Abstract

A general interferometer composed of linear filters (both time stationary and frequency stationary) and a square-law detector is analyzed, and the possibilities for measuring the spectral phase of ultrashort optical pulses are enumerated. It is found that with purely time-stationary filters the phase spectrum cannot be determined with an integrating detector but that a detector with a finite bandwidth permits such a determination. It is also shown that the phase may be measured with a time-nonstationary filter and an integrating detector. The possibilities for realizing the system are evaluated.

© 1994 Optical Society of America

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References

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  1. C. Yan, J.-C. Diels, J. Opt. Soc. Am. B 8, 1259 (1991).
    [CrossRef]
  2. K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
    [CrossRef]
  3. J. L. A. Chilla, O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
    [CrossRef]
  4. D. J. Kane, R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
    [CrossRef]
  5. M. Lai, J.-C. Diels, Opt. Commun. 88, 319 (1992); J.-C. Diels, X. M. Zhao, S. Diddams, Proc. Soc. Photo-Opt. Instrum. Eng. 1861, 120 (1993).
    [CrossRef]
  6. V. Wong, J. Koshel, M. Beck, I. Walmsley, Proc.Soc. Photo-Opt. Instrum. Eng. 1861, 137 (1993).
  7. This form describes the transfer function of a grating pair or the zero-dispersion compressor with a slit at the focal plane of the lens, such as in Ref. 3.
  8. M. Beck, I. A. Walmsley, Opt. Lett. 15, 492 (1990).
    [CrossRef] [PubMed]
  9. M. T. Kauffman, W. C. Banyai, D. M. Bloom, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1993), paper CPD33; M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, “A time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. (to be published).
  10. M. Beck, M. G. Raymer, I. A. Walmsley, V. Wong, Opt. Lett. 18, 2041 (1993).
    [CrossRef] [PubMed]
  11. J. Goodberlet, P. L. Hagelstein, Opt. Lett. 18, 1648 (1993). Although described otherwise in the text, the dispersive delay line used in this interferometer is, in fact, time nonstationary because its transfer function is that of a phase modulator operated near the peak phase shift.
    [CrossRef] [PubMed]
  12. M. Beck, I. A. Walmsley, IEEE J. Quantum Electron. 28, 2274 (1992).
    [CrossRef]

1993 (4)

1992 (2)

M. Beck, I. A. Walmsley, IEEE J. Quantum Electron. 28, 2274 (1992).
[CrossRef]

M. Lai, J.-C. Diels, Opt. Commun. 88, 319 (1992); J.-C. Diels, X. M. Zhao, S. Diddams, Proc. Soc. Photo-Opt. Instrum. Eng. 1861, 120 (1993).
[CrossRef]

1991 (2)

C. Yan, J.-C. Diels, J. Opt. Soc. Am. B 8, 1259 (1991).
[CrossRef]

J. L. A. Chilla, O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[CrossRef]

1990 (1)

1989 (1)

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Banyai, W. C.

M. T. Kauffman, W. C. Banyai, D. M. Bloom, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1993), paper CPD33; M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, “A time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. (to be published).

Beck, M.

M. Beck, M. G. Raymer, I. A. Walmsley, V. Wong, Opt. Lett. 18, 2041 (1993).
[CrossRef] [PubMed]

V. Wong, J. Koshel, M. Beck, I. Walmsley, Proc.Soc. Photo-Opt. Instrum. Eng. 1861, 137 (1993).

M. Beck, I. A. Walmsley, IEEE J. Quantum Electron. 28, 2274 (1992).
[CrossRef]

M. Beck, I. A. Walmsley, Opt. Lett. 15, 492 (1990).
[CrossRef] [PubMed]

Bloom, D. M.

M. T. Kauffman, W. C. Banyai, D. M. Bloom, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1993), paper CPD33; M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, “A time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. (to be published).

Chilla, J. L. A.

J. L. A. Chilla, O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[CrossRef]

Diels, J.-C.

M. Lai, J.-C. Diels, Opt. Commun. 88, 319 (1992); J.-C. Diels, X. M. Zhao, S. Diddams, Proc. Soc. Photo-Opt. Instrum. Eng. 1861, 120 (1993).
[CrossRef]

C. Yan, J.-C. Diels, J. Opt. Soc. Am. B 8, 1259 (1991).
[CrossRef]

Goodberlet, J.

Hagelstein, P. L.

Kane, D. J.

D. J. Kane, R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Kauffman, M. T.

M. T. Kauffman, W. C. Banyai, D. M. Bloom, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1993), paper CPD33; M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, “A time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. (to be published).

Koshel, J.

V. Wong, J. Koshel, M. Beck, I. Walmsley, Proc.Soc. Photo-Opt. Instrum. Eng. 1861, 137 (1993).

Lai, M.

