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All-optical high speed logic gates using SOA
Optics Communications 285 (2012) 2289–2292
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
All-optical high speed logic gates using SOA Mahdi Sahafi a,⁎, Ali Rostami b, Ali Sahafi b a b
Department of Electrical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran Photonics and Nano crystal Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51666, Iran
a r t i c l e
i n f o
Article history: Received 23 June 2011 Received in revised form 27 December 2011 Accepted 13 January 2012 Available online 30 January 2012 Keywords: SOA Optical logic gate Carrier heating Spectral-hole burning
a b s t r a c t In this paper a novel and simple structure of a high speed optical logic gate based on bulk semiconductor optical amplifier (SOA) is presented. The gain dynamic and phase response of bulk SOA using rate equations including the dynamics of carrier heating (CH) and spectral-hole burning (SHB) is investigated numerically. The operation of NOR gate is analyzed by using the presented numerical method, and a NOR gate that can operate up to 1 Tbps is designed. By using the proposed structure, high speed logic gates based on bulk SOA can be realized. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Optical logic gates, such as all-optical NOR, NAND and XOR gates are the key elements for all-optical signal processing. All-optical logic gates fundamentally work on nonlinear characteristics of medium. So far, some methods utilizing the nonlinear operation of optical fiber and semiconductor optical amplifier (SOA) have been used to demonstrate all optical functions. The all-optical logic gate based on nonlinear characteristics of optical fiber has the potential of operating at terabits per second due to very short relaxation times (b100 fs) of its nonlinearity. The disadvantages of optical fiber are its weak nonlinearity and long interaction lengths and high control energy required to achieve reasonable switching efficiency whereas semiconductor optical amplifier has the advantages of high nonlinearity and ease of integration to operate as a logic gate. All optical logic XOR gates at speeds of 20 to 40 Gbps have been demonstrated with semiconductor laser amplifier loop mirror (SLALOM) [1,2], ultrafast nonlinear interferometer (UNI) [3], and SOA based Mach-Zehnder interferometer (SOA-MZI) [4]. The all-optical logic gate based on SOA-MZI is believed to be stable, compact and simple. But, the operating speed of XOR is limited to ~250 Gbps due to the response time of gain saturation in a quantum dot SOA [5]. In this paper, a high performance optical logic gate based on output chirping in SOA is simulated. In other words, instantaneous change in phase of propagating optical pulse for logic operation is used. Using phase variation eliminates the
⁎ Corresponding author. Tel./fax: + 98 411 3860266. E-mail addresses: [email protected] (M. Sahafi), a.sahafi@tabrizu.ac.ir (A. Sahafi). 0030-4018/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2012.01.018
response time limitation of gain saturation, therefore the operating speed increases to more than one tera bit per second. In this paper, we examine the use of output chirping to introduce logic operation theoretically and present some simulated results evaluated numerically. In Section 2, a principle of operation is presented. In Section 3, SOA model is discussed. In Section 4, the model of optical filter is illustrated. Finally the simulation results are illustrated and discussed in Section 5. 2. Principle of operation The proposed structure for logic gate consists of one SOA, one Passive Optical Filter (POF) and two couplers. A continuous wave (CW) beam is injected into the CW port as illustrated in Fig. 1. According to conventional operation of light propagation through bulk SOA, steady state condition is obtained in a few nano second. Two optical control beams are sent into ports A and B of the gate. The wavelengths of the two input signals can be the same or different. Input signals from A and B enter first coupler and combine with CW in second coupler. Then these waves enter the SOA. Existence or non existence of data stream A and B cause different chirping for CW. Optical filter eliminates undesirable part of SOA's output wave and pass others to obtain logic operation. To implement a NOR gate that is the major goal of this paper, output of the gate must be in accordance with Table 1. When A = 0 and B = 0, the SOA output signal is in highest optical frequency (positive chirping) and must pass through designed optical filter to have logic “1” at the output. In other situations, output signal is in lower optical frequency and must be eliminated by optical filter so output will be on “0” state. Considering these explanations, optical filter of this structure must pass high frequency components of output wave.
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t and z, and integrating over the transverse dimensions x and y, the following equations can be obtained [1]:
Fig. 1. Basic configuration of proposed logic gate.
