonly used in many commercial lasers. As a result,
the response of either an LC optical-power-limiting device or of a Z-scan sample
will differ between the first irradiation and after several seconds of irradiation.
These cumulative effects are also the origin for the spatial self-phase-modulation
transverse effects characterized by a slow buildup time. Z-scan measurements
show dependence of the value of nonlinear refraction on the incident intensity,
e.g. at I = 0.36 GW/cm2, n2 (5CB) ≈ −20n2(CS2). Numerical modeling of
the heat diffusion at 10-Hz pulse-repetition-rate confirms sufficient cumulative
heating of LCs by several degree K at the center of a Gaussian beam. Such local
heating is a plausible mechanism for the observed spatial self-phase modulation
rings.
1.5.2. Nonlinear Absorption Measurements at λ = 0.532 µm
• Z-scan measurements of nonlinear absorption under several nanosecond irra-
diation of 1–2-mm layer-thickness, isotropic 5CB and CB15 show an order of
magnitude smaller values in comparison with thin (25–125-µm thickness) layers.
This layer-thickness dependence points toward a key role surfaces (and possible
“damage” of LC-material near the surface (see Sec. 1.3)) play in measurements.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 377
• Measured magnitudes of nonlinear absorption coefficient β depend on the incident
intensity, e.g. β ∼ 4.5–30 cm/GW at I ∼ 0.2–0.9 GW/cm2 for isotropic 5CB and
CB15. That is a more than an order of magnitude higher value than for picosecond
measurements (see Table 2 and Sec. 1.3).
1.5.3. Nonlinear Selective Reflection at λ = 1.064 µm
More detailed results than in Sec. 1.4 will be presented on characterization and
experiments with four cholesteric LC mirrors for laser resonators. Laser irradiation
conditions will be considered for changing the transmission of these mirrors in high-
power laser beam with possible explanation of the effect by athermal helical pitch
dilation and unwinding by the field of a light wave. This remarkable phenomenon of
changing the chirality by a light field only can be used in laser-resonator devices for
temporal (Q-switching) and spatial (soft aperture) profile formation under certain
laser operational regimes.
2. Liquid Crystal Material and Cell Characterization
For Z-scan measurements the well known cyanobiphenyl LCs, 5CB (K15) 4-cyano-
4′-n-pentylbiphenyl,114 and CB15114 (4′-(2-methylbutyl)-4-biphenylcarbonitrile
were used. These materials have identical chemical composition, but CB15, in
difference to 5CB, contains a chiral carbon (Fig. 3) in its pentyl chain.
The E7 mixture of cyanobiphenyl compounds114,115 (Fig. 4(a)) together with
the chiral additive CB15 was used for cholesteric LC mirror preparation.
Fig. 3. Space-filling model of nematic 5CB and chiral additive CB15.
378 S. G. Lukishova
Fig. 4. Molecular structures of the constituents making up the LC E7 (a) and chromophorebis[di-n-butylamino]stilbene (b).
2.1. Nematic and Isotropic LC Layer Preparation
LCs were supplied by BDH. Degassed 5CB served as sample material having been
filtered through a 5-µm filter in a clean room, prior to filling of the cell under regular
laboratory conditions. Samples of 5CB were kept above the nematic/isotropic phase
transition Tc = 35.3◦C114 under control of an Instec heater control unit. CB15 is
isotropic at room temperature.
The two-photon absorbing chromophore bis[di-n-butylamino]stilbene116
(Fig. 4(b)) was added in some experiments of Sec. 6 (7.4 weight %) to a 1:4 mixture
by weight of 5CB and 7CB (Fig. 4(a)).a
For studies of “thick” samples of LCs in the isotropic state, spectroscopic quartz
cells of 0.5, 1 and 2 mm beam pathlength (NSG Precision Cells, Inc.) were used,
as well as for calibration with CS2 (99.9% HPLC grade, Sigma-Aldrich).
“Thin” cells were homemade from glass plates with size ∼ 2.5 cm × 2.5 cm.
Mylar spacers of different thickness (25, 50, 105 and 125-µm) were used between
the two glass plates. For “thin” cells of LCs in the isotropic state Fisher Finest
Premium microscopic slides of 1-mm thickness were used. For oriented nematic
layers of 5CB, planar alignment (Fig. 1(c)) was carried out at room temperature.
To align LC molecules in layer thickness up to 125-µm uniformly in one direction,
spin-coated, rubbed polyimid glass plates (sodalime or borosilicate) were prepared
with the same dimensions as Fisher slides. Coating and rubbing were carried out
in a clean room, but cell assembly and filling with LCs under ordinary laboratory
conditions. Devcon 5-Minute epoxy was used for sealing the “thin” cells.
aChromophore and 7CB and 5CB mixture composition were provided by Prof. J. Perry (Universityof Arizona).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 379
2.2. Chiral Nematic (Cholesteric) LC Mirrors
The liquid-crystal mirrors (Fig. 5) were prepared by the Moscow Organic Inter-
mediates and Dye Institute NIOPIK from photochemically stable mixtures of the
nematic E7 and the chiral twisting agent CB15 (both from E. Merck) with mix
ratio adjusted for maximum reflectivity around the wavelength λ = 1.064 µm (21.4
wt% CB15 + 78.6 wt% E7).91 Materials were prepared, filtered, analyzed, and
processed in a clean room at the Laboratory for Laser Energetics (University of
Rochester). The average refractive index of the mixture was nav = 1.557. The
results of the spectrophotometric measurements of the transmission coefficient of
each of the three, sealed mirrors as a function of wavelength λ for nearly completely
circular-polarized radiation are presented in Fig. 6.
Planar alignment of the cells was achieved by the following methods. It is very
important that at one inner side of the LC-mirror-cell liquid crystalline molecules
are strongly fixed along one direction on the substrate surface (so-called strong an-
choring). On the opposite inner side of the mirror, LC molecules should not be fixed
(weak anchoring). For all mirrors the side of the glass cell with the strong-anchored
director was polyimide coated and then rubbed. The weak-anchoring side was left
unbuffed but covered with (1) polyimide — mirror 1; (2) polyvinylcinnamate and
Fig. 5. Photograph of cholesteric LC mirrors using either mylar spacers (visible) or spacer spheres(invisible).
Fig. 6. Spectral transmittance of three cholesteric LC mirrors.
