Abstract

We present and demonstrate an all-fiber scheme of polarization temporal differentiation (PTD) based on polarization coupling and filtering, which performs well in high-speed optical differentiation, pulse multiplication, and femtosecond-pulse reshaping. Experimental results of the first-order differentiation show the error is 0.1 with an efficiency of 12% for optical signals at 40Gbits/s, while both error and efficiency are proportional to the square of the time delay, which agrees well with the theoretical analysis. By PTD-based two-stage pulse multiplication of a 20GHz optical clock, we obtain an 80GHz picosecond-pulse train with a full width at half maximum of 6.1ps. We further reveal its potential in femtosecond-pulse reshaping, while we retrieve a distorted 250fs original pulse by using a two-stage PTD module. Because of its flexible structure, multifunctionality, and easy integration, the PTD scheme is desirable for photonic signal processing.

© 2011 Optical Society of America

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  1. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
    [CrossRef]
  2. M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
    [CrossRef] [PubMed]
  3. V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
    [CrossRef] [PubMed]
  4. A. Hache and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089–4091(2000).
    [CrossRef]
  5. O. Wada, “Femtosecond all-optical devices for ultrafast communication and signal processing,” New J. Phys. 6, 183 (2004).
    [CrossRef]
  6. J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2, 359–386 (2010).
    [CrossRef]
  7. Y. Park, R. Slavik, and J. Azaa, “Ultrafast all-optical differentiators for generation of orthogonal (sub-) picosecond Hermite–Gaussian waveforms,” in Optical Fiber Communication Conference (OFC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThI2.
  8. Z. Li and C. Wu, “All-optical differentiator and high-speed pulse generation based on cross-polarization modulation in a semiconductor optical amplifier,” Opt. Lett. 34, 830–832(2009).
    [CrossRef] [PubMed]
  9. N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
    [CrossRef]
  10. M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30, 2700–2702 (2005).
    [CrossRef] [PubMed]
  11. J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “All-optical differentiator based on cross-gain modulation in semiconductor optical amplifier,” Opt. Lett. 32, 3029–2031 (2007).
    [CrossRef] [PubMed]
  12. F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, “Compact optical temporal differentiator based on silicon microring resonator,” Opt. Express 16, 15880–15886 (2008).
    [CrossRef] [PubMed]
  13. M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
    [CrossRef]
  14. Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett. 32, 710–712 (2007).
    [CrossRef] [PubMed]
  15. K. Sala, G. Kenney-Wallace, and G. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. 16, 990–996 (1980).
    [CrossRef]

2011

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
[CrossRef]

2010

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2, 359–386 (2010).
[CrossRef]

2009

Z. Li and C. Wu, “All-optical differentiator and high-speed pulse generation based on cross-polarization modulation in a semiconductor optical amplifier,” Opt. Lett. 34, 830–832(2009).
[CrossRef] [PubMed]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

2008

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, “Compact optical temporal differentiator based on silicon microring resonator,” Opt. Express 16, 15880–15886 (2008).
[CrossRef] [PubMed]

2007

2005

2004

O. Wada, “Femtosecond all-optical devices for ultrafast communication and signal processing,” New J. Phys. 6, 183 (2004).
[CrossRef]

N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
[CrossRef]

V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

2000

A. Hache and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089–4091(2000).
[CrossRef]

1980

K. Sala, G. Kenney-Wallace, and G. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. 16, 990–996 (1980).
[CrossRef]

Albert, J.

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
[CrossRef]

Almeida, V.

V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Azaa, J.

Y. Park, R. Slavik, and J. Azaa, “Ultrafast all-optical differentiators for generation of orthogonal (sub-) picosecond Hermite–Gaussian waveforms,” in Optical Fiber Communication Conference (OFC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThI2.

Azaña, J.

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Barrios, C.

V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Bourgeois, M.

A. Hache and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089–4091(2000).
[CrossRef]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Dong, J.

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Foster, M.

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Gaeta, A.

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Geraghty, D.

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Hache, A.

A. Hache and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089–4091(2000).
[CrossRef]

Hall, G.

K. Sala, G. Kenney-Wallace, and G. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. 16, 990–996 (1980).
[CrossRef]

Huang, D.

Kam, C.

N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
[CrossRef]

Kenney-Wallace, G.

K. Sala, G. Kenney-Wallace, and G. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. 16, 990–996 (1980).
[CrossRef]

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Kulishov, M.

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Li, M.

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
[CrossRef]

Li, Z.

Lipson, M.

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Liu, D.

Liu, F.

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Ngo, N.

N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
[CrossRef]

Panepucci, R.

V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

Park, Y.

Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett. 32, 710–712 (2007).
[CrossRef] [PubMed]

Y. Park, R. Slavik, and J. Azaa, “Ultrafast all-optical differentiators for generation of orthogonal (sub-) picosecond Hermite–Gaussian waveforms,” in Optical Fiber Communication Conference (OFC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThI2.

Qiang, L.

Qiu, M.

Sala, K.

K. Sala, G. Kenney-Wallace, and G. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. 16, 990–996 (1980).
[CrossRef]

Salem, R.

