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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 8 — Apr. 12, 2010
  • pp: 7917–7922
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Photonic crystal fiber based Mach-Zehnder interferometer for DPSK signal demodulation

Jiangbing Du, Yongheng Dai, Gordon K. P. Lei, Weijun Tong, and Chester Shu  »View Author Affiliations


Optics Express, Vol. 18, Issue 8, pp. 7917-7922 (2010)
http://dx.doi.org/10.1364/OE.18.007917


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Abstract

We demonstrate a novel fiber-based in-line DPSK demodulator using an in-fiber Mach-Zehnder interferometer (MZI). The device is fabricated by mismatch splicing of a photonic crystal fiber (PCF) with standard single mode fibers. The spectral characteristics at different PCF lengths are analyzed. The envelope of the interference fringes show a period that is inversely proportional to the PCF length, and is attributed to the periodic coupling between the core mode and the cladding mode. Error free demodulations of 10-Gb/s RZ- and NRZ-DPSK signals have been demonstrated using the in-fiber PCF-MZI demodulator with only 3-m PCF to introduce 91-ps delay. Wideband DPSK demodulation has also been achieved.

© 2010 OSA

Introduction

Recently, along with the rapid development of photonic crystal fiber (PCF) technology, a new kind of in-fiber Mach-Zehnder interferometer (MZI) has been demonstrated using methods like mismatch splicing, cladding collapse, long period grating inscription, and hollow-core fiber splicing [1

1. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef] [PubMed]

5

5. J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91(9), 091109 (2007). [CrossRef]

]. The in-fiber PCF-MZI is an in-line, all-fiber, and coupler free device which, as a delay interferometer (DI), has a relative delay governed by the index difference between the core mode and the cladding mode of the PCF. Due to the unique air-hole structure of the PCF, the index difference between the core mode and the cladding mode can be quite large (usually larger than 0.01), which implies that a short PCF can be used to introduce a large delay while keeping optical attenuation of the cladding mode at a relatively low level. Multimode fiber and polarization-maintaining loop mirror can also achieve similar delay interference but a much longer fiber will be required. For a 100-ps relative delay, about 25-m multimode fiber or 110-m birefringent fiber will be needed [6

6. Y. K. Lize, R. Gomma, and R. Kashyap, “Low-cost multimode fiber Mach Zehnder interferometer for differential phase demodulation,” v.6314, p.63140R.1–7, in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications XII, San Diego, USA, August (2006).

,7

7. C. W. Chow and H. K. Tsang, “Polarization-independent DPSK demodulation using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(6), 1313–1315 (2005). [CrossRef]

]. In comparison, the in-fiber and coupler-free PCF-MZI only requires 3-m fiber to introduce 91-ps delay (~3.25 m for 100 ps delay), which indicates a much larger delay efficiency and consequently offers many advantages like compactness and cost reduction [8

8. J. Du, Y. Dai, G. K. P. Lei, W. Tong, and C. Shu, “Demodulation of DPSK signals using in-line Mach-Zehnder interferometer based on photonic crystal fibers,” p.FM6, in the 14th Opto-Electronics and Communications Conference, Hong Kong, July (2009).

]. As an all-fiber device, PCF-MZI also offers enhanced thermal stability and performs favorably for optical sensing [5

5. J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91(9), 091109 (2007). [CrossRef]

]. To date, applications of the in-fiber PCF-MZI is mainly focused on optical sensing rather than on communications, which is the major objective of this work.

In future high-speed optical communications, differential phase shift keying (DPSK) is an attractive modulation format as it offers an improved receiver sensitivity with balanced detection, demonstrates robustness to nonlinear effects, and exhibits high tolerance to dispersion impairments [9

9. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005). [CrossRef]

]. In DPSK communications, demodulation is needed to translate differential phase information into intensity information (for direct detection) using DPSK demodulators such as a MZI. All-fiber MZI has been widely used in optical communications owing to its reliable performance in multiplexing, DPSK signal demodulation, and so on. The conventional all-fiber MZI uses two fiber couplers with a certain length difference between the two arms to introduce a fixed propagation delay. Similar functionalities can also be achieved by using a birefringent loop mirror, photonic bandgap fiber Lyot filter, or a delay-asymmetric nonlinear loop mirror [7

7. C. W. Chow and H. K. Tsang, “Polarization-independent DPSK demodulation using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(6), 1313–1315 (2005). [CrossRef]

,10

10. C. Peucheret, Y. Geng, B. Zsigri, T. T. Alkeskjold, T. P. Hansen, and P. Jeppesen, “Demodulation of DPSK signals up to 40 Gb/s using a highly birefringent photonic bandgap fiber,” IEEE Photon. Technol. Lett. 18(12), 1392–1394 (2006). [CrossRef]

,11

11. M. P. Fok and C. Shu, “Delay-asymmetric nonlinear loop mirror for DPSK demodulation,” Opt. Lett. 33(23), 2845–2847 (2008). [CrossRef] [PubMed]

].