380 S. G. Lukishova
subsequent photoorientation — mirror 2; (3) polyvinylcinnamate and subsequent
photoorientation and additional shearing of the cell — mirror 3; (4) polyimide
only — mirror 4. The liquid-crystal layer thickness in the hermetically sealed cells
(1–3) were 12.8, 13.8, and 6.5-µm, respectively, and in unsealed (open contact with
air) cell (4) — 20-µm.
3. Experimental Set Ups
3.1. Z-scan Measurements of Nonlinear Absorption and
Nonlinear Refraction
Among various methods for measuring n2, e.g. Refs. 51 and 117–120, the Z-scan
method29,121–123 is attractive owing to its simplicity. In this method for measuring
nonlinear refraction and absorption (transmission),29,121–123 a sample is scanned
along the optical, Z-axis through the focus of a lens, while the far-field transmission
is recorded as a function of sample position (Fig. 7). The nonlinear absorption
coefficient is derived by collecting light from the whole beam (open aperture Z-
scan). For determination of nonlinear refraction, a “small” aperture is used in front
of the detector, admitting only rays close to the Z-axis (closed aperture Z-scan).
The ratio of closed-aperture measurement values divided by open-aperture values
yields the “Z-scan curve” for determination of nonlinear refraction.
It should be noted that for pulsed, solid-state lasers with beam quality and
divergence far from the diffraction limit, the Z-scan method, simple in principle,
requires great care in ensuring reliable results.122 Pulse-to-pulse fluctuations in laser
radiation (both in energy, pulse duration and/or in beam diameter) tend to make
the Z-scan method, straightforward as it is for CW, power-stabilized laser sources,
a nontrivial task for pulsed, especially commercial nanosecond lasers with beam
quality far from ideal.
The experimental set up used is shown in Fig. 8. A frequency-doubled,
Q-switched (6–9 ns pulse duration at Gaussian FWHM) Nd:YAG laser (Quantel In-
ternational (Continuum) model YG-682S-10), using a feedback-stabilized, injection-
seeded, single-longitudinal-mode, unstable resonator with Gaussian cavity end
mirror124 and two, single-pass amplifiers, provided, at 2, 5 and 10-Hz repetition
rate, an output beam-spot diameter of ∼ 8 mm at 0.532 µm.
To optimize beam quality, a 1.5-mm-diameter Teflon aperture was placed in the
central part of the beam,125 such that an Airy spot at a reasonable distance from the
Teflon aperture (using mirrors M and beamspliter BS) was formed. A converging,
Sample
Detector
Z
ApertureLens
Fig. 7. Schematic of Z-scan measurements.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 381
Fig. 8. Experimental set up for measurements of nonlinear refraction and absorption by the Z-scanmethod.
9.5 or 10.5-cm focal-length lens L was placed at 4 m from the Teflon aperture.
To remove far-field side lobes caused by the Teflon aperture, a 2.75-mm-diameter,
metal aperture MA was placed in front of the lens. The same aperture MA was
placed at the reference channel. For maintaining a linear incident polarization and
changing the input-pulse energy to the sample, a Glan-prism-polarizer and a quartz
λ/2 waveplate combination was placed in the beam.
Signal D1 and reference D2 pyroelectric joulemeters (Gentec ED-100A with
amplifier EDX-1, vendor recalibrated) or fast photodetectors (Hamamatsu S1722-
01 and Motorola MRD510, respectively) were connected to a digitizing oscilloscope
(Textronix TDS 640). An AT-GPIB/TNT board from National Instruments was
used for data acquisition and processing. Laser pulse shape was monitored by a
sub-ns-risetime Motorola MRD510 photodiode, connected to a Hewlett Packard
HP 54111D digitizing oscilloscope. For closed-aperture Z-scan measurements, a
“small” aperture was placed in front of D1. Sometimes the entire photodetector
was used as the “aperture”. For open-aperture measurements, an additional lens in
front of D1 was used to collect all laser radiation leaving the sample. The samples
were placed on an Aerotech mechanical translation stage controlled by an Unidex
1 motion controller. To measure the average126 beam diameter near the waist
produced by the focusing lens of the Z-scan set up, an 8-bit, WinCam CCD-beam
analyzer by Merchantek (pixel size 8.3 µm × 8.6 µm) was used in a separate, low-
intensity, equivalent channel formed with beamspliter BS and additional lens with
the same focal length as the lens in the Z-scan channel. Beam-waist diameter was
also measured with knife-edge technique and using Z-scan of CS2 with well-known
nonlinear refractive index n2.
The same CCD-camera was also employed for acquisition and analysis of beam
profile on the lens and far-field patterns during the Z-scan. For adjusting the size
of the pattern to the size of the sensor, an additional lens was used between the
sample and the camera. Some far-field patterns were recorded from a screen by
382 S. G. Lukishova
Fig. 9. Beam profile at the lens along X-axis (a) and Y -axis (b); beam diameter in the waistregion (c): • — for X-axis, � — for Y -axis; and pulse shape (d).
a standard video camera/digitizer combination, permitting the recording of each
pulse.
Figure 9 shows near Gaussian spatial distribution of the laser-beam intensity at
the lens in the Z-scan set up (a), (b), typical beam caustic near the waist (c) and
near Gaussian temporal pulse shape (d). Figure 9(d) is a result of storage of ∼ 100
shots.
It must be noted next that both sensitivity and accuracy of the absolute Z-scan
measurements critically depend on the incident beam profile and laser beam quality.
In Ref. 127, numerical modeling showed that, even with a slight deviation from a
perfect Gaussian beam distribution, the Z-scan curve calculation using the standard
formula for the Gaussian beams can yield erroneous, nonlinear optical parameters.
Influence of laser beam quality was studied numerically,122,128 where even for beam
quality factor M2 > 1.2, errors were found in the absolute Z-scan measurements
(M2 (see Ref. 129) expresses in terms of beam divergence as M2 = θ/θ00, where θ
and θ00 are the real beam divergence and TEM00 mode divergence). In difference
to absolute measurements, in relative measurements by Z-scan method even low-
quality beams are found to be useful.130
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 383
In order to remove errors connected with deviation of the spatial profile from
the Gaussian shape,127 relative Z-scan measurements are presented here through
the use of CS2 as a calibration material before and after each measurements of an
LC-sample.
For every translation-stage step (1 mm) 30 irradiation pulses were accumulated,
and, after 5% “windowing”,122 these data were averaged. The accuracy of measure-
ments of n2 and β is estimated to be ∼ ±20% dominated by the incident-intensity
fluctuations.
