Orthogonal tributary channel exchange of 160-Gbit/s pol-muxed DPSK signal

doi:10.1364/OE.18.016995

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Orthogonal tributary channel exchange of 160-Gbit/s pol-muxed DPSK signal

Jian Wang, Omer F. Yilmaz, Scott R. Nuccio, Xiaoxia Wu, and Alan E. Willner »View Author Affiliations

Optics Express, Vol. 18, Issue 16, pp. 16995-17008 (2010)
http://dx.doi.org/10.1364/OE.18.016995

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▸ Article Outline
– Abstract
1. Introduction
2. Concept and operation principle
3. Experimental setup
4. Experimental results
5. Jones matrix analyses and discussions of orthogonal polarization exchange
– References and links

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Abstract

We report the orthogonal tributary channel exchange of a polarization-multiplexed (pol-muxed) differential phase-shift keying (DPSK) optical time-division multiplexed (OTDM) signal by exploiting the Kerr effect-induced nonlinear birefringence in a highly nonlinear fiber (HNLF). We first implement Kerr effect-based 40-to-10, 80-to-10, and 160-to-10 Gbit/s demultiplexing of DPSK OTDM signals with power penalties of less than 0.5, 1.5, and 2.6 dB, respectively, at a bit-error rate (BER) of 10⁻⁹. We further demonstrate 10-Gbit/s tributary channel exchange between two orthogonal polarizations of a 160-Gbit/s pol-muxed DPSK OTDM signal with a power penalty of less than 4 dB at a BER of 10⁻⁹. Moreover, Jones matrix analyses are applied to the orthogonal polarization exchange, indicating the exchange condition of orthogonal polarization exchange with the characteristic of transparency to the modulation format. The exchange performance is analyzed in terms of the extinction ratio (ER) of the newly converted signal to the original residual signal. The dynamic range of the product of nonlinear coefficient, pump power, and effective fiber length, the dynamic range of pump power, the impact and tolerance of pump polarization offset are discussed to characterize and optimize the performance of orthogonal polarization exchange.

1. Introduction

Optical time-division multiplexing (OTDM) provides an effective approach for increasing the transmission capacity of optical communication systems [1

H. G. Weber, R. Ludwig, S. Ferber, C. Schmidt-Langhorst, M. Kroh, V. Marembert, C. Boerner, and C. Schubert, “Ultrahigh-speed OTDM-transmission technology,” J. Lightwave Technol. 24(12), 4616–4627 (2006). [CrossRef]

]. OTDM allows for a high symbol rate at a single wavelength via temporal interleaving of short optical data pulses [1

H. C. Hansen Mulvad, L. K. Oxenløwe, M. Galili, A. T. Clausen, L. Grüner-Nielsen, and P. Jeppesen, “1.28 Tbit/s single-polarisation serial OOK optical data generation and demultiplexing,” Electron. Lett. 45(5), 280–281 (2009). [CrossRef]

]. To further push the limit of bit rate forward on a single wavelength channel and increase the robustness to nonlinearities and dispersion, advanced modulation formats such as differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) can be used in combination with OTDM and polarization-multiplexing technologies [3

A. H. Gnauck, G. Raybon, P. G. Bernasconi, J. Leuthold, C. R. Doerr, and L. W. Stulz, “1-Tb/s (6×170.6 Gb/s) transmission over 2000-km NZDF using OTDM and RZ-DPSK format,” IEEE Photon. Technol. Lett. 15(11), 1618–1620 (2003). [CrossRef]

–5

H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-2-1438. [CrossRef]

]. Although a single wavelength channel can have a transmission speed of over 100 Gbit/s, the optical network may still require traffic grooming to support connections at data rates that are lower than the full wavelength capacity [6

K. Zhu and B. Mukherjee, “A review of traffic grooming in WDM optical networks: architectures and challenges,” Opt. Netw. Mag. 4, 55–64 (2002).

G. Zarris, E. Hugues-Salas, N. A. Gonzalez, R. Weerasuriya, F. Parmigiani, D. Hillerkuss, P. Vorreau, M. Spyropoulou, S. K. Ibrahim, A. D. Ellis, R. Morais, P. Monteiro, P. Petropoulos, D. J. Richardson, I. Tomkos, J. Leuthold, and D. Simeonidou, “Field Experiments With a Grooming Switch for OTDM Meshed Networking,” J. Lightwave Technol. 28(4), 316–327 (2010). [CrossRef]

]. For a spectrally efficient polarization-multiplexed (pol-muxed) optical data signal, each polarization might contain an independent, high-speed data stream that is itself composed of many lower-speed OTDM tributary channels [3

–5

]. In this scenario, tributary channel data traffic grooming exchanges in both the polarization and time domains might be valuable for achieving superior network performance. An effective approach for enabling data traffic grooming of polarization and time is to use optical nonlinearity in fibers. One specific kind of grooming exchange could be the “swapping” of a single OTDM tributary channel from one polarization state with a single OTDM tributary channel on a second orthogonal polarization state.

