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    Orthogonally-polarized optical feedback is known to act on the frequency

    of a semiconductor laser. The coupling of this feedback to a nonlinear filter

    results in bistability in the frequency of the laser output [B. Farias et al.

    Phys. Rev. Lett. 94, 173902 (2005)]. This phenomenon opens the way to the

    development of all-optical devices such as a switch between frequency states

    of the optical emission. For demonstrating this particular application we use

    an AsGaAl monomode laser emitting around 852 nm, together with a warm

    atomic cesium vapor as a resonant filter. The output frequency state of the

    switch is determined by two different frequencies of a control laser operating

    in an exclusive way, i.e. only one of the two control frequencies is able to

    change the switch frequency in a given direction. c 2010 Optical Society of

    America

    OCIS codes: 140.2020, 190.1450, 250.6715, 350.2450.

    1. Introduction

    Optical communications and, more generally, photonics applications with lasers, are

    suitable technologies for their characteristics of high frequency and insensitivity to

    electronic noise. Therefore, it is important to develop schemes where the encoded light

    signal may be changed also by light, avoiding then electronic stages in the apparatus.

    However, practical set-ups demand light-matter interactions, in order to guide or ma-

    nipulate photons, and then information. Nonlinear processes in these interactions are

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    at the very origin of the physical mechanisms to build switches, gates and other pho-

    tonics components for optical circuitry [1]. Therefore, high resonant susceptibilities of

    atomic and molecular media are adequate for one to explore mechanisms and config-

    urations for all-optical network devices [2]. A few proposals and realizations of switch

    prototypes have been made with molecules [35], while the nonlinear media mainly

    investigated for decades are atomic samples, particularly in experiments exploring

    the bistable behavior of the radiation amplitude [68]. Indeed, optical bistability in

    the literature refers to two states of the radiation amplitude of an optical hysteretic

    system [2]. Since the work of Gibbs and collaborators [6], which proposes applications

    of optical bistability as optical amplifier, memory, limiter, etc. an important number

    of schemes exploring optical nonlinearities of atomic resonances have been presented.

    More recently, the goal of building devices for optical computation and communica-

    tion has been extended to the so-called quantum computation, through the promise

    of optical switches working in the regime of one-photon input. As a result, configu-

    rations using atomic media have also been proposed and demonstrated [7, 8] to be

    adapted to the construction of very low intensity optical switches, whose ultimate

    aim is to attain the one-photon level, as required for quantum computation [9]. Thus,

    an expressive number of works have been done on the bistability behavior of light

    interacting with nonlinear systems [10]. Bistable laser light is a particularly suitable

    vehicle to carry binary information in its amplitude as well as in its frequency. How-

    ever, as already emphasized, the physical variable observed is invariably the radiation

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    amplitude, which leads to the production of AM optical switches, memories, etc.

    Recently has been demonstrated the operation of a laser in two or more output fre-

    quencies in the continuous-wave regime [11,12]: A semiconductor laser under atomic-

    filtered orthogonal-polarized feedback can work at various states of its frequency

    output for the same input parameters of that system, and laser emission presenting

    frequency bistability, tristability or multistability (different loops of bistable frequen-

    cies) has been observed, all these features occuring at a constant level of the laser

    emission power. These unique characteristics make this system a candidate for appli-

    cations in all-optical FM logic devices.

    In this paper we demonstrate the all-optical switching of the frequency of a diode

    laser operating in a frequency bistable regime with constant output amplitude. We

    explore the semiconductor laser sensitivity to orthogonal feedback, i.e., as the laser

    emission frequency depends on the intensity sent back into the semiconductor cavity,

    we use a non-linear filter to modulate the amplitude of the feedback beam, yielding

    a hysteretic behavior of the laser frequency. The output frequency has therefore two

    possible values, which can be set through the modification of the transmission of the

    non-linear filter. For this purpose we use a second laser (from now on named control

    laser) to increase/decrease the transmission of the spectral filter. In this scheme the

    control input, which activeness is determined by its frequency, induces frequency-state

    switches in one direction only. The two command signals (increasing or decreasing the

    filters transmission) work with about the same rise time, operate in latch mode [13]

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    and no reset is needed. This is the first scheme of a FM optical switch.

