## Regenerative properties of interferometric all-optical DPSK wavelength converters

Optics Express, Vol. 17, Issue 25, pp. 22639-22658 (2009)

http://dx.doi.org/10.1364/OE.17.022639

Acrobat PDF (1073 KB)

### Abstract

We discuss an all-optical DPSK wavelength conversion scheme comprising a delay-interferometer demodulation stage followed by a Mach-Zehnder interferometer, the arms of which are formed by nonlinear waveguides. If operated properly, the configuration shows regenerative behaviour. This is true for nonlinear waveguides with a dominant cross-gain nonlinearity (e. g., for an electro-absorption amplitude modulator) as well as for the case of a dominant cross-phase nonlinearity (e. g., for Kerr effect based phase modulator). In addition, we show that nonlinear materials exhibiting cross-gain modulation properties can provide a binary phase response so far only known from the transfer functions of digital electronics.

© 2009 OSA

## 1 Introduction

1. A. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64×42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans”, in Technical Digest of OFC 2002, (Anaheim, USA, 2002), FC2.1–FC2.3.

2. V. S. Grigoryan, M. Shin, P. Devgan, J. Lasri, and P. Kumar, “SOA-based regenerative amplification of phase-noise-degraded DPSK signals: dynamic analysis and demonstration,” J. Lightwave Technol. **24**(1), 135–142 (
2006). [CrossRef]

3. I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jaques, and C. R. Giles, “Regenerative all-optical wavelength conversion of 40 Gb/s DPSK signals using a SOA MZI”, in Proc. 31st European. Conf. Optical Communications (ECOC, Glasgow, UK, 2005), Th. 4.3.3.

4. P. Vorreau, A. Marculescu, J. Wang, G. Boettger, B. Sartorius, C. Bornholdt, J. Slovak, M. Schlak, Ch. Schmidt, S. Tsadka, W. Freude, and J. Leuthold, “Cascadability and regenerative properties of SOA all-optical DPSK wavelength converters,” IEEE Photon. Technol. Lett. **18**(18), 1970–1972 (
2006). [CrossRef]

5. P. Johannisson, G. Adolfsson, and M. Karlsson, “Suppression of phase error in differential phase-shift keying data by amplitude regeneration,” Opt. Lett. **31**(10), 1385–1387 (
2006). [CrossRef] [PubMed]

6. C. C. Wei and J. J. Chen, “Convergence of phase noise in DPSK transmission systems by novel phase noise averagers,” Opt. Express **14**(21), 9584–9593 (
2006). [CrossRef] [PubMed]

7. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “'All-optical high-speed signal processing with silicon–organic hybrid slot waveguides*'*,” Nat. Photonics **3**(4), 216–219 (
2009). [CrossRef]

8. M. Matsumoto, “Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators,” IEEE Photon. Technol. Lett. **17**(5), 1055–1057 (
2005). [CrossRef]

11. K. Croussore and G. Li, “Phase and amplitude regeneration of differential phase-shift keyed signals using phase-sensitive amplification,” IEEE J. Sel. Top. Quantum Electron. **14**(3), 648–658 (
2008). [CrossRef]

8. M. Matsumoto, “Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators,” IEEE Photon. Technol. Lett. **17**(5), 1055–1057 (
2005). [CrossRef]

9. K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. **43**(3), 177–178 (
2007). [CrossRef]

11. K. Croussore and G. Li, “Phase and amplitude regeneration of differential phase-shift keyed signals using phase-sensitive amplification,” IEEE J. Sel. Top. Quantum Electron. **14**(3), 648–658 (
2008). [CrossRef]

12. K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. **21**(2), 70–72 (
2009). [CrossRef]

13. M. Suzuki, H. Tanaka, and Y. Matsushima, “InGaAsP electroabsorption modulator for high-bit-rate EDFA system,” IEEE Photon. Technol. Lett. **4**(6), 586–588 (
1992). [CrossRef]

*α*-factor (Henry’s

_{H}*α*-factor [14

_{H}14. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. **18**(2), 259–264 (
1982). [CrossRef]

*α*-factor is indicative for a small refractive index change and thus for a small XPM effect with respect to a given change of the charge carrier concentration. Wavelength converter based on saturated EAM has been demonstrated with regenerative properties in [15

_{H}15. T. Otani, T. Miyazaki, and S. Yamamoto, “40-Gb/s optical 3R regenerator using electroabsorption modulators for optical networks,” J. Lightwave Technol. **20**(2), 195–200 (
2002). [CrossRef]

16. A. Bilenca, R. Alizon, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, D. Gold, J. P. Reithmaier, and A. Forchel, “Broad-band wavelength conversion based on cross-gain modulation and four-wave mixing in InAs-InP quantum dash semiconductor optical amplifiers operating at 1550 nm,” IEEE Photon. Technol. Lett. **15**(4), 563–565 (
2003). [CrossRef]

*α*-factor [19

_{H}19. S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Linewidth enhancement factor in InGaAs quantum-dot amplifiers,” IEEE J. Quantum Electron. **40**(10), 1423–1429 (
2004). [CrossRef]

*α*-factor in QD-SOA is close to zero when the bias is set just above [19

_{H}19. S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Linewidth enhancement factor in InGaAs quantum-dot amplifiers,” IEEE J. Quantum Electron. **40**(10), 1423–1429 (
2004). [CrossRef]

20. H. C. Wong, G. B. Ren, and J. M. Rorison, “Mode amplification in inhomogeneous QD semiconductor optical amplifiers,” Opt. Quantum Electron. **38**(4-6), 395–409 (
2006). [CrossRef]

22. R. Bonk, P. Vorreau, S. Sygletos, T. Vallaitis, J. Wang, W. Freude, J. Leuthold, and R. Brenot, G. H. Duan C. Meuer, S. Liebig, M. Laemmlin, D. Bimberg, “Performing cross-gain modulation with improved signal quality in an interferometric configuration”, in Proc. of OFC 2008 (San Diego, USA, 2008), JWA70.

*α*-factor is discussed. The regenerative potential for the various materials is analyzed in Section 5. In greater detail we report on the regenerative effect on both phase and amplitude for an output signal behind a regenerative DPSK wavelength converter. The following observations will be discussed:

_{H}- • For an ideal DPSK-WC exploiting XPM nonlinearities only, input phase noise may be completely suppressed, while input amplitude noise is reduced due to the sinusoidal amplitude transmission behavior in MZI configurations. This is true as long as the amplitude fluctuations are not too large. For large amplitude fluctuations the phase noise can no longer be completely suppressed.
- • For an ideal DPSK-WC exploiting XGM nonlinearities only, perfect phase regeneration is achieved for any phase and amplitude noise of the input signal, because there are no XPM effects. If the XGM nonlinear elements are operated in a strong saturation regime, also the output amplitude noise can be reduced. Due to the inherently ideal phase regeneration after going through one DPSK-WC stage, amplitude regeneration can be even further improved by cascading another DPSK-WC stage employing XGM nonlinearities.

