Abstract

A free-space optical delay interferometer (DI) featuring a continuously tunable time delay, polarization insensitive operation with high extinction ratios and accurate phase and time delay monitoring scheme is reported. The polarization dependence is actively mitigated by adjusting a birefringent liquid-crystal device. The DI has been tested for reception of D(m)PSK signals.

© 2011 OSA

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  1. R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, J. Hughes, P. A. Jerram, and N. J. Parsons, “10 Gb/s optical differential quadrature phase shift key (DQPSK) transmission using GaAs/AlGaAs integration,” in Proc. Optical Fiber Communication Conference (OFC'02), (Anaheim, CA, USA, 2002), Postdeadline Paper FD6.
  2. A. H. 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. Movassaghi, 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 Proc. Optical Fiber Communication Conference (OFC'02), (Anaheim, CA, USA, 2002), Postdeadline Paper PD FC2.
  3. N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proc. of European Conference on Optical Communication (ECOC’06), (Cannes, France, 2006), paper Th444.
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    [CrossRef] [PubMed]
  5. J. Li, K. Worms, P. Vorreau, D. Hillerkuss, A. Ludwig, R. Maestle, S. Schuele, U. Hollenbach, J. Mohr, W. Freude, and J. Leuthold, “Optical vector signal analyzer based on differential direct detection,” in Proc. of IEEE Photonics Society(LEOS)2009, (Belek-Antalya, Turkey, 2009), Paper TuA4.
  6. 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]
  7. S. Sygletos, R. Bonk, T. Vallaitis, A. Marculescu, P. Vorreau, J. Li, R. Brenot, F. Lelarge, G.-H. Duan, W. Freude, and J. Leuthold, “Filter assisted wavelength conversion with quantum-dot SOAs,” J. Lightwave Technol. 28(6), 882–897 (2010).
    [CrossRef]
  8. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9Issue 9), 9324–9340 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. B. Mikkelsen, C. Rasmussen, P. Mamyshev, and F. Liu, “Partial DPSK with excellent filter tolerance and OSNR sensitivity,” Electron. Lett. 42(23), 1363–1364 (2006).
    [CrossRef]
  11. Y. Nasu, K. Hattori, T. Saida, Y. Hashizume, and Y. Sakamaki, “Silica-based adaptive-delay DPSK demodulator with a cascaded Mach-Zehnder interferometer configuration,” in Proc. European Conference on Optical Communication (ECOC),2010, (Torino, Italy, 2010) paper We.8.E.5.
  12. L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
    [CrossRef]
  13. H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
    [CrossRef]
  14. H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
    [CrossRef]
  15. Z. Tao, A. Isomura, T. Hoshida, and J. C. Rasmussen, “Dither-free, accurate, and robust phase offset monitor and control method for optical DQPSK demodulator” in Proc. European Conference on Optical Communication (ECOC),2007, (Berlin, Germany, 2007) paper Mo.3.D.5.
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    [CrossRef]
  17. A. Cabral and J. Rebordao, ““Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).
  18. S. Schüle, U. Hollenbach, J. Mohr, J. Li, P. Vorreau, A. Efremov, J. Leuthold, and S. Schonhardt, “Modular integration of microactuators and micro-optical benches,” in Proc. of SPIE Conference on Micro-Optics, (Strasbourg, France, April 2008) vol. 6992, pp. 699202–699202–12 (2008).
  19. J. Li, K. Worms, D. Hillerkuss, B. Richter, R. Maestle, W. Freude, and J. Leuthold, “Tunable free space optical delay interferometer for demodulation of differential phase shift keying signals,” in Proc. Optical Fiber Communication Conference (OFC 2010), (San Diego, Ca, USA,2010), paper JWA24.
  20. D. O. Caplan, M. L. Stevens, and J. J. Carney, “High-sensitivity multi-channel single-interferometer DPSK receiver,” Opt. Express 14(23), 10984–10989 (2006).
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    [CrossRef] [PubMed]

2010 (2)

2008 (3)

X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express 16(2), 792–803 (2008).
[CrossRef] [PubMed]

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

2007 (2)

A. Cabral and J. Rebordao, ““Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).

H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
[CrossRef]

2006 (3)

2001 (1)

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]

1998 (1)

L. Rovati, U. Minoni, M. Bonardi, and F. Docchio, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29(3), 121–127 (1998).
[CrossRef]

1995 (1)

Behringer, R.

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]

Ben Ezra, S.

Bonardi, M.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchio, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29(3), 121–127 (1998).
[CrossRef]

Bonk, R.

Bosco, G.

Brenot, R.

Cabral, A.

A. Cabral and J. Rebordao, ““Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).

Caplan, D. O.

