Simulations of a Novel All-Optical Flip-Flop Based on a Nonlinear DFB Laser Cavity Using GPGPU Computing

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1 Optics and Photonics Journal, 06, 6, 03-5 Published Online Auust 06 in SciRes. Simulations of a Novel All-Optical Flip-Flop Based on a Nonlinear DFB Laser Cavity Usin GPGPU Computin Hossam Zoweil Advanced Technoloy and New Materials Research Institute, City of Scientific Research and Technoloy Applications, New Bor EL-Arab City, Eypt Received 5 July 06; accepted Auust 06; published 4 Auust 06 Copyriht 06 by author and Scientific Research Publishin Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). Abstract A new all-optical flip-flop based on a nonlinear Distributed feedback (DFB) structure is proposed. The device does not require a holdin beam. A nonlinear part of the ratin is detuned from the remainin part of the ratin and has neative nonlinear coefficient. Optical ain is provided by an injected electrical current into an active layer. In the OFF state, due to the detuned section, no laser liht is enerated in the device. An injected optical pulse reduces the detunin of the nonlinear section, and the optical feedback provided by the DFB structure enerates a laser liht in the structure that sustains the chane in the detuned section. The device is switched OFF by detunin another section of the ratin by a Reset pulse. The Reset pulse reduces the refractive index of that section by the eneration of electron-hole pairs. The Reset pulse wavelenth is adjusted such that the optical ain provided by the active layer at that wavelenth is zero. The Reset pulse is prevented from reachin the nonlinear detuned section by introducin an optical absorber in the laser cavity to attenuate the pulse. The device is simulated in time domain usin General Purpose Graphics Processin Unit (GPGPU) computin. Set-Reset operations are in nanosecond time scale. Keywords All-Optical Flip-Flop, Bistability, DFB Laser, Urbach Tail. Introduction All-optical flip-flop is required for all optical routin and processin of optical data packets []. All-optical routin and processin of optical data packets eliminates the need to convert the data sinal from optical domain How to cite this paper: Zoweil, H. (06) Simulations of a Novel All-Optical Flip-Flop Based on a Nonlinear DFB Laser Cavity Usin GPGPU Computin. Optics and Photonics Journal, 6,

2 to electronics domain and vice versa, which reduces complexities and increases processin speed. All-optical flip-flop based on coupled laser diodes is investiated in []. All-optical flip-flop based on micro rin lasers is shown in [3]. Low power all-optical flip-flop based on a micro disk laser diode is fabricated and tested in [4]. An all optical flip-flop based on a sinle distributed feedback semiconductor laser is implemented in [5], and it requires also a holdin beam. A device based on vertical cavity semiconductor optical amplifier that requires a holdin beam is shown in [6]. Another device based on active multi-mode interference laser diode is described in [7]. All optical flip-flop based on bistable laser diodes is discussed in [8] [9]. In [0], an all-optical flip-flop based on a chirped DFB laser structure was investiated. The device has bi-stable output optical mode power, and it does not require a holdin beam. The chirp, in [0], is accompanied with a radually increasin neative nonlinear coefficient. The chirp prevents lasin at the OFF state (low liht intensity in the structure). At hih liht intensity in the structure, the nonlinearity reduces the chirp alon the structure, and the optical feedback from the ratin allows for a laser mode to build up. The device is switched OFF by an optical pulse at a wavelenth loner than the wavelenth of the emitted laser liht. This is achieved by reducin the optical ain of the emitted laser mode wavelenth by cross ain modulation (XGM). In [], an all-optical ip-op based on a 3-section DFB laser structure is introduced. Two sections of the DFB structure are detuned from the middle part of the DFB structure. The detuned sections have optical neative nonlinearity. The device is switched ON by an optical pulse that reduced the detunin of both sections. When the detunin is reduced, the DFB structure provides the optical feedback required to start a laser mode. The device is switched OFF by XGM by an optical pulse of a lower frequency than the operatin frequency. In [], an all-optical ip op is investiated where only one section of the DFB laser structure is detuned. However, the ip-op is switched OFF by an optical pulse at a frequency hiher than the operatin frequency by XGM. In this work, an improved nonlinear DFB structure is introduced. The device schematic is shown in Fiure. The wave-uidin layer consists of 3 Sections. Section 3 is a detuned nonlinear section of the DFB ratin. The nonlinear detuned section prevents a laser mode from buildin up at a low liht intensity in the structure. At hih liht intensity in the structure, at wavelenth λ = λ that corresponds to a photon enery just below the band-ap enery in Section 3, the detunin is decreased due to neative nonlinear coefficient. In this case, the optical feedback in the structure increases and allows for an optical laser mode to build up. The laser mode intensity maintains the reduction of the detunin of Section 3, and the laser mode is stable. The device structure is easier to implement than the structure in [0], because it uses a section with a constant detunin instead of a detunin that is due to a radual chane in the refractive index. The device is switched OFF by an optical pulse at wavelenth λ = λ < λ. The optical pulse at λ = λ detunes section by decreasin its averae refractive index, and the optical feedback alon the ratin is reduced. The laser mode decays, and the device is switched OFF. The device presented in this work has advantaes over the device in []. In [], nonlinear sections are needed to achieve bistability, where in this work only one nonlinear section is required. Also, in [], the device is switched OFF by XGM, but in this work, the device is switched OFF by detunin a section of the DFB structure, and the optical ain is not altered. In this case, the switch OFF dynamics is controlled Fiure. Device schematic, the laser mode overlaps with the ratin and the active layer. 04

