Use of State of Polarization Transparent Scheme for Polarization Shift ...

OPTICAL REVIEW Vol. 21, No. 1 (2014) 48–53

Use of State of Polarization Transparent Scheme for Polarization Shift Keying Signal as Optical Phase Conjugator to Improve the Transmission Performance Md. Nur-Al-Safa BHUIYAN1
, Motoharu MATSUURA2 , Hung Nguyen TAN1 , and Naoto KISHI1 1 2

Department of Communication Engineering and Informatics, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan Center for Frontier Science and Engineering, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan

(Received February 15, 2013; revised October 21, 2013; Accepted November 19, 2013) Transmission characteristics of polarization shift keying (PolSK) signal is experimentally demonstrated in this work. Performance degradation due to transmission is improved using optical phase conjugation (OPC) technique. The wavelength converter based on the proposed state of polarization (SOP) transparent scheme for PolSK signal is effective to use it as mid-link optical phase conjugator and which is difficult to achieve using conventional wavelength conversion scheme. It is found that for fiber transmission, the performance of both of the orthogonal SOPs of the PolSK signal is different for their respective chirping characteristics which can be optimized to be similar using proposed OPC technique. # 2014 The Japan Society of Applied Physics Keywords: fiber optics communication, nonlinear optics, four-wave-mixing, phase conjugation

1.

In PolSK, the state of polarization (SOP) of optical signal is used as the information bearing parameter.15) The main advantage of PolSK is its constant envelope, thus showing reduced sensitivity to SPM and cross-phase modulation (XPM). Because of its constant power characteristics, PolSK signal can eliminate the patterning effect in semiconductor optical amplifier (SOA) and thus improves the signal quality.16) PolSK also shows reduced sensitivity to laser phase noise.17) Therefore, PolSK modulation format is very useful in the future photonic network. In a previous research, simple FWM process involving input binary PolSK signal and pump was considered for the wavelength conversion of PolSK signal as the signal SOP was preserved in this effect.18) However, this conventional wavelength converter can not be used as phase conjugator to improve the transmission performance because of a fundamental shortcoming. In the conventional wavelength converter, it is not possible to preserve the SOP of the input PolSK signal on the converted spectral component which is phase-conjugated in FWM process and through which the spectrum of the input signal is inverted. Hence, an improved wavelength converter is required to use it as optical phase conjugator where the phase-conjugated wavelength converted signal can hold the input PolSK signal information. In our previous work, we have demonstrated, for the first time, a fiber-based polarization-insensitive wavelength converter for PolSK signal in which preservation of input signal information on both of the converted spectral components in FWM spectrum is possible.19,20) Hence, our proposed scheme can be called the signal SOP transparent scheme for PolSK. The wavelength converter based on our proposed scheme is suitable for optical phase-conjugator involving PolSK signal and can be used to improve the transmission performance. The additional advantage of the proposed wavelength converter used as optical phase conjugator is polarization-independent operation.20) Before

Introduction

Chromatic dispersion and the optical Kerr effect in a single-mode fiber (SMF) critically limit the maximum transmission length and capacity in a long-haul, high-speed, and high-capacity optical fiber communication system.1,2) A method of dispersion compensation by nonlinear optical phase conjugation (OPC) has been proposed by Yariv et al., in which optical pulses distorted due to dispersion in the first fiber can be reshaped by the following OPC and subsequent propagation through the second fiber with similar dispersive characteristics.3) Mid-link OPC is an attractive method for replacing chromatic dispersion compensating fiber (DCF).4,5) In high bit rate wavelength division-multiplexed (WDM) systems using DCF as chromatic dispersion compensator, the dispersion management has a great impact on the system performance.6,7) In such systems, every link needs its own custom dispersion map which is complicated. However, in mid-link OPC based systems, no custom dispersion map needs to be designed for each specific link. Moreover, different modulation formats and different channel data rates can be used on the same link. It has been experimentally shown that OPC can compensate for chromatic dispersion,8) self-phase modulation (SPM) due to the optical Kerr effect,9) and also intra-channel nonlinear impairments.10,11) Simultaneous processing of multiple channels is another key advantage of OPC.12) Recently, it has been shown that OPC can compensate as well for impairments resulting from nonlinear phase noise.13) Nonlinear phase noise can severely impair the performance of phase shift keyed transmission systems.14) Hence, the application of OPC can relax the link design. However, employing OPC is very difficult with the conventional four-wave mixing (FWM) effect in one of the attractive modulation format called polarization shift keying (PolSK).


