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recovery based on a semiconductor optical amplifier ring cavity
Optics Communications 257 (2006) 334–339 www.elsevier.com/locate/optcom
All-optical frequency multiplication/recovery based on a semiconductor optical amplifier ring cavity Fei Wang, Guang-Qiong Xia, Zheng-Mao Wu
*
School of Physics, Southwest Normal University, Beibei, Chongqing 400715, China Received 3 May 2005; received in revised form 5 July 2005; accepted 19 July 2005
Abstract A novel scheme for all-optical frequency multiplication/recovery based on a semiconductor optical amplifier ring cavity is proposed and investigated numerically. The results show, for a 2.5 GHz driving pulse train, it can be generated 5–25 GHz repetition rate pulse trains with low clock amplitude jitter, polarization independence and high peak power. Furthermore, the extraction of the clock signal from a pseudorandom bit sequence signal can be realized based on the proposed scheme. 2005 Elsevier B.V. All rights reserved. Keywords: Semiconductor optical amplifier; Ring cavity; Interference; All-optical frequency multiplication/recovery
1. Introduction Ultra-short pulses with high repetition rates of several tens of gigahertz are essentially required for optical signal processing in high-speed optical time division multiplexing (OTDM) communications [1]. Recently, rational harmonic mode locking technique, which can generate an optical pulse train at repetition rate integer multiples of the modulation frequency by slightly detuning modulation frequency from its optimal harmonic *
Corresponding author. Tel.: +86 23 6836 7150/6825 4045; fax: +86 23 6825 4608. E-mail address: [email protected] (Z.-M. Wu).
mode-locking value, has received much attention [2–11]. However, with the increase of the order of rational harmonic, the mode-locked pulse amplitude becomes uneven, which gives rise to problems in a real optical communications environment. Some pulse amplitude equalization methods have been presented to solve this problem [6–11]. In this paper, we propose and analyze a novel scheme for all-optical frequency multiplication/ recovery based on a semiconductor optical amplifier (SOA) ring cavity. Compared with the conventional rational harmonic mode-locked lasers, the proposed scheme has some advantages such as the generation of an output pulse train with a small amplitude ripple, high peak power and
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.07.074
F. Wang et al. / Optics Communications 257 (2006) 334–339
polarization independence. Moreover, this scheme can be used to extract the clock signal from a pseudorandom bit sequence (PRBS) signal.
2. Configuration The scheme for all-optical frequency multiplication/recovery based on a SOA ring cavity is shown in Fig. 1. A pulse train output from a mode-locked laser is incident into a ring cavity, whose round trip period can be adjusted to match the period of the input pulse train. However, in order to obtain the pulse train with the p multiple repetition rate of the input signal, the round trip time in the ring cavity should be set to nTp + Tp/p (where n and p are integers, and Tp is the period of the input signal). To better comprehend the procedure of frequency multiplication, the case of frequency doubling (i.e. n = 1, p = 2), is described as follows. For an input mode-locked pulse train entering into the ring cavity, after 1.5 Tp, the feedback pulse train will meet and combine with the input pulse train at the beam splitter R1 with a temporal deviation of Tp/2. After another 1.5 Tp, the feedback pulse will align with the input pulse. Repeating continuously above procedure, frequency doubling can be realized. When an optical pulse passes through a SOA, it is amplified and undergone self-phase modulation (SPM) due to carrier recombination. SPM induces non-linear phase shift proportional to the pulse energy, which results in the
En+1
Ein
R1
SOA Eout
R2
Fig. 1. The proposed configuration for all-optical frequency multiplication/recovery based on a SOA ring cavity.
335
pulse with chirp (the instantaneous carrier frequency varies throughout the pulse) and spectrum shift to lower frequencies. At each round trip, the amplified chirped pulse train is combined with the incident pulse train at the beam splitter R1. Most of energy outputs from the ring cavity via the beam splitter R2, and only relatively low energy circulates inside the ring cavity. By adjusting the system parameters, the high repetition rate pulse train with low clock amplitude jitter (CAJ), polarization independence and high peak power, can be obtained.