A previously proposed scheme for an all-optical time-division add-drop multiplexer used an optical fiber Kerr shutter to perform 10-Gbit/s tributary channel exchange of an 80-Gbit/s pol-muxed signal, showing impressive operation performance. The reported result was for a pol-muxed on-off keying (OOK) OTDM data signal [8

J. Suzuki, K. Taira, Y. Fukuchi, Y. Ozeki, T. Tanemura, and K. Kikuchi, “All-optical time-division add-drop multiplexer using optical fibre Kerr shutter,” Electron. Lett. 40(7), 445–446 (2004). [CrossRef]

]. In regard to robust data traffic grooming, one laudable goal of grooming exchange should be transparency to the modulation format and data rate. It is highly expected that the tributary channel exchange of a pol-muxed signal could be phase-transparent and capable of potentially exchanging DPSK tributary channels. Moreover, DPSK is advantageous in terms of high tolerance to fiber transmission impairments [9

P. J. Winzer and R.-J. Essiambre, “Advanced Modulation Formats for High-Capacity Optical Transport Networks,” J. Lightwave Technol. 24(12), 4711–4728 (2006). [CrossRef]

]. DPSK has been widely used along with pol-muxed OTDM in high-speed large-capacity optical transmission networks [3

]. However, to date little research has been conducted on the grooming exchange of pol-muxed data signal with DPSK format.

In this paper, we experimentally demonstrate the orthogonal tributary channel exchange between two pol-muxed DPSK OTDM data streams by using the Kerr effect-induced nonlinear birefringence in a highly nonlinear fiber (HNLF) [10

J. Wang, O. F. Yilmaz, S. R. Nuccio, X. X. Wu, Z. Bakhtiari, Y. Xiao-Li, J.-Y. Yang, H. Huang, Y. Yue, I. Fazal, R. Hellwarth, and A. E. Willner, “Data traffic grooming/exchange of a single 10-Gbit/s TDM tributary channel between two pol-muxed 80-Gbit/s DPSK channels,” Proc. CLEO’10, San Jose, California, USA, paper CFJ5, 2010.

]. 40/80/160-to-10 Gbit/s DPSK OTDM signal demultiplexing is first implemented with a power penalty of less than 0.5/1.5/2.6 dB at a bit-error rate (BER) of 10⁻⁹. The orthogonal 10-Gbit/s tributary channel exchange of a 160-Gbit/s pol-muxed return-to-zero DPSK (RZ-DPSK) OTDM signal is then demonstrated with a power penalty of less than 4 dB at a BER of 10⁻⁹. Furthermore, Kerr effect-based orthogonal polarization exchange is theoretically analyzed. Fiber length, pump power, and pump polarization offset are discussed for the performance optimization of the orthogonal polarization exchange.

2. Concept and operation principle

Figure 1(a) illustrates the concept and principle of DPSK OTDM signal demultiplexing (demux) based on the optical Kerr effect [11

G. P. Agrawal, Nonlinear Fiber Optics , 3rd Edition (San Diego, CA: Academic, 2002).

]. The DPSK OTDM signal and a strong subrate clock pump are linearly polarized at the HNLF input with a 45° angle between their directions of polarization. When the pump is absent, all the tributary channels of the DPSK OTDM signal will be blocked by a crossed polarizer at the HNLF output. In the presence of the subrate clock pump, which is time aligned with one of the tributary channels of the DPSK OTDM signal, the pump-induced nonlinear birefringence via Kerr effect will cause a polarization change of the selected tributary channel. A 90° polarization rotation could be available through proper adjustment of the pump power, thereby resulting in the selected tributary channel passing through the polarizer and enabling the DPSK OTDM signal demultiplexing [12

V. Marembert, K. Schulze, C. Schubert, C. M. Weinert, H. G. Weber, S. Watanabe, and F. Futami, “Investigations of fiber Kerr switch: nonlinear phase shift measurements and optical time-division demultiplexing of 320 Gbit/s DPSK signals”, Proc. CLEO’05, paper CWK7, 2005.

,13

E. J. M. Verdurmen, A. M. J. Koonen, and H. de Waardt, “Time domain add-drop multiplexing for RZ-DPSK OTDM signals,” Opt. Express 14(12), 5114–5120 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5114. [CrossRef] [PubMed]

Fig. 1 Concept and principle of Kerr effect-based (a) DPSK OTDM signal demultiplexing and (b) orthogonal tributary channel exchange of a pol-muxed DPSK OTDM signal.

Figure 1(b) further depicts the schematic diagram and operation principle of the Kerr effect-based orthogonal tributary channel exchange of a pol-muxed DPSK OTDM signal. The strong subrate clock pump is 45° linearly polarized with respect to the two orthogonal polarizations of a pol-muxed DPSK OTDM signal. With the help of proper pump power control, the pump-induced nonlinear birefringence by Kerr effect could bring the selected tributary channel (aligned with the subrate clock pump) to a 90° polarization rotation for both of the two orthogonal polarizations of the pol-muxed signal, leading to the orthogonal tributary channel exchange when the pump is present. Other unselected orthogonal tributary channels with the pump absent will not experience the nonlinear polarization rotation and hence will be untouched. In addition, simply by shifting the subrate clock pump to be aligned with the tributary channel of interest, it is possible to implement orthogonal tributary channel exchange for all tributary channels of the pol-muxed DPSK OTDM signal.