E-mail address: [email protected] 48

OPTICAL REVIEW Vol. 21, No. 1 (2014)

Md. N.-A.-S. BHUIYAN et al.

employing OPC to PolSK signal, it is also very important to investigate the transmission characteristics of the PolSK signal against different dispersion. So far very few research works have been done on OPC using PolSK signal.21) In this paper, we experimentally demonstrated, the transmission characteristics of the PolSK signal.22) Transmission performance is carried out at different dispersion values. It is found that there exists a large difference in transmission performance for the two orthogonal SOPs of PolSK signal. To improve the transmission performance that means to optimize the performance of both of the orthogonal SOPs of PolSK signal to be similar, investigation is also carried out for mid-link OPC. Using the proposed OPC technique in transmission of PolSK signal, the performances of both of the orthogonal SOPs are found similar. 2.

Preservation of Input SOP of PolSK Signal in Optical Phase Conjugator

FWM is one of the process to realize OPC techniques.3) The condition for a wavelength converter to become an OPC unit is to preserve the input signal information at wavelength converted signal in FWM spectrum which is phase conjugated. Signal amplitude and phase is preserved at the wavelength converted signal in FWM spectrum which is phase conjugated. However, the preservation of signal SOP in FWM process is different from signal amplitude and phase. In PolSK signal, as the information is encoded in the SOP, it is important that the change of SOP of the converted signal should follow that of the input PolSK signal. It is well known that the polarization state of the input optical signals involving in a FWM process determines the SOP of the converted signal. Figure 1 shows the simple FWM between PolSK signal and pump. From Fig. 1 following equations are satisfied:23) F1 ¼ ðFp  F
s ÞFp rð!p  !s Þe jð2!p !s Þt F2 ¼ ðFs 

F
p ÞFs rð!p

 !s Þe

jð2!s !p Þt

ð1Þ ð2Þ

where Fp , Fs , F1 and F2 are vectors representing the fields of the pump, the input signal and the two converted spectral components, Conv.1 and Conv.2, respectively. rð!p  !s Þ is the relative conversion efficiency coefficient. It can be written from these equations that the non-linear coupling between the wave Fp and Fs produces population pulsation at beat frequency (!p  !s ) which in turn produces temporal gain and index gratings. As a result of scattering the wave Fp , by the gratings, the converted wave F1 is created from Eq. (1). Thus, the polarization state of the converted wave F1 is parallel to that of the input wave Fp . Similarly, from Eq. (2) the polarization state of F2 is parallel to that of the input wave Fs .23–26) From the above discussion, it is clear that, the converted signal F2 holds the SOP of the input PolSK signal. On the other hand, the converted signal F1 follows the SOP of the pump signal, which has a fixed SOP. Thus, the converted signal F1 which is phase conjugated and linear converted spectral component with respect to the input signal, is unable to preserve the SOP of the input PolSK signal. In other

Input PolSK signal (

ωs )

FWM in non-linear media

CW Pump ( ω p )

Output with Converted PolSK signals

Data signal

Pump

(Fp )

(Fs )

Conv.1

(F1 ) 2ωp − ωs

49

Conv.2

(F2 ) ωp

ωs

2ωs− ωp

Fig. 1. Schematic diagram of the wavelength conversion for the PolSK signal using simple FWM. Inset: output FWM Spectra for PolSK signal. Conv.1: 1st converted signal and Conv.2: 2nd converted signal.