3.1.1. Evaluation of n2 and β from the Z-scan Data
In light of different definitions of n2 in the literature,51,117,118,131 the value of the
nonlinear refractive index n2 and the nonlinear refractive coefficient γ are defined
in this paper by n = no + 1/2n2|E|2 and n = no + γI. Here n is the total refractive
index of the material, and no is the linear refractive index, E is the (complex) optical
electric field amplitude inside the material, I is the optical intensity. Conversion
between n2 and γ is made via n2[esu] = (cno/40π)[m2/W ], where c is the light
speed (m/s) in vacuum.
For isotropic materials and a linearly polarized laser beam, n2 and the nonlinear
susceptibility χ(3)(−ω, ω, ω,−ω)49–51,117,118,131–134 are related simply by51
n2 = (12π/no)χ(3)1111(−ω, ω, ω,−ω) , (4)
where χ(3)1111 is one of three nonzero elements of χ(3).
For the Gaussian profiles the values of γ and n2 can be calculated from the
Z-scan curves using the following formula29
∆T tr = 0.406|∆Φ|(1− S0.25) , (5)
where ∆T tr is the difference between the maximum value of the normalized trans-
mittance T tr and its minimum value, ∆Φ is the nonlinear phase shift on axis during
Z-scan, S is the linear transmittance of the “small” aperture for a Gaussian input
beam (S = 1 − exp(−2r2a/R
2o)), where ra is the “small” aperture radius, Ro is the
beam radius at the place of “small” aperture in the linear regime).
The nonlinear phase shift ∆Φ = 2πλ−1γIL, where I is the peak axial intensity
at the waist, assuming a temporally and spatially Gaussian-shaped pulse, L is the
sample length.
In this paper intensity is defined as
I(r, t) = 2E(τπ3/2r2o)−1 exp(−2r2/r2
o − t2/τ2) . (6)
Here E is the total energy, the pulse-length full width at half maximum (FWHM)
to = 2τ(ln 2)1/2, ro is the beam waist-radius at 1/e2 level. Using these pulse and
beam parameters,
Ipeak = 4E(ln 2)1/2(toπ3/2r2
o)−1 ≈ 2E/(toπr2o) . (6′)
384 S. G. Lukishova
As to nonlinear absorption, here an assumption is made that two-photon absorp-
tion135 is the principal loss mechanism. The fundamental equation describing this
intensity loss with depth z is
dI/dz = −βI2 . (7)
The solution to (7) at z = L is
I(L) = I(0)/(1 + βI(0)L) = I(0)/(1 +Q) . (7′)
Sample transmittance, T tr(L) = (1 + Q)−1 = 1 −∆T trabs, where ∆T tr
abs is obtained
from the open-aperture Z-scan curve. For a Gaussian spatial and temporal profile
T tr(L) = 2Q−1π−1/2
∫ ∞0
ln(1 +Qe−x2)dx . (8)
Expansion of the logarithmic function yields a linear relationship (valid for small
Q) between T tr(L) and I(0) where the slope is proportional to the nonlinear co-
efficient β:
T tr(L) ≈ 1 + 2−3/2βI(0)L , and ∆T trabs ≈ −23/2βI(0)L . (8′)
3.2. Measurements of Nonlinear Transmittance of
Cholesteric Mirrors
Nonlinear irradiation of cholesteric LC mirrors was carried out by two approaches:
cholesteric LC samples were either irradiated in the focus of a freely propagating
laser beam (for the experimental layout see Fig. 10) or inside a laser resonator
(Fig. 11) in which the cholesteric LC structure served as output coupler.
Nd:YAG laser
Quartz polarizer
Photodiode
λ/4
Glass filters
Lens
CLC mirror
Power meter
Fig. 10. Experimental set up for free-space experiments with cholesteric LC mirrors.
Fig. 11. Schematic of the cholesteric-LC-mirror-equipped laser oscillator.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 385
A Nd:YAG laser operated in two-regimes: (1) in CW mode and (2) in an acousto-
optically Q-switched mode, emitting high-repetition-rate (4.5 kHz) pulse trains,
each pulse being 500-ns long. In either mode, the average power reaching the
cholesteric LC samples was between 0.3 and 1 W.
The incident and transmitted Nd:YAG powers were detected by a calibrated
photodiode and a power meter. Pulse duration and repetition rate were measured
by an avalanche photodiode and a photomultiplier. To increase the incident power
density, a lens with a focal length of about 5-cm was placed in front of the cholesteric
LC mirror in free-space experiments.
Beam cross sections were monitored by a CID 2220A video camera (CID Tech-
nologies Inc.) and video processing set up. From the recorded beam profiles,
1/e2 intensity beam-waist diameters of between 50 and 220-µm were derived for
different sets of measurements. Peak-power densities (for 500-ns pulses) of ∼106 − 107 W/cm2 were used in pulse-repetition rate mode.
For the laser-resonator studies, a plane-parallel cavity was formed by a dielectric
nontransmitting mirror and a cholesteric-LC output coupler (Fig. 11). An active
Nd:YAG element was pumped by a continuously operating arc flashlamp filled with
krypton (the voltage across this lamp was 100 V). Pumping of the active element
generated a thermal lens whose optical power was +1 dioptre kW−1. Switching to
high pulse-repetition rate operation was performed by an acousto-optical switch.
A quartz λ/4 plate was placed inside the cavity between the cholesteric LC
mirror and the active element: in the absence of this plate there was no lasing.
The diameter of the optical beam at the laser output was ∼ 0.8 mm at an average
output power of 1 W.
4. Results of the Z-scan Measurements of Isotropic Liquid Crystals
4.1. Nonlinear Refraction
Results from the Z-scan measurements of 2-mm 5CB samples136 in the isotropic
state at 45◦C for I = 0.66 GW/cm2 are presented in Fig. 12(a)–(c). For comparison,
Z-scan curves for CS2 with 1 and 2-mm cell thickness are shown also for the same ex-
perimental conditions (Fig. 12(d)) for I1 = 1.4 GW/cm2 (•) and I2 = 1.2 GW/cm2
(∆). From data in Fig. 12(c) we derive γ(5CB) = 3.7 γ(CS2) and n2(5CB) = 3.7
n2(CS2). Beam-waist diameter is ∼ 35 µm in these measurements, and to = 7 ns.