3. Experimental setup

Figure 2 shows the experimental setup for the Kerr effect-based demultiplexing of a DPSK OTDM signal and the orthogonal tributary channel exchange of a pol-muxed DPSK OTDM signal. A 10-GHz mode-locked laser (MLL) at 1551.0 nm with a pulse width of ~2.4 ps is used to generate an 80-Gbit/s DPSK OTDM signal through a phase modulator (PM) driven by a 10-Gbit/s 2³¹-1 pseudo-random binary sequence (PRBS) and a subsequent 10:80 multiplexer. A 160-Gbit/s pol-muxed DPSK OTDM signal is then achieved by dividing and recombining the 80-Gbit/s DPSK OTDM signal. Polarization controllers (PCs), tunable optical delay lines (ODLs), and variable optical attenuators (VOAs) are employed to provide the orthogonal polarization control, introduce the relative time delay, and equalize the power level of the pol-muxed signal. Another 10-GHz MLL at 1559.7 nm with a pulse width of ~1.9 ps serves as the subrate clock pump. A 1-nm band-pass filter (BPF) is used after the 10-GHz MLL to broaden the pump pulse width (4.4 ps) for performance optimization. A 330-m piece of HNLF with a nonlinear coefficient (γ) of 25 W⁻¹·km⁻¹ and a zero-dispersion wavelength (ZDW) of ~1562.2 nm is adopted for the DPSK OTDM signal demultiplexing or the orthogonal tributary channel exchange of a pol-muxed DPSK OTDM signal. For the latter case, i.e., tributary exchange of a pol-muxed DPSK OTDM signal, after the orthogonal tributary channel exchange, another 1-km piece of HNLF with a γ of 9.1 W⁻¹·km⁻¹ and a ZDW of ~1552 nm is utilized to demultiplex the DPSK OTDM signal to 10 Gbit/s before BER measurements. The polarizers (Pol.s) after the HNLFs are used to separate the X-/Y-polarization (80-Gbit/s DPSK OTDM) of a pol-muxed signal and extract the tributary channel (10-Gbit/s DPSK) after demultiplexing.

Fig. 2 Experimental setup. MLL: mode-locked laser; EDFA: erbium-doped fiber amplifier; BPF: band-pass filter; ODL: tunable optical delay line; PC: polarization controller; PM: phase modulator; VOA: variable optical attenuator; OC: optical coupler; Pol.: polarizer; Rx: receiver.

4. Experimental results

Figure 3 depicts the results of the BER performance and typical balanced eyes for Kerr effect-based 40-to-10, 80-to-10, and 160-to-10 Gbit/s DPSK OTDM signal demultiplexing. Power penalties of less than 0.5 dB for 40-to-10, 1.5 dB for 80-to-10, and 2.6 dB for 160-to-10 Gbit/s demultiplexing are achieved at a BER of 10⁻⁹.

Fig. 3 BER and balanced eyes of 40/80/160-to-10 Gbit/s DPSK OTDM signal demultiplexing.

We further demonstrate the Kerr effect-based orthogonal tributary channel exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal. Figure 4(a) shows the spectra of 160-Gbit/s pol-muxed DPSK OTDM signal and 10-GHz clock pump at the input of the HNLF. Shown in Fig. 4(b) is the output spectrum of the HNLF after the orthogonal tributary channel exchange. Figure 4(c) depicts the spectrum of the selected X-/Y-polarized 80-Gbit/s DPSK OTDM signal after the orthogonal tributary channel exchange.

Fig. 4 Spectra for orthogonal tributary channel exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal. (a) Before the HNLF (point A in Fig. 2). (b) After the HNLF (point B in Fig. 2). (c) Selected X-/Y-polarization after the orthogonal tributary exchange (point C in Fig. 2).

Figure 5 displays the eye diagrams measured by an optical sampling scope for the typical orthogonal tributary channel (Ch. 1) exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal. The input average and peak power of the 10-GHz clock pump launched into the HNLF are ~19 and ~302 mW, respectively. As the 10-GHz clock pump is time aligned to tributary channel 1 (Ch. 1) of the X- and Y-polarized DPSK OTDM signal, in the absence of the Y-polarization, as shown in Fig. 5(b), Ch. 1 of the X-polarization is blocked by an X-polarizer after the HNLF due to the 90° rotation from the X- to the Y-polarization. When the Y-polarization is present but the X-polarization is absent, Ch. 1 of the Y-polarization is inserted to the X-polarization through the 90° rotation from the Y- to the X-polarization, as shown in Fig. 5(c). In the presence of both the X- and Y-polarizations, the tributary Ch. 1 of the Y-polarization is changed to the X-polarization, as shown in Fig. 5(d). Meanwhile, the original tributary Ch. 1 of the X-polarization is also changed to the Y-polarization, as shown in Fig. 5(h), resulting in the orthogonal tributary channel exchange of a pol-muxed DPSK OTDM signal. Figures 6(a) and 6(b) present another two examples of the orthogonal tributary channel (Ch. 4, Ch. 7) exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal.