3. Theory The amplitude Acnþ1 ðtÞ of the circulating pulse after n + 1 cavity round trips, just after reflection at beam splitter R1, is expressed in terms of the incident pulse amplitude Ain(t) according to Acnþ1 ðtÞ ¼ ð1 r21 Þ1=2 Ain ðtÞ þ r1 r2 Anc ðtÞ ½GðtÞ
1=2
exp½iðUL þ UNL Þ;
ð1Þ
where G(t) is the amplifier gain, UL is the linear phase shift, UNL is the non-linear phase shift, and r1 and r2 are the reflective coefficient of beam splitter R1 and R2, respectively. Assuming that the reflectivity of both facets of the SOA is equal to zero and the SOA is split into 20 sections, the rate equations describing the optical pulse amplification in the jth section of the SOA can be written as [12,13] oN j ðz; T Þ I N j Cg½N j ðz; T Þ ¼ P j; ð2Þ oT qV hxAcross sc oP j ðz; T Þ ¼ fCg½N j ðz; T Þ aint gP j ðz; T Þ; ð3Þ oz o/j 1 ¼ Caj g½N j ðz; T Þ; ð4Þ 2 oz where Nj denotes the carrier density in the j section of the SOA, T(= t z/vg, where vg is the group velocity in the SOA) represents the time in a reference frame moving along with the pulse, I is the injection current, V denotes the volume of the active layer of the SOA, q represents the electron charge, hx is the photon energy, and Across denotes the cross-sectional area of the active layer in the
336
F. Wang et al. / Optics Communications 257 (2006) 334–339
SOA. The spontaneous emission lifetime is defined 1 as sc ¼ ðA þ BN j þ CN 2j Þ , where A, B, and C denote the non-radiative, the bimolecular, and the auger recombination coefficients, respectively. Additionally, aint represents the internal loss of the SOA and P j is the average powers in the jth section of the SOA, which can be calculated as Z jDL 1 Gj 1 P j1 ; Pj ¼ P j1 e½CgðN j Þaint z dz ¼ DL ðj1ÞDL lnðGj Þ ð5Þ ½CgðN j Þaint DL
(if pulse power is too where Gj ¼ e high, the gain compression factor should be taken ½CgðN j Þaint DL into consideration, namely, Gj ¼ exp 1þeP , j1 where e is the gain compression factor which is phenomenologically introduced to describe the effects of the carrier heating and spectral hole burning), nL denotes the length of each SOA section, Pj 1 represents the power output from the (j 1)th section, Meanwhile, a cubic formulas is employed to describe the asymmetric gain, i.e., 2
3
gðN j Þ ¼ a1 ðN j N 0 Þ a2 ðk kN Þ þ a3 ðk kN Þ ; ð6Þ where a1 denotes the differential gain coefficient, a2 and a3 are experimentally determined constants that characterize the width and asymmetry of the gain profile, respectively, N0 represents the transparency carrier density, kN = k0 a4(N N0) is the corresponding wavelength for peak gain, and a4 denotes the empirical constant that shows the shift of the gain peak. The line-width enhancement factor aj for each small section, which is directly related to the frequency chirp, is described as 4p dn dgðN j Þ aj ¼ ; ð7Þ k dN dN j
j
where dn/dN denotes the differential refractive index, and dg(Nj)/dNj is the change rate of gain coefficient with carrier density. Based on Eqs. (1)–(7) and using the fourth-fifthorder Rung–Kutta method, the temporal shape of amplified pulse passing through the SOA can be simulated numerically, then the amplitude of pulse output from the ring cavity via R2 can be obtained by
Anout ðtÞ ¼ ð1 r22 Þ
1=2
1=2
Anc ½GðtÞ
expði/NL Þ.