    2. Experimental Setup

    The switch laser is a single-mode AsAlGa diode laser (DL), stabilized in current and

    temperature (both within 104), emitting around 852 nm, and with no special coating

    on its faces. An optical setup allows to return a fraction of the output power back

    into the semiconductor gain medium, thanks to a high rejection polarizer. The exper-

    imental setup is esquematically shown in Fig.4. The polarization of the output beam

    is slightly elliptical, with an intensity ratio of 800:1 between the TE and TM com-

    ponents (parallel and perpendicular to the laser junction). The beam is sent through

    a polarizer that transmits the TE component and laterally reflects the TM one. We

    use the ejection axis of the polarizer to send back a TM-polarized beam into the DL

    cavity. The feedback intensity is controlled by a half-wave plate. The power of the

    feedback beam is measured, but the effective power coupled into the semiconductor

    cavity is not precisely known, due to the asymmetric and sub-wavelength dimensions

    of the cavity. As the output frequency of the laser experiences a shift that linearly

    depends on the orthogonal feedback power [11], we optimize the alignment through

    maximizing the frequency shift for a given feedback level. This feedback intensity is

    spectrally filtered by a Doppler-broadened atomic absorption line when a thermal

    cesium vapor (T 50C) in a 20 mm-long cell is inserted in the feedback loop. The

    absorption in the filter can be modified through the atomic density, which is adjusted

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    by the temperature of the cell reservoir.

    In our working conditions [11, 12], the current is more than twice the threshold

    one and the switch laser output power is essentially independent of the orthogonal

    feedback [14]. In order to spectrally analyze the emission of the switch laser we use a

    Fabry-Perot (F-P) interferometer and a room-temperature cesium cell (Analyzer in

    Fig.4), both placed externally to the feedback circuit. To avoid any interference with

    the experience, an optical isolator blocks residual reflections (particularly from the

    F-P of analysis) as well as assures the one-way character of the feedback loop.

    The FM switch control is performed by a DBR-type, cw monomode AsAlGa diode

    laser, which frequency is set around 852 nm, in resonance with one of the two hyperfine

    sublevels of the Cs D2 transition. A fraction of the control beam is sent through a

    room-temperature reference cesium cell (not shown in Fig. 4) to monitor the tuning

    of the control laser around the hyperfine transition of interest. A beam of a few

    milliwatts, intensity-modulated by a mechanical chopper, is sent through the atomic

    filter, making a small angle with the switch beam so as to maximize the interaction

    volume with the atoms attenuating this latter.

    3. Results and Discussion

    If one takes into account the linear shift of the laser frequency with the feedback power

    (the higher the feedback power, the larger the red shift) [15] and the modulation of the

    feedback power by the spectral filter, the frequency of the laser with feedback as a

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    function of the solitary (i.e.,without feedback) laser frequency 0 can be written [11]:

    = 0 0[1 f()]P, (1)

    where is the linear coefficient of the frequency shift as a function of the orthogonal

    feedback power; 0 gives the maximum fraction (i.e., out-of-resonance) of the optical

    power P returning into the switch laser, and is the amplitude coefficient of the

    normalized absorptive lineshape. This lineshape is here assumed to be Gaussian,

    f() = exp[f( at)2], where = (4 Log2)/2D, with D the full Gaussian width

    at half maximum. With such a filter lineshape (shown in Fig. 4a) the calculated laser

    frequency for typical values of the experimental variables is shown in Fig. 4b as a

    function of the solitary laser frequency, scanned around the atomic line center, at.

