nonlinear optical refractive indices and absorption coefficients of α, β-unsaturated ketone...

$: Nonlinear optical refractive indices and absorption coefficients of α, β-unsaturated ketone derivatives$
1456 J. Opt. Soc. Am. B/Vol. 18, No. 10 /October 2001 Zhou et al.

Nonlinear optical refractive indices andabsorption coefficients of

a,b-unsaturated ketone derivatives

Jun Zhou

Optoelectronics Research Centre, Department of Electronic Engineering, City University of Hong Kong, Koloow,Hong Kong, and Institute of Engineering Physics, Shandong University of Science & Technology, Taian,

Shandong 271019, China

Edwin Y. B. Pun

Optoelectronics Research Centre, Department of Electronic Engineering, City University of Hong Kong, Koloow,Hong Kong

Xiao Hong Zhang

Institute of Photographic Chemistry, Chinese Academic of Science, Beijing 100101, China

Received January 3, 2001

The nonlinear optical refractive indices and the nonlinear optical absorption coefficients of newly synthesizeda,b-unsaturated ketone derivatives (USKDs) were investigated by use of the intensity-dependent transmit-tance method and the Z-scan technique with a pulsed Nd:YAG laser at 532-nm and 1064-nm wavelengths.Opposite changes of signs of the nonlinear refractive indices are observed at the two wavelengths and can bemainly attributed to the thermal effect and the two-photon absorption mechanism. The origins of the non-linearity of USKDs are discussed, and by establishing a kinetic model for the USKDs, several other nonlinearoptical parameters are obtained, such as the cross section of two-photon absorption, the absorption cross sec-tion of the excited state, and the real part of second-order hyperpolarizability of the ground state. The resultsindicate that USKDs are potential optical limiting materials. © 2001 Optical Society of America

OCIS codes: 160.4330, 160.4890, 190.0190, 190.4180.

1. INTRODUCTIONNonlinear optical effects in organic crystals and polymershave been extensively exploited during the past decade.1,2

In these organic materials the p-conjugated organic mol-ecules are investigated with great interest due to their po-tential applications in optical image processing,3 all-optical switching,4,5 and integrated optical devices.6

Although polymers with sufficiently high second-ordernonlinearity have been developed for electro-opticapplications,7,8 no organic materials have satisfied all therequired conditions for third-order nonlinear optical de-vice applications.9 Thus the quest for new organic mate-rials and fundamental understanding of the structure–property relationship for third-order optical nonlinearityis an important task. In general, large hyperpolarizabili-ties are the result of an optimum combination of variousfactors, such as p-delocalization length, donor–acceptorgroups, dimensionality, conformation, and orientation fora given molecular structure.10

In recent years a great deal of effort has been devotedto the development of optical-limiting materials and de-vices because of the need for automatic protection of hu-man eyes and sensors against intense laser radiation.11

The dominant mechanisms for optical-limiting behaviorhave been established to be two-photon absorption (TPA)and reverse saturable absorption. A number of studies

0740-3224/2001/101456-08$15.00 ©

on optical-limiting effects related to TPA processes havebeen reported to understand the relationship between or-ganic molecular structure and TPA.12,13 Research ondonor–acceptor stilbene derivatives has helped in design-ing donor–acceptor compounds with enhanced two-photonabsorption.14,15 Many researchers have reported on thedesign and the synthesis of a new type of push–pull con-jugated materials with large second-order polarizabilitychromophores. Theoretical and experimental studies onthe structure–polarizability relationship in push–pull-type conjugated materials containing a keto spacer groupwithin the dithienyl-conjugated backbone have beenreported.16 The characterization of new push–pull asym-metrically substituted unsaturated phthalocyanines hasalso been studied.17 However, the third-order nonlinearoptical properties of a,b-unsaturated ketone derivativeswith a keto spacer within the styryl-conjugated pathwayshave not been reported to our knowledge.