In this paper, a simplified dynamic model is used, and the rate equations for carrier density in an SOA are derived and solved for gain and phase recovery. Then the analysis is extended to include the nonlinear effects of carrier heating (CH) and spectral hole burning (SHB). 3. SOA model In simulation step, InGaAsP on InP substrate is considered that is often studied as constituent material for semiconductor optical amplifiers. For simplicity, an ideal facet is assumed and the amplified spontaneous emission (ASE) is neglected. The propagation of an electromagnetic field inside the amplifier is governed by the wave equation: 2 →
2 →
∇ E −
ε∂ E ¼0 c2 ∂t 2
ð1Þ
The dielectric constant is given by: ε¼
2 nb
ω2 ∂2 φ ∂2 φ 2 0 2 þ 2 þ nb −n φ ¼ 0; 2 c2 ∂x ∂y
ð6Þ
∂A 1 ∂A iω0 Γ 1 χA− α int A; þ ¼ c 2n 2 ∂z vg ∂t
ð7Þ
vg ¼
c ; ng
þ ω0 ng ¼ n
∂n ; ∂ω
ð9Þ
where υg is the group velocity, Γ is the confinement factor and αint is the internal loss. The evolution of carrier density, n, can be described by the following Eq. (1): ∂n I n Γg ðnÞ 2 − − jA j ; ¼ ∂t eV τ c dwh ¯ ω0
ð10Þ
In Eq. (10), V is the volume of the active region, I is the injected current, e is the charge of the electron, τc is the carrier lifetime, d is the depth and w is the width of the active region. For pulse propagation, Eqs. (7) and (10) can be further simplified by using the retarded time frame: τ ¼ t−
þ χ;
ð8Þ
z ; υg
ð11Þ
ð2Þ We assume:
c n χ ðnÞ ¼ − ðα þ iÞg ðnÞ ω0
ð3Þ
, ω0, and α are the background refractive index , the suswhere nb, χ, n ceptibility, the effective mode index, the photon angular frequency and the line-width enhancement factor respectively. The optical gain, g(n), is approximately given as: g ðnÞ ¼ aðn−ntr Þ;
ð4Þ
where a is the gain constant, n is the injected carrier density and ntr is the carrier density needed for transparency. The carrier induced refractive index variation is accounted for using the line-width enhancement factor, α, which is the ratio of the change in real part of refractive index to the imaginary part of it. The typical value of α, is in the range of 3–8. The electric field E(x,y,z,t) can be written as [1]: →
1 E ðx; y; z; t Þ ¼ ε^ fφðx; yÞAðz; t Þ exp½iðk0 z−ω0 t Þg; 2
ð5Þ
where ε^ is the polarization unit vector, A(z,t) is the slowly varying ω0 =c. Using Eqs. (1) amplitude of the propagating wave and k0 ¼ n and (5) and neglecting second derivatives of A(z,t) with respect to
Table 1 Truth table of NOR operation. Data A
Data B
NOR
0 0 1 1
0 1 0 1
1 0 0 0
Aðz; τÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi jφðz;τÞ P ðz; τÞe ;
ð12Þ
where P(z, τ) and φ(z, τ) are the instantaneous power and the phase of the propagating pulse respectively. By using Eqs. (3)–(12), the following coupled equations are obtained: ∂g g−g 0 gP − ; ¼− Esat τc ∂τ
ð13Þ
∂P ¼ ðΓg−α int ÞP; ∂z
ð14Þ
Esat ¼
h ¯ ω0 dw ; Γa
Iτc −ntr ; g0 ¼ a eV
ð15Þ ð16Þ
By introducing two additional equations managing gain dynamic, induced by carrier heating and spectral hole burning effects as [6]: ∂g SHB g ε ∂g ∂g ¼ − SHB − SHB g tot P ðτ; zÞ− l − CH ; τ SHB τ SHB ∂τ ∂τ ∂τ
