Optical Bistability in a GaAs-Based Polariton Diode

Daniele Bajoni,* Elizaveta Semenova, Aristide Lemaıtre, Sophie Bouchoule, Esther Wertz, Pascale Senellart,

Sylvain Barbay, Robert Kuszelewicz, and Jacqueline Bloch†

CNRS-Laboratoire de Photonique et Nanostructures, Route de Nozay, 91460 Marcoussis, France(Received 29 July 2008; revised manuscript received 6 November 2008; published 24 December 2008)

We report on a new type of optical nonlinearity in a polariton p-i-n microcavity. Abrupt switching

between the strong and weak coupling regime is induced by controlling the electric field within the cavity.

As a consequence, bistable cycles are observed for low optical powers (2–3 orders of magnitude less than

for Kerr induced bistability). Signatures of switching fronts propagating through the whole 300�300 �m2 mesa surface are evidenced.

DOI: 10.1103/PhysRevLett.101.266402 PACS numbers: 71.36.+c, 42.65.Pc, 73.50.Pz, 78.55.Cr

After its first observation in a Fabry-Perot cavity con-taining Na vapor [1], optical bistability has been widelyexplored in solid state systems for its possible applicationin all optical circuits and optical computing [2]. A commonapproach is the use of a microcavity in which the resonancefrequency depends on the stored optical energy: optical

�ð3Þ nonlinearities, of electronic or thermal origin, havebeen used to obtain bistability in one-dimensional [3,4] andtwo dimensional [5,6] photonic devices, with switchingincident powers around 1 kW=cm2. When part of a spa-tially extended bistable system is switched from one stablestate to the other, a front is formed between spatial regionsin different states. If this front is locked, spatial solitons canbe observed [7,8]; otherwise the front propagates along thesurface until the whole sample has switched state [9].

Recently optical bistability of microcavity polaritonshas been theoretically proposed to generate propagationof switching fronts which can be used for all opticalcomputation [10]. Polaritons are mixed exciton-photonquasiparticles resulting from the strong coupling regimeof excitons with a resonant cavity mode [11]. Polariton-

polariton scattering gives rise to giant �ð3Þ-type nonline-arities [12,13] which have been recently shown to generateoptical bistability [14]; indications of spatial solitons werealso reported [15]. Another approach for optical bistabilityis to use the switch from strong to weak coupling regimedue to exciton bleaching at high pumping power [16,17].This method has been theoretically proposed in 1996 [18],and some experimental indication has been reported in2004 [19].

In this work, we experimentally demonstrate low-poweroptical bistability based on a new nonlinear mechanism.Switching between strong and weak coupling regime isinduced controlling the internal electric field of a p-i-nmicrocavity. Well-defined hysteresis cycles are observedboth scanning the external bias or the optical power. Amodel including the changes of optical and electronicproperties between the strong and weak coupling regimeis developed and gives a good overall description of the

observed cycles. Finally, we show that a local excitationcan produce commutation of the whole mesa.The sample [see Fig. 1(a)] is described in detail in

Ref. [20]. Grown on an n-doped GaAs substrate, anundoped GaAs cavity containing 3 In0:05Ga0:95AsQWs is surrounded by a p- doped and an n-dopedGa0:9Al0:1As=Ga0:1Al0:9As Bragg mirror. 300 �m squaremesas, etched down to the substrate, were connected withmetal contacts. The diode under study, maintained at 10 K,presents a zero detuning between the cavity mode at nor-mal incidence and the QW exciton resonance.Let us first describe the two operating regimes of our

bistable structure. Figure 1(b) summarizes photocurrentspectra under normal incidence measured for differentvalues of the external bias VB. For VB > 0:3 V, two distinctphotocurrent peaks are resolved, attributed to the upper andlower polariton branches (polariton dispersion has beenfully characterized in Ref. [20]): the system operates inthe strong coupling (SC) regime [11]. On the opposite,below 0.2 V, photocurrent spectra exhibit only one peak(the cavity mode): the sample has abruptly switched to theweak coupling (WC) regime. To understand this behavior,the electric field E at the QW position has to be considered:

FIG. 1 (color online). (a) Schematic sample structure.(b) Photocurrent as a function of the laser energy measuredwith an optical power P ¼ 10 W=cm2 and for different voltagebias. Spectra have been vertically shifted for clarity.