## 2 Configuration and operation principle

### 2.1. Configuration of the interferometric DPSK wavelength converter

*λ*

_{cnv}to which the DPSK signal at

*λ*

_{in}will be converted.

3. I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jaques, and C. R. Giles, “Regenerative all-optical wavelength conversion of 40 Gb/s DPSK signals using a SOA MZI”, in Proc. 31st European. Conf. Optical Communications (ECOC, Glasgow, UK, 2005), Th. 4.3.3.

4. P. Vorreau, A. Marculescu, J. Wang, G. Boettger, B. Sartorius, C. Bornholdt, J. Slovak, M. Schlak, Ch. Schmidt, S. Tsadka, W. Freude, and J. Leuthold, “Cascadability and regenerative properties of SOA all-optical DPSK wavelength converters,” IEEE Photon. Technol. Lett. **18**(18), 1970–1972 (
2006). [CrossRef]

### 2.2. Classification of nonlinear elements

*n*and

_{r}*n*, respectively. We first assume that, for a sufficiently narrow spectral range of interest around the carrier wavelength

_{i}*λ*

_{cnv}(frequency

*f*

_{cnv}), the complex refractive index at a position

*z*within a NLE is constant and represented byFor our choice of harmonic time dependence exp(j 2π

*f t*) and for propagation into positive

*z*-direction, gain is described by

*n*< 0.

_{i}*T*

_{NLE}relating the output and input signals of the NLE between the points

*z*=

*L*and

*z*= 0, respectively. As the signal propagates and its power varies along the propagation direction

*z*, the power dependence of the refractive index

*T*

_{NLE}| and phase

*φ*becomeswhere

*k*

_{0}= 2π

*f*

_{cnv}/

*c*

_{0}is the wave number and

*c*

_{0}is the vacuum speed of light. The variable

*t*is the time in a retarded time frame. A power gain requires |

*T*

_{NLE}|

^{2}>1.

*h*(

*t*), termed as the logarithmic power transmission,

*α*factor. A NLE with a large

_{H}-*α*

_{H}mostly produces a phase modulation; in our case we are interested in XPM. In the extreme case where

*α*→ ∞, the device can be understood as an ideal phase modulator. A NLE with a small or close to zero

_{H}*α*mostly causes a gain modulation, and here our interest is in XGM. If

_{H}*α*0, the NLE acts as an ideal gain modulator. Devices with dominant XGM effect are, e. g., QD-SOA or EAMs. A medium with a NLE characterized by 0 <

_{H}=*α*

_{H}< ∞ (e. g., a bulk SOA) will experience both XGM and XPM.

### 2.3. Operation principle of interferometric DPSK wavelength converter with various NLE

*E*

_{in}at

*λ*

_{in}is transformed by the DI stage into an on-off keying (OOK) and an inverted OOK data stream. These on-off signals change the refractive index and the gain of the NLE in the two MZI arms. The two NLE in the MZI arms are assumed to have same gain and

*α*

_{H}-factors. The amplitude transmission functions of the MZI arms are then approximated by Eq. (10).

*E*

_{cnv}at a wavelength

*λ*

_{cnv}is launched in the MZI and distributed to the two arms of the MZI. The two signals in the respective arms are denoted by

*E*

_{cnv,up}and j

*E*

_{cnv,low}. Note that a phase factor j will be added to the signal that couples into the cross output of the coupler. The relative phase and amplitude between

*E*

_{cnv,up}and j

*E*

_{cnv,low}is then controlled by the mark and space bits of the OOK and the inverse OOK via the NLE, similar to the push-pull operation of electrically controlled MZI modulators used in DPSK transmitters [1

1. A. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64×42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans”, in Technical Digest of OFC 2002, (Anaheim, USA, 2002), FC2.1–FC2.3.

*E*

_{cnv,up}and j

*E*

_{cnv,low}signals are recombined at the destructive (difference) output port Δ of the MZI. A filter centred at

*λ*

_{cnv}selects the wavelength-converted signal

*E*

_{Δ}at

*λ*

_{cnv}.

*α*

_{H}-factor at end of Section 2.2. Figures 1(a) and 1(b) show schematically how the two amplitudes

*E*

_{cnv,up}and

*E*

_{cnv,low}in the MZI upper and lower arm evolve with an OOK input signal launched to the respective MZI arms for the two cases with

*α*

_{H}= 0 and

*α*

_{H}>> 0.

*α*

_{H}= 0 we first assume that a logical “1” corresponding to a DPSK state “−1” induces a very strong gain suppression without any nonlinearly induced phase shift in the upper arm at

*λ*

_{in}And there is no gain suppression in the lower arm. The filtered difference output signal at

*λ*

_{cnv}is then

*E*

_{Δ}=

*E*

_{cnv,up}–

*E*

_{cnv,low}< 0. If the gain is reduced in the lower arm by an inverted logical “0”, corresponding to a DPSK state “1”, we have the corresponding relation

*E*

_{Δ}=

*E*

_{cnv,up}–

*E*

_{cnv,low}> 0. Thus, each logical “0” results in a signal with an intensity |

*E*

_{Δ}|

^{2}and an optical phase 0, while each logical “1” generates a signal with the same intensity |

*E*

_{Δ}|

^{2}and an optical phase π. This is illustrated in Fig. 1(b) for a signal inducing an intermediate gain reduction. This situation would hold true for, e. g., a QD-SOA or for an EAM.

*α*

_{H}< ∞ (e. g., for a bulk SOA), both XPM and XGM are effective. The amplitude of the converted signal in the respective arm is both suppressed due to XGM, but also its phase is flipped due to XPM − if the input OOK signal is sufficiently strong to induce a

*π*phase shift. This situation is illustrated in Fig. 1(a). The newly generated signal at the output is actually a PSK signal, where

*E*

_{Δ}> 0 is for a PSK state “1” and

*E*

_{Δ}< 0 is for a PSK state “−1”.