ð8Þ
4. Results and discussion Each pulse of the incident pulse train is supposed to be a Gaussian profile and the power Pin(T) of the incident pulse train can be expressed as P in ðT Þ ¼ P 0
þ1 X
2
C m exp½ðT m=RÞ =T 20 ;
ð9Þ
m¼1
where P0 is the peak power, T0 characterizes the pulse width, R is the bit rate of the incident data, and Cm is the value of code unit. If the incident pulse train is the mode-locked pulse, Cm = 1. However, for a pseudorandom bit sequence (PRBS) signal, Cm can be expressed as 1 P ðam ¼ 1Þ ¼ 1=2; Cm ¼ ð10Þ 0 P ðam ¼ 0Þ ¼ 1=2. Furthermore, the input pulse is assumed to be a single-frequency light of 1.55 lm, which is reasonable because a picosecond pulse has a relative narrow spectral width compared with the bandwidth of the SOA. The data used in calculations are: T0 = 5 ps, P0 = 1 mW, R = 2.5 Gb/s, Cm = 1, L = 0.50 · 103 m, Across = 0.4 · 1012 m2, a1 = 2.5 · 1020 m2, a2 = 7.4 · 1018 m3, a3 = 3.155 · 1025 m4, a4 = 3 · 1032 m4, e = 0.2 W1, N0 = 0.9 · 1024 m3, A = 1 · 108 s1, B = 2.5 · 17 3 10 m /s, C = 9.4 · 1041 m6/s, C = 0.3, aint = 20 cm1, q = 1.6 · 1019 C, c = 3 · 108 m/s, k0 = 1.605 lm, dn/dN = 1.2 · 1026 m3, r21 ¼ 0.7, r22 ¼ 0.01. Fig. 2 shows the evolution of output pulse train as a function of round trip number in double frequency multiplication. From this diagram, it can be seen that the shape of the output pulse varies intensely at the beginning, but after circulating about five round trips in cavity, the amplitude of the output pulse train will be stable, which is significant to quickly extract the clock signal from a pseudorandom signal. If one observes this diagram carefully, uneven pulse amplitude can be found. The quality of pulse–amplitude equilibrium can be measured by the clock amplitude jitter (CAJ) [8]
F. Wang et al. / Optics Communications 257 (2006) 334–339
Fig. 2. Evolution of output pulse train with the round trip number in double frequency multiplication.
r 100ð%Þ; ð11Þ M where is r the standard deviation and M is the mean of the intensity histogram at the peak of the pulses. Normally, CAJ is related to the system parameter. Fig. 3(a) shows CAJ as a function of the bias current of SOA in double frequency multiplication for the base frequency of 2.5 GHz, where the inset is the pulse waveform at several currents. With the increase of the bias current of SOA, CAJ decreases at first, after passes through a minimum value, and then increases again. The pulse–amplitude equilibrium in this scheme is the joint function of gain and non-linear phase shift afforded by SOA, and the loss in ring cavity. If the bias current of SOA is not selected correctly, the quality of pulse–amplitude equilibrium will worsen, and even the pulse may be split. When CAJ ¼
337
the bias current of SOA is 61.3 mA (the SOA small-signal gain g0 = 48.2 dB), the value of CAJ is minimum (0.48%), which indicates that the quality of the pulse–amplitude equilibrium is the best. Therefore, to improve the quality of pulse– amplitude equilibrium, the bias current of the SOA must be optimized if the other parameters of the system have been determined. By the way, it should be pointed out that the base frequency of 2.5 GHz is chosen in this paper only for comparing with the related experimental demonstrations [10,11,14], and the proposed scheme is completely suitable for the base frequency higher than 2.5 GHz. The result for the base frequency of 10 GHz is demonstrated in Fig. 3(b). CAJ curve varying tendency for frequency doubling at 10 GHz is similar to that at 2.5 GHz, and the optimized bias current of SOA increases to 65.7 mA (the SOA small-signal gain g0 = 48.5 dB) due to carrier density decreasing in SOA caused by the incident pulse train with higher base frequency. Fig. 4 shows the temporal waveforms of the input and output pulse train with different frequency multiplication, where Fig. 4(a) is the 2.5 Gb/s input pulse train, and Figs. 4(b)–(f) show the frequency multiplication results of double, triple, four times, 10 times, and 15 times, respectively. Figs. 4(b)–(f) are obtained under the bias current of the SOA being optimized as 61.3, 62, 67 and 75 mA, respectively. From this diagram, it can be seen that, the quality of the pulse–amplitude equilibrium is quite well for the frequency multiplica-
Fig. 3. The clock amplitude jitter (CAJ) as a function of the bias current of SOA in double frequency multiplication.
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F. Wang et al. / Optics Communications 257 (2006) 334–339
Fig. 4. Temporal waveforms of pulse train, where: (a) 2.5 Gb/s input pulse train; (b–f) are for double, triple, four times, 10 times, and 15 times frequency multiplication, respectively.
tion smaller than 10 times, but worsens for more than 10 times frequency multiplication. Additionally, we investigate the all-optical clock recovery from a pseudorandom bit sequence
(PRBS) signal by this scheme. Fig. 5 shows the alloptical clock recovery results for 27–1 PRBS at 2.5 Gb/s. Fig. 5(a) and (b) shows the eye diagram of output clock for 2.5 Gb/s recovery and 2.5 GHz
F. Wang et al. / Optics Communications 257 (2006) 334–339
339
Fig. 5. The eye diagram of: (a) 2.5 GHz recovered clock; (b) 5 GHz recovered clock.