    As the switch laser frequency is scanned (by means of its injection current [16])

    through the Cs D2 line, the modulation of the orthogonal feedback field by the atomic

    line allows the observation of bistability and multistability cycles in the emission

    frequency [11, 12, 15]. Working in a bistable regime (see Fig. 4b), the switch laser

    frequency follows one (branch I in Fig.4b) of the two frequency branches during the

    up scanning and the other one (branch II) during the down scanning. In Fig. 4b one

    can see that jumps between the two branches occur in order to avoid the unstable

    region (d/d0 < 0, dotted part of the S curve [11]) of the filter lineshape, where

    the optical orthogonal feedback amplifies frequency instabilities (positive feedback)

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    and where the laser frequency shows a runaway behavior [?]. Starting from point

    C, common to both up and down scans, increasing the solitary frequency of the

    laser (i.e. decreasing the injection current) makes the system evolve through branch

    I up to point B, where it jumps to B and follows further to point C. From point C,

    decreasing the frequency makes the system return through branch II and, in A, jump

    to point A and then go back to the initial frequency at C. Fig. 4c shows a bistable

    absorption spectrum in the analysis cell, with the corresponding points shown in Fig.

    4b. Stopping the scan at point 1, we can access state 2 by shifting the switch laser

    frequency to the red, reaching the frequency where the system jumps downward.

    Conversely, once at point 2, a blue shift causes the frequency to jump upward back

    to state 1.

    A simple manner to induce the frequency shifts necessary to switch between the

    two states of the switch laser frequency is to change the transmission of the atomic

    filter, modifying thus the feedback power returning to the switch laser. It can be

    all-optically achieved by means of the control laser, when this laser is tuned to the

    convenient hyperfine level of the Cs D2 line. Fig. 4a shows a scheme of the sublevels

    involved in the switching process.

    Let us assume the switch laser is in state 1 of the hyperfine transition F = 4 F =

    3, 4, 5 [18]. If the control laser is tuned to the same hyperfine transition than the switch

    laser, (Fig. 4c), a pulse of this laser momentarily diminishes the population available

    to absorb the light of the switch laser, due to the mechanism of optical pumping [19].

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    Hence, the transmission of the filter increases and the switch laser frequency is red

    shifted, causing it to jump downward and to reach a state between points A and

    C. When the pulse is gone, the switch laser solitary frequency (horizontal axis in

    Figs. 4b and 4c) returns to its initial value, which now corresponds to state 2, i.e.

    to another value of the frequency of the switch laser with feedback (vertical axis in

    Fig. 4b). The frequency jump is one-way only and once it is done the switch laser

    frequency can no longer be affected by the control laser pulses as back and forth

    red shifts cannot induce the return to the previous state (see Fig. 3). Now, if the

    switch laser is in state 2 and the control laser is tuned to the F = 3 F = 2, 3, 4

    transition (Fig. 4d), the control laser optically pumps atoms from the F = 3 to the

    F = 4 hyperfine level, increasing the number of atoms available to absorb the switch

    laser light and thus lowering the transmission of the filter. The resulting decrease of

    the orthogonal feedback intensity shifts the switch laser frequency to the blue and

    induces the upward jump to point B, relaxing to state 1 when the control pulse

    has faded.

    Figure (4) shows the all-optical frequency switching of the switch laser from state

    1 to state 2, when both switch and control lasers are resonant with the F = 4 F

    transition. Figure (4) shows the 2 to 1 switch, when the switch laser is resonant

    with the F = 4 F and the control laser with the F = 3 F transition.

    The upper figures in Fig. (4) and Fig. (4) exhibit the amplitude modulation of the

    control laser by a mechanical chopper, as detected by photodetector PD4, shown in

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    Fig. (4). At t = t0, the control laser beam, initially blocked, is suddenly allowed

    to interact with the filter. The bottom figures in Fig. (4) and Fig. (4) show the

    simultaneously measured absorption of the switch laser beam by an analysis cesium

    vapor cell, as registered by photodetector PD3. In Fig. 4 (Fig. 4) we observe that,

    when the control laser is released, the absorption of the switch laser by the analysis

    cell changes abruptly, reflecting the switching from frequency state 1 (2) to 2 (1).