words, simple FWM effect is not signal SOP transparent for PolSK signal. In the previous study, preservation of input signal SOP was possible only with one of the converted FWM spectral components, namely, the non-linear converted spectral component with respect to the input signal.18) Hence, an improved wavelength converter is required where the linear converted spectral component in FWM spectrum which is phase conjugated with respect to the input signal can hold the input signal SOP. In our previous wavelength converter using polarization diversity scheme for PolSK signal, we achieved the preservation of the SOP of input PolSK signal on both of the converted spectral components of the FWM spectrum.20) This wavelength converter also works as OPC unit as the input signal SOP is preserved in phase conjugated spectral component of the FWM spectrum. The wavelength converter consists of a polarization beam splitter (PBS) and Sagnac loop with highly nonlinear fiber (HNLF) as shown in the lower inset of Fig. 2. PolSK signal consists of two orthogonal SOP components and they are used as information bearing parameter. In each SOP, we have an usual non return to zero (NRZ) intensity modulated signal (the two sequence being inverted). The PBS splits both pump and signal on both the directions of the loop. Each orthogonal polarization component of the PolSK signal is splitted by the PBS and undergoes separate FWM process in the HNLF. During processing inside the HNLF, when one SOP component is present, the orthogonal SOP component is absent and vice versa. As the SOP of pump and signal remain parallel to each other in a particular direction inside the loop, the SOP of both of the converted signals is assumed to follow the same SOP. In this way, both of the converted spectral components preserve the input signal information. Thus, this scheme is called signal SOP transparent scheme for PolSK signal. In addition, this scheme is also called diversity scheme as the converted signal power is independent of change of SOP of the total constellation of the input PolSK signal. This is an additional advantage of this scheme. Detail analysis is also given in our previous paper.20)

50

OPTICAL REVIEW Vol. 21, No. 1 (2014)

Md. N.-A.-S. BHUIYAN et al.

(Transmitting end) 10 Gb/s NRZ Data Stream

SSMF 1 (25 km)

PPG

1555 nm ECL

(Receiving end)

SSMF 2 (25 km) EDFA

Phase Modulator

BPF

PC3

Oscilloscope

POL

OPC

PD

(L1, D1)

(L2, D2) BER Tester

Polarization Rotator

Optical Phase Conjugator (OPC)

Data signal

Pump

PolSK signal at 1555 nm

1549

nm

PC2 Conv.2

Conv.1

1552

nm

1555 1558

nm

nm

B

PBS HNLF

Coupler

ECL CW Pump 1552 nm

EDFA : PC : PBS : BPF : PD :

EDFA

Isolator

ECL : PPG : POL : HNLF :

500 m

D BPF

PC1

Er-Doped Fiber Amplifier Polarization Controller Polarization Beam Splitter Band Pass Filter Photo Diode

C

A

EDFA

BPF

Converted PolSK signal at 1549 nm

External-Cavity Laser Pulse Pattern Generator Polarizer Highly Non-Linear Fiber

Fig. 2. Experimental setup for using the SOP transparent scheme for PolSK signal as optical phase conjugator to improve the transmission performance. Inset: output optical spectrum from port D of PBS. Converted signal, Conv.1 at 1549 nm is the desired phase conjugated PolSK signal.

3.