In this paper, we demonstrate a new solution for DPSK signal demodulation using an in-fiber PCF-MZI. Error free demodulations of 10 Gb/s RZ- and NRZ-DPSK signals have been successfully achieved using only 3-m PCF. Wideband operation capability has also been realized. Compared to the other techniques for DPSK demodulation, the in-fiber PCF-MZI is an in-line, coupler-free, and polarizer-free device that consists of a very short PCF, which offers advantages like simplicity, compactness, and potential cost reduction.

In-fiber PCF-MZI: principle and fabrication

In this work, mismatch splicing method is employed for the fabrication of the in-fiber PCF-MZI. The mismatch between single-mode fiber (SMF) and PCF allows the input light to split into the core and the cladding of the PCF, resulting in light propagating as core mode and cladding mode, respectively. The core mode and cladding mode, which are characterized by different effective indices, ncore and ncladding, have different light propagation speeds in the PCF. Consequently, a relative group delay is developed after the propagation. When the core-mode light and the cladding-mode light are recombined at the PCF output end that is mismatch-spliced with another SMF, interference will take place and result in a transmission spectrum described as follows [1

1. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef] [PubMed]

]:
T(λ)=Icore(λ)+Icladding(λ)+2Icore(λ)Icladding(λ)cos(2πΔnL/λ)
(1)
Δn=ncorencladding=λ2π(βcoreβcladding)
(2)
where βcore and βcladding are the propagation constants, and Icore(λ) and Icladding(λ) are the light intensities of the core mode and the cladding mode at the PCF output, respectively. L is the physical length of the PCF. The operation principle is based on Mach-Zehnder interference with the core and cladding modes taken as the two interference arms, as shown in Fig. 1
Fig. 1 (a) Schematic illustration of the PCF-MZI, (b) cross sectional structure of the PCF, and (c) typical transmission spectrum of the PCF-MZI.
. According to Eq. (1), the transmission is periodic with respect to the frequency and is usually represented by a comb-filtering spectrum as depicted in Fig. 1(c). The spacing Δλ between adjacent constructive peaks (destructive valleys) can be described as:

Δλ=λ2(ncorenclading)L=2πλ(βcoreβcladding)L
(3)

We define a delay coefficient D corresponding to the relative time delay between the core mode and the cladding mode in a one-meter PCF. Thus, the relative delay Δt and the delay coefficient D are given by:

Δt=Lc/ncoreLc/nclading=λ2cΔλ
(4)
D=ΔtL=Δnc=λ2cLΔλ
(5)

Hence, the delay coefficient of the in-fiber PCF-MZI is solely determined by the effective index difference Δn between core-mode light and cladding-mode light, which is in turn governed by the splicing mismatch and the PCF structure.

Figure 1(a) schematically shows the operating principle of the in-fiber PCF-MZI. The cross sectional structure of the PCF used in this work is depicted in Fig. 1(b). The pure silica PCF has a 2.9-μm hole-to-hole spacing, a 1.69-μm hole diameter in the cladding, and a ~3.9-μm core diameter. The air-silica cladding of the PCF has six layers of air-holes with hexagonal distribution. A typical transmission spectrum is shown in Fig. 1(c). The plot shows a wavelength spacing Δλ of 1.29 nm and a relative time delay Δt of 6.2 ps when the PCF length is 20.4 cm. The transmission spectrum is measured using an erbium-doped fiber amplifier (EDFA) as an amplified spontaneous emission (ASE) light source. From the experimental result, a delay coefficient of 30.4 ps/m is obtained. The value is consistent with the experimental results plotted in Fig. 2
Fig. 2 Measured transmission spectra for PCF-MZIs with different PCF lengths: (a) 165.0 cm and (b) 82.3 cm.
showing about 50 and 25-ps relative delays (with 0.16 and 0.32-nm wavelength spacing) for two PCF-MZIs with 165 and 82.3-cm long PCFs, respectively. The delay coefficient of the in-fiber PCF-MZI is much larger than that of multimode fiber based MZI [6

6. Y. K. Lize, R. Gomma, and R. Kashyap, “Low-cost multimode fiber Mach Zehnder interferometer for differential phase demodulation,” v.6314, p.63140R.1–7, in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications XII, San Diego, USA, August (2006).