double/recovery, respectively. It is obvious that the quality of pulse–amplitude equilibrium of the latter is worse than that of the former. The reason is that the quality of pulse–amplitude equilibrium directly depends on the number of consecutive ‘‘0’’ in signal, and the number of consecutive ‘‘0’’ in the frequency multiplication/recovery for the same incident signal is double as that in the frequency recovery, therefore, the CAJ of the frequency multiplication/recovery increases. 5. Conclusion We have proposed and numerically demonstrated all-optical frequency multiplication technique based on a SOA ring cavity. The proposed method has advantages of amplitude equilibrium and polarization-independent all-optical processing, and has potential applications in all-optical clock recovery at very high repetition rates with the help of a proper carrier recovery time reduction scheme such as a CW-holding beam [15,16]. Acknowledgements The authors acknowledge the support from the Commission of Science and Technology of Chongqing City of the PR China, and the Ph.D. fund of Southwest Normal University, PR China.
References [1] T. Houbavlis, K.E. Zoiros, M. Kalyvas, G. Theophilopoulos, C. Bintjas, K. Yiannopoulos, N. Pleros, K. Vlachos, H. Avramopoulos, L. Schares, L. Occhi, G. Guekos, J.R. Taylor, S. Hansmann, W. Miller, IEEE/OSA J. Lightwave Technol. 23 (2005) 781. [2] K. Zoiros, K. Vlachos, T. Stathopoulos, C. Bintjas, H. Avramopoulos, in: Optical Fiber Communication Conference (OFC) 2000, TuR3, p. 254. [3] S.P. Li, C.Y. Lou, K.T. Chan, Electron. Lett. 34 (1998) 375. [4] C.M. Wu, N.K. Dutta, IEEE. J. Quantum Electon. 36 (2000) 145. [5] G.R. Lin, Y.C. Chang, J.R. Wu, IEEE Photon. Technol. Lett. 16 (2004) 1810. [6] M.Y. Jeon, H.K. Lee, J.T. Ahn, D.S. Lim, H.Y. Kim, K.H. Kim, E.H. Lee, Electron. Lett. 34 (1998) 182. [7] M.Y. Jeon, H.K. Lee, J.T. Ahn, K.H. Kim, D.S. Lim, E.H. Lee, Opt. Lett. 23 (1998) 855. [8] H.J. Lee, K. Kim, H.G. Kim, Opt. Commun. 160 (1999) 51. [9] K.K. Gupta, N. Onodera, M. Hyodo, Electron. Lett. 37 (2001) 948. [10] Z.H. Li, C.Y. Lou, K.T. Chan, Y.H. Li, Y.Z. Gao, IEEE. J. Quantum Electon. 37 (2001) 33. [11] Y.J. Kim, C.G. Lee, Y.Y. Chun, C.S. Park, Opt. Express 12 (2004) 907. [12] W.Y. Yang, Z.M. Wu, G.Q. Xia, Opt. Commun. 250 (2005) 384. [13] G.Q. Xia, Z.M. Wu, G.R. Lin, Opt. Commun. 227 (2003) 165. [14] H.J. Lee, C.G. Lee, C.S. Park, Opt. Commun. 198 (2001) 37. [15] R.J. Manning, A.O. Davies, Opt. Lett. 19 (1994) 889. [16] R.J. Manning, G. Sherlock, Electron. Lett. 31 (1995) 307.
All-optical frequency multiplication/recovery based on a semiconductor optical amplifier ring cavity Fei Wang, Guang-Qiong Xia, Zheng-Mao Wu
*
School of Physics, Southwest Normal University, Beibei, Chongqing 400715, China Received 3 May 2005; received in revised form 5 July 2005; accepted 19 July 2005
Abstract A novel scheme for all-optical frequency multiplication/recovery based on a semiconductor optical amplifier ring cavity is proposed and investigated numerically. The results show, for a 2.5 GHz driving pulse train, it can be generated 5–25 GHz repetition rate pulse trains with low clock amplitude jitter, polarization independence and high peak power. Furthermore, the extraction of the clock signal from a pseudorandom bit sequence signal can be realized based on the proposed scheme. 2005 Elsevier B.V. All rights reserved. Keywords: Semiconductor optical amplifier; Ring cavity; Interference; All-optical frequency multiplication/recovery
1. Introduction Ultra-short pulses with high repetition rates of several tens of gigahertz are essentially required for optical signal processing in high-speed optical time division multiplexing (OTDM) communications [1]. Recently, rational harmonic mode locking technique, which can generate an optical pulse train at repetition rate integer multiples of the modulation frequency by slightly detuning modulation frequency from its optimal harmonic *
Corresponding author. Tel.: +86 23 6836 7150/6825 4045; fax: +86 23 6825 4608. E-mail address: [email protected] (Z.-M. Wu).
