Abstract

Orthogonal time division multiplexing (OrthTDM) interleaves sinc-shaped pulses to form a high baud-rate signal, with a rectangular spectrum suitable for multiplexing into a Nyquist WDM (N-WDM)-like signal. The problem with generating sinc-shaped pulses is that they theoretically have infinite durations, and even if time bounded for practical implementation, they still require a filter with a long impulse response, hence a large physical size. Previously a method of creating chirped-orthogonal frequency division multiplexing (OFDM) pulses with a chirped arrayed waveguide (AWG) filter, then converting them into interleaved quasi-sinc pulses using dispersive fiber (DF), has been proposed. This produces a signal with a wider spectrum than the equivalent N-WDM signal. We show that a modification to the scheme enables the spectral extent to be reduced for the same data rate. We then analyse the key factors in designing an OrthTDM transmitter, and relate these to the performance of a N-WDM system. We show that the modified transmitter reduces the required guard band between the N-WDM channels. We also simulate a simpler scheme using an unchirped finite-impulse response filter of similar size, which directly creates truncated-sinc pulses without needing a DF. This gives better system performance than either chirped scheme.

© 2015 Optical Society of America

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    [Crossref]
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2015 (1)

2014 (2)

2013 (1)

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (1)

2010 (1)

2009 (1)

2007 (1)

1992 (1)

M. C. Farries, C. M. Ragdale, and D. C. J. Reid, “Broadband chirped fibre Bragg filters for pump rejection and recycling in erbium doped fibre amplifiers,” Electron. Lett. 28(5), 487–489 (1992).
[Crossref]

1987 (1)

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

1960 (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960).
[Crossref]

1945 (1)

Albersheim, W. J.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960).
[Crossref]

Alem, M.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Alferness, R. C.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Amin Shoaie, M.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Armstrong, J.

Beutler, H. G.

Bosco, G.

Brès, C.-S.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Buhl, L. L.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Carena, A.

Cincotti, G.

Corcoran, B.

Curri, V.

Darlington, S.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960).
[Crossref]

Du, L. B.

Eisenstein, G.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Farries, M. C.

M. C. Farries, C. M. Ragdale, and D. C. J. Reid, “Broadband chirped fibre Bragg filters for pump rejection and recycling in erbium doped fibre amplifiers,” Electron. Lett. 28(5), 487–489 (1992).
[Crossref]

Forghieri, F.

Guan, P.

Hirooka, T.

Kasper, B. L.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Klauder, J. R.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960).
[Crossref]

Koren, U.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Korotky, S. K.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Kumar, S.

Lowery, A. J.

Nakazawa, M.

Poggiolini, P.

Price, A. C.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960).
[Crossref]

Ragdale, C. M.

M. C. Farries, C. M. Ragdale, and D. C. J. Reid, “Broadband chirped fibre Bragg filters for pump rejection and recycling in erbium doped fibre amplifiers,” Electron. Lett. 28(5), 487–489 (1992).
[Crossref]

Raybon, G.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Reid, D. C. J.

M. C. Farries, C. M. Ragdale, and D. C. J. Reid, “Broadband chirped fibre Bragg filters for pump rejection and recycling in erbium doped fibre amplifiers,” Electron. Lett. 28(5), 487–489 (1992).
[Crossref]

Ruan, P.

Schneider, T.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Shimizu, S.

Soto, M. A.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Thévenaz, L.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Tucker, R. S.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Vedadi, A.

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Veselka, J. J.

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

Viterbo, E.

Wada, N.

Yang, D.

Yoshida, M.

Zhu, C.

Bell Syst. Tech. J. (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960).
[Crossref]

Electron. Lett. (2)

R. S. Tucker, G. Eisenstein, S. K. Korotky, U. Koren, G. Raybon, J. J. Veselka, L. L. Buhl, B. L. Kasper, and R. C. Alferness, “Optical time-division multiplexing and demultiplexing in a multigigabit/second fibre transmission system,” Electron. Lett. 23(5), 208–209 (1987).
[Crossref]

M. C. Farries, C. M. Ragdale, and D. C. J. Reid, “Broadband chirped fibre Bragg filters for pump rejection and recycling in erbium doped fibre amplifiers,” Electron. Lett. 28(5), 487–489 (1992).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

M. A. Soto, M. Alem, M. Amin Shoaie, A. Vedadi, C.-S. Brès, L. Thévenaz, and T. Schneider, “Optical sinc-shaped Nyquist pulses of exceptional quality,” Nat. Commun. 4, 2898 (2013).
[Crossref] [PubMed]

Opt. Express (5)

Optica (1)

Other (4)

G. Cincotti, S. Shimizu, T. Murakawa, T. Kodama, K. Hattori, M. Okuno, S. Mino, A. Himeno, T. Nagashima, M. Hasegawa, N. Wada, H. Uenohara, and T. Konishi, “Flexible power-efficient Nyquist-OTDM transmitter, using a WSS and time-lens effect,” in Optical Fiber Communication Conference (Optical Society of America, Los Angeles, California, 2015), paper W3C.5.
[Crossref]