*α*-factor of the NLE, be it

_{H}*α*= 0 or 0 <

_{H}*α*< ∞. While the outcome is same, the physics behind the two NLE media is quite different and thus needs a more detailed discussion. For recovering the original signal from the PSK signal, an electrical encoder needs to be added [4

_{H}4. P. Vorreau, A. Marculescu, J. Wang, G. Boettger, B. Sartorius, C. Bornholdt, J. Slovak, M. Schlak, Ch. Schmidt, S. Tsadka, W. Freude, and J. Leuthold, “Cascadability and regenerative properties of SOA all-optical DPSK wavelength converters,” IEEE Photon. Technol. Lett. **18**(18), 1970–1972 (
2006). [CrossRef]

## 3 Modeling

3. I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jaques, and C. R. Giles, “Regenerative all-optical wavelength conversion of 40 Gb/s DPSK signals using a SOA MZI”, in Proc. 31st European. Conf. Optical Communications (ECOC, Glasgow, UK, 2005), Th. 4.3.3.

**18**(18), 1970–1972 (
2006). [CrossRef]

16. A. Bilenca, R. Alizon, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, D. Gold, J. P. Reithmaier, and A. Forchel, “Broad-band wavelength conversion based on cross-gain modulation and four-wave mixing in InAs-InP quantum dash semiconductor optical amplifiers operating at 1550 nm,” IEEE Photon. Technol. Lett. **15**(4), 563–565 (
2003). [CrossRef]

*P*

_{eq}(the equivalent saturation power) and the

*α*factor are sufficient to describe the media within first order. We will then use these two parameters to derive the DPSK wavelength converter transfer function for arbitrary NLE.

_{H}-### 3.1. Modeling of gain and phase effects in various nonlinear elements

*T*

_{NLE}for a generic NLE. For determining

*T*

_{NLE}in Eq. (10) we need finding Δ

*h*for the respective media. We therefore now discuss the logarithmic gain change for various important media.

*A*)

*Gain and phase change in an SOA.*A signal at wavelength

*λ*

_{cnv}(frequency

*f*

_{cnv}, converting signal in Fig. 1), is launched into the SOA and experiences a gain

*G*

_{cnv}along the SOA. In addition, a strong input control signal, e.g. one of the OOK signals in Fig. 1, enters the SOA and leads to a gain suppression. We assume that the powers of the converting signal

*E*

_{cnv}(power

*P*

_{cnv}) and the power of the control signals

*E*

_{up}or

*E*

_{low}, (power

*P*(

_{s}*t*)) in the NLE simply add, i.e. we assume that the respective coherence times and the frequency difference of converting signal and control signals do not create additional beating terms. Thus the logarithmic power transmission of the cw signal

*h*

_{cnv}and

*h*(

*t*) for the cases with and without control power

*P*(

_{s}*t*) can be described by [24],The quantity

*h*

_{0}is the unsaturated logarithmic power transmission and

*h*

_{0}=

*g*

_{0}

*L*is given by the unsaturated material gain

*g*

_{0}of, e. g., an SOA. For the sake of convenience,

*P*

_{sat}is defined as the input saturation power. If a cw power

*P*

_{cnv}=

*P*

_{sat}ln(2)/(

*h*

_{0}−ln(2)) is applied, the power gain

*G*

_{cnv}= exp(

*h*

_{cnv}) decreases by 3 dB with respect to

*G*

_{0}= exp(

*h*

_{0}). From Eq. (11), the logarithmic power transmission change ∆

*h*takes the form,From Eq. (9) and (12), the phase change is(

*B*)

*Modeling of loss and phase change in a Kerr medium*. In such a medium, the converting signal at

*f*

_{cnv}experiences a power loss, i. e., a (possibly very weak) absorption. This linear power loss is usually described by a linear absorption coefficient

*α*

_{0}[25]. The unsaturated logarithmic power transmission

*h*

_{0}is given as

*h*

_{0}= −

*α*

_{0}

*L*. If a sufficiently strong control signal, e.g. one of the OOK signals in Fig. 1, enters the Kerr-nonlinear element, the absorption changes with the input power due to coherent third-order nonlinear interaction. This interaction is described by a nonlinear power absorption coefficient

*α*

_{2}, also denoted as two photon absorption (TPA) coefficient [25]. The logarithmic power transmission of the converting signal,

*h*

_{cnv}and

*h*(

*t*) for the cases with and without control signal

*P*(

_{s}*t*), can be written asThe factor 2 in front of

*P*

_{s}(

*t*) stems from collecting various third-order nonlinear interaction terms, which belong to the same frequency [25].

*P*

_{eff},where

*A*

_{eff}is the effective area for third-order nonlinear interaction. Equation (14) then becomesThe logarithmic power transmission change ∆

*h*is now given byThe effective power

*P*

_{eff}in a Kerr medium is interpreted as follows. If

*P*

_{cnv}=

*P*

_{eff}ln(2), then the absorption is increased by 3 dB, i. e., the effective power “gain” is decreased by 3 dB. The effective power is very large as a rule, because the nonlinear power absorption coefficient

*α*

_{2}is usually very small.

*P*

_{s}, the nonlinear refractive index change Δ

*n*2

_{r}=*n*

_{2}

*I*is proportional to the intensity

*I*via the nonlinear index coefficient

*n*

_{2}[25]. The factor 2 again comes from the collection of third-order nonlinear interaction terms for XPM. Note that the refractive index change Δ

*n*also varies with higher order nonlinear terms [25], which have been neglected. The phase shift due to XPM is now given asSince

_{r}*α*

_{2}is usually small in Kerr media like quartz glass, the

*α*

_{H,}_{Kerr}-factor is then very large. As an example, an As-Se chalcogenide HNLF was reported to have

*α*

_{H,}_{Kerr}≈29 [26

26. V. G. Ta’eed, L. Fu, M. Pelusi, M. Rochette, I. C. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express **14**(22), 10371–10376 (
2006). [CrossRef] [PubMed]

*C*)

*Generalized saturation power andα*With respect to the gain suppression,

_{H}-factor.*P*

_{eff}is equivalent to the saturation power

*P*

_{sat}in an SOA. For convenience, we subsequently define an equivalent saturation power

*P*

_{eq}by

*α*factor for an SOA-type and Kerr-type medium as

_{H}-### 3.2. Transmission function of a DPSK wavelength converter configuration

*f*

_{in}is expressed by

*E*

_{in}(

*t*)exp(j 2π

*f*

_{in}

*t*). The quantity

*E*

_{in}(

*t*) =

*A*

^{in}(

*t*)exp[jΦ

^{in}(

*t*)] is the complex envelope, where

*A*

^{in}(

*t*) = |

*E*

_{in}(

*t*)| is the amplitude and Φ

^{in}(

*t*) represents the phase. The power of the signal is thus given by,where

*ε*

_{0}is the permittivity of free space and

*n*

_{0}is the refractive index of the medium at low power.

*A*

_{eff}in the amplifier is the mode cross-section with respect to the mode confinement in the waveguide [24].