Over the temperature interval 35.6–50◦C, the value of n2 (5CB) changed little:
it varied from 2.5 to 3.7 n2 (CS2).136,137
Typical Z-scan curves for 2-mm, CB15 cells136,137 at room temperature are
presented in Fig. 13(a)–(c) for I = 0.74 GW/cm2. For comparison, a Z-scan curve
for CS2 with 2-mm thickness is presented as well (Fig. 13(d)) for I = 0.73 GW/cm2.
The results from these curves yield the following values: γ(CB15) = 2.6 γ(CS2) and
n2(CB15) = 2.5n2(CS2). Beam-waist diameter is ∼ 36 µm, and to = 6.8 ns.
In both cases, isotropic 5CB and CB15, self-focusing (converging lens) was ob-
served. Aperture factor was S ∼ 0.1 in these measurements.
386 S. G. Lukishova
0.50.60.70.80.9
11.1
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Nor
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0.9
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Fig. 12. Z-scan curves for isotropic CB15: open aperture (a); closed aperture (b); closed/openaperture (c); and closed aperture for CS2 (d).
Fig. 13. Z-scan curves for isotropic 5CB: open aperture (a); closed aperture (b); closed/openaperture (c); and closed aperture for CS2 (d).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 387
4.2. Nonlinear Absorption
The main results of β-measurements are as follows:
(1) a remarkably large value of β is found for “thin” layers (e.g. for isotropic CB15,
β ∼ 100–150 cm/GW for 25–125-µm cells at I ∼ 0.7–0.8 GW/cm2) in compar-
ison with that from “thick” samples (β ∼ 4.5–30 cm/GW for 1–2-mm cells of
isotropic CB15 and 5CB at 45◦C at I ∼ 0.2–0.9 GW/cm2). Typical curves for
β versus layer thickness136 for isotropic CB15 are presented in Fig. 14(a) at the
same incident intensity I ∼ 0.75–0.78 GW/cm2.
(2) a dependence of β (cm/GW) on incident intensity (Fig. 14(b)) for isotropic 5CB
at 45◦C, “thick” samples.
(3) for isotropic 5CB near the nematic/isotropic phase transition, β values vary by
up to a factor of ∼ 6. Five degrees above the phase transition up to 50◦C, β
does not vary beyond experimental error.
020406080
100120140160
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Layer thickness, mm
, cm
/GW
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1
Intensity, GW/cm2
, cm
/GW
(a)
(b)Fig. 14. Dependence of nonlinear absorption coefficient on layer thickness (a) and the incidentintensity (b).
An explanation of the dependence of β on layer thickness may not rest on the
argument of a Rayleigh length shorter than the sample pathlength. Measurements
of the beam caustic near focus (Fig. 9(c)) show that both “thin” and “thick” cells
388 S. G. Lukishova
used in this experiment were shorter than the Rayleigh length. In addition, for a
sample larger than the Rayleigh length, an open aperture Z-scan curve must be
flat-bottomed.122
5. Results of the Z-scan Measurements of Thin Planar
Nematic Layers
To take into account the well-known nonlinear-absorption anisotropy in the nematic
phase, i.e. nonlinear absorption being larger for incident polarization parallel to the
nematic director and weaker for perpendicular polarization,61 orientation-dependent
measurements were carried out.136–138 Figure 15 shows the results from open (a)
and closed (b) aperture Z-scans for a 5CB layer of 105-µm thickness, irradiated by
a parallel-polarization (I = 0.36 GW/cm2) pulse. Results for the ratio of closed-
aperture data by open-aperture data are presented in Fig. 15(c). For comparison,
0.80.85
0.90.95
11.05
1.1
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Nor
mal
ized
tran
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11.05
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Z, mm
Nor
mal
ized
tran
smitt
ance
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0.940.960.98
11.021.041.06
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orm
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k
Fig. 15. Z-scan curves for planar nematic 5CB: open aperture (a); closed aperture (b); closed/openaperture (c); and closed aperture for CS2 (d).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 389
a closed-aperture Z-scan for CS2 is shown in Fig. 15(d) (I = 1.2 GW/cm2). In all
cases of Fig. 15, S = 0.5.
The results of calculations are as follows: γ = −18.5 γ(CS2). Evaluation of
β yields a value of ∼ 126 cm/GW. The large values of γ (and n2) by themselves
are remarkable, but so is the sign of the nonlinear refraction coefficient (negative).
These data are in good agreement with those of Refs. 34, 66, 67 and 70 where also
a negative nonlinear refraction coefficient was observed for an oriented thin layer of
5CB and parallel-polarized laser light.
The magnitude of β obtained in this measurement for ∼ 105-µm cell probably
cannot be considered as a “true” two-photon absorption coefficient (see Sec. 1.3 and
Sec. 4.2 (Fig. 14(a)).
6. Cumulative Spatial Self-phase Modulation Elliptical
Ring Formation in the Beam and Other Transverse Effects
The LC molecules with their tendency to align with the electric-field direction of
an applied optical wave do in general not experience torque when the LC molecular
dipole is parallel to the linear polarization (nematic cell surface is perpendicular to
the beam propagation direction) of the incident pulse (see Fig. 15, drawing at the
bottom).
Contrary to this expectation, during periodic illumination of planar-nematic
cells in such geometry over time spans of ∼ 0.5–ten seconds the linearly polarized
beam is shown here to experience an imprint of a far-field pattern of high-contrast,
concentric, elliptical diffraction rings whose major axis orients itself perpendicular
to the incident polarization direction.138,139 Once formed, each set of rings may
remain stable for up to several minutes. Upon continued pulsed irradiation over
several minutes, the number of these rings varies systematically with laser intensity
(sometimes between 1–2 and (up to) 20 rings). This ring pattern differs from that
typically obtained from orientational spatial self-phase modulation. In our case,
the ring pattern evolves under polarization conditions for which, in principle, no
orientational effects may occur (polarization of laser light is parallel to the director
orientation). Under CW-irradiation at twice the power density than the average
power density under pulsed illumination, the effect fails to exist.
The key characteristics of the effect are as follows:
• This effect and its development exhibit threshold behavior depending on both the
incident peak intensity and the geometry of irradiation, but not on the average
power density.
• The effect’s evolution depends on the irradiation geometry (focal beam diameter)
and, for a given geometry, on the cell thickness.
• The effect exists at both 2-Hz and 10-Hz pulse repetition rate, however, in the
2-Hz case the threshold increases (cumulative effect).
• Adding the chromophore does not change the character of the effect but only low-
ers its threshold by ∼ 2–2.5 times (for the tested dopant type and concentration).