    After the frequency jump, we note that further modulation of the control laser still

    slightly (8 to 20 % in the measurements of Figs. (4) and (4)) perturbs the switch laser

    frequency but cannot change the frequency state. The residual modulation in Figs.

    (4b) and (4b), as the vapor transparency modulation by the control laser proceeds,

    corresponds to the absorption modulation when the switch laser frequency is varied

    around 1 or 2. The control intensity should be as small as possible and only sufficient

    to change the vapor optical density so that the switch laser frequency change is slightly

    larger than (1 A) (or B 2), triggering the switch. Figs. (4) and (4) have been

    recorded in conditions (Icontrol > Isat) such that the corresponding frequency variation

    is much larger than necessary to operate the switch. Furthermore, in normal working

    conditions (control pulse to trigger the switch), the control laser intensity after the

    pulse is kept off so that the switch laser operates either in state 1 or 2, with no further

    frequency modulation. The switching time is mainly limited by the time response of

    the semiconductor laser to the orthogonal feedback, that we measure to be 10 s.

    The absence of the field that causes the switching does not change the output state,

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    meaning that it is a latching switch, and from Figs. (4) and (4) we can see that a large

    contrast between the two output states is achieved (more than 1 GHz of separation,

    see figure 2b). Unlike other switches that work based on an input modifying the

    level of the output amplitude, we have here an amplitude signal input leading to a

    frequency output signal with stable amplitude. Hence, we have automatically satisfied

    two conditions for scalability [20]: i) input amplitude variations do not affect the

    output amplitude (signal level restoration) and ii) the output cannot have back-action

    on the input (input-output isolation). The remaining condition for this switch to be

    scalable is cascadability, i.e., the capacity that the device output have power enough

    to drive the input of at least two equal devices. However, in the present configuration,

    the issue of getting the right control frequency needs to be addressed.

    4. Conclusion

    We have experimentally demonstrated the operation of a diode-laser-based all-optical

    frequency switch by means of an atomic filter modulating the amount of orthogonally-

    polarized optical feedback into the laser cavity. The switch between two frequencies is

    triggered by an optical pulse whose frequency unambiguously determines the switch

    direction. The laser output amplitude is constant through the frequency switching

    processes. This optical device therefore represents the first development of an all-

    optical FM switch.

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    References

    1. S. D. Smith, Lasers, nonlinear optics and optical computers, Nature 316, 319

    324 (1985).

    2. H. M. Gibbs, Optical bistability: Controlling light with light. Academic Press, Inc.

    Orlando, FL, USA (1985).

    3. G. L. Lippi, H. Grassi, T. Ackemann, A. Aumann, B. Schapers, J. P. Seipenbusch

    and J.R. Tredicce, Bistability and transients in CO2 laser patterns, J. Opt. B:

    Quantum Semiclass. Opt. 1, 161165 (1999).

    4. E. Arimondo, and B.M. Dinelli, Optical bistability of a CO2 laser with intra-

    cavity saturable absorber: Experiment and model, Opt. Commun. 44, 277282

    (1983).

    5. F. M. Raymo and S. Giordani, All-optical processing with molecular switches,

    Proc. Of the Nat. Ac. of Sci. 99, 49414944 (2002).

    6. H. M. Gibbs, S.L. McCall and T.N.C. Venkatesan, Differential gain and bista-

    bility using a sodium-filled Fabry-Perot interferometer, Phys. Rev. Lett. 36,

    11351138 (1976).

    7. Andrew M. C. Dawes, Lucas Illing, Susan M. Clark and Daniel J. Gauthier, All-

    optical switching in rubidium vapor, Science 308, 672674 (2005).