Chirping Characteristics of the Employed Modulator

Modulator used in the current experiment is based on a birefringent LiNbO3 phase modulator whose waveguide is illuminated at 45 to its main axes. The input SOP is thus split up into two orthogonal TE and TM polarization states. When an RF modulation signal is applied, an optical path difference between the TE and TM components is produced resulting in a new SOP for the output light. In this way binary PolSK signal is produced which has two orthogonal SOP components. In the modulator, for the application of electrical signal, we had an ideal phase difference of  between the two orthogonal polarization modes, which produces a binary chirped PolSK. However, the two orthogonal SOPs of PolSK signal have opposite chirping characteristic.27) This makes this format slightly different from the ideal PolSK, which would be unchirped. Therefore, while transmitting through fiber, these two orthogonal SOPs are affected by chromatic dispersion of different extent (a quite similar behavior as what is well known for IM-NRZ signals).27,28) While one SOP component is more resilient to chromatic dispersion, the other is by far more affected than the usual unchirped NRZ (or the corresponding ideal PolSK). So far one research work has been reported based on the result of simple simulation that modeled the effect of chromatic dispersion over a binary PolSK signal.16) In our current research work, we considered single ended receiver where, only one of the two orthogonal SOPs of the PolSK signals is detected using a polarizer. For PolSK signal transmitting through standard single mode fiber (SSMF), single ended receiver can be used to detect the

SOP component which has higher tolerance to chromatic dispersion. However, it is desirable for the balance detection to have the similar performance for both of the orthogonal SOPs of the PolSK signal after fiber transmission. From the above discussion it can be realized that while transmitting through the fiber, the performance of both the SOPs of PolSK signal are very different as they have opposite chirping characteristics. Hence, a practical technique is required where the similar performance of both of the SOPs can be achieved after fiber transmission. Optical phase conjugation can serve the purpose. Even though the two SOPs of the PolSK signal have opposite chirping characteristics, the performance of both of the SOPs are optimized to be similar due to the spectral inversion in OPC.22) 4.

Experimental Setup

The experimental setup is shown in Fig. 2. A LiNbO3 phase modulator (Photline Technologies PS-LN polarization rotators) as polarization rotator is used for encoding a continuous wave light at wavelength of 1555 nm with 10 Gbps (pseudorandom bit sequence of 231  1 ) NRZ data stream. Modulated PolSK signal at the wavelength of 1555 nm is first directly sent to SSMF of 50 km long to observe the performance of both SOPs of PolSK signal. To observe the performance of PolSK signal using OPC, the modulated signal is sent to SSMF of 25 km. Dispersion value for the SSMF in the experiment is 17 ps/km/nm. A mid-link optical phase conjugator which is our proposed SOP transparent scheme for PolSK is used to convert the transmitted input signal to a phase-conjugated signal at a wavelength of 1549 nm. The enlarge portion of Fig. 2 is the optical phase conjugator section. In OPC section, another laser source provides pump light at the wavelength of 1552 nm. The input PolSK signal and pump power are 3 and 5 dBm, respectively. The combined signal is launched into an erbium doped fiber amplifier (EDFA) and the output power is set to produce a total injected power of 22 dBm. A segment of HNLF of 500 mlong with the nonlinear coefficient of 12.6 (Wkm)1 and zero dispersion wavelength of 1552 nm is placed in the loop. The dispersion slope of the HNLF at the wavelength of 1552 nm is 0.032 ps/nm2 /km. The amplified signal enters the PBS through an isolator. Using the polarization controller (PC1), the pump light is polarized at 45 with respect to the PBS axis to split the pump power equally in both directions. The combined signal of input and pump enters the PBS and travels both of the directions inside the loop before entering in the HNLF. Therefore, the signal undergoes separate FWM effect in the HNLF. Using PC2, the SOP of the output signal is controlled to come out from port D of the PBS. The converted spectral component at 1549 nm which is phase conjugated is selected using a BPF having 3-dB bandwidth of 0.6 nm. The selected signal is amplified and sent through another SSMF of 25 km of similar dispersion value. The signal came out from the fiber is amplified to estimate the quality of the signal. PC3 is used to make a

OPTICAL REVIEW Vol. 21, No. 1 (2014)

5.