], birefringent fiber based loop mirror [7

7. C. W. Chow and H. K. Tsang, “Polarization-independent DPSK demodulation using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(6), 1313–1315 (2005). [CrossRef]

] and photonic bandgap fiber based DI [10

10. C. Peucheret, Y. Geng, B. Zsigri, T. T. Alkeskjold, T. P. Hansen, and P. Jeppesen, “Demodulation of DPSK signals up to 40 Gb/s using a highly birefringent photonic bandgap fiber,” IEEE Photon. Technol. Lett. 18(12), 1392–1394 (2006). [CrossRef]

], which possesses delay coefficients of 3.48 ps/m, 0.91 ps/m and 10 ps/m, respectively.

η(λ)=(1+ξ(λ)1ξ(λ))2
(6)

A large extinction ratio is obtained when the value of ξ(λ) is close to unity. In the in-fiber PCF-MZI, the cause of interference periodicity, i.e., the periodic spectral dependence of η(λ) and ξ(λ) in Eq. (6), is the continuous coupling of power between the core mode and the cladding mode along the PCF. This coupling-beating phenomenon is similar to that in a dual-core fiber [12

12. K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11(24), 3188–3195 (2003). [CrossRef] [PubMed]

] and can be characterized with a coupling length L0 that represents the length for a single full coupling process. It is worth noting that L0 is wavelength dependent and polarization sensitive. Due to the variation of L0 with wavelength, the power Icore(λ) and Icladding(λ) are wavelength dependent when the light signal reaches the output end of the PCF. In theory, the spectral period should be inversely proportional to the length of the PCF [12

12. K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11(24), 3188–3195 (2003). [CrossRef] [PubMed]

] which is in agreement with our experimental results. As shown in Fig. 2, decreasing the length of PCF from 165.0 to 82.3 cm leads to an increase of the spectral period of interference from to 6.3 to 13.1 nm.

Demodulation of DPSK signals

Considering the in-fiber PCF-MZI as an in-line delay interferometer (DI), it can be directly used for the demodulation of DPSK signals. We fabricate a PCF-MZI with about 300-cm PCF that introduces 91-ps relative delay. The delay is suitable for the demodulation of 10-Gb/s DPSK signals, which require a 100-ps delay for an ideal demodulation. This ~9-ps delay difference will lead to a narrowing of the demodulated signal pulse but will not significantly affect its quality [13

13. Y. K. Lizé, L. Christen, X. Wu, J. Y. Yang, S. Nuccio, T. Wu, A. E. Willner, and R. Kashyap, “Free spectral range optimization of return-to-zero differential phase shift keyed demodulation in the presence of chromatic dispersion,” Opt. Express 15(11), 6817–6822 (2007). [CrossRef] [PubMed]

]. The spectrum shown in Fig. 3
Fig. 3 Measured transmission spectrum of the 300-cm PCF-MZI
exhibits a maximum extinction ratio of 7.8 dB and a minimum extinction ratio of 1.1 dB (at around 1549.1 nm) for the interference transmission. The variation limits the PCF-MZI demodulator to operate only at periodic wavebands as the demodulation performance is degraded when the extinction ratio is small.

Since the amount of splicing mismatch affects the splitting ratio of the input power, one can adjust the mismatch during the splicing to obtain an optimal transmission spectrum and therefore realize a large extinction ratio at the desired working waveband. Alternatively, the interference extinction ratio can be made tunable through polarization adjustment in the setup. By adjusting the polarization controller (PC) before the demodulator, we have successfully realized DPSK demodulation over the whole waveband with respect to the transmission spectrum in Fig. 3.