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Shao, L.

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
[CrossRef]

Slavik, R.

Y. Park, R. Slavik, and J. Azaa, “Ultrafast all-optical differentiators for generation of orthogonal (sub-) picosecond Hermite–Gaussian waveforms,” in Optical Fiber Communication Conference (OFC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThI2.

Slavík, R.

Su, Y.

Tjin, S.

N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
[CrossRef]

Turner-Foster, A.

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Wada, O.

O. Wada, “Femtosecond all-optical devices for ultrafast communication and signal processing,” New J. Phys. 6, 183 (2004).
[CrossRef]

Wang, T.

Wu, C.

Xu, J.

Yao, J.

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
[CrossRef]

Ye, T.

Yu, S.

N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
[CrossRef]

Zhang, X.

Zhang, Z.

Appl. Phys. Lett.

A. Hache and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089–4091(2000).
[CrossRef]

IEEE J. Quantum Electron.

K. Sala, G. Kenney-Wallace, and G. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. 16, 990–996 (1980).
[CrossRef]

IEEE Photon. J.

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2, 359–386 (2010).
[CrossRef]

Nat. Photon.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Nature

M. Foster, R. Salem, D. Geraghty, A. Turner-Foster, M. Lipson, and A. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef] [PubMed]

V. Almeida, C. Barrios, R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef] [PubMed]

New J. Phys.

O. Wada, “Femtosecond all-optical devices for ultrafast communication and signal processing,” New J. Phys. 6, 183 (2004).
[CrossRef]

Opt. Commun.

N. Ngo, S. Yu, S. Tjin, and C. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Photon. Technol. Lett.

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” Photon. Technol. Lett. 23, 251–253 (2011).
[CrossRef]

Other

Y. Park, R. Slavik, and J. Azaa, “Ultrafast all-optical differentiators for generation of orthogonal (sub-) picosecond Hermite–Gaussian waveforms,” in Optical Fiber Communication Conference (OFC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThI2.

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Figures (6)

Fig. 1
Fig. 1

Principle diagram of the nth-order PTD module: PC, polarization controller; PBS, polarization beam splitter; PMF, polarization-maintaining fiber; PBC, polarization beam coupler; PF, polarization filter.

Fig. 2
Fig. 2

Normalized polarization differentiation d p ( t ) and calculated differentiation d c ( t ) of 40 Gbits / s optical signal pulses: (a)  1 bit , (b)  4 bits . (c) Magnitude and phase of the spectral transfer function for the PTD module with a time delay of 8 ps (lines, calculated; marks, experimental data).

Fig. 3
Fig. 3

(a) Experimental setup of PTD for the data rate at 40 Gbits / s , (b)  40 Gbits / s super-Gaussian input optical signal with fixed data “1010 0011 1100 1000 1011,” (c) measured and (d) calculated differentiation of optical signal in (b).

Fig. 4
Fig. 4

Differential errors and efficiencies for different time delays with related diagrams of the input and outputs.

Fig. 5
Fig. 5

(a) Magnitude and phase of the spectral transfer functions for the first-stage PTD (1st-Stage) and the second-stage PTD (2nd-Stage). (b), (c) Optical spectrums of pulse trains after the first- and second-stage differentiation, respectively. (d) RF spectrum and waveforms (inset) of the pulse train after the first-stage differentiator. (e) RF spectrum and autocorrelation trace (inset) of the pulse train after the second-stage differentiator.

Fig. 6
Fig. 6

(a) Principle and experimental setup of femtosecond-pulse reshaping. (b)–(e) Autocorrelation waveforms ( 650 fs / div ) of the (b) initial femtosecond pulse and (c) its distorted pulse. (d) Retrieved pulse shapes from the first- and (e) second-stage PTD.

Equations (7)

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

S c ( t ) = exp ( i ω t ) [ E ( t Δ t 1 ) exp ( i ω Δ t 1 ) , E ( t ) ] T .
S d ( t ) = M P · S c ( t ) = 1 / 2 exp ( i ω t ) [ ( 1 + cos 2 θ ) E ( t Δ t 1 ) + sin 2 θ E ( t ) , sin 2 θ E ( t Δ t 1 ) + ( 1 cos 2 θ ) E ( t ) ] T .
S d ( t ) = 1 / 2 exp ( i ω t ) ( E ( t ) E ( t Δ t 1 ) ) [ 1 , 1 ] T Δ t 1 / 2 exp ( i ω t ) ( d E ( t ) / d t ) [ 1 , 1 ] T ,
I d ( t ) = | S d ( t ) | 2 ( Δ t 1 ) 2 / 2 | d E ( t ) / d t | 2 .
I in ( t ) = I a ( t ) = | S a ( t ) | 2 = 2 | E ( t ) | 2 .
η = I out A ( t ) / I in A ( t ) ( Δ t / 2 ) 2 | ( d E ( t ) / d t ) A | 2 ,
ε = T | I d I c | d t / T = T | S d 2 S c 2 | d t / T = | R 1 | T | S d + S c | d t / T = C ( Δ t / 2 ) 2 ,

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