Abstract

Complex envelope measurement using coherent linear optical sampling with mode-locked sources is investigated. It is shown that reliable measurement of the phase requires that one of the optical modes of the mode-locked laser be locked to the optical carrier of the data signal to be measured. Carrier-envelope offset (CEO) is found to have negligible effect on the measurement. Measurement errors of the intensity profile and phase depend on the pulsewidth and chirp of the sampling pulses as well as the detuning between the carrier frequencies of the data signal and the center frequency of sampling source.

© 2004 Optical Society of America

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References

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  1. M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, �??Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,�?? IEEE Photon. Technol. Lett. 12, 82�??84 (2000).
    [CrossRef]
  2. S. Diez, R. Ludwig, C. Schmidt, U. Feiste, and H. G. Weber, �??160-Gb/s optical sampling by gain-transparent four-wave mixing in a semiconductor optical amplifier,�?? IEEE Photon. Technol. Lett. 11, 1402�??1404 (1999).
    [CrossRef]
  3. S. Kawanishi, T.Yamamoto, M. Nakawawa, and M. M. Fejer, �??High sensitivity waveform measurement with optical sampling using quasi-phasematched mixing in LiNbO3 waveguide,�?? Electron. Lett. 37, 842�??844 (2001).
    [CrossRef]
  4. J. Li, J. Hansryd, P. O. Hedekvist, P. A. Andrekson, and S. N. Knudsen, �??300 Gb/s eye-diagram measurement by optical sampling using fiber-based parametric amplification,�?? IEEE Photon. Technol. Lett. 13, 987�??989 (2001).
    [CrossRef]
  5. S. Nogiwa, H. Ohta,Y. Kawaguchi, and Y. Endo, �??Improvement of sensitivity in optical sampling system,�?? Electron. Lett. 35, 917�??918 (1999).
    [CrossRef]
  6. J. Li, M. Westlund, H Sunnerud, B. Olsson, M. Karsson, and P. A. Adnrekson, �??0.5-Tb/s eye-diagram measurement by optical sampling using XPM-induced wavelength shifting in highly nonlinear fiber,�?? IEEE Photon. Technol. Lett. 16, 566-568 (2004).
    [CrossRef]
  7. C. Dorrer, C. R. Doerr, I. Kang, R. Ryfand, and P. J. Winzer, �??High-sensitivity high-resolution sampling using linear optics and waveguide optical hybrid,�?? OFC 2004, PDP18.
  8. A. H. Gnauck, S. Chandrasekhar, J. Leuthold, and L. Stulz, �??Demonstration of 42.7-Gb/s DPSK receiver with 45 photons/bit sensitivity,�?? IEEE Photon. Technol. Lett. 15, 99-101 (2003).
    [CrossRef]
  9. R. A. Griffin, R. L. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, �??10 Gb/s optical differential quadrature phase shift key (DQPSK) transmission using GaAs/AlGaAs integration,�?? OFC 2002, FD6-1.
  10. C. Dorrer, J. Leuthold, and C. R. Doerr, �??Direct measurement of constellation diagrams of optical sources,�?? OFC 2004, PDP33.
  11. S. T. Cundiff, �??Phase stabilization of ultrashort optical pulses,�?? J. Phys. D: Appl. Phys. 35. R43-R59 (2002).
    [CrossRef]
  12. A. Takada and W. Imajuku, �??Linewidth narrowing and optical phase control of mode-locked semiconductor ring laser employing optical injection locking,�?? IEEE Photon. Technol. Lett. 9, 1328-1330 (1997).
    [CrossRef]
  13. R. F. Kalman, J. C. Fan, and L. G. Kazovsky, �??Dynamic range of coherent analog fiber-optic links,�?? J. Lightwave. Technol. 12, 1263-1277 (1994).
    [CrossRef]

Electron. Lett. (2)

S. Kawanishi, T.Yamamoto, M. Nakawawa, and M. M. Fejer, �??High sensitivity waveform measurement with optical sampling using quasi-phasematched mixing in LiNbO3 waveguide,�?? Electron. Lett. 37, 842�??844 (2001).
[CrossRef]

S. Nogiwa, H. Ohta,Y. Kawaguchi, and Y. Endo, �??Improvement of sensitivity in optical sampling system,�?? Electron. Lett. 35, 917�??918 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

A. H. Gnauck, S. Chandrasekhar, J. Leuthold, and L. Stulz, �??Demonstration of 42.7-Gb/s DPSK receiver with 45 photons/bit sensitivity,�?? IEEE Photon. Technol. Lett. 15, 99-101 (2003).
[CrossRef]

J. Li, J. Hansryd, P. O. Hedekvist, P. A. Andrekson, and S. N. Knudsen, �??300 Gb/s eye-diagram measurement by optical sampling using fiber-based parametric amplification,�?? IEEE Photon. Technol. Lett. 13, 987�??989 (2001).
[CrossRef]

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, �??Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,�?? IEEE Photon. Technol. Lett. 12, 82�??84 (2000).
[CrossRef]

S. Diez, R. Ludwig, C. Schmidt, U. Feiste, and H. G. Weber, �??160-Gb/s optical sampling by gain-transparent four-wave mixing in a semiconductor optical amplifier,�?? IEEE Photon. Technol. Lett. 11, 1402�??1404 (1999).
[CrossRef]

A. Takada and W. Imajuku, �??Linewidth narrowing and optical phase control of mode-locked semiconductor ring laser employing optical injection locking,�?? IEEE Photon. Technol. Lett. 9, 1328-1330 (1997).
[CrossRef]

J. Lightwave. Technol. (1)

R. F. Kalman, J. C. Fan, and L. G. Kazovsky, �??Dynamic range of coherent analog fiber-optic links,�?? J. Lightwave. Technol. 12, 1263-1277 (1994).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

S. T. Cundiff, �??Phase stabilization of ultrashort optical pulses,�?? J. Phys. D: Appl. Phys. 35. R43-R59 (2002).
[CrossRef]

OFC 2002 (1)

R. A. Griffin, R. L. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, �??10 Gb/s optical differential quadrature phase shift key (DQPSK) transmission using GaAs/AlGaAs integration,�?? OFC 2002, FD6-1.