*A*

_{eff}in the fibre is the effective area for third-order nonlinear interaction [25]. The input is a DPSK signal, whose phase difference between two consecutive bits carries the information. This phase difference is then expressed asFor a logical “0” we have ΔΦ

^{in}= 0, and ΔΦ

^{in}= ± π for a logical “1”.

*A*)

*Impulse response matrix for a delay interferometer.*Following [27

27. J. Leuthold, B. Mikkelsen, G. Raybon, C. H. Joyner, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and R. Behringer, “All-optical wavelength conversion between 10 and 100 Gb/s with SOA delayed-interference configuration,” Opt. Quantum Electron. **33**(7/10), 939–952 (
2001). [CrossRef]

*E*

_{up},

*E*

_{low}and the input field

*E*

_{in}as assigned in Fig. 1 as

*t*of the DI in Fig. 1. A multiplicative phase factor exp(j 2π

*f*

_{in}

*τ*) modifies the amplitude transmission in the “long” arm taking into account the phase shift of the optical carrier. The time delay Δ

*t*of the “long” arm is adjusted such that Δ

*t*approximates the bit period

*T*

_{b}, and

*f*

_{in}Δ

*t*is an integer number.

*t*=

*T*

_{b}lead us to the output signals behind the DI,

*E*

_{cnv}(as specified in Fig. 1) and guided to the corresponding NLE in the upper and lower arms of the MZI.

*B*)

*Amplitude transmission function of the MZI with a generic NLE*. The amplitude transmission function

*T*(

*t*) below relates the output signal

*E*

_{Δ}of the destructive output port Δ of the MZI with the input signal

*E*

_{cnv}, see Fig. 1. The transmission function of the MZI comprises the NLE defined in Eq. (10) on its arms. Depending on the NLE media another logarithmic power transmission

*h*

_{cnv}and logarithmic power transmission change ∆

*h*

_{up/low}will be needed, such as given by Eqs. (11), (12), (16) and (17). The

*α*–factor in Eq. (10) is defined by Eq. (9). This leads us to the general MZI amplitude transmission function

_{H}*T*(

*t*),In this transmission function γ is the coupler link loss.

## 4 Regenerative properties for various nonlinear elements

*α*= 0), (B) by modulators showing amplitude and phase modulation, and (C) by ideal phase modulators (

_{H}*α*→ ∞), respectively. The left column of Fig. 2, marked with (I), shows the power and phase responses with increasing input DPSK signal power. The right column of Fig. 2, marked with (II), displays the power and phase response if the relative phase difference ∆Φ between two consecutive DPSK bits at the input increases from –π to π.

_{H}*P*

_{eq}, defined in Eq. (19). For generating the plots in Fig. 2, we used a moderate non-zero equivalent saturation power in case (A) and (B), which is 20 dB below the equivalent saturation power

*P*

_{eq}used in case (C).

*P*

_{in}(horizontal axes of the subfigures in the left column of Fig. 2) to a common reference power level

*P*

_{in,ref}. This reference power level

*P*

_{in,ref}is the power required to induce a π-phase shift onto an input signal

*P*

_{cnv}= 0 dBm launched in SOAs with

*α*= 8, with

_{H}*P*

_{eq}= 10 dBm (i.e. 0 <

*P*

_{eq}< ∞) and

*G*

_{0}= 30 dB, see Fig. 2(B). The resulting output powers in Fig. 2 have also been normalized with respect to the maximum output power γ

^{2}exp(

*h*

_{cnv})/4 of

*P*

_{cnv}. All plots in Fig. 2(II) have been generated with the input powers at the respective optimum operating points, marked with short arrows pointing to filled circles (●) in Fig. 2(I).

*α*= 8 for the SOAs is based on modeling and experimental results [28

_{H}28. J. Wang, A. Maitra, C. G. Poulton, W. Freude, and J. Leuthold, “Temporal dynamics of the alpha factor in semiconductor optical amplifiers,” J. Lightwave Technol. **25**(3), 891–900 (
2007). [CrossRef]

*α*-factor has been dropped, as we assume (see beginning of Section 3) that the time constants of the respective nonlinear effects are negligible on the scale of the bit period under consideration.

_{H}*NLE with pure amplitude modulation*(

*α*= 0). With

_{H}*α*= 0 the amplitude transmission function

_{H}*T*(

*t*) in Eq. (25) simplifies toThe conversion efficiency is best for highest input powers. The phase of the converted signal is not changed when increasing the power of input DPSK signal, since

*α*is virtually zero.

_{H}*P*

_{in}≈6

*P*

_{in,ref}varies from −π to 0 and from 0 to + π. In fact, the converted signal at the output will have a phase with either 0 or π. The plot also shows the output powers if the input signals phases varies between −π and π.

17. T. Akiyama, M. Ekawa, M. Sugawara, K. Kawaguchi, H. Sudo, A. Kuramata, H. Ebe, and Y. Arakawa, “An ultrawide-band semiconductor optical amplifier having an extremely high penalty-free output power of 23 dBm achieved with quantum dots,” IEEE Photon. Technol. Lett. **17**(8), 1614–1616 (
2005). [CrossRef]

*amplitude and phase modulation*(e.g.

*α*≈8). In this case, the converting signal experiences both XGM and XPM in the NLE, and the transmission function from Eq. (25) provides the power and phase responses. This is a typical situation encountered with normal bulk SOAs. The transmission functions of Fig. 2(B,I) and (B,II) show that these wavelength converters with this type of NLE potentially could offer power and phase regeneration. The power and phase responses in Fig. 2(B,I) show oscillations with increasing signal power. These oscillations will appear if the nonlinear phase shift exceeds several π. Furthermore, one observes a damping of the transmission peaks of the converted signal. This is due to saturation effects in the nonlinear elements.

_{H}*Pure phase modulation*(

*α*→ ∞). In this case, the quantity effective power

_{H}*P*

_{eq}derived in Eq. (15) is large (

*P*

_{eq}→ ∞). NLE such as an organic material [12

12. K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. **21**(2), 70–72 (
2009). [CrossRef]

5. P. Johannisson, G. Adolfsson, and M. Karlsson, “Suppression of phase error in differential phase-shift keying data by amplitude regeneration,” Opt. Lett. **31**(10), 1385–1387 (
2006). [CrossRef] [PubMed]

6. C. C. Wei and J. J. Chen, “Convergence of phase noise in DPSK transmission systems by novel phase noise averagers,” Opt. Express **14**(21), 9584–9593 (
2006). [CrossRef] [PubMed]

*P*

_{eff}which is 20 dB above that used in case (B), and we assumed an

*α*-factor

_{H}*α*= 500.