In this paper the nonlinear optical refractive indicesand the nonlinear optical absorption coefficients of newlysynthesized a,b-unsaturated ketone derivatives (USKDs)have been investigated by use of the intensity-dependenttransmittance method18 and the Z-scan technique.19,20

The measurements were performed with a nanosecondNd:YAG laser working at 1064-nm and 532-nm wave-lengths. The relationship between the push–pull struc-

2001 Optical Society of America

Zhou et al. Vol. 18, No. 10 /October 2001 /J. Opt. Soc. Am. B 1457

ture characteristic of electron–donor and electron–acceptor groups and the hyperpolarizabilities ofchromophores were also studied. By establishing a ki-netic model for the USKDs, several other nonlinear opti-cal parameters were also obtained.

2. EXPERIMENTSA. Sample Preparation and CharacterizationThe chemical structures of a,b-unsaturated ketone de-rivative molecules are shown in Fig. 1. They were syn-thesized by a general method described in Ref. 21. Theirstructures were confirmed by 1H NMR and mass spec-trometry. USKD-1 and USKD-2 are distinguished struc-turally by the difference in the electron–acceptor groupsonly [nitro group (-NO2) and nitrile group (-CN)].USKDs exhibit a large nonlinear optical refractive indexand a nonlinear optical absorption because their struc-tures have an intensive transfusion of charge with donorand acceptor functional group and delocalized p-electroneffects.

The linear-absorption spectra of USKD samples areshown in Fig. 2. All the filtered sample solutions wereprepared with toluene as the solvent and measured by aspectrometer at room temperature. The concentration ofUSKD in toluene varies from 5 3 1023 mol/L to 23 1022 mol/L. There is a strong linear absorption in the300–350-nm range and another strong absorption peak inthe 400–450-nm range. However, there is no strong ab-sorption in the spectral range from 600 nm to 1200 nm ex-cept for a weak peak at 1175 nm due to the toluene used.

The photoluminescence spectra of USKD solutions areshown in Fig. 3. The spectra were measured with a Per-kin Elmer LS50B luminescence spectrometer, and the ex-citing wavelength was 400 nm. The yellow-greenfluorescence-emission peak at 550 nm implies that short-wavelength absorption will lead to a fast relaxation fromthe upper Sn to the S1 state and a transition emission ofthe S1 → S0 state. A combined analysis of the linear-absorption and the photoluminescence spectra result in afive-level model that is described in Section 3.

Fig. 1. Molecule structures of a,b-unsaturated ketone deriva-tives: (a) USKD-1; (b) USKD-2.

B. Experimental ArrangementThe experimental setup, as shown in Fig. 4, can performboth the intensity-dependent transmittance and theZ-scan measurements. The exciting light source was aQ-switched Nd:YAG laser providing a single pulse at ei-ther a 1064-nm or a second-harmonic 532-nm wave-length, and typical pulse duration was 7 ns. A variableoptical attenuator consisting of a rotating half-wave plate(HP) and a Glan–Thomson polarizing prism (P) attenu-ates the laser beam intensity without changing the tem-poral and spatial structures of the laser radiation. A175-mm focal-length lens (L1) provided a tight focusing ofthe laser beam, and the beam-waist radii, v0 , were 45 mmand 36 mm at 1064 nm and 532 nm, respectively. BS1

Fig. 2. Absorption spectra of USKD.

Fig. 3. Fluorescence spectra of USKD.

Fig. 4. Experimental setup for the intensity-dependent trans-mitted measurement and the Z-scan technique.


and BS2 were beam splitters. D1 was the probe of alaser-energy meter (Lambda Physik Lasertechnik), D2was a 1-cm-diameter silicon photodiode, and D3 was ahigh-speed photodetector (Newport, Model 875). D1 wasused to monitor the incident pulse energy, and D2 and D3were used to detect the Z-scan signals of the open and theclosed aperture measurements, respectively. L2 was alens ensuring that all the reflected light was collected bythe detector D2. D3 was mounted at a position 110 cmfrom the focal plane z 5 0, and for closed-aperture Z-scanmeasurements an aperture A was used in front of the de-tector.

