Theoretical modeling of an improved all-optical flip flopbased on a nonlinear semiconductor distributed

feedback laser structure

Hossam ZoweilAdvanced Technology and New Materials Research Institute, Mubarak City for Scientific Research

and Technology Applications, Alexandria, Egypt (zoweil@gmail.com)

Received 18 May 2010; revised 21 August 2010; accepted 25 August 2010;posted 26 August 2010 (Doc. ID 128561); published 21 September 2010

A new, improved design of an all-optical flip flop is proposed. The waveguiding layer of the device consistsof a phase-shifted nonlinear grating. The grating layers of a high refractive index have a negative non-linear coefficient. A phase-shift section exists at the middle of the waveguiding layer. The optical gain isprovided by current injection into an active layer. Nonlinearity in the waveguiding layer is achieved bydirect absorption at the edge of the absorption band (Urbach tail). In the “OFF” state, the waveguidinglayer forms a weak grating with an optical feedback below the laser threshold. In the “ON” state, thedevice functions as a distributed feedback (DFB) laser due to an induced strong grating in the nonlinearwaveguiding layer. The improvements of the device performance by reducing the set pulse energyand accelerating the switch-off process are discussed. Field simulations in the time domain wereperformed. © 2010 Optical Society of AmericaOCIS codes: 140.3490, 130.4815, 130.4310, 070.4340, 130.3750.

1. Introduction

Optical internet requires fast processing of data inthe electronic and optical domain. The data aretransferred from the optical domain to the electronicdomain, processed via electronic VLSI circuits, thentransferred again to the optical domain. Processingdata in the optical domain directly without transfer-ring it to the electronic domain eliminates the needfor VLSI processing circuits and leads to a faster pro-cessing speed. Routing an optical data packet in theoptical domain requires the availability of an opticalmemory element, or simply an all-optical flip flopthat changes its state from “OFF” to “ON” and viceversa by applying only an optical pulse to it [1–3].Much research had been conducted toward buildingan all-optical flip flop. In Ref. [4], a low-power high-speed all-optical flip flop (memory element) based ona disk laser was fabricated. The device switches froma clockwise to counterclockwise gallery whispering

mode. The device is generating a laser light in bothstates. In Ref. [5], an all-optical flip flop based on twoinjection-locked single-mode Fabry–Perot laserdiodes was introduced. A fast coherent all-optical flipflop memory based on a bistable system composed oftwo gain-clamped semiconductor laser amplifierswas introduced in Ref. [6]. An all-optical flip flopbased on a single distributed feedback (DFB) laserdiode that requires a holding beam was investigatedin Ref. [7]. These devices require more than one laserdiode/amplifier, or generate laser light in both states,or require a holding beam.

In Ref. [8], an all-optical flip flop that does not re-quire a holding beam and that is based on a singlenonlinear DFB laser was introduced. The output la-ser mode is OFF in one state and ON in the second.The waveguiding layer of the device consists of a lin-ear grating followed by a phase-shift section followedby a nonlinear periodic feedback structure section.The nonlinear feedback section consists of a constantlinear refractive index and a periodic negativenonlinearity [Fig. 1(a)]. At low light intensity inthe structure, only the linear grating section pro-

0003-6935/10/285199-06$15.00/0© 2010 Optical Society of America

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vides an optical feedback that is not enough for thelaser field to build up. At high light intensity in thestructure, an optical grating is induced in the secondsection, and it forms a phase-shifted DFB laser withthe phase-shift section and the linear grating section.In this case, the optical feedback allows for the laserfield to build up. The device is switched from the OFFstate to the ON state with an optical pulse that in-duces a grating in the second section. The negativenonlinearity is due to generated electron-hole pairsby direct absorption at the edge of the conductionband (Urbach tail), which decreases the refractive in-dex of the grating nonlinear layers. The wavelengthof the set pulse lies within the reflection band ofthe grating. Once the laser fields build up, the lightintensity in the structure maintains the electron-hole densities required to induce the grating. Thedevice is switched OFF by reducing the gain bycross-gain modulation (XGM). An optical pulse, atlonger wavelength, reduces the gain and does notproduce large electron-hole densities in the wave-guiding layer.

In this paper, the design in Ref. [8] is improved by:(a) a set pulse of a wavelength shorter than the grat-ing central frequency is used, and hence, due to lar-ger absorption, a lower energy pulse is required togenerate the electron-hole pair densities needed toinduce the grating; (b) instead of using a linear sec-tion and a nonlinear section in the waveguidinglayer, only one nonlinear grating structure is used,which can facilitate the fabrication; and (c) theswitching-off process is accelerated by assuming aweak phase-shifted grating in the guiding layer. Athigh light intensity in the grating, the weak gratingis reversed and a strong grating is induced. When theoptical gain is reduced by XGM, the induced changein the refractive index is reduced, and the gratingcoupling at an intermediate electron-hole pair den-sity is null. Therefore, the laser fields and the gener-ated electron-hole pair densities decay fast. Thisleads to a shorter switch-off time.