ð17Þ
∂g CH g ε ¼ − CH − CH g tot P ðτ; zÞ; τ CH τ CH ∂τ
ð18Þ
where τSHB is the carrier-carrier scattering rate while τCH is the temperature relaxation rate, εSHB and εCH are the nonlinear gain suppression factors due to spectral hole burning and carrier heating respectively [6] and renaming g(τ) and α with gl(τ) and αl, the total gain is given by: g tot ðτ Þ ¼ g l ðτ Þ þ g CH ðτÞ þ gSHB ðτÞ;
ð19Þ
M. Sahafi et al. / Optics Communications 285 (2012) 2289–2292
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Solution of Eq. (14) with neglecting internal loss is: P ðτ; LÞ ¼ P ðτ; 0Þ expðhtot ðτÞÞ;
ð20Þ
where L
htot ðτ Þ ¼ Γ∫ g tot ðτ; zÞdz; 0
ð21Þ
and htot(τ) is the total integrated net gain, hl(τ), hSHB(τ) and hCH(τ) are the integrated net gain due to linear gain, spectral hole burning and carrier heating respectively. Integrating both sides of Eqs. (13), (17), and (18) and using: L
hl ðτ Þ ¼ Γ∫ gl ðτ; zÞdz; 0
L
ð22Þ
hSHB ðτ Þ ¼ Γ∫ g SHB ðτ; zÞdz;
ð23Þ
L
ð24Þ
0
hCH ðτ Þ ¼ Γ∫ g CH ðτ; zÞdz; 0
Eqs. (25)–(27) can be obtained: ∂hl Γg 0 L−hl P ðτÞ −½ expðhtot Þ−1 in ; ¼ Esat τc ∂τ
ð25Þ
∂hSHB h ε ∂h ∂h ¼ − SHB − SHB ½ expðhtot Þ−1P in ðτÞ− − CH ; τSHB τSHB ∂τ ∂τ ∂τ
ð26Þ
∂hCH h ε ¼ − CH − CH ½ expðhtot Þ−1P in ðτ Þ; τCH τCH ∂τ
ð27Þ
The optical gain as a function of time can be solved numerically considering coupled Eqs. (25)–(27). The time dependence phase is given as follows [6]: 1 φðτÞ ¼ − ðα l hl ðτ Þ þ α CH hCH ðτ ÞÞ; 2
ð28Þ
A time dependent phase variation leads to a variation in optical frequency content of the propagating pulse. The instantaneous variation in frequency, known as the frequency chirp Δν(τ) is given by [6]: ΔνðτÞ ¼ −
1 dφ 1 dh dh ¼ α þ α CH CH ; 2π dτ 4π dτ dτ
ð29Þ
and output frequency of SOA is: f out ðτÞ ¼ f in ðτÞ þ Δυðτ Þ;
Fig. 3. Data train of A or B.
This phenomenon is used to produce logic operation in this paper. 4. Optical filter model For simplicity, the following equation for modeling the optical filter is used. ω−ωC 4 H ðωÞ ¼ exp − ln2 ; Δω=2
ð31Þ
where ωc and Δω are the central frequency and the full width at half maximum value of H(ω). If we want to show the operation on frequency domain, the following curve should be considered (Fig. 2). It should be mentioned that ωrf is the frequency difference between 1% and 99% of the maximum value of H(ω). In this simulation, Δω is set to 24 GHz and soωrf is 15 GHz. 5. Numerical results We illustrate here the case of logic operation for NOR gate by numerical evaluation of the proposed structure. It should be mentioned that Gaussian pulse is used as the input signal (Fig. 3). The investigated device is a typical bulk InGaAsP-InP region with parameters given in Table 2 [7,8] and pumped with 200 mA. Fig. 4 shows 1 Tbps process and includes five traces of simulated results. In this figure, (a) and (b) show data streams enter to ports A and B. (c) is the output pulse of SOA and (d) is frequency shifting of output signal. (e) shows the final output after optical filter.
ð30Þ Table 2 Parameters used in simulation.
Fig. 2. Operation at frequency domain.