Using the 300-cm PCF-MZI, we have realized error free demodulation of both RZ- and NRZ-DPSK signals. The measured results are shown in Fig. 4
Fig. 4 Measured spectra and eye diagrams of the demodulated 10-Gb/s RZ-DPSK signals at (a) 1547.094 and 1547.046 nm; (b) 1549.204 and 1549.155 nm; (c) 1551.318 and 1551.268 nm. The upper and lower plots show constructive and destructive interferences, respectively.
to Fig. 6
Fig. 6 Bit-error rate performance on the demodulation of 10 Gb/s RZ- and NRZ-DPSK signals.
. The 10 Gb/s RZ-DPSK signals, with 231-1 pseudo random binary sequence (PRBS), are generated at different wavelengths of 1547.094, 1549.204 and 1551.318 nm using a tunable laser and a phase modulator. After demodulation, clear and widely opened eye diagrams are obtained as shown in Fig. 4. It is worth mentioning that in Fig. 4(b), the demodulated eye diagrams at 1549.204 nm exhibit no degradation compared to those at 1547.094 and 1551.318 nm shown in Fig. 4(a) and (c), even though the interference extinction ratio at 1549.204 nm is only 1.1 dB and is much smaller than the values of 7.4 and 7.1 dB at the other two wavelengths. Results of the bit error rate (BER) measurement are shown in Fig. 6. The BER performances at these three wavelengths are similar and the receiver sensitivity is even slightly better at 1549.204 nm. By tuning the polarization to optimize the demodulation performance during the BER measurement, we observe that the required power for error-free demodulation deviates within only 1.5 dB over the whole wavelength range from 1547 to 1552 nm, which covers one period of the variation in interference extinction ratio. Similar demodulation performance has also been achieved and measured for NRZ-DPSK signals using the same PCF-MZI, as shown in Fig. 5
Fig. 5 Measured spectra and eye diagrams of the demodulated 10-Gb/s NRZ-DPSK signals at (a) 1547.101 and 1547.148 nm; (b) 1549.078 and 1549.121 nm (c) 1551.241 and 1551.190 nm. The upper and lower plots show constructive and destructive interferences, respectively.
and Fig. 6. These results indicate that the in-fiber PCF-MZI, as a DPSK demodulator, can operate over a wide band regardless of the variation of interference extinction ratio that occurs at a fixed polarization. Compared to demodulation with a typical conventional DI built with fiber couplers, we obtain a 1.1-dB power penalty using our PCF-MZI [8

8. J. Du, Y. Dai, G. K. P. Lei, W. Tong, and C. Shu, “Demodulation of DPSK signals using in-line Mach-Zehnder interferometer based on photonic crystal fibers,” p.FM6, in the 14th Opto-Electronics and Communications Conference, Hong Kong, July (2009).

].

In this work, the in-fiber PCF-MZI has only one output port which limits the demodulator for use in balanced detection. This difficulty can be solved by splicing a dual-core fiber at the output end and detecting the demodulated signals in the two cores, while increasing the complexity of the device. There is also a tradeoff issue between polarization insensitivity and wideband demodulation. Using the cladding collapse method for fabrication can significantly reduce the polarization sensitivity; however, the power coupling ratio will be wavelength dependent, thus limiting the wideband demodulation performance owing to the variation of the interference extinction ratio. By carefully controlling the collapse of cladding during fabrication, it is possible to tailor the transmission spectrum. Thus, wideband operation can still be optimized while maintaining reduced polarization sensitivity.

Conclusion

We have demonstrated a novel DPSK demodulator based on an in-fiber PCF-MZI fabricated by mismatch splicing of a PCF with SMFs at both ends. The interference property of the in-fiber PCF-MZI is investigated and the result indicates periodically varied interference extinction ratio caused by coupling-beating phenomenon between the cladding mode and the core mode. Error free demodulations of 10 Gb/s RZ- and NRZ-DPSK signals are achieved. Wideband operation of the demodulator can be anticipated as the BER measurement shows similar performance (<1.5 dB variation) at different wavelengths over one period of variation in the interference extinction ratio. Compared to other DPSK demodulators, the PCF-MZI presented in this work is an in-line all-fiber device, which offers advantages of simplicity, compactness, and potential cost reduction.

Acknowledgment

The PCF used in this work is provided by YOFC Ltd. This project is supported by the Research Grants Council of Hong Kong (Projects CUHK 415907 and 416808, and 416509).

References

1.

H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef] [PubMed]

2.

J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15(4), 1491–1496 (2007). [CrossRef] [PubMed]

3.

J. H. Lim, H. S. Jang, K. S. Lee, J. C. Kim, and B. H. Lee, “Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings,” Opt. Lett. 29(4), 346–348 (2004). [CrossRef] [PubMed]

4.

Y. Jung, S. Lee, B. H. Lee, and K. Oh, “Ultracompact in-line broadband Mach-Zehnder interferometer using a composite leaky hollow-optical-fiber waveguide,” Opt. Lett. 33(24), 2934–2936 (2008). [CrossRef] [PubMed]

5.

J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91(9), 091109 (2007). [CrossRef]

6.

Y. K. Lize, R. Gomma, and R. Kashyap, “Low-cost multimode fiber Mach Zehnder interferometer for differential phase demodulation,” v.6314, p.63140R.1–7, in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications XII, San Diego, USA, August (2006).