Fig. 5 Eye diagrams of orthogonal tributary channel (Ch. 1) exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal.

Fig. 6 Eye diagrams of orthogonal tributary channel exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal. (a) Ch. 4. (b) Ch. 7.

Figure 7 further depicts the BER performance and typical balanced eyes for the orthogonal tributary channel exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal. The approximately 3.3-dB power penalty at a BER of 10⁻⁹ is observed during the orthogonal tributary channel exchange, which can be ascribed to the beating effect between the newly inserted signal and the original residual signal. Figure 8 plots the power penalties of the orthogonal tributary exchange for 8 tributary channels. Less than 4-dB power penalty at a BER of 10⁻⁹ is obtained for all 8 tributary channels with a fluctuation of <1.5 dB. Figure 9 presents the impact of the orthogonal tributary exchange on the neighboring channels. Taking the tributary exchange of Ch. 4 as an example, less than 1-dB power penalty at a BER of 10⁻⁹ is observed for the neighboring Ch. 3 and Ch. 5 due to the orthogonal tributary channel exchange.

Fig. 7 BER and balanced eyes of orthogonal tributary channel exchange of a 160-Gbit/s pol-muxed DPSK OTDM signal.

Fig. 8 Power penalties of orthogonal tributary exchange for 8 tributary channels.

Fig. 9 Impact of the orthogonal tributary exchange on the neighboring channels.

5. Jones matrix analyses and discussions of orthogonal polarization exchange

The Kerr-effect based orthogonal polarization exchange can be described using the Jones matrix method. In the demonstrated orthogonal polarization exchange experiments, the pump was always kept 45° linearly polarized with respect to the two orthogonal polarizations of a pol-muxed signal [8

,10

]. In general, the pump polarization may suffer a slight offset (ϕ). As shown in the inset of Fig. 1(b), when considering the pump polarization and its orthogonal direction respectively as the y- and x-axes (x-y coordinates), Jones matrix formulations connecting Jones vectors of the output and input signals can be written as

(\begin{array}{l} E_{x 1}^{'} \\ E_{y 1}^{'} \end{array}) = (\begin{array}{l} 1 0 \\ 0 \exp (j Δ φ_{N L}) \end{array}) \cdot (\begin{array}{l} E_{x 10} \\ E_{y 10} \end{array}) = (\begin{array}{l} 1 0 \\ 0 \exp (j Δ φ_{N L}) \end{array}) \cdot (\begin{array}{l} \cos θ \cdot E_{10} \\ \sin θ \cdot E_{10} \end{array})

(1a)

(\begin{array}{l} E_{x 2}^{'} \\ E_{y 2}^{'} \end{array}) = (\begin{array}{l} 1 0 \\ 0 \exp (j Δ φ_{N L}) \end{array}) \cdot (\begin{array}{l} E_{x 20} \\ E_{y 20} \end{array}) = (\begin{array}{l} 1 0 \\ 0 \exp (j Δ φ_{N L}) \end{array}) \cdot (\begin{array}{l} - \sin θ \cdot E_{20} \\ \cos θ \cdot E_{20} \end{array})

(1b)

where

θ = π / 4 - ϕ

E_{10}

and

E_{20}

are the amplitudes of the X- (subscript “1”) and Y-polarizations (subscript “2”) of the incident pol-muxed signal.

E_{x 10}

(

E_{x 20}

) and

E_{y 10}

(

E_{y 20}

) are the corresponding x and y components of the input X-(Y-) polarized electrical field in the x-y coordinates.

E_{x 1}^{'}

(

E_{x 2}^{'}

) and

E_{y 1}^{'}

(

E_{y 2}^{'}

) are the x and y components of the output X-(Y-) polarized electrical field after passing through the fiber. The nonlinear phase shift

Δ φ_{N L}

caused by the pump-induced nonlinear birefringence can be expressed as [11

G. P. Agrawal, Nonlinear Fiber Optics , 3rd Edition (San Diego, CA: Academic, 2002).

]

Δ φ_{N L} = 2 π / λ \cdot L_{e f f} \cdot n_{2 B} \cdot {| E_{P} |}^{2} = 4 / 3 \cdot γ \cdot P_{P} \cdot L_{e f f}

(2)

where λ is the wavelength.