Carney, J. J.

Chandrasekhar, S.

Christen, L.

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

Docchio, F.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchio, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29(3), 121–127 (1998).
[CrossRef]

Dreyer, K.

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]

Duan, G.-H.

Frejlich, J.

Freschi, A. A.

Freude, W.

Hillerkuss, D.

Itoh, T.

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

Joyner, C. H.

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]

Kawakami, H.

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
[CrossRef]

Lelarge, F.

Leuthold, J.

Leven, A.

Li, J.

Liu, F.

B. Mikkelsen, C. Rasmussen, P. Mamyshev, and F. Liu, “Partial DPSK with excellent filter tolerance and OSNR sensitivity,” Electron. Lett. 42(23), 1363–1364 (2006).
[CrossRef]

Liu, X.

Lize, Y. K.

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

Mamyshev, P.

B. Mikkelsen, C. Rasmussen, P. Mamyshev, and F. Liu, “Partial DPSK with excellent filter tolerance and OSNR sensitivity,” Electron. Lett. 42(23), 1363–1364 (2006).
[CrossRef]

Marculescu, A.

Mikkelsen, B.

B. Mikkelsen, C. Rasmussen, P. Mamyshev, and F. Liu, “Partial DPSK with excellent filter tolerance and OSNR sensitivity,” Electron. Lett. 42(23), 1363–1364 (2006).
[CrossRef]

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]

Miller, B. I.

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]

Minoni, U.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchio, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29(3), 121–127 (1998).
[CrossRef]

Miyamoto, Y.

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
[CrossRef]

Narkiss, N.

Nuccio, S.

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

Oguma, M.

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
[CrossRef]

Paraschis, L.

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

Pleumeekers, J. L.

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]

Poggiolini, P.

Rasmussen, C.

B. Mikkelsen, C. Rasmussen, P. Mamyshev, and F. Liu, “Partial DPSK with excellent filter tolerance and OSNR sensitivity,” Electron. Lett. 42(23), 1363–1364 (2006).
[CrossRef]

Raybon, G.

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]

Rebordao, J.

A. Cabral and J. Rebordao, ““Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).

Rovati, L.

L. Rovati, U. Minoni, M. Bonardi, and F. Docchio, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29(3), 121–127 (1998).
[CrossRef]

Sigurdsson, G.

Stevens, M. L.

Sygletos, S.

Teschke, M.

Vallaitis, T.

Vorreau, P.

Willner, A. E.

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

Winter, M.

Worms, K.

Yoshida, E.

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
[CrossRef]

Electron. Lett. (3)

B. Mikkelsen, C. Rasmussen, P. Mamyshev, and F. Liu, “Partial DPSK with excellent filter tolerance and OSNR sensitivity,” Electron. Lett. 42(23), 1363–1364 (2006).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, and M. Oguma, “Analysing the penalty induced by PD of MZI in DQPSK receiver using novel measuring technique,” Electron. Lett. 43(2), 121–122 (2007).
[CrossRef]

H. Kawakami, E. Yoshida, Y. Miyamoto, M. Oguma, and T. Itoh, “Simple phase offset monitoring technique for 43 Gbit/s optical DQPSK receiver,” Electron. Lett. 44(6), 437–438 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. Christen, Y. K. Lize, S. Nuccio, L. Paraschis, and A. E. Willner, “Experimental demonstration of reduced complexity 43-Gb/s RZ-DQPSK rate-tunable receiver,” IEEE Photon. Technol. Lett. 20(13), 1166–1168 (2008).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. (1)

L. Rovati, U. Minoni, M. Bonardi, and F. Docchio, “Absolute distance measurement using comb-spectrum interferometry,” J. Opt. 29(3), 121–127 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

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]

Other (9)

Y. Nasu, K. Hattori, T. Saida, Y. Hashizume, and Y. Sakamaki, “Silica-based adaptive-delay DPSK demodulator with a cascaded Mach-Zehnder interferometer configuration,” in Proc. European Conference on Optical Communication (ECOC),2010, (Torino, Italy, 2010) paper We.8.E.5.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, J. Hughes, P. A. Jerram, and N. J. Parsons, “10 Gb/s optical differential quadrature phase shift key (DQPSK) transmission using GaAs/AlGaAs integration,” in Proc. Optical Fiber Communication Conference (OFC'02), (Anaheim, CA, USA, 2002), Postdeadline Paper FD6.

A. H. 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. Movassaghi, 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 Proc. Optical Fiber Communication Conference (OFC'02), (Anaheim, CA, USA, 2002), Postdeadline Paper PD FC2.

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proc. of European Conference on Optical Communication (ECOC’06), (Cannes, France, 2006), paper Th444.