    8. Jiepeng Zhang, Gessler Hernandez, and Yifu Zhu, All-optical switching at ul-

    tralow light levels, Opt. Lett. 32, 13171319 (2007).

    12

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    9. D. Lukin, Trapping and manipulating photon states in atomic ensembles, Rev.

    Mod. Phys. 75, 457472 (2003).

    10. Andrew M. C. Dawes, Daniel J. Gauthier, Stefan Schumacher, N. H. Kwong,

    R. Binder and Artur L. Smirl, Transverse optical patterns for ultra-low-light-

    level all-optical switching, Laser & Photon. Rev., DOI: 10.1002/lpor.200810067

    (2010).

    11. B. Farias, T. Passerat de Silans, M. Chevrollier and M. Oria, Frequency bistabil-

    ity of a semiconductor laser under a frequency-dependent feedback, Phys. Rev.

    Lett. 94, 173902 (2005).

    12. M. Oria, B. Farias, T. Sorrentino and M. Chevrollier, Multistability in the emis-

    sion frequency of a semiconductor laser, J. Opt. Soc. Am. B 24, 18671873

    (2007).

    13. G. Langholtz, A. Kandel, and J. Mott, Foundations of Digital Logic Design, p.340,

    World Scientific, Singapore, 1998.

    14. T. Heil, A. Uchida, P. Davis and T. Aida, TE-TM dynamics in a semiconductor

    laser subject to polarization-rotated optical feedback, Phys. Rev. A 68, 033811

    (2003).

    15. C. Masoller, T. Sorrentino, M. Chevrollier and M. Oria, Bistability in semicon-

    ductor lasers with polarization-rotated frequency-dependent optical feedback,

    IEEE J. Quantum Electron. 43, 261268 (2007).

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    16. The current scanning is small enough not to produce any appreciable amplitude

    modulation.

    17. A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier and M. Oria, Diode laser

    coupled to an atomic line by incoherent optical negative feedback, Appl. Phys.

    Lett. 84, 179181 (2004).

    18. The Doppler FWHM of the Cs D2 lineshape in a Cs vapor cell is larger than the

    separation between the excited hyperfine sublevels, so that the linear absorption

    on this transition consists of a single broad line.

    19. Spontaneous emission from the excited F levels takes place towards F = 4 and

    F = 3 with similar probabilities. In the absence of a mechanism to redistribute

    the populations between the two ground sublevels, the population piles up in

    the uncoupled state (optical pumping process). However, in ordinary (glass or

    metallic) optical cells, a certain amount of population thermalization is achieved

    through collisions of the atoms with the cell walls. See, for example H.N. de

    Freitas, A. F. A. da Rocha, M. Chevrollier and M. Ori a, Radiation trapping and

    spin relaxation of cesium atoms at cell walls, Appl. Phys. B 76, 661666 (2003).

    20. R. W. Keyes, Information, computing technology, and quantum computing, J.

    Phys.: Condens. Matter 18, S703S719 (2006).

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    FIGURES CAPTIONS

    Fig.1 (Color online) Experimental setup. The switch laser frequency is turned

    bistable through filtered, orthogonally polarized, optical feedback. The control laser

    operates the switch through manipulation of the atomic filters transparency at the

    switch laser frequency. DL, diode laser; BS, beam splitter; PM, power meter; G-F,

    Glan-Foucault polarizer; M, mirror; OI, optical isolator; /2, half-wave plate; PD,

    photodetector; F-P, Fabry-Perot interferometer.

    Fig.2 (Color online) Frequency bistability of the switch laser. (a) Filter Gaussian

    spectral profile. (b) Laser emission frequency as a function of the solitary frequency

    (Eq. 1), for =1.5 GHz/mW, =0.32 and 0 = 5.4 102. (c) Laser absorption of

    the switch laser beam by an analysis Cs vapor cell, as a function of the solitary laser

    frequency scanned around the 6S1/2F = 4 6P3/2F Cs D2 transition, showing an

    hysteretical behavior and frequency bistable states 1 and 2.