L_{e f f}

denotes the effective fiber length, defined as

L_{e f f} = [1 - \exp (- α \cdot L)] / α

, in which α is the fiber loss and L is the fiber length. Meanwhile,

n_{2 B} = 4 / 3 \cdot n_{2}

is the Kerr coefficient,

n_{2}

is the nonlinear-index coefficient,

{| E_{P} |}^{2}

is the pump intensity, and

P_{P}

is the pump power. The parameter

γ = 2 π \cdot n_{2} / (λ \cdot A_{e f f})

represents the nonlinear coefficient in which

A_{e f f}

is the effective area.

According to the Eqs. (1)a) and (1b), under the following exchange condition,

Δ φ_{N L} = (2 N + 1) π, N = 0, 1, 2, ...

θ = π / 4 (ϕ = 0)

(3)

the complete exchange between X- and Y-polarizations of a pol-muxed signal is obtained as

(\begin{array}{l} E_{x 1}^{'} \\ E_{y 1}^{'} \end{array}) = - (\begin{array}{l} E_{x 20} \\ E_{y 20} \end{array})

(4a)

(\begin{array}{l} E_{x 2}^{'} \\ E_{y 2}^{'} \end{array}) = - (\begin{array}{l} E_{x 10} \\ E_{y 10} \end{array})

(4b)

Since the electrical field contains both amplitude and phase information, it is expected that the proposed Kerr effect-based orthogonal polarization exchange has the characteristic of transparency to the modulation format.

One of the most important parameters for characterizing the exchange performance is the extinction ratio (ER) of the newly converted signal to the original residual signal. The larger the achievable ER, the better the exchange performance expected. We can further derive the following formulations for the newly converted signal and original residual signal in the X-/Y- polarizations.

X-to-Y conversion:

$(- \sin θ, \cos θ) \cdot (\begin{array}{l} E_{x 1}^{'} \\ E_{y 1}^{'} \end{array}) = (- \sin θ \cdot \cos θ + \sin θ \cdot \cos θ \cdot \exp (j Δ φ_{N L})) \cdot E_{10}$

(5a)
X-polarization residual:

$(\cos θ, \sin θ) \cdot (\begin{array}{l} E_{x 1}^{'} \\ E_{y 1}^{'} \end{array}) = (\cos^{2} θ + \sin^{2} θ \cdot \exp (j Δ φ_{N L})) \cdot E_{10}$

(5b)
Y-to-X conversion:

$(\cos θ, \sin θ) \cdot (\begin{array}{l} E_{x 2}^{'} \\ E_{y 2}^{'} \end{array}) = (- \sin θ \cdot \cos θ + \sin θ \cdot \cos θ \cdot \exp (j Δ φ_{N L})) \cdot E_{20}$

(6a)
Y-polarization residual:

$(- \sin θ, \cos θ) \cdot (\begin{array}{l} E_{x 2}^{'} \\ E_{y 2}^{'} \end{array}) = (\sin^{2} θ + \cos^{2} θ \cdot \exp (j Δ φ_{N L})) \cdot E_{20}$

(6b)

Based on Eqs. (5a), (5b), (6a), and (6b), the ER of the orthogonal polarization exchange can be deduced as

Y-to-X polarization exchange:

${ER}_{Y - to - X} = \frac{\sin^{2} 2 θ \cdot \sin^{2} \frac{Δ φ_{N L}}{2}}{1 - \sin^{2} 2 θ \cdot \sin^{2} \frac{Δ φ_{N L}}{2}} \cdot \frac{{| E_{20} |}^{2}}{{| E_{10} |}^{2}}$

(7a)
X-to-Y polarization exchange:

${ER}_{X - to - Y} = \frac{\sin^{2} 2 θ \cdot \sin^{2} \frac{Δ φ_{N L}}{2}}{1 - \sin^{2} 2 θ \cdot \sin^{2} \frac{Δ φ_{N L}}{2}} \cdot \frac{{| E_{10} |}^{2}}{{| E_{20} |}^{2}}$

(7b)

5.1 Without pump polarization offset

We first investigate the ER performance of the Kerr effect-based orthogonal polarization exchange when the pump is linearly polarized at 45° with respect to the two orthogonal polarizations of the incident pol-muxed signal (without pump polarization offset, i.e.,

ϕ = 0

θ = π / 4

). As shown in Fig. 10(a) , the ER is a function of the product of the nonlinear coefficient, pump power, and effective fiber length (i.e.,

γ \cdot P_{P} \cdot L_{e f f}

). A desired >20 dB ER requires

γ \cdot P_{P} \cdot L_{e f f}

to be limited to 1.83-2.88 rad with a dynamic range of 1.05 rad. The perfect exchange is achieved by adjusting

γ \cdot P_{P} \cdot L_{e f f} = 3 π / 4

(i.e.,

Δ φ_{N L} = π

). Assuming the two orthogonal polarization components of the incident pol-muxed signal have the same amplitude, i.e.,