Symbol
Parameter
Value
d w L ntr a ng λ Γ αl αCH τC τCH τSHB εCH εSHB
thickness of the amplifier active region width of the amplifier active region length of the amplifier active region carrier density needed for transparency gain constant group refractive index wave lengh of beam confinement factor line-width enhancement factor line-width enhancement factor due to carrier heating carrier lifetime carrier temperature relaxation rate carrier-carrier scattering rate gain suppression factor due to carrier heating gain suppression factor due to spectral hole burning
0.1 μm 1 μm 1 mm 1.28e + 24 2.75e − 20 3.42 1.55 μm 0.4 7 1 250 ps 300 fs 100 fs 0.2 W− 1 0.2 W− 1
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M. Sahafi et al. / Optics Communications 285 (2012) 2289–2292
beam are filtered by designed optical filter and output is exactly NOR function of A and B (Fig. 4e). 6. Conclusion In this paper, a new promising plan of high speed logic gate using bulk SOA is presented and a NOR gate to achieve speeds as high as 1 Tbps to be used in all-optical signal processing is introduced. The filter used in this method is simple and practical. Since a simple structure is used, the characteristics of the filter can be changed to obtain other fundamental gates such as XOR and NAND. References [1] G.P. Agrawal, N.A. Olsson, Quantum Electronics 25 (1989) 2297. [2] T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, R. Dall'Ara, Electronics Letters 35 (1999) 1650. [3] C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, R. Dall'Ara, Photonics Technology Letters 12 (2000) 834. [4] T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, M. Renaud, Electronics Letters 22 (2000) 1863. [5] H. Sun, Q. Wang, H. Dong, N.K. Dutta, Optics Express 6 (2005) 1892. [6] A. Mecozzi, J. Mørk, Selected Topics in Quantum Electronics 5 (1997) 1190. [7] J.M. Tang, K.A. Shore, Quantum Electron. 11 (1999) 1704. [8] M.J. Connelly, Quantum Electron. 1 (2007) 47.
Fig. 4. Simulation results for 1 ps pulse width (1Tbps). (a) Input power of port A. (b) Input power of port B. (c) Normalized power of SOA output. (d) Frequency shifting of SOA output. (e) Normalized output power of optical filter.
It should be mentioned that in these simulations P0 is considered to be −5 dBm for CW, A and B pulses. In this condition the maximum frequency shifting is 20 GHz as shown in (d). Undesirable sections of
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
All-optical high speed logic gates using SOA Mahdi Sahafi a,⁎, Ali Rostami b, Ali Sahafi b a b
Department of Electrical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran Photonics and Nano crystal Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51666, Iran
a r t i c l e
i n f o
Article history: Received 23 June 2011 Received in revised form 27 December 2011 Accepted 13 January 2012 Available online 30 January 2012 Keywords: SOA Optical logic gate Carrier heating Spectral-hole burning
a b s t r a c t In this paper a novel and simple structure of a high speed optical logic gate based on bulk semiconductor optical amplifier (SOA) is presented. The gain dynamic and phase response of bulk SOA using rate equations including the dynamics of carrier heating (CH) and spectral-hole burning (SHB) is investigated numerically. The operation of NOR gate is analyzed by using the presented numerical method, and a NOR gate that can operate up to 1 Tbps is designed. By using the proposed structure, high speed logic gates based on bulk SOA can be realized. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Optical logic gates, such as all-optical NOR, NAND and XOR gates are the key elements for all-optical signal processing. All-optical logic gates fundamentally work on nonlinear characteristics of medium. So far, some methods utilizing the nonlinear operation of optical fiber and semiconductor optical amplifier (SOA) have been used to demonstrate all optical functions. The all-optical logic gate based on nonlinear characteristics of optical fiber has the potential of operating at terabits per second due to very short relaxation times (b100 fs) of its nonlinearity. The disadvantages of optical fiber are its weak nonlinearity and long interaction lengths and high control energy required to achieve reasonable switching efficiency whereas semiconductor optical amplifier has the advantages of high nonlinearity and ease of integration to operate as a logic gate. All optical logic XOR gates at speeds of 20 to 40 Gbps have been demonstrated with semiconductor laser amplifier loop mirror (SLALOM) [1,2], ultrafast nonlinear interferometer (UNI) [3], and SOA based Mach-Zehnder interferometer (SOA-MZI) [4]. The all-optical logic gate based on SOA-MZI is believed to be stable, compact and simple. But, the operating speed of XOR is limited to ~250 Gbps due to the response time of gain saturation in a quantum dot SOA [5]. In this paper, a high performance optical logic gate based on output chirping in SOA is simulated. In other words, instantaneous change in phase of propagating optical pulse for logic operation is used. Using phase variation eliminates the
⁎ Corresponding author. Tel./fax: + 98 411 3860266. E-mail addresses: [email protected] (M. Sahafi), a.sahafi@tabrizu.ac.ir (A. Sahafi). 0030-4018/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2012.01.018
response time limitation of gain saturation, therefore the operating speed increases to more than one tera bit per second. In this paper, we examine the use of output chirping to introduce logic operation theoretically and present some simulated results evaluated numerically. In Section 2, a principle of operation is presented. In Section 3, SOA model is discussed. In Section 4, the model of optical filter is illustrated. Finally the simulation results are illustrated and discussed in Section 5. 2. Principle of operation The proposed structure for logic gate consists of one SOA, one Passive Optical Filter (POF) and two couplers. A continuous wave (CW) beam is injected into the CW port as illustrated in Fig. 1. According to conventional operation of light propagation through bulk SOA, steady state condition is obtained in a few nano second. Two optical control beams are sent into ports A and B of the gate. The wavelengths of the two input signals can be the same or different. Input signals from A and B enter first coupler and combine with CW in second coupler. Then these waves enter the SOA. Existence or non existence of data stream A and B cause different chirping for CW. Optical filter eliminates undesirable part of SOA's output wave and pass others to obtain logic operation. To implement a NOR gate that is the major goal of this paper, output of the gate must be in accordance with Table 1. When A = 0 and B = 0, the SOA output signal is in highest optical frequency (positive chirping) and must pass through designed optical filter to have logic “1” at the output. In other situations, output signal is in lower optical frequency and must be eliminated by optical filter so output will be on “0” state. Considering these explanations, optical filter of this structure must pass high frequency components of output wave.
2290
M. Sahafi et al. / Optics Communications 285 (2012) 2289–2292
t and z, and integrating over the transverse dimensions x and y, the following equations can be obtained [1]:
Fig. 1. Basic configuration of proposed logic gate.
In this paper, a simplified dynamic model is used, and the rate equations for carrier density in an SOA are derived and solved for gain and phase recovery. Then the analysis is extended to include the nonlinear effects of carrier heating (CH) and spectral hole burning (SHB). 3. SOA model In simulation step, InGaAsP on InP substrate is considered that is often studied as constituent material for semiconductor optical amplifiers. For simplicity, an ideal facet is assumed and the amplified spontaneous emission (ASE) is neglected. The propagation of an electromagnetic field inside the amplifier is governed by the wave equation: 2 →
2 →
∇ E −
ε∂ E ¼0 c2 ∂t 2
ð1Þ
The dielectric constant is given by: ε¼
2 nb
ω2 ∂2 φ ∂2 φ 2 0 2 þ 2 þ nb −n φ ¼ 0; 2 c2 ∂x ∂y