7.

C. W. Chow and H. K. Tsang, “Polarization-independent DPSK demodulation using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(6), 1313–1315 (2005). [CrossRef]

8.

J. Du, Y. Dai, G. K. P. Lei, W. Tong, and C. Shu, “Demodulation of DPSK signals using in-line Mach-Zehnder interferometer based on photonic crystal fibers,” p.FM6, in the 14th Opto-Electronics and Communications Conference, Hong Kong, July (2009).

9.

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005). [CrossRef]

10.

C. Peucheret, Y. Geng, B. Zsigri, T. T. Alkeskjold, T. P. Hansen, and P. Jeppesen, “Demodulation of DPSK signals up to 40 Gb/s using a highly birefringent photonic bandgap fiber,” IEEE Photon. Technol. Lett. 18(12), 1392–1394 (2006). [CrossRef]

11.

M. P. Fok and C. Shu, “Delay-asymmetric nonlinear loop mirror for DPSK demodulation,” Opt. Lett. 33(23), 2845–2847 (2008). [CrossRef] [PubMed]

12.

K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11(24), 3188–3195 (2003). [CrossRef] [PubMed]

13.

Y. K. Lizé, L. Christen, X. Wu, J. Y. Yang, S. Nuccio, T. Wu, A. E. Willner, and R. Kashyap, “Free spectral range optimization of return-to-zero differential phase shift keyed demodulation in the presence of chromatic dispersion,” Opt. Express 15(11), 6817–6822 (2007). [CrossRef] [PubMed]

OCIS Codes
(060.2400) Fiber optics and optical communications : Fiber properties
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 27, 2010
Revised Manuscript: March 5, 2010
Manuscript Accepted: March 6, 2010
Published: March 31, 2010

Citation
Jiangbing Du, Yongheng Dai, Gordon K. P. Lei, Weijun Tong, and Chester Shu, "Photonic crystal fiber based Mach-Zehnder interferometer for DPSK signal demodulation," Opt. Express 18, 7917-7922 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-7917


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References

  1. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef] [PubMed]
  2. J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15(4), 1491–1496 (2007). [CrossRef] [PubMed]
  3. J. H. Lim, H. S. Jang, K. S. Lee, J. C. Kim, and B. H. Lee, “Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings,” Opt. Lett. 29(4), 346–348 (2004). [CrossRef] [PubMed]
  4. Y. Jung, S. Lee, B. H. Lee, and K. Oh, “Ultracompact in-line broadband Mach-Zehnder interferometer using a composite leaky hollow-optical-fiber waveguide,” Opt. Lett. 33(24), 2934–2936 (2008). [CrossRef] [PubMed]
  5. J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91(9), 091109 (2007). [CrossRef]
  6. Y. K. Lize, R. Gomma, and R. Kashyap, “Low-cost multimode fiber Mach Zehnder interferometer for differential phase demodulation,” v.6314, p.63140R.1–7, in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications XII, San Diego, USA, August (2006).
  7. C. W. Chow and H. K. Tsang, “Polarization-independent DPSK demodulation using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(6), 1313–1315 (2005). [CrossRef]
  8. J. Du, Y. Dai, G. K. P. Lei, W. Tong, and C. Shu, “Demodulation of DPSK signals using in-line Mach-Zehnder interferometer based on photonic crystal fibers,” p.FM6, in the 14th Opto-Electronics and Communications Conference, Hong Kong, July (2009).
  9. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005). [CrossRef]
  10. C. Peucheret, Y. Geng, B. Zsigri, T. T. Alkeskjold, T. P. Hansen, and P. Jeppesen, “Demodulation of DPSK signals up to 40 Gb/s using a highly birefringent photonic bandgap fiber,” IEEE Photon. Technol. Lett. 18(12), 1392–1394 (2006). [CrossRef]
  11. M. P. Fok and C. Shu, “Delay-asymmetric nonlinear loop mirror for DPSK demodulation,” Opt. Lett. 33(23), 2845–2847 (2008). [CrossRef] [PubMed]
  12. K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11(24), 3188–3195 (2003). [CrossRef] [PubMed]
  13. Y. K. Lizé, L. Christen, X. Wu, J. Y. Yang, S. Nuccio, T. Wu, A. E. Willner, and R. Kashyap, “Free spectral range optimization of return-to-zero differential phase shift keyed demodulation in the presence of chromatic dispersion,” Opt. Express 15(11), 6817–6822 (2007). [CrossRef] [PubMed]

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