E_{10}

E_{20}

, Eqs. (7a) and (7b) imply that both Y-to-X and X-to-Y polarization exchanges have the same ER performance; thus, only one will be depicted in the following figures. Figure 10(b) shows the dependence of the dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

on the desired minimal ER. The dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

decreases as the desired minimal ER increases. For example, the dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

decreases from 1.05 rad for a desired >20 dB ER to 0.66 rad for a desired >30 dB ER. For practical applications, pump power and fiber length are two flexible parameters that can be adjusted to optimize the exchange performance. Figure 10(c) plots the ER as functions of the fiber length and pump power with the given nonlinear coefficient γ = 25 W⁻¹·km⁻¹ and fiber loss α = 0.5 dB/km. According to Fig. 10(c), it is possible to choose the proper fiber length and pump power for different required ER. The marked ranges within pairs of dashed lines shown in Fig. 10(c) indicate the optimized fiber length and pump power enabling >20 dB ER. The neighboring optimized ranges have an increase of

2 π

for

Δ φ_{N L}

(e.g., from range ① to range ②). For a desired >20 dB ER, as shown in Fig. 10(d), both the optimized pump power and the dynamic range of pump power decrease as the fiber length increases. Figure 10(e) shows an example of the dependence of ER on the pump power under different fiber lengths. To achieve the desired >20 dB ER, the available pump power (L = 300m: 247.9-391.3 mW, L = 400m: 187.0-295.2 mW, L = 500m: 150.4-237.5 mW) and the dynamic range of pump power (L = 300m: 143.4 mW, L = 400m: 108.2 mW, L = 500m: 87.1 mW) decrease as the fiber length increases. Figure 10(f) depicts the dynamic range of pump power as a function of the desired minimal ER under different fiber lengths. With the increased ER requirement, the corresponding dynamic range of pump power decreases.

Fig. 10 ER performance for Y-to-X and X-to-Y polarization exchanges without pump polarization offset. (a) ER vs.

γ \cdot P_{P} \cdot L_{e f f}

. (b) Dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

vs. desired minimal ER. (c) ER vs. fiber length and pump power (ER>20dB within pairs of dashed lines). (d) Optimized pump power and dynamic range of pump power (ER>20 dB) vs. fiber length. (e) ER vs. pump power under different fiber lengths of L = 300, 400, 500 m. (f) Dynamic range of pump power vs. desired minimal ER under different fiber lengths of L = 300, 400, 500 m. γ = 25 W⁻¹·km⁻¹ and α = 0.5 dB/km are given for (c)-(f).

5.2 With pump polarization offset

We further investigate the ER performance of the Kerr effect-based orthogonal polarization exchange when the pump polarization is offset (i.e.,

ϕ \neq 0

θ \neq π / 4

). As shown in Fig. 11(a) , the ER and dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

(ER>20 dB) decrease as the pump polarization offset increases. In particular, as the pump polarization offset increases beyond ± 10.1°, the desired >20 dB ER becomes unavailable. Thus, the tolerance of the pump polarization offset is assessed to be ± 10.1° in order to achieve a >20 dB ER. Figure 11(b) depicts the tolerance of pump polarization offset as a function of the desired achievable ER. As indicated, the pump polarization offset tolerance decreases as the desired achievable ER increases. For example, the tolerance of the pump polarization offset decreases from ± 10.1° for a desired achievable ER of 20 dB to ± 6.3° for a desired achievable ER of 30 dB. As shown in Fig. 11(c), the pump polarization offset impacts the dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

under different requirements of ER. The dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

decreases as the desired ER increases. The pump polarization offset also reduces the dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

, which drops quickly for a large value of pump polarization offset. For a pump polarization offset of ± 9°, Fig. 11(d) further plots the ER as functions of the fiber length and pump power with the given nonlinear coefficient γ = 25 W⁻¹·km⁻¹ and fiber loss α = 0.5 dB/km. The optimized ranges with >20 dB ER are also marked within pairs of dashed lines, as shown in Fig. 11(d), an increase of

2 π

for

Δ φ_{N L}

is introduced between neighboring optimized ranges (e.g., from range ① to range ②). In addition, by comparing these results in Fig. 11(d) with those shown in Fig. 10(c), it becomes evident that the pump polarization offset shrinks the optimized ranges of fiber length and pump power. As shown in Fig. 11(e), both the optimized pump power and dynamic range of pump power decrease as the fiber length increases. Compared to Fig. 10(d), a negligible change of optimized pump power but significant reduction of pump power dynamic range is observed when the pump polarization is offset ( ± 9°). Figure 11(f) depicts the dependence of the dynamic range of pump power on the desired minimal ER under different fiber lengths (L = 300, 400, 500 m) and pump polarization offsets (ϕ = ± 6°, ± 9°, ± 13°). The dynamic range of pump power decreases as the desired minimal ER, fiber length, and pump polarization offset increase. It can be clearly seen that the pump polarization offset imposes a great limitation on the achievable ER.

Fig. 11 ER performance for Y-to-X and X-to-Y polarization exchanges with pump polarization offset. (a) ER vs.