_{H}*P*

_{in,ref}for generating Fig. 2(C,II) is at the optimum operating point. However, the phase of the converted signal linearly depends on the input power, Fig. 2(C,I). In fact, the phase response in Fig. 2(C,II) will vary considerably for different operating points.

## 5 Noise suppression properties with various nonlinear elements

### 5.1. Constellation maps

*α*-factor and effective power. Best conversion efficiencies are obtained with schemes employing high

_{H}*α*-factors, as shown in Fig. 2(C). Yet, schemes with a high

_{H}*α*-factor are also very prone to power fluctuations. In fact, the transmission function for a small

_{H}*α*-factor becomes flatter, resulting in a more favourable regenerative behaviour around the two DPSK states. Unfortunately, this regenerative behaviour most often comes at the price of higher input powers that are required to reach the optimum operation point of low-

_{H}*α*devices.

_{H}*E*

_{in,0}=

*A*

_{0}

^{in}exp(jΦ

_{0}

^{in}), where

*A*

_{0}

^{in}is the amplitude and Φ

_{0}

^{in}is the absolute phase of the optimum operating point. Note that the phase Φ

_{0}

^{in}is either 0 or π. The perturbation which adds to the phasor

*E*

_{in,0}is defined by

*δE*

_{in}=

*δA*exp(jδΦ), where

*δA*is the amplitude perturbation and δΦ is the absolute phase perturbation. Thus, the phasor of the perturbed signal

*E*

_{in}isIn generating the shaded areas in Fig. 3(a), we used equally distributed values of the relative amplitude perturbation

*δA*/

*A*

_{0}

^{in}within an interval 0% to 25%, 50% and 75%, respectively, and equally distributed phase perturbation δΦ within [−π, π].

*α*-factor of 0, 8 and 500. The amplitude of the subfigures in Fig. 3(b) is now normalized to the amplitude value of the output signal at the operating point. For the calculations in Fig. 3(b) we have used the same effective (or saturation) powers as for the corresponding calculations performed in column II of Fig. 2(A, B, C).

_{H}*α*-factor leads to better conversion efficiency, as shown in Fig. 2(C), it does not necessarily provide better performance. As seen in the subfigures of Fig. 3(b), both amplitude and phase perturbations are visually more confined near the ideal “1” and “−1” states for the device with

_{H}*α*= 8 compared to the device with

_{H}*α*→∞. The figure on the left of Fig. 3(b) shows an ideal phase regeneration for devices with

_{H}*α*= 0..

_{H}### 5.2. Mathematical description of noise suppression properties

*E*

_{in}(

*t*) is sampled in the middle of each bit slot. The

*n*-th sample is now indexed by a subscript “

*n*” asThe amplitude consists of an unperturbed term

*A*

_{0}

^{in}and a noise term

*δA*

_{n}^{in}. To characterize the amplitude noise, we use a quantity

_{n}^{in}is also a random variable, which comprises a signal phase term ΔΦ

_{n,s}^{in}= {0, ± π} according to the logical information {0, 1} and a phase noise term

*δ*Φ

_{n}^{in},The phase error

*δ*Φ

_{n}^{in}is characterized by its standard deviation σ

_{ph}

^{in}.

#### 5.2.1 Noise after delay-interferometer stage

*P*

_{up}and δ

*P*

_{low}of the OOK signals in front of the NLE in the upper and lower arms of the MZI can also be calculated. They are obtained by neglecting the quadratic terms in Eqs. (31) and (32), and by normalizing the power variation to a power level

*P*

_{s,}_{0}= (

*A*

_{0}

^{in})

^{2}of a noiseless OOK pulse before the NLE,

#### 5.2.2 Noise after MZI stage

*n*-th sample of the output signal is denoted aswhere

*A*

_{n}^{out}and Φ

_{n}^{out}are the amplitude and phase of the output signal. In the noiseless case, amplitude and phase of the output signal are denoted by

*A*

_{0}

^{out}and Φ

_{0}

^{out}. The amplitude and phase errors can be calculated through the transmission function of the MZI in Eq. (25). We write the MZI transmission function between the noiseless input and output signals as

*T*

_{0}=

*E*

_{0}

^{out}/

*E*

_{0}

^{in}, and that between the

*n-*th input and output signals as

*T*=

_{n}*E*

_{n}^{out}/

*E*

_{n}^{in}, respectively. The relative output amplitude error then becomesSubsequently, we will discuss the cases of ideal amplitude modulators (

*α*= 0) and of ideal phase modulators (

_{H}*α*→∞) in the MZI arms. These two wavelength converters based on different ideal modulators predict the performance limits of amplitude and phase noise suppression. The problem then reduces to finding the respective

_{H}*T*

_{0}and

*T*for these two types of nonlinear elements.

_{n}*P*and output noise

_{S}*P*

_{N}of one single SOA, OSNR

_{XGM}=

*P*/

_{S}*P*

_{N}. For XPM, and assuming comparable operating conditions, on the other hand, the coherent addition of (nearly) equal fields in both arms leads to a four-fold output signal power 4

*P*, while the (virtually equal) noise powers of both NLE add up to 2

_{S}*P*

_{N}. Therefore, the OSNR for XPM-dominated wavelength conversion would be better by a factor of 2, OSNR

_{XPM}= 2 OSNR

_{XGM}= 2

*P*/

_{S}*P*

_{N}. If the XGM extinction ratio is not infinite but 20 dB, as long as the time constants of the respective nonlinear effects are negligible on the scale of the bit period e.g. shown in [16

16. A. Bilenca, R. Alizon, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, D. Gold, J. P. Reithmaier, and A. Forchel, “Broad-band wavelength conversion based on cross-gain modulation and four-wave mixing in InAs-InP quantum dash semiconductor optical amplifiers operating at 1550 nm,” IEEE Photon. Technol. Lett. **15**(4), 563–565 (
2003). [CrossRef]

_{XPM}/ OSNR

_{XGM}factor would increase from 2 (3dB) to 2.4 (3.9dB).

*(*α

_{H}= 0

*)*based MZI

*α*= 0. This transmission function takes on positive or negative values only, depending on the difference between the logarithmic power transmission changes Δ

_{H}*h*

_{up}−Δ

*h*

_{low}, see Eq. (26). This actually corresponds to a perfect phase response as depicted in Fig. 2(A). That is, the output phase only takes on the values zero or π, but no other values in-between.