3 the neative optical nonlinearity process in the wave-uidin layer. The neative optical nonlinearity is achieved by direct absorption of a part of the incident liht at a photon enery slihtly less than the band ap enery of the semiconductor. Hence, by alterin the semiconductor properties the switch OFF process could be controlled. In the next section, the device desin and ON/OFF switchin dynamics were described.. Device Description and Switchin Dynamics Fiure shows the schematic of the device includin input sinals and output laser mode. The optical ain in the device is provided by electrical current injection in the active layer Fiure. The wave-uidin layer of the device consists of a phase shifted nonlinear ratin of period Λ= nλg. where n is the averae refractive index alon the ratin, and λ G is the wavelenth at the center of the reflection band of the ratin. The device is switched ON by a SET pulse, and it is switched OFF, by a RESET pulse at a different wavelenth. The ratin and the neative nonlinear refractive index distribution at the laser mode wavelenth λ = λ ( λ = λ G ) is shown in Fiure. The neative nonlinear coefficient in section 3 of the nonlinear wave-uidin layer is provided by direct photon absorption at the Urbach tail, Fiure 3. The absorption coefficient at Urabch tail is expressed as α = α0 exp (( ħω ħ ω ) E0), ħ ω = E is the band ap enery (all eneries are expressed in electron. volt) α is the direct optical loss, α 0 is the band-ap optical loss at ħω = ħ ω, and E 0 is chosen to be 0.0 e.v., [3] [4]. The absorbed photons produce electron-hole pairs in the nonlinear waveuidin section 3. The electron-hole pairs enerated reduce the refractive index at photon enery just below the band-ap enery. At low liht intensity in the structure, the optical feedback is not enouh to produce a lasin mode due to a detuned part (section 3 ) of the ratin. When an optical pulse of a wavelenth λ = λ is sent throuh the structure, part of the pulse enery is absorbed in section 3, and it produces electron-hole pairs that reduce the refractive index. When the detunin of the nonlinear section is reduced, the reflection band of this section overlaps with the reflection band of the other part of the ratin and more photons are reflected from section 3 to the rest of the ratin. This increases the optical feedback in the structure which allows for a laser mode to build up. More photons are reflected back to sections and of the ratin which increases optical feedback and reduces the number of photons leavin the cavity from the terminal end of the ratin. To switch the laser OFF, section of the ratin as in Fiure is detuned from the ratin center reflection band wavelenth λ by eneratin electron-hole pairs to reduce refractive index of that section. Whence Fiure. Linear and nonlinear refractive index distribution at ω ω = ( ) λ = λ. 05