γ \cdot P_{P} \cdot L_{e f f}

under different pump polarization offsets. (b) Tolerance of pump polarization offset vs. desired achievable ER. (c) Dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

vs. pump polarization offset under different desired ER. (d) ER vs. fiber length and pump power under a pump polarization offset of ± 9° (ER>20dB within pairs of dashed lines). (e) Optimized pump power and dynamic range of pump power (ER>20 dB) vs. fiber length under a pump polarization offset of ± 9°. (f) Dynamic range of pump power vs. desired minimal ER under different fiber lengths (L = 300, 400, 500 m) and different pump polarization offsets ( ± 6°, ± 9°, ± 13°). γ = 25 W⁻¹·km⁻¹ and α = 0.5 dB/km are given for (d)-(f).

For the Kerr effect-based orthogonal polarization exchange, fiber length, pump power, and the pump polarization offset in particular are important parameters for optimizing the exchange performance. The derived Eqs. (1)-(7) assisted by the Jones matrix method and Figs. 10 and 11 provide the theoretical analyses of the orthogonal polarization exchange in terms of the ER performance. The product of the nonlinear coefficient, pump power, and effective fiber length (i.e.,

γ \cdot P_{P} \cdot L_{e f f}

) completely determine the nonlinear phase shift (

Δ φ_{N L}

), which impacts the ER performance. For practical applications, we can choose proper fiber length and pump power according to the optimized ranges marked in Fig. 10(c) and Fig. 11(d). The characterization and optimization of the dynamic range of

γ \cdot P_{P} \cdot L_{e f f}

, the dynamic range of the pump power, and the tolerance of pump polarization offset could be helpful for better understanding and further improving the performance of the orthogonal polarization exchange. Additionally, the Kerr effect-based orthogonal polarization exchange has the characteristic of transparency to the modulation format. With future improvement, it is possible to further implement the orthogonal tributary channel exchange of a pol-muxed differential quadrature phase-shift keying (DQPSK) OTDM signal or a pol-muxed quadrature amplitude modulation (QAM) OTDM signal.

Acknowledgments

We acknowledge Lin Zhang, Zahra Bakhtiari, Yinying Xiao-Li, Jeng-Yuan Yang, Hao Huang, Yang Yue, Irfan Fazal, and Dr. Robert W. Hellwarth for the helpful discussions and the generous support of the Defense Advanced Research Projects Agency (DARPA) under the contract number FA8650-08-1-7820 and the NSF ERC CIAN.

References and links

1.	H. G. Weber, R. Ludwig, S. Ferber, C. Schmidt-Langhorst, M. Kroh, V. Marembert, C. Boerner, and C. Schubert, “Ultrahigh-speed OTDM-transmission technology,” J. Lightwave Technol. 24(12), 4616–4627 (2006). [CrossRef]
2.	H. C. Hansen Mulvad, L. K. Oxenløwe, M. Galili, A. T. Clausen, L. Grüner-Nielsen, and P. Jeppesen, “1.28 Tbit/s single-polarisation serial OOK optical data generation and demultiplexing,” Electron. Lett. 45(5), 280–281 (2009). [CrossRef]
3.	A. H. Gnauck, G. Raybon, P. G. Bernasconi, J. Leuthold, C. R. Doerr, and L. W. Stulz, “1-Tb/s (6×170.6 Gb/s) transmission over 2000-km NZDF using OTDM and RZ-DPSK format,” IEEE Photon. Technol. Lett. 15(11), 1618–1620 (2003). [CrossRef]
4.	H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006). [CrossRef]
5.	H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-2-1438. [CrossRef]
6.	K. Zhu and B. Mukherjee, “A review of traffic grooming in WDM optical networks: architectures and challenges,” Opt. Netw. Mag. 4, 55–64 (2002).
7.	G. Zarris, E. Hugues-Salas, N. A. Gonzalez, R. Weerasuriya, F. Parmigiani, D. Hillerkuss, P. Vorreau, M. Spyropoulou, S. K. Ibrahim, A. D. Ellis, R. Morais, P. Monteiro, P. Petropoulos, D. J. Richardson, I. Tomkos, J. Leuthold, and D. Simeonidou, “Field Experiments With a Grooming Switch for OTDM Meshed Networking,” J. Lightwave Technol. 28(4), 316–327 (2010). [CrossRef]
8.	J. Suzuki, K. Taira, Y. Fukuchi, Y. Ozeki, T. Tanemura, and K. Kikuchi, “All-optical time-division add-drop multiplexer using optical fibre Kerr shutter,” Electron. Lett. 40(7), 445–446 (2004). [CrossRef]
9.	P. J. Winzer and R.-J. Essiambre, “Advanced Modulation Formats for High-Capacity Optical Transport Networks,” J. Lightwave Technol. 24(12), 4711–4728 (2006). [CrossRef]
10.	J. Wang, O. F. Yilmaz, S. R. Nuccio, X. X. Wu, Z. Bakhtiari, Y. Xiao-Li, J.-Y. Yang, H. Huang, Y. Yue, I. Fazal, R. Hellwarth, and A. E. Willner, “Data traffic grooming/exchange of a single 10-Gbit/s TDM tributary channel between two pol-muxed 80-Gbit/s DPSK channels,” Proc. CLEO’10, San Jose, California, USA, paper CFJ5, 2010.
11.	G. P. Agrawal, Nonlinear Fiber Optics , 3rd Edition (San Diego, CA: Academic, 2002).
12.	V. Marembert, K. Schulze, C. Schubert, C. M. Weinert, H. G. Weber, S. Watanabe, and F. Futami, “Investigations of fiber Kerr switch: nonlinear phase shift measurements and optical time-division demultiplexing of 320 Gbit/s DPSK signals”, Proc. CLEO’05, paper CWK7, 2005.
13.	E. J. M. Verdurmen, A. M. J. Koonen, and H. de Waardt, “Time domain add-drop multiplexing for RZ-DPSK OTDM signals,” Opt. Express 14(12), 5114–5120 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5114. [CrossRef] [PubMed]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(190.3270) Nonlinear optics : Kerr effect
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(230.1150) Optical devices : All-optical devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 24, 2010
Revised Manuscript: July 11, 2010
Manuscript Accepted: July 15, 2010
Published: July 26, 2010