In the following sections, the device structure isdescribed, and a set of differential equations is intro-duced to model the device. The optical output versuscurrent bistability relation and the ON/OFF opera-tion of the device in the time domain are simulated,and the results are discussed.

2. Device Layout

An all-optical flip flop device investigated in Ref. [8]is shown in Fig. 1(a). The waveguiding layer consistsof a linear grating section followed by a phase-shiftsection followed by a nonlinear grating section. Inthe OFF state, only the linear grating section contri-butes to the distributed feedback in the device. In theON state, the linear section, the phase-shift section,and the nonlinear grating section contribute to thedistributed feedback in the device. The grating inthe nonlinear section is induced by direct absorptionof the laser mode (or an input pulse) at the edge of theconduction band. The input set pulse wavelength lies

within the reflection band of the grating—set pulse(a) in Fig. 2. The reset pulse is sent through the sameinput or face, and its wavelength lies at the lowerphoton energy (longer wavelength) to ensure thatit does not generate many electron-hole pairs in thewaveguiding layer. The reset pulse decreases the op-tical gain in the device, and the optical mode decaysuntil the induced grating in the nonlinear section isreduced.

In this paper, an improved all-optical flip flopstructure is introduced. The guiding layer consistsof a weak refractive index grating and a periodicnegative nonlinearity [Fig. 1(b)]. The negative non-linear coefficient is distributed such that the layer ofhigh refractive index has a negative nonlinear coeffi-cient, and no optical nonlinearity exists in the layerof low refractive index. In the OFF state, the weakrefractive index grating does not provide enoughoptical feedback to build up a laser mode. The deviceis switched ON by an optical pulse at a photon energyhigher than the center frequency of the grating,[Fig. 2, set pulse (b)]. Because of the large absorption,at high photon energy at the Urbach tail, a lowerenergy pulse is required to set the flip flop ON.

Fig. 1. (a) All-optical flip flop introduced in Ref. [8], (b) proposedflip flop.

Fig. 2. Set pulse (a), set pulse (b), reset pulse, and Urbach tailversus incident photon energy.

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The refractive index in the nonlinear layer is reduceddue to electron-hole pairs generated by the set pulse.The refractive index decreases and becomes lowerthan the refractive index in the linear layer, andan induced grating is developed. Once the laser modebuilds up, it generates electron-hole pairs and main-tains the induced grating in the nonlinear guidinglayer. The flip flop is switched OFF by an opticalpulse of photon frequency lower than the grating cen-ter frequency (Fig. 2). The optical reset pulse reducesthe optical gain at the laser mode wavelength bycross-gain modulation (XGM). The laser mode powerdecreases, and the electron-hole pair densities in theguiding layer decrease. The refractive index of thenonlinear layer increases until it is equal to the re-fractive index in the linear layer, hence the gratingcoupling is null. Then, the refractive index increasesagain and becomes higher than refractive index inthe linear layer. The switch-off process is acceleratedbecause the refractive index in the nonlinear layerbecomes equal to the refractive index of the linearlayer in a short time during the relaxation time ofthe electron-hole densities, and the coupling coeffi-cient becomes negligible at that time. The laser modeintensities decrease quickly during the reset pulsedue to the fast disappearing of the grating coupling,and the device switches OFF in a short time.

A. Mathematical Model

In Fig. 3, the distribution of linear refractive indexand negative nonlinearity is shown. Based on thisconfiguration, the coupled mode equations that mod-el the field propagation in the device were derived.The coupled mode equations are coupled with therate equations of the charge densities and the gainin the nonlinear waveguiding layer and the activelayer [8–10] as follows:

i∂Eþ∂z

þ i�nc∂Eþ∂t

¼�Γ1 þ i

g2ð1 − iγÞ − i

αcav2

�Eþ

− e−iϕðzÞ−i2δβzðK þ Γ2ÞE−; ð1Þ

− i∂E−

∂zþ i

�nc∂E−

∂t¼

�Γ1 þ i

g2ð1 − iγÞ − i

αcav2

�E−

− eiϕðzÞþi2δβzðK þ Γ2ÞEþ ð2Þ

Γ1 ¼ 2πλG

�� δnδNcar

�ð1 − iξÞNcar

�− i

α4; ð3Þ

Γ2 ¼ 4λG

� δnδNcar

�ð1 − iξÞNcar − i

α2π ; ð4Þ

∂Ncar

∂t¼ −

Ncar

τcar− BN2

car − CN3car þ

αIintℏω ; ð5Þ

∂Ng

∂t¼ I

eV−Ng

τ − BN2g − CN3

g − vgΘgS; ð6Þ

g ¼ ~gðNg −NgtrÞ1þ ϵS ; ð7Þ

where the total electric field in the device is in theform ofEðz;tÞ¼Eþðz;tÞe−iβzþiωtþE−ðz; tÞeþiβzþiωtþ c:c:,where Eþ is the field propagating in the positive zdirection, and E− is the field propagating in the ne-gative z direction. δn=δNcar ¼ −10−26 m3, which is therate of change in the refractive index due to thechange in electron-hole pair density at photonenergy ℏω≃ Eg − 0:1 e:V: [8,11,12]. Δn ¼ 0:0006,K ¼ 4Δn=λG is the grating coupling. Ncarðz; tÞ andNgðz; tÞ are the charge carrier distributions in thenonlinear guiding layer and the active layer, respec-tively. ξ ¼ 0:033 is the ratio between the inducedchange in the refractive index and the induced lossdue to free electron-hole pairs generated in the guid-ing layer. ϕðzÞ ¼ 0 for 0 < z < L=2, and ϕðzÞ ¼ π forL=2 < z < L. δβ ¼ β − βG, where βG ¼ 2π�n=λG andβ ¼ 2π�n=λ. Iint is the mode intensity. S is the photondensity.

Equations (1) and (2) are the coupled mode equa-tions of the forward and backward fields. Equation(5) is the rate equation of the charge carrier densityin the nonlinear guiding layer. Equation (6) is therate equation of the charge carrier density in the ac-tive layer. The coupled differential equations aresolved by the Rung–Kutta techniques. The structureis divided into 20 sections, and in each section, spon-taneous emission fields are added to the forward andbackward fields in the simulations. It was assumedthat no reflections are at either end of the device.

3. Simulations

The optical output mode power is normalized toP0 ¼ 1:352 mW. The carrier density in the guidinglayer is normalized to Ncar0 ¼ 6 × 1023 m−3, and thecarrier density in the active layer is normalized toNgtr. All time domain simulations were performedfor a time period of 7.5 ns. The absorption loss inthe waveguiding layer at the edge of the conductionband (Urbach tail) is assumed to have the form α ¼α0 expððE − EgÞ=E0Þ [13,14]. α0 is the absorptionFig. 3. Refractive index distribution in the waveguiding layer.

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coefficient at the conduction band edge.E ¼ ℏω is theincident photon energy. It is assumed that the wave-guiding layer is fabricated from InGaAsP alloy,where the bandgap energy is Eg ≃ 0:9 e:V:[15], andE0 ¼ 0:01 e:V:. The output optical mode photon en-ergy was assumed to be ≈0:1 e:V: less than Eg. Theset pulse was tuned to λ ¼ 1:482 μm, and the resetpulse was tuned to λ ¼ 1:518 μm. The direct absorp-tion loss coefficients at each wavelength are shown inTable 1. It was assumed that the optical gain atλ ¼ 1:518 μm is half the gain at λ ¼ 1:5 μm and atλ ¼ 1:482.

A. Current Optical Bistability

The optical output mode power versus input injectedcurrent relation is obtained by increasing the injectedcurrent linearly in 12.5 ns from 0 to 76:048 mA, thendecreasing again linearly in 12.5 ns to 0. The simula-tion parameters are shown in Table 1. The simulationresult is shown in Fig. 4. TheON/OFF power level dif-ference is more than 20 dB. In the following time do-main simulations, the current injected to the device is

Fig. 4. Current (in ampere)/output optical power hysteresis loop.

Table 1. Simulation Parameters

Symbol Description Value

α Urbach tail absorption at 1:5 μm 80 cm−1

Urbach tail absorption at 1:518 μm 28:8 cm−1

Urbach tail absorption at 1:482 μm 218 cm−1

αcav Intrinsic cavity loss 25 cm−1

τcar Nonradiative recombination time innonlinear layer

1 ns

τ Nonradiative recombination time inactive layer

3 ns

ϵ Gain saturation 1:5 × 10−23 m3

V Cavity volume 0:36 × 10−16 m3

Θ Overlap factor 0.35vg Group velocity 108 m=sγ Linewidth enhancement −0:5B Radiative recombination 10−16 m3=sC Auger recombination 3 × 10−40 m6=sI Injected current 46:85 mA~g Differential gain 4 × 10−20 m2

Ngtr Transparency carrier density 1024 m−3

�n Average refractive index 3L Cavity length 250 μm

Fig. 5. Optical output power in (a) “OFF” state, (b) “ON” state.