4 Fiure 3. Direct absorption loss in Section 3 (Urbach tail) and optical ain spectrum. the section is detuned, the distributed optical feedback cannot provide enouh optical feedback to sustain the laser mode. The laser mode decays and the electron-hole pairs density in section 3 decreases with time. The detunin of section 3 is restored to its value in the OFF state. The device will remain in the OFF state till another optical pulse at λ = λ triers the device ON aain. The reduction of refractive index in section is done by injectin an optical pulse of wavelenth λ where ħ ω is just below the band ap enery in this section. In the same time, ω is chosen such that the ain of the active layer ( ω ) = 0, Fiure 3, [5]. ħ ω is reater than ħ ω, so it can reduce the refractive index in section 3 by eneratin more electron-hole pairs. To avoid this, the semiconductor band ap enery in section is adjusted to provide a lare absorption loss at ω, so that the photons of enery ħ ω are absorbed in section before reachin section 3. The absorption coefficients and correspondin band aps alon the nonlinear ratin are shown in Fiure 4 and Fiure 5. The device could be built usin InGaAsP alloy on InP substrate. The band ap eneries in each section could be adjusted by alterin the percentae of each element of the InGaAsP semiconductor [6]. Also, the device could be built from 3 DFB laser devices, where each device has its wave-uidin layer altered as described in Fiure 4 and Fiure 5. In the followin simulations, wavelenths are set as follow: λ = 500 nm and λ = 470 nm. In the next section a mathematical model of the device is introduced. Equations describin optical fields and electron-hole densities in the active layer and nonlinear wave-uidin layers are presented. Also, simulations parameters are tabulated. 3. Mathematical Model and Simulation Parameters Coupled mode equations describe the optical fields in the structure [7]. Rate equations describe the electron-hole pairs density in both the active layer and the nonlinear wave-uidin layer. The RESET pulse is modeled by an analytic model where the power of the device decays due to an attenuation coefficient that depends on the section throuh which the pulse is propaatin. ( ) = reset ( ) [ β ω ] ( α( ) ) ERESET zt, E zt, exp i z i t exp d z z. The total electric field of the laser mode propaatin in the device is described by a sum of a forward and backward propaatin field; 06

5 Fiure 4. Semiconductor band-ap alon the wave-uidin layer, and Set and Reset pulses photon eneries. Fiure 5. Direct absorption loss ( ) the wave-uidin structure. α λ at (a) λ = λ, and (b) λ = λ alon ( ) ( ) [ β ω ] ( ) [ β ω ] E zt, = E zt, exp i z i t + E zt, exp i z i t + cc... + The laser mode is modeled at ω = ω. The RESET pulse was assumed a wavelenth λ = 470 nm E+ n E+ αcav + = iγ + ( + iγ ) E + ( iγ exp iφ ( z) + iδβ z ) E z c t + () 07