Results and Discussions

Figure 3 shows the investigated characteristics of the employed modulator to show its response to different dispersion values without using mid-link optical phase conjugator. To investigate this characteristic, a tunable dispersion compensating module (TDCM) is used. The TDCM has the range from +500 to 500 ps/nm. To carry out the investigation up to higher dispersion (positive) values, SSMF is added after TDCM. As the orthogonal SOPs of the PolSK signal have different chirping characteristics, they also show different performance against dispersion. One of the orthogonal SOPs has better performance at positive dispersion. This performance improvement is due to the interplay of chirp and dispersion.16) Negative power penalty is observed for this SOP component up to dispersion of 400 ps/nm. For dispersion of 200 ps/nm, the power penalty of 0:27 dB is observed. This orthogonal SOP component is called the negatively chirped, as better performance is observed against positive dispersion. Power penalties for this negatively chirped component is 0.4 and 2.6 dB for dispersion of 850 and 1095 ps/nm, respectively. For higher dispersion values the power penalty is very high and difficult to observe. It can be realized that for positive dispersion of limited range, negatively chirped SOP component showed performance improvement. However, for higher dispersion values, performance degradation occurred. On the other hand, another orthogonal SOP component showed drastic performance degradation at positive dispersion and it is called the positively chirped component. Power penalties for this positively chirped component is 0.6 and 1.8 dB for dispersion of 100 and 200 ps/nm, respectively. With higher values of positive dispersion, for this component, the power penalty is very high to be observed. For negative dispersion, both of the orthogonal SOPs showed just the opposite characteristics. The eye pattern for both of the orthogonal SOPs are shown for different values of positive dispersion in Fig. 4. It can be seen from the eye pattern that the signal is distorted by chromatic dispersion during transmission. It is also seen from the eye pattern that the two orthogonal SOPs experienced opposite chirping characteristics. It is observed that at the positive dispersion value of 200 ps/nm, the eye of the negatively chirped component is comparatively more open than the positively chirped component. However, at the higher positive dispersion of 1095 ps/nm, the performance for both of the orthogonal SOPs degraded rapidly. For fiber transmission of PolSK signal, detecting the negatively chirped SOP component is suitable option for single ended receiver scheme using a polarizer. However, to achieve the advantage from the PolSK signal regarding receiver sensitivity, balanced detection is very much required. For balanced detection of PolSK signal, the

51

3

Negatively chirped SOP 2.5

Power Penalty (dB)

linear-polarized signal at the input of the rotatable polarizer (POL). The converted PolSK signal is demodulated to conventional on-off keying (OOK) signal using the POL. By carefully rotating the POL, both of the orthogonal SOPs of the converted signal are detected.

Md. N.-A.-S. BHUIYAN et al.

Positively chirped SOP

2 1.5 1 0.5 0 -0.5 -600 -400 -200

0

200

400

600

800

1000 1200

Dispersion (ps/nm)

Fig. 3. Power penalty for positively and negatively chirped SOP component of PolSK signal against dispersion.

One SOP (negatively chirped)

Orthogonal SOP (positively chirped)

(a)

(b)

(c)

Fig. 4. Eye patterns for both of the orthogonal SOPs of PolSK signal for different values of positive dispersion of 0 ps/nm (a), 200 ps/nm (b), 1095 ps/nm (c). Eye patterns are for 20 ps/div.

performances of both of the orthogonal SOPs are required to be similar. OPC is one of the techniques where similar performance for both of the orthogonal SOPs of the PolSK signal is achieved after transmission of signal through fiber. The BER characteristics for both of the orthogonal SOPs are shown in Fig. 5 with their corresponding back to back when the PolSK signal is transmitted through the SSMF of length 50 km without using mid-link optical phase conjugator. The negatively chirped SOP is more tolerant to chromatic dispersion and shows better performance at positive dispersion. The power penalty for this negatively chirped SOP at BER of 109 is found to be 0.4 dB. However, the positively chirped SOP is by far more affected by the chromatic dispersion. It is difficult to measure the power penalty for this positively chirped SOP as there exists very

52

OPTICAL REVIEW Vol. 21, No. 1 (2014)

Md. N.-A.-S. BHUIYAN et al.