Fig. 6. Input optical set pulse power.

Fig. 7. Free carrier distribution Ncar at (a) z ¼ L=2, (b) z ¼ 0, andNg at (c) z ¼ 0, (d) z ¼ L=2.

Fig. 8. Set and reset pulse.

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chosen to be at the middle of the hysteresis loop;I ¼ 46:85 mA.

B. OFF State

TheOFF state fields inside the device were simulatedin the time domain using the simulation parametersin Table 1, and the simulation results are shown inFig. 5(a).

C. ON State

The device is switched ON by applying an input op-tical pulse of 1:352 mW for 375 ps (0.507 pJ) andwavelength λ ¼ 1:482 μm (Fig. 6). The set pulse gen-erates electron-hole pairs in the nonlinear layers ofthe grating. The refractive index of these gratinglayers is reduced to below the refractive index ofthe linear refractive index layers. A strong gratingcoupling is produced in the waveguiding layer. Theoutput mode power is shown in Fig. 5(b). The lasermode builds up quickly after the set pulse. The lasermode sustains the carrier density level in the wave-guiding layer. The carrier densities in both the wave-guiding layer and the active layer are shown inFig. 7, at z ¼ 0 and at z ¼ L=2.

D. Set-Reset Operation

The set-reset operation is simulated in the timedomain. Input set and reset pulses are shown inFig. 8. A set pulse of 1:352 mW, 375 ps width (0.507pJ), and a wavelength of λ ¼ 1:482 μm was applied.Later, a reset pulse of 1:352 mW, 1.875 ns width(2.535 pJ) and a wavelength of λ ¼ 1:518 μm was in-jected to the same input to switch the device OFF. Theoutput optical mode power is shown in Fig. 9. The re-set pulse reduces the optical gain at the laser modefrequency. Also, the pulse does not generate manyelectron-hole pairs due to a low direct absorption ata longer wavelength. Hence, the laser mode ceasesto exist, and the density of carriers Ncar is reduceddue to the electron-hole relaxation. The grating cou-pling also decreases until it almost reaches zero at anintermediate Ncar electron-hole pair density, then itstarts to increase slightly to its OFF state value.The output optical power falls by more than 20 dBduring the reset pulse time period. The carrier densi-ties in the waveguiding layer and the active layer are

shown in Fig. 10. The simulation shows fast decay ofthe carrier density in the waveguiding layer.

4. Discussion

In Ref. [8] [Fig. 1(a)], the nonlinear waveguiding sec-tion has a constant real refractive index in both thelinear and the nonlinear layer. However, in this pa-per, the structure in Fig. 1(b) requires that the layerof negative nonlinearity has a higher refractive indexthan adjacent layers, which is easier to achieve. InRef. [8], the input set pulse energy was more than3 pJ, while in this work, the input set pulse energywas reduced to 0.5 pJ by using a shorter wavelengthpulse. Even a lower energy pulse could be used toswitch the device ON if a shorter wavelength pulsewas applied. The flip flop changes its state fromON to OFF by reducing the optical gain by XGM.An optical pulse at a longer wavelength reducesthe gain in the devices of Figs. 1(a) and 1(b). In device(a), a reset pulse of a ≃3:75 ns width was required toensure that the electron-hole density in the non-linear waveguiding layer is reduced to its OFF statevalue and the grating coupling induced is reduced toalmost zero. However, in device (b), to reduce thegrating coupling to almost zero in the waveguidinglayer, the electron-hole density does not need to bereduced to its OFF state value. It needs to be reducedto an intermediate value that makes the grating cou-pling almost zero. Hence, the laser mode is reducedquickly, and this leads to a fast switching to the OFFstate. Though in Ref. [8], the reset pulse was a 3.75 nswidth, in this work, a reset pulse of a 1.875 ns widthis required.

5. Conclusion

An improved design of an all-optical flip flop is intro-duced. The device performance was improved byusing a low energy set pulse of a shorter wavelength.The switch-off process was accelerated by introdu-cing a weak grating in the nonlinear waveguidinglayer. The optical nonlinearity based on the direct ab-sorption at the edge of the conduction band (Urbachtail) allows for effective change in the refractive in-dex of the grating layers. Because of the high opticalnonlinearity of the refractive index, a relatively low

Fig. 9. Output optical power after set and reset pulses.Fig. 10. Free carrier distribution after set and reset pulses; Ncarat (a) z ¼ L=2, (b) z ¼ 0, and Ng at (c) z ¼ 0, (d) z ¼ L=2.

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injected current (I ¼ 46:85 mA) and a low opticalmode output power (≈ 1:352 mW) are achieved.The device could be built from InGaAsP alloy onan InP substrate.

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