Abstract

Picosecond pulses from semiconductor lasers are chirped (have time-dependent wavelengths) due to the effect of free carriers on the refractive index of the laser material. For optically pumped ultrashort-cavity semiconductor film lasers, the chirp is large (>1 nm/psec) and nonlinear in time because of the very high carrier concentration (> 1020 carriers/cm3) present during the operation of the laser. Experimentally, the chirp of film lasers is measured by optical upconversion sampling of the laser pulse followed by spectral filtering. This paper presents a mathematical model of this detection scheme which is used to extract the instantaneous time-dependent laser wavelength λ(t) from the measured data. Coefficients for the linear and quadratic terms of a power-series expansion of λ(t) are obtained for two InGaAsP film lasers. These parameters are used to compute time-averaged pulse spectra, which are compared with measured spectra. A formula is presented for the compression of chirped pulses in dispersive optical media which is used for comparison with experimental pulse compression results obtained by passing the film laser pulse through a short dispersive optical fiber. Finally, the time-dependent wavelength is related to the instantaneous carrier concentration in semiconductor material.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
    [CrossRef]
  2. F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
    [CrossRef]
  3. K. Kishino, S. Aoki, Y. Suematsu, IEEE J. Quantum Electron. QE-18, 343 (1982).
    [CrossRef]
  4. J. van der Ziel, IEEE J. Quantum Electron. QE-15, 1277 (1979).
    [CrossRef]
  5. C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
    [CrossRef]
  6. K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
    [CrossRef]
  7. J. M. Wiesenfeld, J. Stone, Opt. Lett. 8, 262 (1983).
    [CrossRef] [PubMed]
  8. G. H. B. Thompson, Opto-electronics 4, 257 (1972).
    [CrossRef]
  9. M. Ito, T. Kimura, IEEE J. Quantum Electron. QE-16, 910 (1980).
    [CrossRef]
  10. K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
    [CrossRef]
  11. J. S. Manning, R. Olshansky, Electron. Lett. 17, 506 (1981).
    [CrossRef]
  12. T. Suzuki, T. Fukumoto, Electron. Commun. Jpn. 59C, 117 (1976).
  13. D. Marcuse, Appl. Opt. 20, 3573 (1981).
    [CrossRef] [PubMed]
  14. J. V. Wright, B. P. Nelson, Electron. Lett. 13, 361 (1977).
    [CrossRef]
  15. J. Stone et al.Opt. Lett. 6, 534 (1981).
    [CrossRef] [PubMed]
  16. J. M. Wiesenfeld, J. Stone, to be published.
  17. R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
    [CrossRef]
  18. D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980).
    [CrossRef]

1983

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

J. M. Wiesenfeld, J. Stone, Opt. Lett. 8, 262 (1983).
[CrossRef] [PubMed]

1982

K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
[CrossRef]

K. Kishino, S. Aoki, Y. Suematsu, IEEE J. Quantum Electron. QE-18, 343 (1982).
[CrossRef]

1981

F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
[CrossRef]

D. Marcuse, Appl. Opt. 20, 3573 (1981).
[CrossRef] [PubMed]

J. Stone et al.Opt. Lett. 6, 534 (1981).
[CrossRef] [PubMed]

J. S. Manning, R. Olshansky, Electron. Lett. 17, 506 (1981).
[CrossRef]

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

1980

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980).
[CrossRef]

B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
[CrossRef]

M. Ito, T. Kimura, IEEE J. Quantum Electron. QE-16, 910 (1980).
[CrossRef]

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

1979

J. van der Ziel, IEEE J. Quantum Electron. QE-15, 1277 (1979).
[CrossRef]

1977

J. V. Wright, B. P. Nelson, Electron. Lett. 13, 361 (1977).
[CrossRef]

1976

T. Suzuki, T. Fukumoto, Electron. Commun. Jpn. 59C, 117 (1976).

1972

G. H. B. Thompson, Opto-electronics 4, 257 (1972).
[CrossRef]

Adams, A. R.

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

Aoki, S.

K. Kishino, S. Aoki, Y. Suematsu, IEEE J. Quantum Electron. QE-18, 343 (1982).
[CrossRef]

Arai, A.

F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
[CrossRef]

Arai, S.

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

Asada, M.

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

Burrus, C. A.

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Fork, R. L.

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Fukumoto, T.

T. Suzuki, T. Fukumoto, Electron. Commun. Jpn. 59C, 117 (1976).

Greene, B. I.

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Hakki, B. W.

B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
[CrossRef]

Ito, M.

M. Ito, T. Kimura, IEEE J. Quantum Electron. QE-16, 910 (1980).
[CrossRef]

Iwashita, K.

K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
[CrossRef]

Kimura, T.

M. Ito, T. Kimura, IEEE J. Quantum Electron. QE-16, 910 (1980).
[CrossRef]

Kishino, K.

K. Kishino, S. Aoki, Y. Suematsu, IEEE J. Quantum Electron. QE-18, 343 (1982).
[CrossRef]

F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
[CrossRef]

Koyoma, F.

F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
[CrossRef]

Lee, T. P.