M. Lai, J.-C. Diels, Opt. Commun. 88, 319 (1992); J.-C. Diels, X. M. Zhao, S. Diddams, Proc. Soc. Photo-Opt. Instrum. Eng. 1861, 120 (1993).
[CrossRef]

Martinez, O. E.

J. L. A. Chilla, O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[CrossRef]

Mogi, K.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Raymer, M. G.

Trebino, R.

D. J. Kane, R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Walmsley, I.

V. Wong, J. Koshel, M. Beck, I. Walmsley, Proc.Soc. Photo-Opt. Instrum. Eng. 1861, 137 (1993).

Walmsley, I. A.

Wong, V.

V. Wong, J. Koshel, M. Beck, I. Walmsley, Proc.Soc. Photo-Opt. Instrum. Eng. 1861, 137 (1993).

M. Beck, M. G. Raymer, I. A. Walmsley, V. Wong, Opt. Lett. 18, 2041 (1993).
[CrossRef] [PubMed]

Yamada, H.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Yan, C.

IEEE J. Quantum Electron. (4)

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

J. L. A. Chilla, O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[CrossRef]

D. J. Kane, R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

M. Beck, I. A. Walmsley, IEEE J. Quantum Electron. 28, 2274 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

M. Lai, J.-C. Diels, Opt. Commun. 88, 319 (1992); J.-C. Diels, X. M. Zhao, S. Diddams, Proc. Soc. Photo-Opt. Instrum. Eng. 1861, 120 (1993).
[CrossRef]

Opt. Lett. (3)

Proc.Soc. Photo-Opt. Instrum. Eng. (1)

V. Wong, J. Koshel, M. Beck, I. Walmsley, Proc.Soc. Photo-Opt. Instrum. Eng. 1861, 137 (1993).

Other (2)

This form describes the transfer function of a grating pair or the zero-dispersion compressor with a slit at the focal plane of the lens, such as in Ref. 3.

M. T. Kauffman, W. C. Banyai, D. M. Bloom, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1993), paper CPD33; M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, “A time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. (to be published).

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Figures (2)

Fig. 1.
Fig. 1.

Schematic description of a general linear frequency-domain phase-measurement interferometer.Ni(t, t′) (i = 1, 2, 3, 4) are the time-domain response functions of linear, causal filters.

Fig. 2.
Fig. 2.

Schematic description of the spectral shearing interferometer for phase measurement.

Equations (8)

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E fi ( t ) = d t N i ( t , t ) E in ( t ) ,
N ˜ ˜ i ( t , ω ) = d t exp ( i ω t ) N i ( t , t ) ,
I ( Ω , τ ) = d t exp ( i Ω t ) | E f 1 ( t ) | 2 + d t exp ( i Ω t ) | E f 2 ( t + τ ) | 2 + d t exp ( i Ω t ) [ E f 1 ( t ) E f 2 * ( t + τ ) + c . c . ] = I 1 + I 2 + I I ,
I I ( Ω , τ ) = d ω 1 d ω 2 d ω 3 d ω 4 E ˜ in ( ω 3 ) E ˜ in * ( ω 4 ) × [ d t N ˜ ˜ 2 ( t , ω 1 ) N ˜ ˜ 4 * ( t + τ , ω 2 ) exp ( i Ω t ) ] × [ d t N ˜ ˜ 1 ( t , ω 3 ) exp ( i ω 1 t ) ] × [ d t N ˜ ˜ 3 * ( t , ω 4 ) exp ( i ω 2 t ) ] + c . c . ( Ω Ω ) ,
I I ( Ω , τ ) = d ω E ˜ in ( ω ) E ˜ in * ( ω Ω ) N ˜ 1 ( ω ) N ˜ 2 ( ω ) × N ˜ 3 * ( ω Ω ) N ˜ 4 * ( ω Ω ) exp [ i ( ω Ω ) τ ] + c . c . ( Ω Ω ) .
I ( Ω , τ ) | E ˜ in ( ω c + Ω 2 ) | | E ˜ in ( ω c Ω 2 ) | × exp ( τ f 2 2 Ω 2 ) × exp [ i ( ϕ ω c Ω / 2 τ 2 ) Ω + i ψ rf ] × [ exp ( i τ 2 Ω ) + exp ( i τ 2 Ω ) + 2 exp ( τ 2 8 τ f 2 ) cos ( ω c τ ) ] ,
I I ( τ ; ω c ) = Re [ d ω E ˜ in ( ω + δ ω ) E ˜ in * ( ω ) | N ˜ ( ω ) | 2 exp ( i ω τ ) ] .
I ( τ ; ω c ) | E ˜ in ( ω c ) | 2 + | E ˜ in ( ω c + δ ω ) | 2 + 2 | E ˜ in ( ω c ) | × | E ˜ in ( ω c + δ ω ) | exp ( τ 2 8 τ f 2 ) × cos ( ω c τ + δ ω ϕ ω c ) ,

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