mode-locking value, has received much attention [2–11]. However, with the increase of the order of rational harmonic, the mode-locked pulse amplitude becomes uneven, which gives rise to problems in a real optical communications environment. Some pulse amplitude equalization methods have been presented to solve this problem [6–11]. In this paper, we propose and analyze a novel scheme for all-optical frequency multiplication/ recovery based on a semiconductor optical amplifier (SOA) ring cavity. Compared with the conventional rational harmonic mode-locked lasers, the proposed scheme has some advantages such as the generation of an output pulse train with a small amplitude ripple, high peak power and
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.07.074
F. Wang et al. / Optics Communications 257 (2006) 334–339
polarization independence. Moreover, this scheme can be used to extract the clock signal from a pseudorandom bit sequence (PRBS) signal.
2. Configuration The scheme for all-optical frequency multiplication/recovery based on a SOA ring cavity is shown in Fig. 1. A pulse train output from a mode-locked laser is incident into a ring cavity, whose round trip period can be adjusted to match the period of the input pulse train. However, in order to obtain the pulse train with the p multiple repetition rate of the input signal, the round trip time in the ring cavity should be set to nTp + Tp/p (where n and p are integers, and Tp is the period of the input signal). To better comprehend the procedure of frequency multiplication, the case of frequency doubling (i.e. n = 1, p = 2), is described as follows. For an input mode-locked pulse train entering into the ring cavity, after 1.5 Tp, the feedback pulse train will meet and combine with the input pulse train at the beam splitter R1 with a temporal deviation of Tp/2. After another 1.5 Tp, the feedback pulse will align with the input pulse. Repeating continuously above procedure, frequency doubling can be realized. When an optical pulse passes through a SOA, it is amplified and undergone self-phase modulation (SPM) due to carrier recombination. SPM induces non-linear phase shift proportional to the pulse energy, which results in the
En+1
Ein
R1
SOA Eout
R2
Fig. 1. The proposed configuration for all-optical frequency multiplication/recovery based on a SOA ring cavity.
335
pulse with chirp (the instantaneous carrier frequency varies throughout the pulse) and spectrum shift to lower frequencies. At each round trip, the amplified chirped pulse train is combined with the incident pulse train at the beam splitter R1. Most of energy outputs from the ring cavity via the beam splitter R2, and only relatively low energy circulates inside the ring cavity. By adjusting the system parameters, the high repetition rate pulse train with low clock amplitude jitter (CAJ), polarization independence and high peak power, can be obtained.
3. Theory The amplitude Acnþ1 ðtÞ of the circulating pulse after n + 1 cavity round trips, just after reflection at beam splitter R1, is expressed in terms of the incident pulse amplitude Ain(t) according to Acnþ1 ðtÞ ¼ ð1 r21 Þ1=2 Ain ðtÞ þ r1 r2 Anc ðtÞ ½GðtÞ
1=2
exp½iðUL þ UNL Þ;
ð1Þ
where G(t) is the amplifier gain, UL is the linear phase shift, UNL is the non-linear phase shift, and r1 and r2 are the reflective coefficient of beam splitter R1 and R2, respectively. Assuming that the reflectivity of both facets of the SOA is equal to zero and the SOA is split into 20 sections, the rate equations describing the optical pulse amplification in the jth section of the SOA can be written as [12,13] oN j ðz; T Þ I N j Cg½N j ðz; T Þ ¼ P j; ð2Þ oT qV hxAcross sc oP j ðz; T Þ ¼ fCg½N j ðz; T Þ aint gP j ðz; T Þ; ð3Þ oz o/j 1 ¼ Caj g½N j ðz; T Þ; ð4Þ 2 oz where Nj denotes the carrier density in the j section of the SOA, T(= t z/vg, where vg is the group velocity in the SOA) represents the time in a reference frame moving along with the pulse, I is the injection current, V denotes the volume of the active layer of the SOA, q represents the electron charge, hx is the photon energy, and Across denotes the cross-sectional area of the active layer in the