*T*

_{0}and

*T*respectively for

_{n}*α*= 0 and for the logical “1” state. Without any noise, we have from Eq. (12) Substituting Eq. (37) into Eq. (26) results in the MZI transmission function

_{H}*T*

_{0}for

*α*= 0,Under the influence of noise, the respective values of Δ

_{H}*h*

_{up}and Δ

*h*

_{low}will change. If noise is included, the respective perturbations of the logarithmic transmissions of the upper and lower arms are denoted as

*δh*

_{up}and

*δh*

_{low}, respectively. They can be calculated by substituting δ

*P*

_{up}and δ

*P*

_{low}from Eq. (34) in Eq. (12) and Eq. (37), respectively,

*δP*

_{low}and

*δP*

_{up}are neglected in the denominators of Eq. (39) . This assumption is generally valid since the power perturbations

*δP*

_{low}and

*δP*

_{up}are usually smaller than the power of the converting signal and the OOK control signals. Indeed, if these power perturbations are added in the denominators of Eq. (39), the respective values of the logarithmic transmission perturbations

*δh*

_{up}and

*δh*

_{low}, are smaller, which results in less amplitude/phase errors at the output. Equation (26) then provide the transmission function

*T*of the

_{n}*n-*th output signal

*E*

_{n}^{out}

*α*= 0. When the NLE in the upper arm (e. g., a QD-SOA) sees an OOK pulse, it becomes strongly saturated, while the other NLE in the lower arm is less saturated. So, the change of the logarithmic transmission Δ

_{H}*h*

_{up}in the strongly saturated NLE (

*P*

_{s,0}>>

*P*

_{cnv}) approaches –

*h*

_{cnv}according to Eq. (37), and exp(–Δ

*h*

_{up}/2) ≈exp(

*h*

_{cnv}/2) >>1. Also,

*δh*

_{low}>>

*δh*

_{up}holds. Thus, from Eq. (41), we see that the amplitude error at the output signal mainly comes from the power perturbation in the lower arm

*δh*

_{low}.

*P*

_{s,}_{0}and of the converting signal power

*P*

_{cnv}. In order to keep the noise low, Eq. (41), one needs minimizing

*δh*

_{up}and especially

*δh*

_{low.}The quantity

*δh*

_{low}is small as long as

*δP*

_{low}is small. A small

*δP*

_{low}in Eq. (34) means a small

*P*

_{s,}_{0}at a given input relative error. On the other hand, to achieve a good conversion efficiency (i. e., a large

*T*

_{0}) at the operating point, a high

*P*

_{s}_{,0}is also needed to saturate QD-SOAs. This can be also seen from Eqs. (37) and (38): A large

*P*

_{s}_{,0}leads to a small exp(Δ

*h*

_{up}/2) and thus to a large

*T*

_{0}. So the value

*P*

_{s}_{,0}needs optimization. From Eq. (39),

*δh*

_{low}is also small as long as the converting power

*P*

_{cnv}is high. However, a high

*P*

_{cnv}also suppresses the single pass gain and gives a smaller exp(

*h*

_{cnv}/2), with other QD-SOA parameters fixed. Consequently, from Eq. (38), a large

*P*

_{cnv}leads to a smaller eye opening of the converted signal. So an optimum exists for

*P*

_{cnv}, too.

*G*

_{0}= 30 dB, saturation power

*P*

_{sat}= 10 dBm, cw converting signal power (before MZI in Fig. 1) is 6 dBm, and optimized power of the input DPSK signal (before DI)

*P*

_{in}= 15 dBm.

5. P. Johannisson, G. Adolfsson, and M. Karlsson, “Suppression of phase error in differential phase-shift keying data by amplitude regeneration,” Opt. Lett. **31**(10), 1385–1387 (
2006). [CrossRef] [PubMed]

_{ph}

^{in}(in radians) before the first stage are indicated in the legends in Figs. 4(b) and 4(c).

^{2}(

*P*

_{up}and δ

*P*

_{low}in Eq. (34). As the input amplitude noise is growing and exceeds a certain value, the input amplitude noise is becoming the dominant noise source. This amplitude regeneration could be totally destroyed for high input phase noise, even if the input amplitude noise is zero, as seen on the blue and green lines for

_{ph}

^{in}before the first stage.

*(*α

_{H}

*→ ∞)*

*α*in Eq. (20) approaches infinity, and

_{H}*P*

_{eff}→ ∞ from Eq. (15), but

*α*/

_{H}*P*

_{eff}= 4

*k*

_{0}

*n*

_{2}/(

*α*

_{0}

*A*

_{eff}) is a constant. The transmission function from Eq. (27) behaves as a linear MZI.

*T*

_{0}for the logical “1” state without noise. We apply Eq. (17) for the two arms in the MZI and substitute them into Eq. (27),The power

*P*

_{s}_{,0}of the OOK pulse is assumed to be noiseless. From Fig. 2(C), the optimum operating point will be chosen so that the phase shift of the converting signal on the upper arm isand the transmission function in Eq. (27) becomesNext we are interested in the transmission function

*T*for the logical “1” state with noise. By inserting the power perturbations with respect to

_{n}*P*

_{s,0}from Eq. (34) in Eq. (17), we have the respective perturbations in the logarithmic transmissionWith Eq. (45) and ∆

*h*

_{up}= –2

*π*/

*α*, Eq. (27) becomesSubstituting Eqs. (44) and (46) in Eq. (36), we now obtain the relative output amplitude error and the output phase error.From Eq. (47), first, it is interesting to see that the output phase error comprises only the input amplitude error. The output phase error follows a similar distribution compared to the input amplitude error, see Eqs. (33) and (47). Any transfer of the input phase error to an output phase error is totally suppressed. This is because the gain fluctuations

_{H}*δh*

_{low}and

*δh*

_{up}due to an input phase error are compensated, see Eq. (45). The second observation when inspecting Eq. (47) is that the conversion from the input phase noise to output amplitude noise is also suppressed by the nonlinear cosine function. The distribution of the output amplitude error is modified by the wavelength conversion. For two consecutive bits with a larger amplitude error in-between, the output amplitude is smaller than for the noiseless case. Also, if the perfect interference condition as assumed in Eq. (43) is not satisfied, the output amplitude is smaller than that in the noiseless case. So, the output amplitude is close to but never exceeds the output amplitude in the noiseless case, as can be seen in Fig. 3(b). As a result, the distribution function of the output amplitude error changes too.

*α*= 500. Also, the effective power

_{H}*P*

_{eff}= 27.5 dBm, the input DPSK signal (before DI)

*P*

_{in}= 1.5 dBm, and the clock converting signal

*P*

_{cnv}= 0 dBm was used. The remaining parameters are identical with those from before.