A. J. Lowery and P. C. R. Gurney, “270-km 10 Gbit/s WDM dispersion compensation using a chirped AWGM,” in Optical Fiber Communication Conference (OFC), (OSA, 1999), paper FD5–1.
[Crossref]

T. Murakawa, G. Cincotti, S. Shimizu, T. Nagashima, M. Hasegawa, K. Hattori, M. Okuno, S. Mino, A. Himeno, N. Wada, H. Uenohara, and T. Konishi, “Fractional OFDM based transmitter and receiver for time/frequency multiplexing in gridless, elastic networks,” in Optical Fiber Communication Conference (Optical Society of America, Los Angeles, California, 2015), paper W3C.1.
[Crossref]

J. W. Goodman, Introduction to Fourier optics, 3rd ed (Roberts and Company, 2005).

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Figures (11)

Fig. 1
Fig. 1

(Left) Block diagrams of three methods that use all-optical pulse shaping to generate one wavelength channel of time-multiplexed quasi-sinc pulses. (Right) Associated spectra (blue) with neighboring WDM channels (green, red) (* means convolution).

Fig. 2
Fig. 2

Cincotti’s method of creating an OrthTDM signal using chirped OFDM transmitter followed by a DF [5]. The signal processing equivalent to the arrayed grating waveguide device is at the bottom of the figure, and also shows the full arrangement of the mode-locked laser (MLL), optical modulators (Mod) and DF.

Fig. 3
Fig. 3

Alternative scheme for generating OrthTDM, but with a narrower output spectrum than that of Fig. 2. The AWGR is fed with optically time-division multiplexed signal pulses. Mod is a modulator, typically a complex (I,Q) modulator for QPSK and QAM.

Fig. 4
Fig. 4

Generation of one quasi-sinc pulse using a chirped finite-impulse response (FIR) filter followed by a DF. The output of the FIR is the convolution (*) of the MLL pulse with the impulse response of the filter. Because the FIR imposes a frequency chirp upon the MLL pulse, the DF can compress the pulse.

Fig. 5
Fig. 5

Effect of the shape factor, S, on the FIR filter’s spectrum when the bandwidth B = 160 GHz. The solid lines are from Eq. (1). The thick magenta/cyan dashed lines are from a MATLAB calculation of the FT of a chirped rectangular pulse.

Fig. 6
Fig. 6

Simulated system for generating quasi-Nyquist WDM using FIR filters and a DF. (DSP: digital signal processor).

Fig. 7
Fig. 7

Comparison of the Q factors for S = 10, 40 for QPSK and 16-QAM modulation (TMLL = 100 ps). The solid lines are for QPSK modulation. The dashed lines are for 16-QAM modulation. The red and black lines are for S = 40 and S = 10, respectively. The green line is for Cincotti’s system using a chirped AWGR as in Fig. 1(a).

Fig. 8
Fig. 8

Required shape factor to support QPSK and 16-QAM versus guard band ratio.

Fig. 9
Fig. 9

Generation of OrthTDM (or one N-WDM channel) using an unchirped FIR filter and no DF.

Fig. 10
Fig. 10

(a) Comparison of the quasi-sinc pulse generated by a chirped FIR and Cincotti’s chirped AWGR with a DF (VPItransmissionMaker simulation with S = 10, TMLL = 100 ps, ∆T = 6.25 ps), truncated-sinc pulse generated by a truncated-sinc FIR (VPItransmissionMaker) and ideal sinc pulse simulated in MATLAB. (b) Comparison of the Q factors for QPSK systems using the three different transmitters in single-channel systems.

Fig. 11
Fig. 11

(a) Comparison of the Q factors for QPSK systems using three different transmitters. (b) The Q factors for three WDM channels with respect to guard band ratio using truncated-sinc FIR of Fig. 1c, chirped FIR of Fig. 1b and unmodified chirped systems of Fig. 1a (OSNR = 20 dB).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

F(f)= 1 4C exp( j( π 4 + π ( f A f) 2 C ) )× ( erf( π 2C f B f 2 +j 2π C f B f 2 )erf( 2π C f A f 2 +j 2π C f A f 2 ) )
M= T MLL /ΔT.
FSR= 1 Δt =k.B= k ΔT
N=1+ T chirp Δt =1+k. T chirp ΔT .
θ i =K ( i N+1 2 ) 2
K=Cπ ( T chirp N ) 2
T group =D.L.Δλ
D.L= T chirp .ΔT. f 0 2 c
h(t)=sinc( t T MLL /2 ΔT ). rect T MLL ( t T MLL 2 )
γ out,i = 1 A ( sinc( ( (i1)Δt T MLL 2 )/ΔT ) ) 2 1iN

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