In the Z-scan experiments a 1-mm path-length quartzcell was filled with USKD samples that had a concentra-tion of ;1023 mol/L. Thin-sample approximation wasused in the measurements because the thickness is thincompared with the Rayleigh length of the laser beam.Each experimental point was taken with an average of atleast 32 shots with a 1-Hz repetition rate by means of adigital storage oscilloscope (Hewlett Packard 54520A).To verify the accuracy of the experimental setup, a stan-dard sample CS2 was used for calibration purposes. Thetheoretical fitting values to the closed-aperture Z-scan ex-perimental data were n2 5 1.56 3 10211 esu at 1064 nmand n2 5 1.45 3 10211 esu at 532 nm. These values arein close agreement with the values given in Ref. 19 (n25 1.30 3 10211 esu at 1064 nm and n2 5 1.203 10211 esu at 532 nm).

In the intensity-dependent transmittance measure-ments, variable input laser powers (up to 0.5 GW cm22)were obtained without changing the pulse polarization byrotating the half-wave plate (HP) within the damagethreshold of the quartz cell, and the input pulses were fo-cused with a 25-cm focal-length lens. A 10-mm path-length quartz cell filled with USKD solutions was used,and the laser beam passed through the sample with its fo-cus spot near the middle of the sample cell. The probe(LMP10I) of a laser-energy meter (Coherent Labmaster)with a large detection area was placed behind the sample.To ensure that all the transmitted pulse energy was cap-tured by the energy meter, there was no diaphragm orpinhole between the sample and the detector.

3. RESULTS AND DISCUSSIONA. Intensity-Dependent Transmittance MeasurementThe USKD samples displayed the nonlinear absorption asa function of input fluence at 532-nm and linear absorp-tion at 1064-nm wavelengths. In the scope of this paper,only the experimental results of the nonlinear absorptionat 532 nm are shown in Fig. 5. In Fig. 5(a), USKD-1 dis-plays a linear absorption at low input fluence initially,then a nonlinear absorption (RSA or TPA) at high inputfluence, and finally a saturable absorption at higher flu-ence. In Fig. 5(b), USKD-2 displays a nonlinear absorp-tion only (RSA and TPA) with increasing input fluence.The effective absorption coefficient of USKD solutions,aeff , is presented in Table 1. aeff is determined by the re-lation Iout /I in 5 exp(2aeffL), where L is the samplelength, and Iout /I in was obtained by a linear fit to the dy-namic transmittance data.

A multilevel energy diagram, as shown in Fig. 6, can be

used to explain the absorption behaviors of USKD. Thefive-level structure shows the possibility of both excitedsinglet- and triplet-state absorption. In this scheme themolecules are optically pumped with single-photon ab-sorption cross section s0 and a TPA averaged cross sections2P from the single state S0 to the excited single state S1 .The population in the excited state can either undergosingle-photon absorption to higher states S2 with a cross

Fig. 5. Output versus input fluences at 532 nm for (a) USKD-1and (b) USKD-2 in a 10-mm quartz cell. Straight lines are lin-ear fits of the fluence transmittance. Solid curves are theoreti-cal fitting curves for the nonlinear absorption.

Fig. 6. Energy-level diagram for USKD.

Table 1. Effective Absorption Coefficients ofUSKD Solutions

Sample aeff (cm21) I in (J cm22) aeff (cm21) I in (J cm22)

USKD-1 0.462 ,0.073 3.08 .1.05USKD-2 0.274 ,0.23 1.36 .1.34


section sS , or cross over to the lowest triplet state T1with an intersystem crossing time tST , or decay to theground state with a characteristic time t10 . An uppertriplet T2 can be populated from the lowest triplet stateby one-photon absorption with a cross section sT . Thereare a lot of vibrational and rotational substates locatedabove the electronic energy levels in the single and tripletmanifolds.