Citation
Jian Wang, Omer F. Yilmaz, Scott R. Nuccio, Xiaoxia Wu, and Alan E. Willner, "Orthogonal tributary channel exchange of 160-Gbit/s pol-muxed DPSK signal," Opt. Express 18, 16995-17008 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16995

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References

H. G. Weber, R. Ludwig, S. Ferber, C. Schmidt-Langhorst, M. Kroh, V. Marembert, C. Boerner, and C. Schubert, “Ultrahigh-speed OTDM-transmission technology,” J. Lightwave Technol. 24(12), 4616–4627 (2006). [CrossRef]
H. C. Hansen Mulvad, L. K. Oxenløwe, M. Galili, A. T. Clausen, L. Grüner-Nielsen, and P. Jeppesen, “1.28 Tbit/s single-polarisation serial OOK optical data generation and demultiplexing,” Electron. Lett. 45(5), 280–281 (2009). [CrossRef]
A. H. Gnauck, G. Raybon, P. G. Bernasconi, J. Leuthold, C. R. Doerr, and L. W. Stulz, “1-Tb/s (6×170.6 Gb/s) transmission over 2000-km NZDF using OTDM and RZ-DPSK format,” IEEE Photon. Technol. Lett. 15(11), 1618–1620 (2003). [CrossRef]
H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006). [CrossRef]
H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-2-1438 . [CrossRef]
K. Zhu and B. Mukherjee, “A review of traffic grooming in WDM optical networks: architectures and challenges,” Opt. Netw. Mag. 4, 55–64 (2002).
G. Zarris, E. Hugues-Salas, N. A. Gonzalez, R. Weerasuriya, F. Parmigiani, D. Hillerkuss, P. Vorreau, M. Spyropoulou, S. K. Ibrahim, A. D. Ellis, R. Morais, P. Monteiro, P. Petropoulos, D. J. Richardson, I. Tomkos, J. Leuthold, and D. Simeonidou, “Field Experiments With a Grooming Switch for OTDM Meshed Networking,” J. Lightwave Technol. 28(4), 316–327 (2010). [CrossRef]
J. Suzuki, K. Taira, Y. Fukuchi, Y. Ozeki, T. Tanemura, and K. Kikuchi, “All-optical time-division add-drop multiplexer using optical fibre Kerr shutter,” Electron. Lett. 40(7), 445–446 (2004). [CrossRef]
P. J. Winzer and R.-J. Essiambre, “Advanced Modulation Formats for High-Capacity Optical Transport Networks,” J. Lightwave Technol. 24(12), 4711–4728 (2006). [CrossRef]
J. Wang, O. F. Yilmaz, S. R. Nuccio, X. X. Wu, Z. Bakhtiari, Y. Xiao-Li, J.-Y. Yang, H. Huang, Y. Yue, I. Fazal, R. Hellwarth, and A. E. Willner, “Data traffic grooming/exchange of a single 10-Gbit/s TDM tributary channel between two pol-muxed 80-Gbit/s DPSK channels,” Proc. CLEO’10, San Jose, California, USA, paper CFJ5, 2010.
G. P. Agrawal, Nonlinear Fiber Optics, 3rd Edition (San Diego, CA: Academic, 2002).
V. Marembert, K. Schulze, C. Schubert, C. M. Weinert, H. G. Weber, S. Watanabe, and F. Futami, “Investigations of fiber Kerr switch: nonlinear phase shift measurements and optical time-division demultiplexing of 320 Gbit/s DPSK signals”, Proc. CLEO’05, paper CWK7, 2005.
E. J. M. Verdurmen, A. M. J. Koonen, and H. de Waardt, “Time domain add-drop multiplexing for RZ-DPSK OTDM signals,” Opt. Express 14(12), 5114–5120 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5114 . [CrossRef] [PubMed]

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