390 S. G. Lukishova
• When the LC cell was rotated around the light-propagation direction, the ellipti-
cal rings’ major and minor axes rotated in the same handedness, but the number
of rings diminished as the angle between LC director and incident linear polar-
ization increased. However, when the LC director was oriented perpendicular to
the light polarization, the effect vanished entirely at incident intensities below
∼ 1 GW/cm2.
6.1. Large-beam Diameter (Slow Focus)
At 160-µm beam diameter, cells of thickness 25–50-µm did not permit evolution of
the effect (only chaotic break-up of the beam was observed), while larger thickness
(105–125-µm) cells did. The elliptical ring pattern developed from the original beam
spot through several “rays” of scattered light (Fig. 16). Images in Fig. 16 (105-µm
layer thickness of 5CB and 7CB mixture with chromophore, I = 0.5 GW/cm2) were
obtained by recording from the screen elliptical ring patterns onto magnetic tape
at full repetition rate, and digitizing each frame afterwards.
Figure 17 shows the evolution of the ring-image with diminishing incident in-
tensity for layer thickness 125-µm. As well as in Fig. 16, for lowering the effect
Fig. 16. Slow focus irradiation: time evolution of the elliptical ring pattern in the far-field.
Fig. 17. Slow focus irradiation: set of elliptical ring patterns with diminishing incident intensityfrom (a) to (g).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 391
threshold doping of the mixture of 5CB and 7CB LCs with the two-photon ab-
sorbing chromophore (see Sec. 2.1 and Fig. 4(b)) was used. The same patterns are
observed in pure 5CB (or mixture), but at incident intensity levels twice larger than
used here.
6.2. Small-beam Diameter (Tight Focusing).
Asymmetric Scattering, “Dark” Spot and
Cross-structure Formation
For tight focusing (35–50-µm beam-waist diameter), the effect of elliptical ring for-
mation was observed for all used cell-thicknesses (25–30, 50, 105, 125-µm). In all
tight-focusing experiments no chromophores were used. In this case, the evolution
of the far-field pattern from the initial beam spot into the elliptical rings passed
through the appearance of what is referred to here as “dark ” spot (Fig. 18) or
wide dark ring (“donut” shape) around the initial beam spot and a stage of asym-
metric scattering (Fig. 19).138,139 Figure 18 (for 5CB sample with 125-µm layer
thickness) shows changes of the far-field pattern with increasing intensity from
I < 0.3 GW/cm2 (high-contrast, narrow-diffraction-ring on beam diameter is a
result of spatial self-phase modulation) to I ∼ 0.6 GW/cm2 (“dark spot” instead of
a bright beam, “negative” of the original beam spot). This “dark” spot effect was
observed only for small-beam diameter (tight focusing). It can be explained by the
additional widening of the far-field diffraction angle in the self-defocusing medium
in the divergent beam. It should be noted that the same “dark ” spot was observed
not only under “parallel” polarization, but under “perpendicular” as well and even
for the LC in the isotropic state. In the latter two cases, the threshold of the effect
doubled over that for “parallel” polarization and neither asymmetric scattering nor
elliptical rings were observed. The “dark”-spot effect was also reported in Ref. 140
for thermal self-defocusing of CW-radiation in an absorbing isotropic liquid. Theo-
retical analysis140 has shown that the “dark”-spot formation is a common feature of
a divergent Gaussian beam transmitted through an arbitrary defocusing medium.
The scattering asymmetry (Fig. 19) follows a simple rule: the scattered intensity
is always highest in the direction orthogonal to the incident polarization direction.
The buildup time of such scattering near its threshold was measured (using magnetic
tape recording and digitizing each frame afterward) of the order of ∼ 0.3–1 second.
Figure 19 (5CB sample with 30-µm layer thickness, I = 0.43 GW/cm2) shows
(a) (b)
Fig. 18. Tight focusing: far-field patterns at low incident intensity (a); “dark spot” (b).
392 S. G. Lukishova
Fig. 19. Tight focusing: far-field asymmetric scattering CCD-image (a); 3D-rendering of spatialbeam profile (b); X-axis spatial intensity distribution (c); Y -axis spatial intensity distribution (d).
Fig. 20. Tight focusing: elliptical rings in the far-field with increasing incident intensity from leftto right.
details of asymmetric scattering and the “donut ”-shape “dark ” spot at the beam
initial spot. The central bright spot and the “donut” black ring are circles. At the
1/e2 level, the asymmetric scattering spot diameter at the X-direction (parallel to
the incident polarization) is ∼ 1.5 times larger than that in the Y -direction.
At higher intensity (I ∼ 0.5 GW/cm2), asymmetric scattering becomes stronger,
and the first ring appears (Fig. 20, left for 25-µm pathlength of 5CB). At still
higher intensities (∼ 0.7 GW/cm2), asymmetric scattering evolves into the multiple-
elliptical ring pattern whose major axis is oriented perpendicular to the incident po-
larization (Fig. 20, right for 105-µm pathlength of 5CB). Under certain conditions,
the divergence angle of the elliptical fringes abruptly increases, exceeding the spa-
tial capture range of the CCD-camera’s detector. This necessitates capturing the
fringe pattern on a white paper screen, and imaging the screen on to the detector
by a conventional objective. Figure 20, right is the result of such imaging. For scale
comparison, the absolute size of the initial beam spot observed in Fig. 20 left and
right does not change throughout the evolution of the pattern.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 393
Fig. 21. Tight focusing: far-field elliptical ring pattern (left) and result of 45◦ rotation (right).
Fig. 22. Different types of the cross-structure in the far-field.
When the LC cell was rotated around the light-propagation direction, the ellip-
tical rings’ major and minor axes rotated in the same handedness, but the number
of rings diminished as the angle between LC director and incident, linear polar-
ization increased (Fig. 21, 50-µm cell thickness: left I = 0.77 GW/cm2, right
I = 0.88 GW/cm2). By the time the LC director is oriented fully perpendicular to
the light polarization, the effect vanishes entirely.
At the highest employed intensity (I ∼ 0.8–1 GW/cm2 for tight focusing), the
elliptical ring pattern may develop into a cross structure139 for both tight focusing
and slow focus. Figure 22 shows different versions of such cross structures (left —
for tight focusing (5CB, 25-µm layer thickness), right — for slow focus (5CB and
7CB mixture with chromophore, 125-µm layer thickness)), depending on specific
laser-pulse or irradiation-geometry parameters. Each specific form is reproducible
for a defined laser operational mode. Equally important, the polarization state
of the far-field laser light depicted in Fig. 22 remains the same as in the incident
beam, in difference with cross patterns resulting from the sample being held between
crossed-polarizers, reported, e.g. in Ref. 141. Under CW-excitation of equivalent
power, we did not observe any of the above described effects.