_{ph}

^{in}varies for 0 and 0.25 radians. Figure 5(b) shows the standard deviation of the output phase noise σ

_{ph}

^{out}(left-axis) versus the standard deviation of the input phase noise σ

_{ph}

^{in}(bottom-axis), where the standard deviation of the input amplitude noise

## 6 Conclusion

## Acknowledgements

## References and Links

1. | A. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64×42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans”, in Technical Digest of OFC 2002, (Anaheim, USA, 2002), FC2.1–FC2.3. |

2. | V. S. Grigoryan, M. Shin, P. Devgan, J. Lasri, and P. Kumar, “SOA-based regenerative amplification of phase-noise-degraded DPSK signals: dynamic analysis and demonstration,” J. Lightwave Technol. |

3. | I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jaques, and C. R. Giles, “Regenerative all-optical wavelength conversion of 40 Gb/s DPSK signals using a SOA MZI”, in Proc. 31st European. Conf. Optical Communications (ECOC, Glasgow, UK, 2005), Th. 4.3.3. |

4. | P. Vorreau, A. Marculescu, J. Wang, G. Boettger, B. Sartorius, C. Bornholdt, J. Slovak, M. Schlak, Ch. Schmidt, S. Tsadka, W. Freude, and J. Leuthold, “Cascadability and regenerative properties of SOA all-optical DPSK wavelength converters,” IEEE Photon. Technol. Lett. |

5. | P. Johannisson, G. Adolfsson, and M. Karlsson, “Suppression of phase error in differential phase-shift keying data by amplitude regeneration,” Opt. Lett. |

6. | C. C. Wei and J. J. Chen, “Convergence of phase noise in DPSK transmission systems by novel phase noise averagers,” Opt. Express |

7. | C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “'All-optical high-speed signal processing with silicon–organic hybrid slot waveguides |

8. | M. Matsumoto, “Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators,” IEEE Photon. Technol. Lett. |

9. | K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. |

10. | M. Matsumoto and H. Sakaguchi, “DPSK signal regeneration using a fiber-based amplitude regenerator,” Opt. Express |

11. | K. Croussore and G. Li, “Phase and amplitude regeneration of differential phase-shift keyed signals using phase-sensitive amplification,” IEEE J. Sel. Top. Quantum Electron. |

12. | K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. |

13. | M. Suzuki, H. Tanaka, and Y. Matsushima, “InGaAsP electroabsorption modulator for high-bit-rate EDFA system,” IEEE Photon. Technol. Lett. |

14. | C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. |

15. | T. Otani, T. Miyazaki, and S. Yamamoto, “40-Gb/s optical 3R regenerator using electroabsorption modulators for optical networks,” J. Lightwave Technol. |

16. | A. Bilenca, R. Alizon, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, D. Gold, J. P. Reithmaier, and A. Forchel, “Broad-band wavelength conversion based on cross-gain modulation and four-wave mixing in InAs-InP quantum dash semiconductor optical amplifiers operating at 1550 nm,” IEEE Photon. Technol. Lett. |

17. | T. Akiyama, M. Ekawa, M. Sugawara, K. Kawaguchi, H. Sudo, A. Kuramata, H. Ebe, and Y. Arakawa, “An ultrawide-band semiconductor optical amplifier having an extremely high penalty-free output power of 23 dBm achieved with quantum dots,” IEEE Photon. Technol. Lett. |

18. | M. Laemmlin, G. Fiol, M. Kuntz, F. Hopfer, D. Bimberg, A. R. Kovsh, and N. N. Ledentsov, “Dynamical properties of quantum dot semiconductor optical amplifiers at 1.3 μm fiber-coupled to quantum dot mode-locked lasers”, in Conf. on Lasers and Electro-Optics (Long Beach, USA, 2006), CThGG2. |

19. | S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Linewidth enhancement factor in InGaAs quantum-dot amplifiers,” IEEE J. Quantum Electron. |

20. | H. C. Wong, G. B. Ren, and J. M. Rorison, “Mode amplification in inhomogeneous QD semiconductor optical amplifiers,” Opt. Quantum Electron. |

21. | T. Vallaitis, C. Koos, B.-A. Bolles, R. Bonk, W. Freude, M. Laemmlin, C. Meuer, D. Bimberg, and J. Leuthold, “Quantum dot semiconductor optical amplifier at 1.3μm for ultra-fast cross-gain modulation”, in Proc. 33rd European Conf. Opt. Commun. (ECOC, Berlin, Germany, 2007), We8.6.5. |

22. | R. Bonk, P. Vorreau, S. Sygletos, T. Vallaitis, J. Wang, W. Freude, J. Leuthold, and R. Brenot, G. H. Duan C. Meuer, S. Liebig, M. Laemmlin, D. Bimberg, “Performing cross-gain modulation with improved signal quality in an interferometric configuration”, in Proc. of OFC 2008 (San Diego, USA, 2008), JWA70. |

23. | R. Bonk, S. Sygletos, R. Brenot, T. Vallaitis, A. Marculescu, P. Vorreau, J. Li, W. Freude, F. Lelarge, G.-H. Duan, and J. Leuthold, “Optimum Filter for Wavelength Conversion with QD-SOA”, in Proc. of CLEO/IQEC (Baltimore, USA 2009), CMC6. |

24. | G. P. Agrawal, and N. K. Dutta, |

25. | G. P. Agrawal, |

26. | V. G. Ta’eed, L. Fu, M. Pelusi, M. Rochette, I. C. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express |

27. | J. Leuthold, B. Mikkelsen, G. Raybon, C. H. Joyner, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and R. Behringer, “All-optical wavelength conversion between 10 and 100 Gb/s with SOA delayed-interference configuration,” Opt. Quantum Electron. |

28. | J. Wang, A. Maitra, C. G. Poulton, W. Freude, and J. Leuthold, “Temporal dynamics of the alpha factor in semiconductor optical amplifiers,” J. Lightwave Technol. |

29. | G. K. Grau, and W. Freude, |

30. | K.-P. Ho, |

**OCIS Codes**

(060.5060) Fiber optics and optical communications : Phase modulation

(250.5980) Optoelectronics : Semiconductor optical amplifiers

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: August 28, 2009

Revised Manuscript: October 29, 2009

Manuscript Accepted: November 19, 2009

Published: November 25, 2009

**Citation**

Jin Wang, Ayan Maitra, Wolfgang Freude, and Juerg Leuthold, "Regenerative properties of interferometric
all-optical DPSK wavelength converters," Opt. Express **17**, 22639-22658 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22639