336
F. Wang et al. / Optics Communications 257 (2006) 334–339
SOA. The spontaneous emission lifetime is defined 1 as sc ¼ ðA þ BN j þ CN 2j Þ , where A, B, and C denote the non-radiative, the bimolecular, and the auger recombination coefficients, respectively. Additionally, aint represents the internal loss of the SOA and P j is the average powers in the jth section of the SOA, which can be calculated as Z jDL 1 Gj 1 P j1 ; Pj ¼ P j1 e½CgðN j Þaint z dz ¼ DL ðj1ÞDL lnðGj Þ ð5Þ ½CgðN j Þaint DL
(if pulse power is too where Gj ¼ e high, the gain compression factor should be taken ½CgðN j Þaint DL into consideration, namely, Gj ¼ exp 1þeP , j1 where e is the gain compression factor which is phenomenologically introduced to describe the effects of the carrier heating and spectral hole burning), nL denotes the length of each SOA section, Pj 1 represents the power output from the (j 1)th section, Meanwhile, a cubic formulas is employed to describe the asymmetric gain, i.e., 2
3
gðN j Þ ¼ a1 ðN j N 0 Þ a2 ðk kN Þ þ a3 ðk kN Þ ; ð6Þ where a1 denotes the differential gain coefficient, a2 and a3 are experimentally determined constants that characterize the width and asymmetry of the gain profile, respectively, N0 represents the transparency carrier density, kN = k0 a4(N N0) is the corresponding wavelength for peak gain, and a4 denotes the empirical constant that shows the shift of the gain peak. The line-width enhancement factor aj for each small section, which is directly related to the frequency chirp, is described as 4p dn dgðN j Þ aj ¼ ; ð7Þ k dN dN j
j
where dn/dN denotes the differential refractive index, and dg(Nj)/dNj is the change rate of gain coefficient with carrier density. Based on Eqs. (1)–(7) and using the fourth-fifthorder Rung–Kutta method, the temporal shape of amplified pulse passing through the SOA can be simulated numerically, then the amplitude of pulse output from the ring cavity via R2 can be obtained by
Anout ðtÞ ¼ ð1 r22 Þ
1=2
1=2
Anc ½GðtÞ
expði/NL Þ.
ð8Þ
4. Results and discussion Each pulse of the incident pulse train is supposed to be a Gaussian profile and the power Pin(T) of the incident pulse train can be expressed as P in ðT Þ ¼ P 0
þ1 X
2
C m exp½ðT m=RÞ =T 20 ;
ð9Þ
m¼1
where P0 is the peak power, T0 characterizes the pulse width, R is the bit rate of the incident data, and Cm is the value of code unit. If the incident pulse train is the mode-locked pulse, Cm = 1. However, for a pseudorandom bit sequence (PRBS) signal, Cm can be expressed as 1 P ðam ¼ 1Þ ¼ 1=2; Cm ¼ ð10Þ 0 P ðam ¼ 0Þ ¼ 1=2. Furthermore, the input pulse is assumed to be a single-frequency light of 1.55 lm, which is reasonable because a picosecond pulse has a relative narrow spectral width compared with the bandwidth of the SOA. The data used in calculations are: T0 = 5 ps, P0 = 1 mW, R = 2.5 Gb/s, Cm = 1, L = 0.50 · 103 m, Across = 0.4 · 1012 m2, a1 = 2.5 · 1020 m2, a2 = 7.4 · 1018 m3, a3 = 3.155 · 1025 m4, a4 = 3 · 1032 m4, e = 0.2 W1, N0 = 0.9 · 1024 m3, A = 1 · 108 s1, B = 2.5 · 17 3 10 m /s, C = 9.4 · 1041 m6/s, C = 0.3, aint = 20 cm1, q = 1.6 · 1019 C, c = 3 · 108 m/s, k0 = 1.605 lm, dn/dN = 1.2 · 1026 m3, r21 ¼ 0.7, r22 ¼ 0.01. Fig. 2 shows the evolution of output pulse train as a function of round trip number in double frequency multiplication. From this diagram, it can be seen that the shape of the output pulse varies intensely at the beginning, but after circulating about five round trips in cavity, the amplitude of the output pulse train will be stable, which is significant to quickly extract the clock signal from a pseudorandom signal. If one observes this diagram carefully, uneven pulse amplitude can be found. The quality of pulse–amplitude equilibrium can be measured by the clock amplitude jitter (CAJ) [8]
F. Wang et al. / Optics Communications 257 (2006) 334–339
Fig. 2. Evolution of output pulse train with the round trip number in double frequency multiplication.