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E ¼ �i � VB þ ZI

Lcav

; (1)

where �i ’ 1:48 V is the built in potential, I the current, Zthe load resistance, and Lcav ¼ 237:6 nm the intrinsicregion thickness. In the measures of Fig. 1(b), Z ¼ 50 �is the coupling impedance of the voltmeter and ZI can beneglected.

For VB ¼ 0:2 V, E lies around 55 kV=cm so that theStark effect is too small to induce the loss of SC regime[21]. The abrupt switch between SC andWC regime can beunderstood considering the enhanced tunneling of elec-trons and holes out of the QW in presence of the electricfield. The tunneling time �itunnel (i ¼ e, h) is given by [22]

�itunnel ¼2m�

i L2QW

@�exp

�4

3@eE

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m�

i U3i

q �; (2)

where m�i and Ui are, respectively, the effective mass and

confinement barrier of electrons and holes, LQW ¼ 8 nmthe QW width and e the electron charge. In the presentQWs the barrier height is rather small : Ue ¼ 42 meV,Uh ¼ 5 meV. For E ¼ 55 kV=cm Eq. (2) yields �htunnel �0:15 ps and �etunnel � 0:4 ps, so that �htunnel is comparable to

the Rabi oscillation period (�0:12 ps). The sampleswitches from SC to WC because the exciton is destroyedby carrier tunneling out of the QW before a Rabi oscilla-tion can be completed. Notice that the physics governingthe switch is completely different than in previous reports[19]. Instead of bleaching the exciton by Coulomb inter-action screening and phase space filling [16,17], here thelight matter interaction is modified by the internal electricfield. This mechanism is more similar to the self-electro-optic effect device (SEED) [23,24], in which the electricfield changes the QW absorption by quantum-confinedStark effect.

The abrupt change in reflectivity described above can beexploited to generate optical bistability. Let us considerexperiments where the laser is resonant to the lower polar-iton energy and its power P is modulated by a symmetrictriangular wave. It is focused into a 50 �m diameter spotwith a 10� angular aperture. The photocurrent is measuredwith an oscilloscope across a Z ¼ 10 k� load resistance.In Figs. 2(a)–2(c), VB is constant and chosen so that in thedark the sample operates in the WC regime. Clear hystere-sis cycles are observed in the photocurrent. Indeed, when Pis increased starting from zero (forward ramp), the sampleis initially in the WC regime and the reflectivity dip lies atthe energy of the uncoupled cavity mode so that the laser isout of resonance. The photocurrent (proportional to P),being negative, progressively reduces E through the ZIterm of Eq. (1). Eventually E becomes low enough forthe sample to switch into the SC regime. As a result, thelaser becomes resonant and an increased power is trans-mitted with a further reduction of E, providing a positivefeedback loop. Notice that once in the SC regime, thecurrent tends to saturate; when ZI approaches the value

VB ��i [see Eq. (1)], E tends to zero and the tunnelingtimes out of the QW [given by Eq. (2)] become muchgreater than the radiative recombination time. In this re-gime increasing the pumping power increases the flux ofemitted photons rather than the photocurrent. When P isreduced, starting from the SC regime (backward ramp), theinitial transmission of the laser is high. Thus, for the samevalue of P, the photocurrent is more intense and E is lowerthan in the forward ramp. This means that the switchoccurs at a lower P, thus opening the bistable cycle.To support this interpretation, pump and probe experi-

ments were performed. The sample was biased at VB ¼0:21 V, and two collinear beams were used: a constantpump and a chopped tunable probe (with Pprobe ¼5 W=cm2). The photocurrent was then filtered with alock-in amplifier to isolate the differential signal generatedby the probe. Such differential photocurrent spectra oneach side of the hysteresis cycle are shown in Fig. 2(d)

FIG. 2 (color online). (a) and (b) experimental (black) andsimulated (green) photocurrent as a function of the excitationpower for to values of the bias. (c) Photocurrent as a function ofexcitation power for VB ¼ 0:22 V. (d) and (e) Differential pho-tocurrent spectra measured for VB ¼ 0:22 V with a choppedprobe (Pprobe � 5 W=cm2), (d) P ¼ 0 and (e) P ¼ 25 W=cm2.