6 E n E αcav = iγ + ( + iγ ) E ( iγ exp iφ ( z) iδβ z ) E z c t + ( z, ω) π dn α Γ = δn( z) Nc ( iξ) + i λg dn 4 Γ = n (4) λ c G (, ) N α(, ω ) α(, ω ) N zt z I + z I t (, ) c 3 = BNc CNc + τc N zt I N t ( ω ) ħω ( ω ) current 3 = BN CN v ΘS qv τ ( ω )( tr ) N N = + ε S Equations () and () describe the two coupled mode equations of the two counter propaatin fields. The phase shift φ ( z) is zero for 0 z L and φ = π for L z L. c is the liht speed in vacuum, and n is the averae refractive index in the laser cavity. Λ= nλg, where Λ is the ratin period. λg = λ = 500 nm. Γ 6 3 presents the detunin and the direct optical loss alon the ratin. dn dn = 0 m is the chane in the refractive index due to the injected electron-hole pairs density by direct absorption at photon enery slihtly less than the band ap enery of the semiconductor ( E ħω 0. electron-volt) [8] [9]. The ratio between the induced loss due to electron-hole pairs enerated and the chane in the refractive index is ξ = In this device model, δ n( z) = for ( 34) L z L, and 0 otherwise. Γ presents the couplin between the forward mode and the backward mode, and n = α cav = 5 cm is the intrinsic cavity loss. Equation (5) presents the rate equations electron-hole pairs density in the nonlinear wave-uidin layer. α( z, ω( or λ ) ) and α( z, ω( or λ ) ) present the direct absorption loss in the nonlinear wave-uidin layer of the laser mode and the reset pulse respectively. α( z, ω ) = 480 cm for ( 34) L z L and 0 otherwise. α( z, ω ) = 4800 cm for 0 z L. For L z ( 34) L, α( z, ω ) = 48 0 cm. For 3 z ( 34) L, we assumed that the pulse sinal at ω = ω( or λ) has zero intensity due to absorptions at section and, so α( z, ω ) is not modeled in the simulations in section 3. I and I are the power densities of the laser modes at ω = ω ( λ ), and the power density of the RESET pulse at ω = ω ( λ ) respectively. I current is the current injected to the active layer. q is the electron chare. V is the optical laser cavity volume. S is the photon density in the cavity at ω = ω. Equation (6) presents the rate equation of the injected carriers density in the active layer. The other simulation parameters are tabulated in Table. In the followin sections, numerical simulations of optical bistability and switchin dynamics in time domain are performed. The mathematical model is solved usin Fourth order Rune-Kutta technique. The lenth of the device is divided into 80 sections, and the time step is Ln 80c. The spontaneous emission optical fields are added as random sinals at each interation step to the forward and backward fields. General purpose raphics processin unit (GPGPU) computin is used to accelerate the numerical simulations of the device. The lenth of the device is devided into 80 sections alon the z direction. The interations of the backward and forward fields alon each the 80 sections are done by assinin a thread on the GPU to each section. All the interations alon the 80 sections are done in parallel to reduce the total computation time. The computation time is reduced about 5 times. NVIDIA GTX 670 raphics processin unit is used to perform parallel computin of the forward and backward fields at each one of the 80 sections alon the z direction. The code is written usin CUDA C [0]. () (3) (5) (6) (7) 4. Simulations Results P N c0 = 0 m. The elec- 3 3 = 0 m. In all the followin numerical simulations the laser mode power is normalized to electron-hole pairs density in the nonlinear wave-uidin layer is normalized to tron-hole pairs density of carriers injected into the active layer N is normalized to N tr = 3 Watt. The

7 Table. Simulation parameters. Symbols Description Value L Lenth 87.5 µ m I current Current injected in the active layer Ampere n Averae ref. index 3 v Group velocity 0 8 m/sec γ Line-width enhancement 0.5 Gain saturation.5 0 m 3 3 Θ Overlap factor 0.35 V Cavity volume m 6 3 τ car Non-radiative recombination in nonlinear sections nsec τ Non-radiative recombination in the active layer 3 nsec B C Radiative Recombination Auer recombination m sec m sec ( ω ) Differential ain at 0 ω 4 0 m N tr Transparency carrier density m 4.. Optical Bistability Loop A mathematical experiment is performed to find the injected current to the laser device at which the device has stable optical outputs levels at the same injected current. The injected current to the device is increased linearly with time from 0 to Ampere in 37.5 nanosecond, then, the current decreases linearly from to 0 Ampere in 37.5 nanosecond. A part of the output optical power versus injected current relation is shown in Fiure 6. An injected current of Ampere is used in all of the followin simulations to insure bistable operation of the device. 4.. OFF State and On State Simulations of the output optical power are performed for a lon simulation time to test the stability of the device output in the OFF state and the ON state. The output power of the device in the OFF state is simulated in the time domain for 75 nanosecond, Fiure 7. To switch the device from OFF state to the ON state an optical pulse at λ = λ is injected to the device at z = 0. The pulse is injected at simulation time t = nanosecond. The pulse width is nanosecond and has a peak power of P = P 0 = Watt ( picojoule). The input optical pulse induces electron-hole pairs in section 3 on the nonlinear wave-uidin layer. The electron- hole pairs reduces the detunin of this section, the reflection band of this section overlaps with the reflection band of the rest of the ratin. The number of photons reflected back from section 3 increases. The optical feedback is increased and the structure allows for a laser mode to build up. The laser mode provides photons at λ = λ, part of these photons is absorbed in section 3 to maintain the number of electron-hole pairs in this section. The electron-hole pairs enerated in section 3 maintain the chane in detunin that allows the laser mode to exist. The chanes in the refractive index (normalized to n ) alon the structure at the end of the simulation time (at t = 75 nanosecond) for both ON state and OFF state are shown in Fiure 7. The output power in the ON state is shown in Fiure 8. N c at z = 7L 8, and N at z = 7L 8, are plotted in Fiure 9 and Fiure 0. 09