7. Numerical Modeling of Cumulative Effects and Explanation
of Spatial Self-phase Modulation Effects
For an explanation of the slow buildup time spatial self-phase modulation as well
as of its absence under CW irradiation of comparable power density, the
394 S. G. Lukishova
heating of LC was further scrutinized. In a pure LC-material, the major contrib-
utor to heating is radiationless decay from excited states addressed by two-photon
absorption and excited-state absorption17,27 (see Sec. 1.3). Assuming that the glass
substrates do not absorb at all, numerical solutions have been sought for the heat
balance equation. The finite-element solutions were obtained using the commercial
ANSYS/Thermal code),b including thermal conduction in the LC-material and the
two glass-walls of the LC-cells, convection from the glass walls to air, and enthalpy
effects at the phase-transition temperature. Two-dimensional transient thermal
analysis was carried out for the initial condition of a Gaussian spatial temperature
distribution written by the laser pulse into the material. Temperature-dependent
material parameters for 5CB (thermal conductivity, specific heat) were provided in
file form by the authors of Ref. 142.
For lack of literature data on radiationless energy coupling efficiencies from two-
photon and excited-state absorption, here the assumption is made of a Gaussian
temperature profile equivalent to the in-focus laser-beam profile (1/e2 diameter =
160 µm) with maximum temperature Tmax. Other device parameters used in
the simulation were: LC layer thickness L = 125 µm, glass substrate thickness
Lglass = 375 µm, room temperature Troom = 26◦C. In order to comply with the
experimental 10-Hz repetition rate, the decay evolution of the initial temperature
profile was followed out to 0.1 seconds, with the smallest time step set at 10−6
seconds. Values for Tmax = ∆Tmax + Troom were chosen such that throughout a
sequence of equal pulses, Tmax at any node did not exceed the temperature limit
set by the available material-parameter142 lookup table (44.9◦C maximum). This
Fig. 23. Numerical modeling of the heat diffusion: center-node temperature relaxation in timeafter first pulse.
bNumerical modeling was made by Dr. A. Schmid (University of Rochester, Laboratory for LaserEnergetics) using code of ANSYS, Inc., PA.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 395
∆∆∆∆Tmax = 10oC ∆∆∆∆Tmax = 5oC
Short number
Cen
ter-
node
tem
pera
ture
, oC
Fig. 24. Numerical modeling of the heat diffusion: center-node temperature versus the numberof pulses.
constraint is strictly methodological and is not to imply that in an actual experiment
the temperature did not exceed, or could not have exceeded, the values chosen here.
Figure 23 shows the temperature relaxation with time after the first pulse at the
central node of the 5CB-cell (∆Tmax = 5◦C). During the first 10 milliseconds the
temperature relaxes fast, followed by slower relaxation thereafter. Even after 100
milliseconds the temperature remains ∆T ∼ 0.15◦C above room temperature.
Numerical calculations of heating as cumulative action of many, 10-Hz repetition-
rate pulses yield results presented in Fig. 24, ∆Tmax = 10◦C (solid curve) and
∆Tmax = 5◦C (dotted curve). After 60 pulses (∼ 6 s of irradiation) the tempera-
ture in the center of the LC-cell increased by ∆T = 5◦C for ∆Tmax = 10◦C, and
∆T ∼ 4.5◦C for ∆Tmax = 5◦C. The slopes of the curves increase faster for the first
15–20 pulses, and for ∆Tmax = 5◦C, ∆T is close to the temperature saturation
value at the end of the sequence.
Evaluation of the phase shift caused in a laser beam by this temperature increase
is equal to ∆Ψ = 2π∆nL/λ, where ∆n = ∆Tdn/dT . The number of rings as a
result of self-phase modulation in space on the transverse profile of a beam134 is
equal to N = ∆Ψ/2π = ∆TL(dn/dT )/λ. For 5CB in the region from 26◦C to
31◦C dn/dT ∼ 2.5 · 10−3 grad−1. For λ = 0.532 µm, L = 125 µm, and ∆T =
5◦C, N = 3. A temperature increase after single pulse irradiation (∆T ∼ 0.15◦C)
results in no diffraction rings in the beam. Only the cumulative action of many
pulses approaching a steady-state value yields a stable spatial self-phase modulation
elliptical ring picture as displayed in Figs. 16 and 17. Given the approximations
in the model, this apparent agreement between simulation and experiment cannot
serve as a rigorous proof of the cumulative heating mechanism. Instead, it provides
substantial plausibility for such a mechanism to be active in this situation.
396 S. G. Lukishova
The observation of the effect only for incident polarization parallel to the LC-
director is explained by two-photon absorption dichroism,61 and more effective LC
heating by “parallel” — polarization light, and approximately twice larger absolute
value of dn/dT for “parallel” polarization in comparison with “perpendicular”.
The scattering asymmetry and ellipticity of the ring pattern can be explained by
the anisotropy of the thermal diffusion constant, which has for 5CB a ∼ 1.6 times
larger value along the long molecular axis than perpendicular to it.142,143
The nature of the cross-structure is not yet clear. Stresses similar to those con-
sidered in Ref. 144 can create movement of LC fluid in two perpendicular directions
and destruction of the planar structure in these directions.
8. Changes of Reflectivity of Cholesteric Mirror by Light Field
Near Selective Reflection Conditions
8.1. Free-space Results
An increase in cholesteric LC-mirror transmittance was observed in free space,
i.e. outside the cavity, when laser radiation with 500-ns pulse duration and a repe-
tition rate of 4.5 kHz was focused into the cholesteric LC layer. The mirror trans-
mittance increased from 5% up to 30–80% for mirrors 1–3 and from 15% up to
25–50% for mirror 4. The intensity drop appeared 30 s–10 min after irradiation
onset (Fig. 25 for two mirrors (a) and (b)), depending on the peak power density
of the incident radiation, which was different for each mirror.
It is interesting, that the effect did not depend on the average power density. Just
as in Refs. 103–104, in the CW lasing mode no reflectance drop was observed, even
for a power density twice as high as the high-repetition rate average pulsed mode.