(f) Experimental (full symbols) and simulated (open symbols)pump powers for the SC ! WC and WC ! SC. (g) and(h) photocurrent measured varying the bias at fixed excitationpower.

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and Fig. 2(e) (corresponding to P ¼ 0 and 25 W=cm2).The transition from a single photocurrent peak (WC re-gime) to a double peaked spectrum (SC regime) is clearlyevidenced. The observed bistability cycles at fixed biashave been reproduced using a phenomenological model.We describe the transition from SC to WC driven by theelectric field considering the associated changes in severalphysical quantities and in carrier dynamics. Across thetransition, the cavity transmission T, the conversion effi-ciency of photons into carriers �, and the radiative lifetime�rad vary between their WC and SC values. To simulate thetransition from WC to SC, transmission spectra were com-puted for increasing values of the exciton dephasing time(�X). The transfer matrix method [18,25] was used, solvingMaxwell equations in each layer and imposing continuityconditions at each interface. The evolution with �X of thecalculated transmission coefficient at the energy of thelaser pump is well reproduced using

T ¼ TSC þ TWC � TSC

1þ � � �X (3)

with � ¼ 4:7� 1011 s�1. TWC ¼ 0:01, while in the SCregime the cavity transmission under normal incidenceamounts to 65%. However due to the 10� angular apertureof the excitation beam, the polariton resonance acts as anangular filter: we estimate that TSC ¼ 0:02. To model thetransition for � and �rad, the same dependence on �X as inEq. (3) is used. In WC regime �WC ¼ 0:02 corresponds tothe 2% QW absorption. In SC regime all photons enteringthe cavity become polaritons and �SC ¼ 1. In WC regime�WCrad ¼ 200 ns is the carrier radiative recombination time

for a density around 109 cm�2 [26]. In SC regime �SCrad ¼2 ps is the polariton recombination time, given by twice thecavity lifetime.

For a given photocurrent, the electric field E is given byEq. (1). The exciton dephasing time is therefore driven bythe competition between phonon dephasing and tunnelingout of the QW

�XðEÞ ¼�1

�X0þ 1

�etunnelðEÞþ 1

�htunnelðEÞ��1

; (4)

where �X0 ¼ 10 ps is the exciton dephasing time due tointeraction with phonons for E ¼ 0. Under steady stateconditions the photocurrent I is linked to the populationof electrons and holes through

I ¼ Ie þ Ih ¼ e

�neðEÞ

�etunnelðEÞþ nhðEÞ

�htunnelðEÞ�; (5)

where e is the elementary charge. Moreover, since elec-trons and holes injected by the laser can either recombineradiatively with decay time �radðEÞ or tunnel out of the QW,we get

niðEÞ ¼ �ðEÞTðEÞ P

@!

�radðEÞ�itunnelðEÞ�radðEÞ þ �itunnelðEÞ

; (6)

where @! ¼ 1467:5 meV is the laser energy.

From Eqs. (5) and (6), we deduce the explicit depen-dence of the pump intensity on I:

P ¼ @!I

e�T

ð�rad þ �etunnelÞð�rad þ �htunnelÞ�radð2�rad þ �etunnel þ �htunnelÞ

: (7)

A good overall agreement is found between simulated andexperimental curves as shown in Figs. 2(a) and 2(b) [27].The width of the hysteresis cycles is well reproduced.Notice that there is a small discrepancy in the additionalfeature that appears in the experiment as a small bump atI ¼ �70 �A in Fig. 2(a) or at I ¼ �40 �A in Fig. 2(b).The simulated curves also present a feature at these currentvalues, coming from the interplay between the increase ofT and of �itunnel during the switch. However a detailed

microscopic model is needed to obtain a complete agree-ment. We define PWC!SC and PSC!WC as the pump powersof the switch between WC and SC and vice versa.Simulated and experimental values of these two quantitiesare summarized in Fig. 2(f). The very good agreementbetween the model and the experiment further supportthe interpretation of the observed cycles in terms of switch-ing between SC and WC regime.The sample can also be driven varying the bias at fixed