OFC 2004 (2)

C. Dorrer, J. Leuthold, and C. R. Doerr, �??Direct measurement of constellation diagrams of optical sources,�?? OFC 2004, PDP33.

C. Dorrer, C. R. Doerr, I. Kang, R. Ryfand, and P. J. Winzer, �??High-sensitivity high-resolution sampling using linear optics and waveguide optical hybrid,�?? OFC 2004, PDP18.

Photon. Technol. Lett. (1)

J. Li, M. Westlund, H Sunnerud, B. Olsson, M. Karsson, and P. A. Adnrekson, �??0.5-Tb/s eye-diagram measurement by optical sampling using XPM-induced wavelength shifting in highly nonlinear fiber,�?? IEEE Photon. Technol. Lett. 16, 566-568 (2004).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the linear optical sampling. Data and sampling pulses have the same polarization. (b) Walk off in the time domain between the sampling pulse (narrow) and data pulse (broad). (c) Schematic of the optical spectra of the data and sampling source: (ωsc is the center frequency of the sampling source, ωd is the optical carrier frequency of the data signal, ΔΩ, called carrier frequency offset, is the offset of the optical carrier of the data signal from the closest mode of the sampling source, and Δω, called carrier frequency detuning, is the detuning of the optical carrier of the data signal from the center frequency of the sampling source).

Fig. 2.
Fig. 2.

Constellation diagram when the data phase is constant, (a) ΔΩ=0 and (b) ΔΩ≠0.

Fig. 3.
Fig. 3.

Numerical simulation of measurement of the envelope profile and phase with linear optical sampling. The sampling pulse bandwidths are 3.769 nm (a) and 1.767 nm (b).

Equations (18)

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E s ( t ) = m a m e j ( ω s , m t + ϕ m ) , with ω s , m = 2 π m T s + α
E s ( t ) = { m a m e j ( ( ω s , m ω sc ) t + ϕ m ) } e j ω sc t = { m a m e j ( 2 π ( m m 0 ) T s t + ϕ m ) } e j ω sc t
E s ( t ) = l ε s ( t l T s ) e j ω sc t
E d ( t ) = l ε d ( t l T d ) e j ( ω d t + ϕ do )
χ ( k ) = ( k 0.5 ) T s ( k + 0.5 ) T s E s ( t ) * E d ( t ) dt
= ( k 0.5 ) T s ( k + 0.5 ) T s ε s ( t k T s ) * ε d ( t k T s + t 0 ( k ) ) e j ( ( ω d ω sc ) t + ϕ do ) dt
χ ( k ) = ( k 0.5 ) T s ( k + 0.5 ) T s ε s ( t k T s ) * ε d ( t k T s + t o ( k ) ) e j ( ( ω s , n ω sc ) t + Δ Ω t + ϕ do ) dt
= e j ϕ do 0.5 T s 0.5 T s ε s ( t ) * ε d ( t + t o ( k ) ) e j [ 2 π ( n m 0 ) T s t ] e j Δ Ω ( t + k T s ) dt
= e j ϕ do e j Δ Ω k T s 0.5 T s 0.5 T s ε s ( t ) * ε d ( t + t o ( k ) ) e j Δ ω t dt
χ ( k ) ε d ( t o ( k ) ) e j ϕ do e j Δ Ω k T s ε s ( t ) * e j Δ ω t dt ( for Δ t s Δ t d )
= ε d ( t o ( k ) ) e j ϕ do ε ˜ s ( Δ ω ) * e j Δ Ω k T s
ε s ( t ) = ε s 0 e ( 1 + iC ) ( 2 ln 2 t 2 Δ t s 2 ) π Δ t s 2 ln 2
Δ t d Δ t d [ 1 + 1 2 ( 1 + C 2 ) ( Δ t s Δ t d ) 2 ] , ( Δ t s 2 Δ t d 2 )
= Δ t d [ 1 + 8 ( ln 2 ) 2 Δ t d 2 Δ ω s 2 ] , ( Δ t s = 4 ln 2 1 + C 2 Δ ω s )
ε s 0 2 Δ ω s e ( 4 ln 2 ) ( Δ ω Δ ω s ) 2 ( Δ t s 2 Δ t d 2 )
Φ ( t o ) 2 ln 2 C Δ t s 2 t o 2 Δ t d 2 Δ ω t o Δ t s 2 ( 1 + C 2 ) Δ t d 2 , ( Δ t s 2 Δ t d 2 , t o < Δ t d 2 )
= 32 ( ln 2 ) 3 C t o 2 t d 2 16 ( ln 2 ) 2 Δ ω t o Δ ω s 2 Δ t d 2
E s ( t ) = l ε s ( t l T s ) e j [ ω sc t + ϕ N ( t ) ]

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