Sort: Year | Journal | Reset

### References

- A. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agarwal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maywar, M. Movassghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, “2.5 Tb/s (64×42.7 Gb/s) transmission over 40×100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in Technical Digest of OFC 2002, (Anaheim, USA, 2002), FC2.1–FC2.3.
- V. S. Grigoryan, M. Shin, P. Devgan, J. Lasri, and P. Kumar, “SOA-based regenerative amplification of phase-noise-degraded DPSK signals: dynamic analysis and demonstration,” J. Lightwave Technol. 24(1), 135–142 (2006). [CrossRef]
- I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jaques, and C. R. Giles, “Regenerative all-optical wavelength conversion of 40 Gb/s DPSK signals using a SOA MZI,” in Proc. 31st European. Conf. Optical Communications (ECOC, Glasgow, UK, 2005), Th. 4.3.3.
- P. Vorreau, A. Marculescu, J. Wang, G. Boettger, B. Sartorius, C. Bornholdt, J. Slovak, M. Schlak, Ch. Schmidt, S. Tsadka, W. Freude, and J. Leuthold, “Cascadability and regenerative properties of SOA all-optical DPSK wavelength converters,” IEEE Photon. Technol. Lett. 18(18), 1970–1972 (2006). [CrossRef]
- P. Johannisson, G. Adolfsson, and M. Karlsson, “Suppression of phase error in differential phase-shift keying data by amplitude regeneration,” Opt. Lett. 31(10), 1385–1387 (2006). [CrossRef] [PubMed]
- C. C. Wei and J. J. Chen, “Convergence of phase noise in DPSK transmission systems by novel phase noise averagers,” Opt. Express 14(21), 9584–9593 (2006). [CrossRef] [PubMed]
- C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “'All-optical high-speed signal processing with silicon–organic hybrid slot waveguides',” Nat. Photonics 3(4), 216–219 (2009). [CrossRef]
- M. Matsumoto, “Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators,” IEEE Photon. Technol. Lett. 17(5), 1055–1057 (2005). [CrossRef]
- K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. 43(3), 177–178 (2007). [CrossRef]
- M. Matsumoto and H. Sakaguchi, “DPSK signal regeneration using a fiber-based amplitude regenerator,” Opt. Express 16(15), 11169–11175 (2008). [CrossRef] [PubMed]
- K. Croussore and G. Li, “Phase and amplitude regeneration of differential phase-shift keyed signals using phase-sensitive amplification,” IEEE J. Sel. Top. Quantum Electron. 14(3), 648–658 (2008). [CrossRef]
- K. Croussore and G. Li, “Phase-regenerative wavelength conversion for BPSK and DPSK signals,” IEEE Photon. Technol. Lett. 21(2), 70–72 (2009). [CrossRef]
- M. Suzuki, H. Tanaka, and Y. Matsushima, “InGaAsP electroabsorption modulator for high-bit-rate EDFA system,” IEEE Photon. Technol. Lett. 4(6), 586–588 (1992). [CrossRef]
- C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982). [CrossRef]
- T. Otani, T. Miyazaki, and S. Yamamoto, “40-Gb/s optical 3R regenerator using electroabsorption modulators for optical networks,” J. Lightwave Technol. 20(2), 195–200 (2002). [CrossRef]
- A. Bilenca, R. Alizon, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, D. Gold, J. P. Reithmaier, and A. Forchel, “Broad-band wavelength conversion based on cross-gain modulation and four-wave mixing in InAs-InP quantum dash semiconductor optical amplifiers operating at 1550 nm,” IEEE Photon. Technol. Lett. 15(4), 563–565 (2003). [CrossRef]
- T. Akiyama, M. Ekawa, M. Sugawara, K. Kawaguchi, H. Sudo, A. Kuramata, H. Ebe, and Y. Arakawa, “An ultrawide-band semiconductor optical amplifier having an extremely high penalty-free output power of 23 dBm achieved with quantum dots,” IEEE Photon. Technol. Lett. 17(8), 1614–1616 (2005). [CrossRef]
- M. Laemmlin, G. Fiol, M. Kuntz, F. Hopfer, D. Bimberg, A. R. Kovsh, and N. N. Ledentsov, “Dynamical properties of quantum dot semiconductor optical amplifiers at 1.3 μm fiber-coupled to quantum dot mode-locked lasers,” in Conf. on Lasers and Electro-Optics (Long Beach, USA, 2006), CThGG2.
- S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Linewidth enhancement factor in InGaAs quantum-dot amplifiers,” IEEE J. Quantum Electron. 40(10), 1423–1429 (2004). [CrossRef]
- H. C. Wong, G. B. Ren, and J. M. Rorison, “Mode amplification in inhomogeneous QD semiconductor optical amplifiers,” Opt. Quantum Electron. 38(4-6), 395–409 (2006). [CrossRef]
- T. Vallaitis, C. Koos, B.-A. Bolles, R. Bonk, W. Freude, M. Laemmlin, C. Meuer, D. Bimberg, and J. Leuthold, “Quantum dot semiconductor optical amplifier at 1.3μm for ultra-fast cross-gain modulation,” in Proc. 33rd European Conf. Opt. Commun. (ECOC, Berlin, Germany, 2007), We8.6.5.
- R. Bonk, P. Vorreau, S. Sygletos, T. Vallaitis, J. Wang, W. Freude, J. Leuthold, and R. Brenot, G. H. Duan C. Meuer, S. Liebig, M. Laemmlin, D. Bimberg, “Performing cross-gain modulation with improved signal quality in an interferometric configuration,” in Proc. of OFC 2008 (San Diego, USA, 2008), JWA70.
- R. Bonk, S. Sygletos, R. Brenot, T. Vallaitis, A. Marculescu, P. Vorreau, J. Li, W. Freude, F. Lelarge, G.-H. Duan, and J. Leuthold, “Optimum Filter for Wavelength Conversion with QD-SOA,”in Proc. of CLEO/IQEC (Baltimore, USA 2009), CMC6.
- G. P. Agrawal, and N. K. Dutta, Semiconductor Lasers, (Reinhold, NewYork, 2nd Ed. 1993).
- G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 3rd Ed. 2001).
- V. G. Ta’eed, L. Fu, M. Pelusi, M. Rochette, I. C. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express 14(22), 10371–10376 (2006). [CrossRef] [PubMed]
- J. Leuthold, B. Mikkelsen, G. Raybon, C. H. Joyner, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and R. Behringer, “All-optical wavelength conversion between 10 and 100 Gb/s with SOA delayed-interference configuration,” Opt. Quantum Electron. 33(7/10), 939–952 (2001). [CrossRef]
- J. Wang, A. Maitra, C. G. Poulton, W. Freude, and J. Leuthold, “Temporal dynamics of the alpha factor in semiconductor optical amplifiers,” J. Lightwave Technol. 25(3), 891–900 (2007). [CrossRef]
- G. K. Grau, and W. Freude, Optische Nachrichtentechnik (Springer, Berlin, 1991).
- K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, New York, 2005).

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