ð6Þ
∂A 1 ∂A iω0 Γ 1 χA− α int A; þ ¼ c 2n 2 ∂z vg ∂t
ð7Þ
vg ¼
c ; ng
þ ω0 ng ¼ n
∂n ; ∂ω
ð9Þ
where υg is the group velocity, Γ is the confinement factor and αint is the internal loss. The evolution of carrier density, n, can be described by the following Eq. (1): ∂n I n Γg ðnÞ 2 − − jA j ; ¼ ∂t eV τ c dwh ¯ ω0
ð10Þ
In Eq. (10), V is the volume of the active region, I is the injected current, e is the charge of the electron, τc is the carrier lifetime, d is the depth and w is the width of the active region. For pulse propagation, Eqs. (7) and (10) can be further simplified by using the retarded time frame: τ ¼ t−
þ χ;
ð8Þ
z ; υg
ð11Þ
ð2Þ We assume:
c n χ ðnÞ ¼ − ðα þ iÞg ðnÞ ω0
ð3Þ
, ω0, and α are the background refractive index , the suswhere nb, χ, n ceptibility, the effective mode index, the photon angular frequency and the line-width enhancement factor respectively. The optical gain, g(n), is approximately given as: g ðnÞ ¼ aðn−ntr Þ;
ð4Þ
where a is the gain constant, n is the injected carrier density and ntr is the carrier density needed for transparency. The carrier induced refractive index variation is accounted for using the line-width enhancement factor, α, which is the ratio of the change in real part of refractive index to the imaginary part of it. The typical value of α, is in the range of 3–8. The electric field E(x,y,z,t) can be written as [1]: →
1 E ðx; y; z; t Þ ¼ ε^ fφðx; yÞAðz; t Þ exp½iðk0 z−ω0 t Þg; 2
ð5Þ
where ε^ is the polarization unit vector, A(z,t) is the slowly varying ω0 =c. Using Eqs. (1) amplitude of the propagating wave and k0 ¼ n and (5) and neglecting second derivatives of A(z,t) with respect to
Table 1 Truth table of NOR operation. Data A
Data B
NOR
0 0 1 1
0 1 0 1
1 0 0 0
Aðz; τÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi jφðz;τÞ P ðz; τÞe ;
ð12Þ
where P(z, τ) and φ(z, τ) are the instantaneous power and the phase of the propagating pulse respectively. By using Eqs. (3)–(12), the following coupled equations are obtained: ∂g g−g 0 gP − ; ¼− Esat τc ∂τ
ð13Þ
∂P ¼ ðΓg−α int ÞP; ∂z
ð14Þ
Esat ¼
h ¯ ω0 dw ; Γa
Iτc −ntr ; g0 ¼ a eV
ð15Þ ð16Þ
By introducing two additional equations managing gain dynamic, induced by carrier heating and spectral hole burning effects as [6]: ∂g SHB g ε ∂g ∂g ¼ − SHB − SHB g tot P ðτ; zÞ− l − CH ; τ SHB τ SHB ∂τ ∂τ ∂τ
ð17Þ
∂g CH g ε ¼ − CH − CH g tot P ðτ; zÞ; τ CH τ CH ∂τ
ð18Þ
where τSHB is the carrier-carrier scattering rate while τCH is the temperature relaxation rate, εSHB and εCH are the nonlinear gain suppression factors due to spectral hole burning and carrier heating respectively [6] and renaming g(τ) and α with gl(τ) and αl, the total gain is given by: g tot ðτ Þ ¼ g l ðτ Þ þ g CH ðτÞ þ gSHB ðτÞ;
ð19Þ
M. Sahafi et al. / Optics Communications 285 (2012) 2289–2292
2291
Solution of Eq. (14) with neglecting internal loss is: P ðτ; LÞ ¼ P ðτ; 0Þ expðhtot ðτÞÞ;
ð20Þ
where L
htot ðτ Þ ¼ Γ∫ g tot ðτ; zÞdz; 0
ð21Þ
and htot(τ) is the total integrated net gain, hl(τ), hSHB(τ) and hCH(τ) are the integrated net gain due to linear gain, spectral hole burning and carrier heating respectively. Integrating both sides of Eqs. (13), (17), and (18) and using: L
hl ðτ Þ ¼ Γ∫ gl ðτ; zÞdz; 0
L
ð22Þ
hSHB ðτ Þ ¼ Γ∫ g SHB ðτ; zÞdz;
ð23Þ
L
ð24Þ
0
hCH ðτ Þ ¼ Γ∫ g CH ðτ; zÞdz; 0
Eqs. (25)–(27) can be obtained: ∂hl Γg 0 L−hl P ðτÞ −½ expðhtot Þ−1 in ; ¼ Esat τc ∂τ
ð25Þ
∂hSHB h ε ∂h ∂h ¼ − SHB − SHB ½ expðhtot Þ−1P in ðτÞ− − CH ; τSHB τSHB ∂τ ∂τ ∂τ
ð26Þ
∂hCH h ε ¼ − CH − CH ½ expðhtot Þ−1P in ðτ Þ; τCH τCH ∂τ
ð27Þ
The optical gain as a function of time can be solved numerically considering coupled Eqs. (25)–(27). The time dependence phase is given as follows [6]: 1 φðτÞ ¼ − ðα l hl ðτ Þ þ α CH hCH ðτ ÞÞ; 2
ð28Þ
A time dependent phase variation leads to a variation in optical frequency content of the propagating pulse. The instantaneous variation in frequency, known as the frequency chirp Δν(τ) is given by [6]: ΔνðτÞ ¼ −
1 dφ 1 dh dh ¼ α þ α CH CH ; 2π dτ 4π dτ dτ
ð29Þ
and output frequency of SOA is: f out ðτÞ ¼ f in ðτÞ þ Δυðτ Þ;
Fig. 3. Data train of A or B.