    Fig.3 (Color online) Scheme of the energy levels of Cs involved in the switch

    process, with the populations of each ground-state hyperfine sublevels represented

    by dots of diameter proportional to the respective population, for a few lasers

    configurations. (a) The equilibrium populations in the fundamental sublevels F = 3

    and F = 4 in the absence of incident radiation are proportional to their respective

    level degeneracy (g4/g3 = 9/7).(b), (c) and (d): The non-saturating switch laser

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    beam is resonant with the 6S1/2F = 4 6P3/2F transition. (b) The switch laser

    beam slightly depletes the F = 4 population in favor of F = 3 [19]. (c) The control

    laser beam, resonant with the same F = 4 F

    transition, further depletes the

    F = 4 population, decreasing the medium opacity for the first laser. (d) The control

    laser beam, resonant with the F = 3 F transition, ensures re-equilibration of the

    ground sublevels populations [19]

    Fig.4 Demonstration of the control pulse-induced switch from state 1 to state

    2: (a) The control laser amplitude incident on the atomic filter is modulated by a

    chopper. At t = t0, the first control pulse makes the switch laser frequency jump from

    state 1 to state 2, as evidenced in (b) by the sudden variation of the absorption in

    the analysis cell. After the switching, the control laser does not change the switch

    laser frequency state anymore.

    Fig.5 Demonstration of the control pulse-induced switch from state 2 to state

    1: (a) The control laser amplitude incident on the atomic filter is modulated by a

    chopper. At t = t0, the first control pulse makes the switch laser frequency jump from

    state 2 to state 1, as evidenced in (b) by the sudden variation of the absorption in

    the analysis cell.

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    ChopperCs vapor cell

    (Filter)Oven

    BS

    BS

    BS

    BS

    l/2

    M

    M

    BS

    M

    MOI

    DL

    G-F

    F-P (Analyzer)

    PD2

    PD1

    PD3

    PM

    PD4

    Cs vapor cell

    (Analyzer)

    Control Laser

    DL

    M M

    Switch Laser

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    2 3 4 5

    -1.5

    0.0

    1.5

    0.5 1.0

    -1.5

    0.0

    1.5

    C

    n2

    II

    n0-nat (GHz)

    n-nat(GHz)

    f(n)

    A

    B

    C'

    B'

    (b)

    I

    (arb. units)

    A' n1

    (a)

    1 2 3

    0.0

    0.1

    0.2

    0.3

    0.4

    0.5

    C'

    n0-nat (GHz)

    (c)

    n2

    Absorption(arb

    .units)

    n1

    A

    A'

    B

    B'

    C

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    controllaser

    F=4

    switch laser

    F=4

    F'

    F=4

    F'(a) (b)

    F=3

    switch laser

    F=4

    F'

    switch laser

    F'

    controllaser

    (c)

    F=3 F=3

    F=3

    (d)

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    0 20 40 60 80 100-2,2

    -2,1

    -2,0

    -1,9

    -1,8

    -1,7

    -1,6

    -1,5

    b)Absorption(arb.units)

    Time (ms)t

    0

    a)

    on

    0 20 40 60 80 1000,05

    0,00

    -0,05

    -0,10

    -0,15

    -0,20

    -0,25

    offIntensity(arb

    .units)

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    0 25 50 75 100

    -0,6

    -0,5

    -0,4

    -0,3

    -0,2

    -0,1

    0,0

    0 25 50 75 100-0,65

    -0,60

    -0,55

    -0,50

    -0,45

    -0,40

    b)

    Intensity(arb.

    units)

    a)

    t0

    on

    off

    Absorptio

    n(arb.units)

    Time (ms)

    21