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Lin, C.

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Manning, J. S.

J. S. Manning, R. Olshansky, Electron. Lett. 17, 506 (1981).
[CrossRef]

Marcuse, D.

Miller, D. A. B.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980).
[CrossRef]

Nakagawa, K.

K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
[CrossRef]

Nakano, Y.

K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
[CrossRef]

Nelson, B. P.

J. V. Wright, B. P. Nelson, Electron. Lett. 13, 361 (1977).
[CrossRef]

Olshansky, R.

J. S. Manning, R. Olshansky, Electron. Lett. 17, 506 (1981).
[CrossRef]

Shank, C. V.

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Smith, S. D.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980).
[CrossRef]

Stone, J.

Stubkjaer, K.

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

Suematsu, Y.

K. Kishino, S. Aoki, Y. Suematsu, IEEE J. Quantum Electron. QE-18, 343 (1982).
[CrossRef]

F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
[CrossRef]

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

Suzuki, T.

T. Suzuki, T. Fukumoto, Electron. Commun. Jpn. 59C, 117 (1976).

Suzuki, Y.

K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
[CrossRef]

Thompson, G. H. B.

G. H. B. Thompson, Opto-electronics 4, 257 (1972).
[CrossRef]

van der Ziel, J.

J. van der Ziel, IEEE J. Quantum Electron. QE-15, 1277 (1979).
[CrossRef]

Wherrett, B. S.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980).
[CrossRef]

Wiesenfeld, J. M.

Wright, J. V.

J. V. Wright, B. P. Nelson, Electron. Lett. 13, 361 (1977).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Electon. Lett.

F. Koyoma, A. Arai, Y. Suematsu, K. Kishino, Electon. Lett. 17, 938 (1981).
[CrossRef]

Electron. Commun. Jpn.

T. Suzuki, T. Fukumoto, Electron. Commun. Jpn. 59C, 117 (1976).

Electron. Lett.

J. V. Wright, B. P. Nelson, Electron. Lett. 13, 361 (1977).
[CrossRef]

K. Iwashita, K. Nakagawa, Y. Nakano, Y. Suzuki, Electron. Lett. 18, 873 (1982).
[CrossRef]

K. Stubkjaer, Y. Suematsu, M. Asada, S. Arai, A. R. Adams, Electron. Lett. 16, 895 (1980).
[CrossRef]

J. S. Manning, R. Olshansky, Electron. Lett. 17, 506 (1981).
[CrossRef]

IEEE J. Quantum Electron.

M. Ito, T. Kimura, IEEE J. Quantum Electron. QE-16, 910 (1980).
[CrossRef]

K. Kishino, S. Aoki, Y. Suematsu, IEEE J. Quantum Electron. QE-18, 343 (1982).
[CrossRef]

J. van der Ziel, IEEE J. Quantum Electron. QE-15, 1277 (1979).
[CrossRef]

J. Appl. Phys.

B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
[CrossRef]

Opt. Commun.

D. A. B. Miller, S. D. Smith, B. S. Wherrett, Opt. Commun. 35, 221 (1980).
[CrossRef]

Opt. Lett.

Opto-electronics

G. H. B. Thompson, Opto-electronics 4, 257 (1972).
[CrossRef]

Other

J. M. Wiesenfeld, J. Stone, to be published.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Experimental schematic. The chirp is measured by upconversion followed by spectral filtering.

Fig. 2
Fig. 2

Comparison of experimentally acquired data (solid curve) and digitally smoothed data (dashed curve). The trace shows the broadband 1.151-μm pulse.

Fig. 3
Fig. 3

Upconverted and spectrally filtered pulses from the l.151-μm laser. Monochromator wavelengths are indicated.

Fig. 4
Fig. 4

Experimentally derived time-dependent wavelength curves for the 1.151-μm laser. The curves are vertically offset to coincide at λ = 1.15 μm at t = 0.

Fig. 5
Fig. 5

Model time-dependent wavelength curves for the l.151-μm laser. The average parameters of Table I are used with Eq. (20), dashed curve, and Eq. (21), solid curve. Also shown is the model of the broadband pulse shape, Eq. (25).

Fig. 6
Fig. 6

Computed time-averaged spectra of the 1.151-μm laser. The solid curve uses the average Δλ1 and Δλ2 values of Table I. For the dashed curve, Δλ2 = 0.

Fig. 7
Fig. 7

Experimental pulse compression results for the 1.151-μm laser. The cross-correlation traces were taken without spectral filtering. Pulse widths (FWHM) are indicated. The time origin is arbitrary.

Fig. 8
Fig. 8

Upconverted and spectrally filtered pulses for the 1.261-μm laser. Monochromator wavelengths are indicated.

Fig. 9
Fig. 9

Experimentally derived time-dependent wavelength curves for the 1.261-μm laser. The curves are vertically offset to coincide at λ = 1.255 μm and t = 0.

Fig. 10
Fig. 10

Model time-dependent wavelength curves for the 1.261-μm laser. The average parameters of Table II are used with Eq. (20), dashed curve, and Eq. (21), solid curve. Also shown are two model approximations to the broadband pulse shape. The curve labeled exponential is computed from Eq. (25). The curve labeled Gaussian has a Gaussian decay for t > 0.