3

3 Back to Back (One SOP)

Back to Back (One SOP)

Converted without transmission

Back to Back (Orthogonal SOP)

Back to Back (Orthogonal SOP)

Converted without transmission

(Negatively chirped SOP ) (Positively chirped SOP )

50 km without OPC

4

50 km with OPC

4

(Negatively chirped SOP )

50 km without OPC

(Negatively chirped SOP )

50 km with OPC

5 6

(Negatively chirped SOP ) (20 ps/div)

7

(Positively chirped SOP )

-log(BER)

-log(BER)

(Positively chirped SOP )

5 6

(Negatively chirped SOP) (20 ps/div)

7

8

8

(Positively chirped SOP ) (20 ps/div)

(Positively chirped SOP )

9 10 11 4

5

6

7

8

9

9 10 11

10 11 12 13 14

(20 ps/div)

4

5

6

Received Power (dBm) Fig. 5. BER characteristics for 10 Gbps PolSK signal through 50 km transmission without OPC.

large error floor in its BER characteristic. The eye pattern for both of the SOPs after 50 km transmission is shown in the inset of Fig. 5. The power penalties at the converted wavelength of 1549 nm without using any fiber transmission are 1.65 and 1.73 dB at the BER of 109 , respectively for both of the orthogonal SOPs of the PolSK signal and is shown in Fig. 6. Figure 6 also summarized, the BER characteristics for both of the orthogonal SOPs of PolSK signal when OPC is used at the middle of the transmission link of 50 km. With mid-link OPC for 50 km transmission, the power penalties at the BER of 109 are found to be 2.45 and 2.69 dB, respectively for both of the orthogonal SOPs of the PolSK signal. In the inset of Fig. 6, the eye patterns for 50 km transmission with OPC are shown at the converted wavelength of 1549 nm. It is seen from the BER results and eye patterns that the signal quality for both the SOPs are very similar and significantly improved by the effect of spectral inversion in OPC. However, without OPC, the signal qualities for the SOPs are very different which is explained in Fig. 5. In the results of Fig. 6, even though the two SOPs of the PolSK signal have opposite chirping characteristics, the qualities for both of the SOPs are similar by the spectral inversion after transmission. Chirping introduced in the first part of the transmission link is mitigated by the transmission of the signal through the second link using the function of optical phase conjugation. Received power in the horizontal axes of Figs. 5 and 6 signifies that it is the optical power before the photodiode in Fig. 2, which is varied using a tunable optical attenuator for BER measurement. In the horizontal axes of Figs. 5 and 6, it is seen that to reach the BER of 109 level for back to back and converted signal, the received power is very high. It is due to the high power level of EDFA used before

7

8

9

10 11 12 13 14

Received Power (dBm) Fig. 6. BER characteristics for 10 Gbps PolSK signal through 50 km transmission with OPC. Eye patterns are for 50 km transmission with OPC for both of the orthogonal SOP of PolSK signal.

photodiode. For high power level of EDFA, the amplified spontaneous emission (ASE) can be a degrading factor. However, in this case, it is not high enough to hinder the performance. For, both of the back to back and wavelength converted signals, the BER is measured in the same scale of high received power level. The important issue is the difference in performance between back to back and wavelength converted signal. The additional advantage of the proposed optical phase conjugator is polarizationinsensitivity.20) Hence, it has better performance in case of practical situation when the SOP of the input PolSK signal is rotated. 6.

Conclusions

We demonstrated experimentally, the investigation of transmission performance of PoSK signal using optical phase conjugation. The wavelength converter based on our proposed signal SOP transparent scheme can preserve the input signal SOP at the wavelength converted spectral component which is phase conjugated. Hence, it can be used as an optical phase conjugator for PolSK signal which is not possible otherwise in conventional wavelength converter. Moreover, the optical phase conjugator based on our proposed signal SOP transparent scheme is also polarization-insensitive. It can be realized from the results that for fiber transmission, the performance of both of the orthogonal SOPs of the PolSK signal is different for their respective chirping characteristics which can be optimized to be similar using proposed OPC technique. Our proposed optical phase conjugation scheme can be employed to increase the signal robustness in PolSK long-haul transmission system for future photonic network.