This phenomenon is used to produce logic operation in this paper. 4. Optical filter model For simplicity, the following equation for modeling the optical filter is used. ω−ωC 4 H ðωÞ ¼ exp − ln2 ; Δω=2
ð31Þ
where ωc and Δω are the central frequency and the full width at half maximum value of H(ω). If we want to show the operation on frequency domain, the following curve should be considered (Fig. 2). It should be mentioned that ωrf is the frequency difference between 1% and 99% of the maximum value of H(ω). In this simulation, Δω is set to 24 GHz and soωrf is 15 GHz. 5. Numerical results We illustrate here the case of logic operation for NOR gate by numerical evaluation of the proposed structure. It should be mentioned that Gaussian pulse is used as the input signal (Fig. 3). The investigated device is a typical bulk InGaAsP-InP region with parameters given in Table 2 [7,8] and pumped with 200 mA. Fig. 4 shows 1 Tbps process and includes five traces of simulated results. In this figure, (a) and (b) show data streams enter to ports A and B. (c) is the output pulse of SOA and (d) is frequency shifting of output signal. (e) shows the final output after optical filter.
ð30Þ Table 2 Parameters used in simulation.
Fig. 2. Operation at frequency domain.
Symbol
Parameter
Value
d w L ntr a ng λ Γ αl αCH τC τCH τSHB εCH εSHB
thickness of the amplifier active region width of the amplifier active region length of the amplifier active region carrier density needed for transparency gain constant group refractive index wave lengh of beam confinement factor line-width enhancement factor line-width enhancement factor due to carrier heating carrier lifetime carrier temperature relaxation rate carrier-carrier scattering rate gain suppression factor due to carrier heating gain suppression factor due to spectral hole burning
0.1 μm 1 μm 1 mm 1.28e + 24 2.75e − 20 3.42 1.55 μm 0.4 7 1 250 ps 300 fs 100 fs 0.2 W− 1 0.2 W− 1
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beam are filtered by designed optical filter and output is exactly NOR function of A and B (Fig. 4e). 6. Conclusion In this paper, a new promising plan of high speed logic gate using bulk SOA is presented and a NOR gate to achieve speeds as high as 1 Tbps to be used in all-optical signal processing is introduced. The filter used in this method is simple and practical. Since a simple structure is used, the characteristics of the filter can be changed to obtain other fundamental gates such as XOR and NAND. References [1] G.P. Agrawal, N.A. Olsson, Quantum Electronics 25 (1989) 2297. [2] T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, R. Dall'Ara, Electronics Letters 35 (1999) 1650. [3] C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, R. Dall'Ara, Photonics Technology Letters 12 (2000) 834. [4] T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, M. Renaud, Electronics Letters 22 (2000) 1863. [5] H. Sun, Q. Wang, H. Dong, N.K. Dutta, Optics Express 6 (2005) 1892. [6] A. Mecozzi, J. Mørk, Selected Topics in Quantum Electronics 5 (1997) 1190. [7] J.M. Tang, K.A. Shore, Quantum Electron. 11 (1999) 1704. [8] M.J. Connelly, Quantum Electron. 1 (2007) 47.
Fig. 4. Simulation results for 1 ps pulse width (1Tbps). (a) Input power of port A. (b) Input power of port B. (c) Normalized power of SOA output. (d) Frequency shifting of SOA output. (e) Normalized output power of optical filter.
It should be mentioned that in these simulations P0 is considered to be −5 dBm for CW, A and B pulses. In this condition the maximum frequency shifting is 20 GHz as shown in (d). Undesirable sections of