Since the upper singlet- and triplet-state lifetimes aregenerally much shorter than the S1-state lifetime t10 , thepopulation of the upper states can be neglected. In addi-tion, the typical value of the intersystem crossing time tSTis larger than that of the laser pulsewidth used in our ex-periments; thus the population of the triplet states can beignored.22 For simplicity we shall not solve all the rateequations on the model described above; instead we cal-culate numerically the nonlinear-absorption processes ofthe USKD molecules using the following equations23,24:

dN0

dt5 2

s0

hnN0I 2

s2P

hnN0I2 1

N1

t10, (1)

dN1

dt5

s0

hnN0I 1

s2P

hnN0I2 2

N1

t10, (2)

dI

dz5 2~ s0N0 1 sSN1!I 2 s2PN0I2, (3)

where N0 and N1 are the populations in energy levels S0and S1 , respectively, I is the incident intensity, and z isthe direction of propagation at frequency n. The bound-ary conditions are given by

N0~z, r, t 5 2`! 5 N,

N1~z, r, t 5 2`! 5 0, (4)

N 5 N0 1 N1 ,

I~z 5 0, r, t ! 5 I08 expF2S t

tpD 2GexpF2S 2r

v0D 2G , (5)

where N is the total population density, I08 is the peak-on-axis irradiance of the incident laser pulse of duration tp ,and v0 is the spot size at focus. The population N corre-sponds to a concentration of 1.12 3 1022 M/L and 6.83 1023 M/L, and I08 were 0.13 GW/cm2 and 0.21 GW/cm2

for USKD-1 and USKD-2, respectively. From the lineartransmittance fit in Fig. 5, the cross sections s0 were de-termined to be 6.97 3 10220 cm2 and 6.68 3 10220 cm2 forUSKD-1 and USKD-2, respectively.

It is very difficult to obtain the analytical solutions ofthe time–space-dependent differential equation system.Therefore the standard Runge–Kutta–Fehlberg methodcan be used to solve Eqs. (1)–(5) with the parameterspresented above. The numerical solution is then appliedto fit the experimental data by adjusting the values ofthe variable parameters sS and s2P . The decrease intransmittance with increasing transmitted-beam diver-gence due to nonlinear refractive effects and surface re-flection of the quartz cell were ignored in the theoreticalfit. The solid curves in Fig. 5 are the theoretical fittingcurves with sS 5 2.27 3 10219 cm2 and s2P 5 5.183 10218 cm4/GW for USKD-1 and sS 5 1.15

3 10219 cm2 and s2P 5 7.68 3 10219 cm4/GW forUSKD-2. However, it is worth remembering that theconversion behavior of RSA to saturable absorption usesUSKD-1 for the optical-limiting application, and the inci-dent intensity threshold25 at the turning point Ic is only1.75 J/cm2.

B. Open-Aperture Z-Scan MeasurementThe nonlinear absorption of USKD solutions is measuredby use of the open-aperture Z-scan technique at a 532-nmwavelength and is shown in Fig. 7. From the results inSubsection 3.A, s2P is the dominant parameter in deter-mining the curvature of the nonlinear-transmissioncurve. Therefore the nonlinear absorption of USKD inan open-aperture Z-scan can be explained mainly by theTPA mechanism, and the total absorption coefficient canbe written as

a~I ! 5 a0 1 bI, (6)

where a0 is the linear-absorption coefficient and b is theTPA coefficient. The normalized transmittance T(z) inFig. 7 was analyzed theoretically with the following equa-tions that are integrated with respect to time t19:

T~z ! 51

Apq~z !E

2`

1`

ln@1 1 q~z !exp~2t 2!#dt, (7)

Fig. 7. Open-aperture Z-scan data: Normalized transmittanceof (a) USKD-1 and (b) USKD-2. Scatter points are experimentaldata, and solid curves are theoretical fitting results.