r 100ð%Þ; ð11Þ M where is r the standard deviation and M is the mean of the intensity histogram at the peak of the pulses. Normally, CAJ is related to the system parameter. Fig. 3(a) shows CAJ as a function of the bias current of SOA in double frequency multiplication for the base frequency of 2.5 GHz, where the inset is the pulse waveform at several currents. With the increase of the bias current of SOA, CAJ decreases at first, after passes through a minimum value, and then increases again. The pulse–amplitude equilibrium in this scheme is the joint function of gain and non-linear phase shift afforded by SOA, and the loss in ring cavity. If the bias current of SOA is not selected correctly, the quality of pulse–amplitude equilibrium will worsen, and even the pulse may be split. When CAJ ¼
337
the bias current of SOA is 61.3 mA (the SOA small-signal gain g0 = 48.2 dB), the value of CAJ is minimum (0.48%), which indicates that the quality of the pulse–amplitude equilibrium is the best. Therefore, to improve the quality of pulse– amplitude equilibrium, the bias current of the SOA must be optimized if the other parameters of the system have been determined. By the way, it should be pointed out that the base frequency of 2.5 GHz is chosen in this paper only for comparing with the related experimental demonstrations [10,11,14], and the proposed scheme is completely suitable for the base frequency higher than 2.5 GHz. The result for the base frequency of 10 GHz is demonstrated in Fig. 3(b). CAJ curve varying tendency for frequency doubling at 10 GHz is similar to that at 2.5 GHz, and the optimized bias current of SOA increases to 65.7 mA (the SOA small-signal gain g0 = 48.5 dB) due to carrier density decreasing in SOA caused by the incident pulse train with higher base frequency. Fig. 4 shows the temporal waveforms of the input and output pulse train with different frequency multiplication, where Fig. 4(a) is the 2.5 Gb/s input pulse train, and Figs. 4(b)–(f) show the frequency multiplication results of double, triple, four times, 10 times, and 15 times, respectively. Figs. 4(b)–(f) are obtained under the bias current of the SOA being optimized as 61.3, 62, 67 and 75 mA, respectively. From this diagram, it can be seen that, the quality of the pulse–amplitude equilibrium is quite well for the frequency multiplica-
Fig. 3. The clock amplitude jitter (CAJ) as a function of the bias current of SOA in double frequency multiplication.
338
F. Wang et al. / Optics Communications 257 (2006) 334–339
Fig. 4. Temporal waveforms of pulse train, where: (a) 2.5 Gb/s input pulse train; (b–f) are for double, triple, four times, 10 times, and 15 times frequency multiplication, respectively.
tion smaller than 10 times, but worsens for more than 10 times frequency multiplication. Additionally, we investigate the all-optical clock recovery from a pseudorandom bit sequence
(PRBS) signal by this scheme. Fig. 5 shows the alloptical clock recovery results for 27–1 PRBS at 2.5 Gb/s. Fig. 5(a) and (b) shows the eye diagram of output clock for 2.5 Gb/s recovery and 2.5 GHz
F. Wang et al. / Optics Communications 257 (2006) 334–339
339
Fig. 5. The eye diagram of: (a) 2.5 GHz recovered clock; (b) 5 GHz recovered clock.
double/recovery, respectively. It is obvious that the quality of pulse–amplitude equilibrium of the latter is worse than that of the former. The reason is that the quality of pulse–amplitude equilibrium directly depends on the number of consecutive ‘‘0’’ in signal, and the number of consecutive ‘‘0’’ in the frequency multiplication/recovery for the same incident signal is double as that in the frequency recovery, therefore, the CAJ of the frequency multiplication/recovery increases. 5. Conclusion We have proposed and numerically demonstrated all-optical frequency multiplication technique based on a SOA ring cavity. The proposed method has advantages of amplitude equilibrium and polarization-independent all-optical processing, and has potential applications in all-optical clock recovery at very high repetition rates with the help of a proper carrier recovery time reduction scheme such as a CW-holding beam [15,16]. Acknowledgements The authors acknowledge the support from the Commission of Science and Technology of Chongqing City of the PR China, and the Ph.D. fund of Southwest Normal University, PR China.
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