Moreover, even in the high-repetition-rate mode the bleaching effect was recorded
only when the reflection occurred from the side of the cholesteric LC mirror with
the strong anchoring. No bleaching was observed in the case of reflection from the
weak-anchoring side (flipping of the cell by 180◦).
It should first be noted that a high-quality beam reflection was obtained only
from the strong-surface-anchoring side of the cholesteric LC mirror, while a beam
reflected from the other, weak-anchoring side, had poor quality (e.g. amplitude
inhomogeneities were observed in beam cross-section).107
According to measurements, the temperature shift of the selective-reflection
curve of the experimental cholesteric LC mixture is approximately +1 nm/◦C, i.e. to
obtain a transmittance of ∼ 70% for CLC mirrors at λ = 1.064 µm the prepared
cholesteric LC mirrors must be heated to a temperature above 50◦C. Monitoring the
cell temperature by an attached thermocouple, no increase in the cell temperature
was recorded.
In the case of weak bleaching, it was observed that the transmittance of the
cholesteric LC mirror returned to its previous state after the laser was either
switched off or switched to the CW mode (Fig. 25(b)).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 397
(a)
(b)
Time interval , minTr
ansm
ittan
ce, %
Time interval, min
Tran
smitt
ance
, %
Fig. 25. Dependence of two cholesteric LC mirrors ((a) and (b)) transmittance on irradiation timeunder high repetition rate, pulsed irradiation. For mirror (b) lasing action intentionally terminated(*) and restarted again (**).
8.2. Cholesteric LC Mirror in an Nd:YAG Laser Cavity
No significant difference was observed between the slope efficiency of the laser with
dielectric or cholesteric LC output mirrors when the reflection coefficients were the
same. The advantage of the cholesteric LC mirror was a lower sensitivity of the
laser operation to cavity misalignment. At low pumping rate and in the pulsed
high-repetition-rate regime, the slope efficiency and the lasing stability were the
same for cholesteric LC and dielectric mirrors. At high pumping rates, the average
output power obtained in the high-repetition-rate decayed rapidly and disappeared
after 0.5–5 min from switching, but only when the side of the cholesteric LC mirror
with strong surface anchoring was facing the gain medium. The pump threshold
(i.e. the current to the flashlamp) at which lasing was suppressed was a function of
the mirror characteristics (method of their fabrication): it was 28.5–29.5 A for the
output mirrors 1–3 with R = 95% and ∼ 24.5 A for the mirror 4 with R = 85%.
398 S. G. Lukishova
Time interval, min
Out
put P
ower
, W
t1 t2t1 t2 t2t1
Fig. 26. Time dependence of the average output power of a laser with cholesteric mirror withchanging the regime from CW to high-repetition rate (t1) and back to CW (t2). Solid and dashedcurves present results for different mirrors.
Figure 26 depicts the time dependence of the laser output power obtained for
two cholesteric LC mirrors differing in the method of their fabrication (different
degrees of surface anchoring) when a change from the CW to the pulsed regime
occurred above the pump threshold. Turning on the acousto-optical switch (at t1)
quenched the lasing action because of a drop in the reflection coefficient of the
cholesteric LC mirror. Turning off the switch (at t2) gradually restored the lasing
action. A second change to the pulsed regime suppressed lasing again and it was
restored when the laser was made to operate in the CW regime again. Adjustment
of the polarization of the radiation by rotating the λ/4 wave plate in the pulsed
regime sometimes increased the output power only slightly.
The observed reflectivity drop of the cholesteric LC mirror can be explained on
the basis of a model in which the pitch of the cholesteric helix increases in the electric
field of light pulses with high power density (intensity) ∼ (1 − 10) × 106 W/cm2.
Indeed, according to the calculations in Ref. 96, for a “thick” cholesteric LC layer
of thickness L > 2λ/(π∆n) the critical field for unwinding the cholesteric helix by
the light field is determined by the expression
|E|2cr = 4π(ω/c)2(εa/ε)K22 , (9)
where ∆n = npar − nperp, ε ∼ n2av, and the dielectric anisotropy at optical fre-
quencies is
εa = εpar − εperp = n2par − n2
perp ≈ 2∆nnav . (10)
Using the relation (10), we obtain from Eq. (9)
|E|2cr ≈ (32π3K22/λ2)(∆n/nav) . (11)
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 399
For λ = 1.064 µm, ∆n = 0.174, nav = 1.6, and K22 = 5 × 10−7 dyn we obtain
Ecr = 2.1× 104 V/cm and 2λ/(π∆n) = 3.9 µm, i.e. less than L for all four mirrors.
In the described experiments the electric field strength at the center of the beam is
∼ (2.2–7) ×104 V/cm, i.e. higher than Ecr.
The unwinding of the cholesteric helix by the field of a powerful light wave in
the region of selective reflection is substantially different from the unwinding of the
helix in a low-frequency field, since in the latter case E2cr ∼ ε−1
a (Refs. 145 and
146). In contrast to the field with a constant direction in the low-frequency case,
the direction of the electric field vector of a circularly polarized light wave changes
over the thickness of the cholesteric LC layer. The field of the light wave decays
exponentially over a distance Lc ∼ ε−1a and does not “see” the remaining thickness
of the cholesteric LC.96 Comparing results described here with the experimental
investigations of the pitch increase in a low-frequency electric field lying in the
plane of the cholesteric LC layer,145–147 it is possible to say that the electric field
reached in our experiments was much higher than the unwinding field in Refs. 145–
147 (∼ 104 V/cm).
It should be noted that in Ref. 148, the pitch of the cholesteric helix in a
cholesteric LC layer on whose surfaces the director was anchored increased in a
nonmonotonic, step-like manner. Apparently, this explains the nonmonotonic (step)
dependence of the cholesteric LC-mirror transmittance on the irradiation time in
the experiments described here (Fig. 25). The smearing of the steps is due to the ra-
dial intensity distribution in the beam and the corresponding change in electric-field
magnitude cross the beam. Deformation energy is accumulated in the cholesteric
LC layer over the interaction time of a single laser pulse (500 ns), and this energy
is partially dissipated during the “quiet” period between the pulses (200 µs), since
the relaxation time of the deformed helix is of the order of 1000 µs. Therefore,
the unwinding of a cholesteric helix in an optical field occur only over quite a long
time (accumulation of nonlinear changes149) during pulsed high-repetition rate laser
irradiation.
For a complete picture it should be noted that step-like changing the trans-
mittance was observed in Ref. 150, owing to pitch changes by heating. In difference
to our experiments, the authors of Ref. 150 used LCs with large temperature
sensitivity.