q~z ! 5bI0Leff

1 1 ~z/z0!2, (8)

where I0 is the input intensity at the focus z 5 0, Leff5 @1 2 exp(2a0L)#/a0 , where L is the sample length, z isthe distance of the sample from the focus, t 5 t/t0 is thetime normalized by the pulse duration (half-width at 1/epulse maximum), and z0 5 pv0

2/l is the Rayleigh diffrac-tion length. The numerical calculations were performedby choosing the most fitted values for parameter b. Fromthe solid curves in Fig. 7, the best-fitting values for b atI0 5 0.28 GW/cm2 are 39 cm GW21 and 4.3 cm GW21 forUSKD-1 and USKD-2, respectively. In addition, the TPAcross section s2P 5 b/N and the imaginary part of thethird-order nonlinear susceptibility Im x(3) 5 lce0n0

2b/2p

Fig. 8. Normalized transmittance of closed-aperture Z-scandata at 1064 nm for (a) USKD-1 and (b) USKD-2 with I05 2.25 3 1012 W/m2. Squares represent experimental data,and solid curves are theoretical fitting curves, resulting in an ap-erture of linear transmittance S 5 0.035.

Table 2. TPA Coefficient b, Cross Section s2P ,and Im x(3) of USKD Solutions

Sampleb

(cm/GW)s2P 3 10218

(cm4/GW)Im x(3) 3 10211

(esu)

USKD-1 39 5.88 (5.18)a 1.41USKD-2 4.3 1.04 (0.768) 0.155

a The values in parentheses correspond to the fitting values in Subsec-tion 3.A.

are listed in Table 2. In comparison with the values ofs2P reported in Ref. 23, they were of the same order ofmagnitude for the organic molecules of USKD and DCB(;10218 cm4/GW). However, the values given in Table 2are larger than the one reported in Refs. 12 and 13; a pos-sible explanation is the contribution of other effects, suchas the nonlinear refractive index, a multiresonance pro-cess involving one- or two-photon resonance (S0 → Sn)and the excited-state absorption as well as the triplet–triplet absorption of the sample molecules in the nanosec-ond regime, which are absent from the model in Subsec-tion 3.A.15,23 Moreover, the amount of aggregateformation in USKD solutions and the effect of solvent po-larity are not considered here.13 However, the deviationis no more than 630%, which is within the experimentalerrors. The results demonstrate that TPA is the domi-nant mechanism causing the observed nonlinear-absorption behavior and also that the values of b varywith different substitute groups.

C. Closed-Aperture Z-Scan MeasurementThe nonlinear refractive index n2 was measured by use ofthe closed-aperture Z-scan technique at 1064-nm and532-nm laser wavelengths. The technique can providenot only the magnitude of the real part of the nonlinearsusceptibility but also the sign. The experimental re-sults are shown in Figs. 8 and 9. The Z-scan curves ex-hibit a dispersionlike configuration, with a valley followedby a peak at the 1064-nm wavelength and a peak-to-

Fig. 9. Normalized transmittance of closed-aperture Z-scanmeasurement at 532 nm for (a) USKD-1 and (b) USKD-2 withI0 5 2.81 3 1012 W/m2. The squares represent experimentaldata, and the solid curves are theoretical fitting curves, resultingin an aperture of linear transmittance S 5 0.068.


valley configuration at the 532-nm wavelength. Thus thenonlinearity changes from self-focusing (Dn . 0) to self-defocusing (Dn , 0).

In Fig. 9 the signals of the closed-aperture Z-scan showa peak-suppression configuration at z , 0 side owing tothe strong nonlinear-absorption effect under 532-nm laserexcitation. To simplify the analysis, normalized Z-scandata induced by purely nonlinear refraction were ob-tained by dividing the closed-aperture data with the cor-responding open-aperture data, as shown in Fig. 10.Only the third-order optical nonlinearity in a purely re-fractive effect is examined under certain approximationconditions.19 The refractive part of the nonlinearity ischaracterized by the nonlinear refractive index g, and

n~I ! 5 n0 1 gI, (9)

where n0 is the linear refractive index and I denotes theirradiance of the laser beam within the sample. The fit-ted curves are given by19,26