J. Li, K. Worms, P. Vorreau, D. Hillerkuss, A. Ludwig, R. Maestle, S. Schuele, U. Hollenbach, J. Mohr, W. Freude, and J. Leuthold, “Optical vector signal analyzer based on differential direct detection,” in Proc. of IEEE Photonics Society(LEOS)2009, (Belek-Antalya, Turkey, 2009), Paper TuA4.

Z. Tao, A. Isomura, T. Hoshida, and J. C. Rasmussen, “Dither-free, accurate, and robust phase offset monitor and control method for optical DQPSK demodulator” in Proc. European Conference on Optical Communication (ECOC),2007, (Berlin, Germany, 2007) paper Mo.3.D.5.

A. Cabral and J. Rebordao, ““Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).

S. Schüle, U. Hollenbach, J. Mohr, J. Li, P. Vorreau, A. Efremov, J. Leuthold, and S. Schonhardt, “Modular integration of microactuators and micro-optical benches,” in Proc. of SPIE Conference on Micro-Optics, (Strasbourg, France, April 2008) vol. 6992, pp. 699202–699202–12 (2008).

J. Li, K. Worms, D. Hillerkuss, B. Richter, R. Maestle, W. Freude, and J. Leuthold, “Tunable free space optical delay interferometer for demodulation of differential phase shift keying signals,” in Proc. Optical Fiber Communication Conference (OFC 2010), (San Diego, Ca, USA,2010), paper JWA24.

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Figures (11)

Fig. 1
Fig. 1

Schematic of an optical delay interferometer (DI). Inputs (E in, 1, and E in,2) are split by a coupler (SI ) into two paths with A and B as the respective power loss factors. A time delay ΔT is introduced between the two paths. The signals interfere on the other coupler (SII ) where two outputs (E out, 1 and E out,2) are generated.

Fig. 2
Fig. 2

Transfer function of the DI for different upper-arm power losses A = 1 and A = 0.64. The case A = 1 denotes an ideal DI (blue). The case A = 0.64 denotes an imbalanced DI with excess losses in the delayed arm (red). The three plots show (a) the power transfer functions |H 1,2 (f)|2, (b) the phase response Φ1, 2(f) and (c) the group delay τ 1, 2 (f) for the constructive output port (dashed lines) and the destructive port (straight lines), respectively.

Fig. 3
Fig. 3

Practical implementation of DI (a) Schematic of the Mach-Zehnder-DI with two non-polarizing beam splitters (BS) combined in one unit, and one reflector. (b) Schematic of the Michelson DI with single non-polarizing BS and two reflectors. A liquid crystal compensates a polarization dependent frequency shift. (c) Photograph of a prototype of the Michelson DI.

Fig. 4
Fig. 4

Spectral response for vertical (blue) and horizontal (red) polarizations. (a) Large PDFS, (b) LC is used to undo birefringence, (c) PDFS of DI for different voltages applied onto the LC (the precision of the measured offset phase is limited by the resolution of the measurement equipment). The plots show the output 2 (dashed lines) and output 1 (straight lines).

Fig. 5
Fig. 5

Measured average squared magnitude of the transfer function for all possible polarizations (blue), of PDL (green), and of DGD (green) at DI output 1(solid line) and 2 (dashed line); FSR ≈42.7 GHz. For minimized PDFS: (a) average loss and PDL. (b) DGD versus wavelength. For large PDFS: (c) average squared magnitude of the transfer function and PDL. (d) DGD versus wavelength.

Fig. 6
Fig. 6

, Schematic of control circuit (a) Time delay and phase control setup of DI, (b) ideal power transfer function between DI “Input” and “Output 2”

Fig. 7
Fig. 7

Average spectral responses (blue) of the two outputs (solid line for output 1 and dashed line for output 2) over all possible polarizations and PDL (green) at FSR = 10 GHz (a), 28 GHz (b) and 100 GHz (c).

Fig. 8
Fig. 8

Average spectral responses (blue) of the two outputs (solid line for output 1 and dashed line for output 2) over all possible polarizations and PDL at wavelength 1525 nm – 1530 nm (a), 1545 nm – 1555 nm (b), and 1570 nm – 1575 nm (c) with FSR = 42.7 GHz

Fig. 9
Fig. 9

, The plots (a) the accuracy for setting the absolute time delay (blue curve) when setting the FSR to particular value (red curve) for a measurement cycle between 800 GHz and 20 GHz, (b) the accuracy for setting a particular two delays with FSR = 40 GHz —•— red, FSR = 80 GHz —•— blue for a measurement cycle from 0 to 360 degrees and (c) absolute deviation from set value over time when using the stabilization setup.