9. Conclusion and Future Developments
9.1. χ(3)(− ω,ω,ω,−ω) Measurements of Liquid Crystals
The main result of this paper is a warning of caution that, to date, results of
nanosecond and picosecond χ(3) measurements of cyanobiphenyl LCs remain in a
state of unsettlement that all but precludes the effective use of these materials in
the device engineering of power-limiting and other χ(3)-based applications. In par-
ticular, several nanosecond laser irradiation experiments involving such LCs under
400 S. G. Lukishova
two-photon absorption conditions need to be rethought. The unresolved challenges
are these:
• “Thin” (≤ 100 µm thickness) layer measurements, including the ones reported
here, tend to overestimate values of nonlinear optical parameters, in particular
when purification of “as received” materials by degassing and other means is
omitted. In the benign case, transient, micrometer-sized bubble formation will
cause wide-angle scattering that the detector will “interpret” as enhanced nonlin-
ear absorption. In the more aggravated case, microscopic carbonization will float
and remain in the medium with the potential for massive damage and device loss
later on. Both effects do “limit”, but quantification of such artifacts is tedious,
and reproducibility between devices based on such artifacts is impossible.
• Planar-nematic layers irradiated by pulses at moderate repetition-rate (2–10 Hz)
with linear polarization parallel to the director seem to experience cumulative,
laser-driven heating effects. Among the consequences of this local heating is
the important difference in LC response between first irradiation and much later
ones. LC devices, such as power limiters, that are expected to show specified
performance on the first shot without preconditioning, cannot be based on mea-
surements that do not distinguish this difference.
• Critical emphasis needs to be placed on irradiation geometry (beam-waist diam-
eter) and its precise knowledge as the nanosecond nonlinear response of “thick”
LC layers changes not only magnitude but even sign, depending on the geometry.
With much of this information absent or guessed in past measurements, reliable
χ(3) values are sparse indeed.
• It remains a vexing puzzle why the value for nonlinear absorption coefficient β in
the nanosecond case is ten- to hundred times larger than in the picosecond case.
Moreover, β depends on the incident intensity in both cases. Whether this is a
manifestation of a “clean” effect such as added triplet-state absorption or another
“dirt” effect (either bubbles or carbonization) needs to be clarified.
I would like to mark the importance of studies of materials with high two-photon
absorption, especially in optical power limiting application. It is also important to
mention that in difference with linear absorption, the two-photon absorption process
has a quadratically increase the absorption rate. This property allows activation of
photo-chemical or physical processes with high spatial resolution in 3D,151 e.g. for
data recording and storage application. Recently LCs doped with two-photon ab-
sorbing chromophores began to be used under short-pulse laser irradiation. A large
enhancement of the nonlinear absorption properties of dye molecules was observed,
dissolved in cyanobiphenyl nematic LCs.151
9.2. Cholesteric Mirrors
This paper shows the possibility to control the chiral-nematic (cholesteric) pitch
length (up to its unwinding) by a light-field alone under irradiation conditions
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 401
without either two-photon or linear absorption. Macroscopically this effect mani-
fests itself as a reflectivity drop of planar-aligned cholesteric mirrors. Previous at-
tempts to observe this drop failed because the threshold intensity (∼ MW/cm2)
must be maintained for the entire unwinding time ∼millisecond. Experiments
should also be able to distinguish between light-field-induced and thermal effects
that are present even at very low absorption coefficients of the LC medium.
Experiment described in this paper succeeded owing to specially chosen irradia-
tion conditions (∼ 4.5 kHz high-repetition rate) that enabled the cumulative action
of many pulses, each with above-threshold peak intensity. Low average power den-
sity did not permit heating of the sample.
Further development in this field should distinguish between “slow” (1) and
“fast” (2) unwinding experiments. (1) “Slow” unwinding, at near-threshold inten-
sities (I ∼ 2.2–10 MW/cm2) is presented in this paper. At such “low” intensities,
several minutes duration unwinding time offers the possibility to observe the un-
winding process in the microscope, i.e. imaging of how the chiral order changes
during the unwinding process. (2) Fast unwinding observed in Refs. 112 and 113 at
I ∼ 0.1–1 GW/cm2 opens the opportunity to use a cholesteric mirror for temporal
pulse shaping in a laser resonator with Q-switching or as the Q-switcher. It should
be added that nonlinear pitch dilation in cholesteric LC mirrors in laser resonator
gives the possibility to improve mode composition and output power stability of
CW and repetitively pulsed laser sources.
Acknowledgments
The author is very grateful to Prof. P. Palffy-Muhoray (Liquid Crystal Institute,
Kent State University) for his hospitality and help, Dr. A. Schmid (Laboratory for
Laser Energetics, the University of Rochester) for numerical simulations, providing
purified chiral mixture, and numerous discussions and help, Prof. S. Belyaev and N.
Malimonenko (Moscow Organic Intermediate and Dyes Institute (NIOPIK), Russia)
for fabrication cholesteric LC mirrors and discussions, K. Lebedev and E. Magu-
lariya (former students of Moscow Institute of Physics and Technology, Russia) for
assistance in chiral nematic experiments, Dr. T. Kosa (Liquid Crystal Institute) for
providing software and help, Dr. M. Groom (Liquid Crystal Institute) for the help
in maintaining electronics, Dr. B. Taheri (Liquid Crystal Institute) for the help in
maintaining laser system, Prof. J. Perry (University of Arizona) for providing chro-
mophore for some experiments, Prof. F. Scudiery and Dr. M. Marinelli (University
of Roma II) for providing their data in electronic form, Prof. V. Zolin, Dr. C.
Briskina, Dr. A. Lichmanov, Dr. V. Markushev, Dr. N. Ter-Gabrielyan from the
Institute of Radioengineering and Electronics of the Russian Academy of Sciences
(Moscow, Russia) for valuable advice and/or technical assistance, Dr. A. Zolot’ko
and Prof. V. Kitaeva from the P. N. Lebedev Institute of the Russian Academy of
Sciences (Moscow, Russia) for valuable references and advice.
This work was supported by NSF under ALCOM grant DMR-890147 and Cal-
ifornia Institute of Technology/AFOSR NoPC218970. In Russia this work was
402 S. G. Lukishova
partially supported by the International Science (Soros) Foundation (Grants Nos
MF2000 and MF2300), the Government of the Russian Federation (Grant No
MF2300), and the Russian Foundation for Basic Research (Grant No 96-02-18762).
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