8 Fiure 6. Optical bistability loop. Fiure 7. Output optical power in: (a) OFF state, (b) ON state. Fiure 8. Normalized refractive index distribution in OFF state and ON state. 0

9 Fiure 9. Normalized N in the ON state at z = 7L 8. c Fiure 0. Normalized N in the ON state at z = 7L ON/OFF Switchin Dynamics ON/OFF switchin dynamics are investiated in the time domain. The device is simulated for.5 nanosecond. 3 At simulation time t =.5 nanosecond, an optical pulse at λ = λ of peak power P = P 0 = Watt and nanosecond width ( picojoule) sets the device ON. At simulation time t = 7.5 nanosecond, an optical pulse at λ = λ of peak power of 0P 0 = Watt and.875 nanosecond width ( picojoule) resets the device to the OFF state. The input optical power pulses are shown in Fiure. The output optical mode is shown in Fiure. The set pulse switches the device ON by eneratin electronhole pairs in section 3 and the electron-hole pairs reduce the detunin of the refractive index in this section. More photons are reflected back at section 3, and a laser mode builds up and maintains the detunin by providin electron-hole pairs in section 3. The RESET pulse switches the device OFF. The photons at λ = λ are absorbed in section and produce electron-hole pairs. The enerated electron-hole pairs reduce the averae refractive index alon section. Hence, the reflection band of the ratin section does not overlap effectively with the reflection band of sections and. More photons escape the laser cavity throuh section. The structure can no loner sustain a laser mode at λ = λ. As laser mode decreases quickly inside the laser cavity, N c in section decays with time and the refractive index in section is restored to its value before the SET pulse. After the RESET pulse elapses, the refractive index in section is restored to its value in the OFF state, and the

10 Fiure. Input optical pulses at z = 0. Fiure. Output optical laser mode power at z = L durin ON/OFF simulations. device remains in the OFF state. Fiure 3 shows N c evolution with time at z = 7L8 durin Set/Reset operation. The evolution of N with time at z = 7L 8 is shown in Fiure 4. The detunin of refractive index normalized to n, ( δ n( z) dndnnc) n, is shown in Fiure 5. The detunin at t = nanosecond, t = nanosecond, t = nanosecond, and t = durin the RESET pulse is plotted. The detunin at the end of the simulation time t =.5 nanosecond is shown in Fiure 5. The neative peak at z = L corresponds to the chane in refractive index due to electron-holes pairs enerated by the direct absorption at the beinnin of section. While the SET operation takes about 0.5 nanosecond to stabilize the output mode power in the ON state, resettin the device to the OFF state takes about nanosecond. In the SET operation the input sinal is amplified, while in the RESET operation the RESET pulse is not amplified. Durin the RESET operation, the RESET pulse does not alter N directly. N is restored to its value in the OFF state due to the decrease of liht intensity at λ = λ in the optical cavity. 5. Discussion In this work, an all-optical ip-op is simulated. The lenth of the device is 87:5 μm. In comparison with an