T~z ! 5 1 14^DF0~t !&x

~1 1 x2!~9 1 x2!1

^DF0~t !&2

~9 1 x2!1 ... ,

(10)

with

DF0~t ! 5 kDn0~t !Leff , (11)

Fig. 10. Closed-aperture Z-scan data (in Fig. 9) divided by cor-responding open-aperture Z-scan data (in Fig. 7) at 532 nm for(a) USKD-1 and (b) USKD-2. Solid curves are theoretical fittingcurves.

where x 5 z/z0 , ^DF0(t)& represents the time-averagedon-axis phase shift at focus, k and Leff have been definedpreviously, and Dn0(t) 5 gI0(t), where I0(t) is the on-axis excitation intensity at focus and g is the nonlinear re-fractive index. In addition, ^Dn0(t)& 5 Dn0 /A2 for atemporally Gaussian pulse, representing the peak-on-axisindex change at the focus.

Equation (10) was used to fit numerically the curves ofthe closed-aperture Z-scan to determine the value of g ateach I0 . The fourth and higher terms on the right-handside of Eq. (10) were neglected in the process becauseu^DF0(t)&u < 1. Table 3 shows the fitted values of g un-der different measured wavelengths. It also contains thenonlinear refractive index n2 and the third-order suscep-tibility components Re x(3), and they are converted fromthe formula n2(esu) 5 (cn0/40p)g (m2/W) and Re x(3)

5 2n02e0cg, where c is the speed of light in vacuum. The

linear refractive index of the sample solutions was mea-sured to be ;1.497 with an Abbe refractometer.

There are two kinds of possible contributions to thenonlinear refractive index induced by the nanosecondpulse laser, i.e., the purely optical Kerr effect and thethermo-optical effect. If we consider the case of n2 . 0in Table 3, it can be concluded that the transient nonlin-earity is caused mainly by the electronic effect, and theorigin of positive sign is related to the p-electrondelocalization.2,10 From Fig. 2 and the intensity-dependent transmittance measurement the linear absorp-tion of USKD materials at a 1064-nm wavelength can beneglected; thus the thermal effect due to absorption bythe material is negligible. Operation at very low pulse-repetition frequency may not give rise to a cumulative ef-fect to show thermal nonlinearity. However, from thecomparison of Fig. 10 with Fig. 8 there is sign reversal ofthe nonlinear refractive index under laser excitation withdifferent wavelengths. Thus the closed-aperture Z-scandata are determined both by the linear and the nonlinear

Table 3. Nonlinear Index g, n2 and Re x(3) of USKDSolutions

Sample g 3 10217

(m2/W)n2 3 10210

(esu)Re x(3) 3 10210

(esu)

USKD-1 3.81a 1.36 0.32624.84 21.73 20.413

USKD-2 6.26 2.24 0.53522.38 20.852 20.203

a Upper values correspond to l51064 nm, and lower values correspondto l5532 nm.

Table 4. Physical Parameters of Toluene Used inthe Numerical Calculations

Quantitya Valueb Quantitya Valueb

n0(20 °C) 1.4961 k (W/m•K) 0.1342r0 (g/cm3) 0.8669 vs (m/s) 1333Cp (J/g•K) 1.804 g 1.35(dn/dT)p(K21) 2 5.6 3 1024

a See text for notation.b Refs. 25 and 26.


optical responses of the materials, and also by the pos-sible thermal effect caused by very low single- ormultiple-photon absorption at 532-nm pulse laser energy.To estimate how the thermal-lens effect produces the re-sults of a negative nonlinear refractive index, we can as-sume that, other than absorption, the thermal propertiesof sample solutions are governed by the solvent toluene.Some physical parameters of toluene used in the follow-ing computation are listed in Table 4.