OPTICAL REVIEW Vol. 21, No. 1 (2014) References 1) G. P. Agrawal: Nonlinear Fiber Opfics (Academic, New York, 1989). 2) A. F. Elrefaie, R. E. Wagner, D. A. Atlas, and D. G. Daut: Electron. Lett. 23 (1987) 756. 3) A. Yariv, D. Fekete, and D. M. Pepper: Opt. Lett. 4 (1979) 52. 4) S. L. Jansen, S. Spalter, G.-D. Khoe, H. de Waardt, H. E. Escobar, L. Marshall, and M. Sher: IEEE Photonics Technol. Lett. 16 (2004) 1763. 5) S. L. Jansen, S. Spalter, G.-D. Khoe, H. de Waardt, D. Zhou, Q. Shu, and L. Marshall: Proc. ECOC, 2004, paper Th 2.5.6. 6) G. Mohs, L. Didier Coelho, E. Gottwald, and C. Scheerer: Proc. OECC/IOOC, 2001, p. 262. 7) G. Lehmann and E. Meissnere: Proc. Asian Pacific Optical and Wireless Communication Conf. 4906 (2002) 253. 8) S. Watanabe, T. Naito, and T. Chikama: IEEE Photonics Technol. Lett. 5 (1993) 92. 9) S. Watanabe and M. Shirasaki: J. Lightwave Technol. 14 (1996) 243. 10) I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski: Proc. OFC, 2000, paper PD33. 11) A. Chowdhury, G. Raybon, R.-J. Essiambre, and C. R. Doerr: Proc. ECOC, 2004, paper Th 4.5.6. 12) J. Yamawaku, H. Takara, T. Ohara, K. Sato, A. Takada, T. Morioka, O. Tadanaga, H. Miyazawa, and M. Asobe: Electron. Lett. 39 (2003) 1144. 13) S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P. M. Krummrich, G. D. Khoe, and H. de Waardt: IEEE

Md. N.-A.-S. BHUIYAN et al.

53

Photonics Technol. Lett. 17 (2005) 923. 14) T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara: J. Lightwave Technol. 21 (2003) 1933. 15) S. Benedetto, R. Gaudino, and P. Poggiolini: IEEE Trans. Commun. 45 (1997) 1269. 16) E. Ciaramella, A. D’Errico, R. Proietti, and G. Contestabile: J. Lightwave Technol. 24 (2006) 4039. 17) S. Benedetto, R. Gaudino, and P. Poggiolini: IEEE Trans. Commun. 43 (1995) 1603. 18) L. Han, H. Wen, H. Zhang, and Y. Guo: Opt. Eng. 46 (2007) 090501. 19) Md. Bhuiyan, M. Matsuura, H. N. Tan, and N. Kishi: Proc. OECC, 2009, paper FE2. 20) Md. Bhuiyan, M. Matsuura, H. N. Tan, and N. Kishi: Opt. Express 18 (2010) 2467. 21) A. L. Y. Low, Y. K. Chan, S. F. Chien, A. H. You, and T. S. Guan: IEICE Electron. Express 1 (2004) 386. 22) Md. Bhuiyan, M. Matsuura, H. N. Tan, and N. Kishi: Proc. OECC, 2011, paper 7C4-2 450. 23) J. M. Tang and K. A. Shore: IEEE Photonics Technol. Lett. 11 (1999) 1123. 24) G. P. Agrawal: J. Opt. Soc. Am. B 5 (1988) 147. 25) K. Inoue: IEEE J. Quantum Electron. 28 (1992) 883. 26) J. P. R. Lacey, M. A. Summerfield, and S. J. Madden: J. Lightwave Technol. 16 (1998) 2419. 27) A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford, and D. T. Moser: IEEE Photonics Technol. Lett. 3 (1991) 916. 28) A. H. Gnauck, R. W. Tkach, and M. Mazurczyk: Proc. ECOC, 1999, paper TuC. 4.4.