Fig. 10
Fig. 10

Measurement results of the proposed DI at various bit rates and comparison with a commercial DI (a) eye diagrams of NRZ-DQPSK I channel at 11.7 GBd, 28 GBd, and 42.7 GBd, (b) BER versus received power at 28 GBd (▲Δ green, for I and Q channels at polarization 1, blue for I and Q channels at polarization 2), and 42.7 GBd (■□ black for I and Q channels at polarization 1, ●○, red for I and Q channels at polarization 2)for orthogonal polarizations of the tunable DI and single polarization of the typical DI (◄ magenta for I and Q channels), and (c) BER versus received power at 42.7 GBd at different wavelengths (■□ black for I and Q channels at 1545.56 nm, ●○ red at 1550.12 nm, and ▲Δ green at 1560.61 nm)

Fig. 11
Fig. 11

, Schematics of polarization diversity self-coherent receivers (a) conventional configuration with 4 DIs, (b) I and Q DIs combined configuration with 2 DIs, (c) free-space micro-optical implementation where all elements are folded into 1 DI only.

Equations (9)

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[ E out,2 E out,1 ] = ( S I I T S I ) * [ E in,2 E in,1 ] ,         where ​       S I = [ a ( 1 s I ) j a s I exp ( j δ θ 12 I ) j a s I exp ( j δ θ 21 I ) a ( 1 s I ) ] , T = [ A δ ( t Δ T ) ​ ​ ​ ​ ​ 0 0 ​ ​ ​ ​ ​ B δ ( t ) ] ,         and     S I I = [ b ( 1 s I I ) j b s I I exp ( j δ θ 12 I I ) j b s I I exp ( j δ θ 21 I I ) b ( 1 s I I ) ] .
E out,1 ( t ) = [ A a b s I s I I δ ( τ Δ T ) exp [ j ( δ θ 21 I I + δ θ 12 I ) ] + B a b ( 1 s I ) ( 1 s I I ) δ ( τ ) ] E in,1 ( t τ ) d τ , E out,2 ( t ) = j [ A a b s I ( 1 s I I ) δ ( τ Δ T ) exp ( j δ θ 12 I ) + B a b s I I ( 1 s I ) δ ( τ ) exp ( j δ θ 12 I I ) ] E in,1 ( t τ ) d τ .
| H 1 ( f ) | 2 B a b [ B a b s I + B a b s I I ( A + B ) a b s I s I I + 2 S cos ( 2 π f Δ T δ θ 21 I I δ θ 12 I ) ] , | H 2 ( f ) | 2 B a b s I I + A b s I ( A + B ) a b s I s I I + 2 S cos ( 2 π f Δ T + δ θ 12 I I δ θ 12 I ) , where S = a b A B s I s I I ( 1 s I ) ( 1 s I I ) .
Φ 1 ( f ) = tan 1 [ A a b s I s I I sin ( 2 π f Δ T δ θ 21 I I δ θ 12 I ) B a b ( 1 s I ) ( 1 s I I ) A a b s I s I I cos ( 2 π f Δ T δ θ 21 I I δ θ 12 I ) ] , Φ 2 ( f ) = tan 1 [ A a b s I ( 1 s I I ) cos ( 2 π f Δ T δ θ 12 I ) + B a b s I I ( 1 s I ) cos ( δ θ 12 I I ) A a b s I ( 1 s I I ) sin ( 2 π f Δ T δ θ 12 I ) B a b s I I ( 1 s I ) sin ( δ θ 12 I I ) ] .
τ 1 ( f ) = Δ T A a b s I s I I S cos ( 2 π f Δ T δ θ 21 I I δ θ 12 I )   | H 1 ( f ) | 2 , τ 2 ( f ) = Δ T A a b s I [ A a b s I s I I S cos ( 2 π f Δ T + δ θ 12 I I δ θ 12 I ) ] | H 2 ( f ) | 2 .
A , B , a , b = 1 , s I , s I I = 1 2 ,   and   δ θ 12 I , δ θ 21 I , δ θ 12 I I , δ θ 21 I I = 0 .
PDL = | 10 log 10 ( | H pol  v ( f ) | 2 | H pol  h ( f ) | 2 ) | , DGD = | τ pol  v ( f ) τ pol  h ( f ) | .
| δ T | = m max + m min 2 f p .
I a c ( t ) J 1 ( 2 π δ ν d Δ T ) sin ( 2 π Δ f p Δ T ) sin ( 2 π ν FM t )           + J 2 ( 2 π δ ν d Δ T ) cos ( 2 π Δ f p Δ T ) cos ( ν FM t ) + ...

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