P: similar bistable cycles are observed as shown inFigs. 2(g) and 2(h). In these conditions, bistability hasbeen observed for P as low as 0:7 W=cm2 [Fig. 2(h)].Although still greater than the pumping powers used inSEEDs (in which bistable cycles have been observed foroptical powers as low as 100 �W=cm2 [24]), our device ismore than 2 orders of magnitude more efficient than pre-

FIG. 3 (color online). Real space image (in logarithmic colorscale) of the pump spot reflected on the sample surface. VB ¼�2 V and Ppump � 2 kW=cm2 setting the system in the bistable

region. (a) the sample is in WC regime; (b) similar than (a) butwith the writing laser beam shone in region 1: the whole surfacehas switched into the WC regime; (c) reflected intensitiesaveraged on region 1, 2 and 3 during the sequence indicatedon top.

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viously reported cavity based devices [3–6]. It is indeed thefirst demonstration of low-power optical bistability forpolaritonics [10,14,19].

Bistability curves have been observed tuning the laser toboth the lower and upper polariton branches. On the con-trary, when tuning the laser to the cavity mode energy, thefeedback between the photocurrent and the laser trans-mission is negative, and no bistability was observed. Thesample switching time between the two states could not bemeasured : the present diodes have a cut-off frequency of�1 kHz due to their large areas. This effect should how-ever be greatly reduced by patterning the diodes in the formof micron-sized micropillars [28].

Let us finally consider regions prepared in differentstates and address the existence and the propagation ofswitching fronts connecting them. The sample was homo-geneously illuminated by a laser tuned to the lower polar-iton energy. A spatial image of the reflected light intensityis shown in Fig. 3(a). P� 2 kW=cm2 and VB ¼ �2 Vwere chosen to set the sample in the bistable region,initially in the WC state. Awriting laser beam was focusedon a �20 �m spot in region 1 within the pump spot. Itsintensity is high enough to switch the sample to the SCstate. As shown in Fig. 3(b), the writing beam induces areflectivity drop on the whole surface. This is furtherillustrated in Fig. 3(c) where the reflected intensity aver-aged over each of the three regions labeled 1,2 and 3 aresummarized. Regions 2 and 3 are 40 �m apart from region1. Initially, the whole sample is in the WC and presents ahigh reflectivity. At t ¼ 1:1 s the writing beam is turned onand all three regions switch to the SC state with lowerreflectivity (this is not visible in region 1 because thereflectivity drop is compensated by the reflected writingbeam). At t ¼ 2:7 s the writing beam is turned off and allregions remain in the same state. The pump is turned off att ¼ 5:1 s and on again at t ¼ 5:5 s: the sample has comeback to theWC state and the previous sequence is repeated.These measurements highlight that commuting a smallarea within the pump spot induces a switch of the wholeexcited region. This necessarily occurs through the propa-gation of a switching front across the sample [9]. In ourcase, it propagates over distances of several tens ofmicrons.

In conclusion, we have demonstrated pronounced opti-cal bistability in a p-i-n microcavity based on a newelectro-optic mechanism. Driving the internal electric fieldwithin the cavity produces a strong nonlinearity with apositive feed back, due to abrupt switching between strongand weak coupling regime. Signatures of switching frontspropagating over long distances are evidenced. Such frontscould in the future be guided by lateral patterning of thediodes into 1D structures. This opens the way toward therealization of new polariton based optical logic gates asproposed in ref. [10]. Devices with fast switching timescould be achieved by lateral processing of the microcavity

into micron-sized pillars. The observed low-power bista-bility relies on the bleaching of the strong coupling regimedue to the internal electric field, and could easily be trans-ferred into large band gap materials [29] for room tem-perature operation.This work was funded by ‘‘C’nano Ile de France’’ and

‘‘Conseil General de l’Essonne.’’ We thank Paul Voisin andChristophe Minot for fruitful discussions.

*Present address: CNISM UDR Pavia and Dipartimento diElettronica, Universita degli studi di Pavia, via Ferrata 1,27100 Pavia, Italy.†jacqueline.bloch@lpn.cnrs.fr

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