In our experiments at a 532-nm wavelength the ther-mal effect is in the transient regime and not in the quasi-steady-state regime; i.e., the condition

tp < trise,trelax (12)

is satisfied,27 where trise is the rise time of the thermalnonlinearity and is ;25 ns from the relation trise' v0 /vs , where vs is the acoustic velocity, tp is the pulse

duration time, and trelax is the thermal-relaxation timeand is ;3.37 ms from the relation trelax 5 v0

2rCp/4k,where r is the toluene density, Cp is the specific heat, andk is the thermal conductivity. Hence the building up ofthe thermal lens is dominated not only by the acoustic-density change but also by the thermal diffusive effect.In this case, and following the theoretical treatment givenin Ref. 28, the on-axis time-averaged effective indexvariation induced by the thermal mechanism during theGaussian temporal pulse duration can be written as

^Dn0 eff& ' ^Dn0qss&expS 2m

2.7D , (13)

with

^Dn0qss& 5 21

2

aeffF0

r0Cp

dn

dT, (14)

where ^Dn0qss& is the on-axis time-averaged index changeunder quasi-steady-state approximation, m 5 triseAg/t0with g 5 Cp /Cv being the ratio between constant pres-sure and constant volume caloric capacities, t0 is the 1/epulse width, F0 is the on-axis incident fluence at focus,and dn/dT is the change in index with temperature.

Under our experimental conditions, t0 5 4.19 ns(tp 5 1.67t0 , the full width at half-maximum) andF0 5 1.95 J/cm2, and the computed values ^Dn0 eff&5 28.34 3 1025 and 23.68 3 1025, which are in closeagreement with experimental results ^Dn0& 5 29.583 1025 and 24.71 3 1025 for USKD-1 and USKD-2, re-spectively. The large negative refractive nonlinearity ismainly attributed to the thermal-contribution mecha-nism. The differences between the calculated values andexperimental data are due to the effective two-photon (ortwo-step) absorption and the electronic-origin nonlinear-ity. In addition, the discrepancies arise essentially fromthe uncertainty of the calibration of the peak irradianceand the beam-waist value in the Z-scan setup.

4. CONCLUSIONIn summary, the nonlinear refractive indices and the ab-sorption coefficients of newly synthesized a,b-unsaturated ketone derivatives have been characterizedwith the intensity-dependent transmittance method and

the Z-scan technique. The differentiation of the magni-tude of the third-order nonlinear coefficients is due to theability of electron withdrawing and electron pushing inthe nonlinear optical chromophores. This indicates thatthe electron donor and acceptor play an important role inthe structure–susceptibility relationship. The sign re-versal of the nonlinear refractive index induced by twokinds of wavelengths can be mainly attributed to thechange from the electronic-origin mechanism (at 1064nm) to the thermal effect and the two-photon-absorptionmechanism (at 532 nm). The computed values of thenegative nonlinear refractivity are in close agreementwith the experimental data.

In addition, the nonlinear optical absorption at 532 nmwas investigated by use of the nonlinear-transmittancemeasurement combined with the opened-aperture Z-scantechnique. Several nonlinear optical parameters, suchas the effective absorption cross section of the groundstate, the cross section of the excited state, the cross sec-tion of TPA, and the imaginary part of third-order nonlin-earity, were obtained. A kinetic model has been devel-oped to explain the results of the intensity-dependenttransmittance and open Z-scan experiments. The pa-rameters obtained suggest that USKDs have good pros-pects for applications in optical-limiting devices. Besidethe nonlinear-absorption phenomenon, the presence of anegative nonlinear refractive index (i.e., defocusing ef-fects) is also helpful in protecting optical elements fromdamage by intense laser light.

ACKNOWLEDGMENTSThis research is supported in part by the Third WorldAcademy of Sciences under Research Grant Agreement98-150 RG/PHYS/AS and by a Competitive EarmarkedResearch Grant, Research Grant Council, Hong Kong.The authors thank H. P. Ho for help in using the Nd:YAGlaser and Y. Liu for helpful discussions.

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nonlinear optical refractive indices and absorption coefficients of α, β-unsaturated ketone...

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