11 Fiure 3. Electron-hole pairs density N c at z = 7L 8 durin ON/OFF simulations. Fiure 4. N at z = 7L 8 in the active layer durin ON/OFF simulations. another work in [0] where the device lenth is 375 μm. Also the operatin current in this work was 0:0965 Ampere and in [0] the injected current is 0:94358 Ampere. The device simulated in this work has a shorter lenth and operates at a lower injection current. The Reset pulse width in [0] is 9:375 nanosecond, while in this work a Reset pulse of :875 nanosecond switches the device OFF. In eneral, the desin described in this work shows fast operation compared to [0]. The device investiated in [0] requires a wave-uidin layer that increases linearly alon the device. Also it requires havin a direct optical loss that increases linearly with distance too. However in this device only one section of the wave-uidin layer has a slihtly hiher refractive index and has a direct absorption loss. Hence, in this work, the device fabrication is easier. In this work, the device is Reset by detunin part of the laser cavity which is a section of the DFB structure, and the optical ain is not altered. In [0], the Reset pulse reduces the optical ain by cross ain modulation that switches OFF the output laser mode and allows the refractive index to return to its oriinal distribution in the OFF state. 3

12 6. Conclusion Fiure 5. Detunin alon the structure durin Reset pulse and at the end of the simulation time. An all-optical flip-flop based on a nonlinear wave-uidin layer is suested and simulated in the time domain. The nonlinearity in the wave-uidin layer is achieved by direct absorption of photons at the Urbach tail at photons enery just below the band-ap enery of the semiconductor. The device is switched ON by an optical pulse of nanosecond width ( picojoule), and is switched OFF by an optical pulse of.875 nanosecond width ( picojoule). The switchin dynamics are in nanoseconds time scale which could be useful for all optical data packet switchin and routin. The device could be built usin semiconductor alloy In- GaAsP, where by chanin the percentaes of elements in the alloy the band-ap could be altered. Parallel computin usin GPGPU card is used to reduce the computation time of the set of equations that describes the mathematical model of the device. References [] Dorren, H.J.S., Hill, M.T., Liu, Y., Calabretta, N., Srivatsa, A., Huijskens, F.M., de Waardt, H. and Khoe, G.D. (003) Optical Packet Switchin and Bufferin by Usin All-Optical Sinal Processin Methods. Journal of Lihtwave Technoloy,, -. [] Martin, T.H., de Waardt, H., Khoe, G.D. and Dorren, H.J.S. (00) All-Optical Flip-Flop Based on Coupled Laser Diodes. IEEE Journal of Quantum Electronics, 37, [3] Hill, M.Y., Dorren, H.J.S., de Vries, T., Leijtens, X.J.M., den Besten, J.H., Smalbrue, B., Oei, Y.S., Binsma, H., Khoe, G.D. and Smit, M.K. (004) A Fast Low-Power Optical Memory Based on Coupled Micro-Rin Lasers, Nature, 43, [4] Liu, L., Kumar, R., Huybrechts, K., Spuesens, T., Roelkens, G., Geluk, E.J., de Vries, T., Rereny, P., Thourhout, D.V., Baets, R. and Morthier, G. (00) An Ultra-Small, Low-Power, All-Optical Flip-Flop Memory on a Silicon Chip. Nature Photonics, 00, [5] Huybrechts, K., Morthier, G. and Baet, R. (008) Fast All-Optical Flip-Flop Based on a Sinle Distributed Feedback Laser Diode. Optics Express, 6, [6] Kaplan, A.M., Arawal, G.P. and Maywar, D.N. (009) All-Optical Flip-Flop Operation of VCSOA. Electronics Letters, 45, 7-8. [7] Takenaka, M., Raburn, M. and Nakano, Y. (005) All-Optical Flip-Flop Multimode Interference Bistable Laser Diode. IEEE Photonics Technoloy Letters, 7, [8] Kawauchi, H. (997) Bistable Laser Diodes and Their Applications: State of the Art. IEEE Journal of Selected Topics in Quantum Electronics, 3,

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