Fig. 11
Fig. 11

Computed time-averaged spectra for the 1.261-μm laser: (a) Δλ1 = 1 nm/psec, Δλ2 = −0.075 nm/psec2, and the Gaussian pulse shape of Fig. 10 are used; (b) Δλ1 = 1 nm/psec, Δλ2 = −0.056 nm/psec2, and the exponential pulse shape of Fig. 10 are used.

Fig. 12
Fig. 12

Experimental pulse compression results for the 1.261-μm laser. The cross-correlation traces were taken without spectral filtering. Pulse widths (FWHM) are indicated. The time origin is arbitrary.

Tables (2)

Tables Icon

Table I Chirp Parameters for the 1.151-μm Pulse

Tables Icon

Table II Chirp Parameters for the 1.261-μm Pulse

Equations (35)

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

ψ s ( τ , t ) = ψ L ( τ + t ) ψ p ( τ ) ,
ψ f ( τ , t ) = - ψ L ( τ 1 + t ) ψ p ( τ 1 ) H ( τ - τ 1 ) d τ 1 .
ψ L ( τ ) = ϕ L ( τ ) exp { i [ w L τ + χ ( τ ) ] } ,
ψ p ( τ ) = ϕ p ( τ ) exp ( i w p τ ) ,
ψ f ( τ , t ) = exp ( i w L t ) ϕ L ( t ) × - ϕ p ( τ 1 ) H ( τ - τ 1 ) × exp { i [ ( w L + w p ) τ 1 + χ ( τ 1 + t ) ] } d τ 1 .
G ( w , t ) = 1 2 π - ϕ p ( τ 1 ) exp { i [ ( w p + w L ) τ 1 + χ ( τ 1 + t ) ] } × exp ( - i w τ 1 ) d τ 1
F ( w - w f ) = 1 2 π - H ( τ 2 ) exp ( - i w τ 2 ) d τ 2
ψ f ( τ , t ) = 2 π ϕ L ( t ) exp ( i w L t ) - G ( w , t ) × F ( w - w f ) exp ( i w τ ) d w .
P d ( t ) = 4 π 2 ϕ L ( t ) 2 × - d τ - d w - d w G ( w , t ) × G * ( w , t ) F ( w - w f ) F * ( w - w f ) exp [ i ( w - w ) τ ] .
P d ( t ) = ( 2 π ) 3 P L ( t ) - G ( w , t ) 2 F ( w - w f ) 2 d w
P L ( t ) = ϕ L ( t ) 2 .
ϕ p ( τ ) = exp [ - 2 ( τ D p ) 2 ]
F ( w - w f ) 2 = exp [ - 4 ( w - w f ) 2 W 2 ] .
w u v ( t ) = w L + w p + ( d χ ( τ ) d τ ) τ = t
G ( w , t ) 2 = D p 2 8 π exp { - D p 2 4 [ w u v ( t ) - w ] 2 } .
P d ( t ) = π 5 / 2 D P 2 W / 2 [ 1 + ( D p W / 4 ) 2 ] 1 / 2 P L ( t ) × exp { - ( D p / 2 ) 2 1 + ( D p W / 4 ) 4 [ w u v ( t ) - w f ] 2 } .
w u v ( t ) = 1 2 ( w f 1 + w f 2 ) + 1 + ( W D p / 4 ) 2 2 ( D p / 2 ) 2 ( w f 2 - w f 1 ) ln [ P 2 ( t ) P 1 ( t ) ] .
λ ( t ) = 2 π c w u v ( t ) - w p .
F ^ ( w ) = 1 1 + exp ( w - w c Δ w ) .
λ ( t ) = λ 0 + Δ λ 1 t + Δ λ 2 t 2
λ ( t ) = A + B [ 1 - exp ( - C t ) ] .
A = λ 0 ,
C = - 2 Δ 2 / Δ λ 1 ,
B = Δ λ 1 / C .
P L = ψ L 2 = exp [ - ( t + t 0 ) / Δ t 1 ] - exp [ - ( t + t 0 ) / Δ t 2 ] exp ( - t 0 / Δ t 1 ) - exp ( - t 0 / Δ t 2 ) ,
t 0 = Δ t 1 Δ t 2 Δ t 2 - Δ t 1 ln ( Δ t 2 Δ t 1 ) .
G c h ( w ) = | 1 2 π - ϕ L ( t ) exp [ i 2 π c λ ( t ) t ] exp ( - i w t ) d t | 2 .
w ( t ) = w 0 + Δ w 1 t + Δ w 2 t 2 ,
Δ w 1 = - 2 π c λ 0 2 Δ λ 1 ,
Δ w 2 = 2 π c λ 0 2 [ - Δ λ 2 + ( Δ λ 1 ) 2 λ 0 ] .
σ σ 0 = [ ( 1 + β ¨ L Δ w 1 ) 2 + ( 4 β ¨ L T 2 ) 2 + ( 1 2 T β ¨ L Δ w 2 ) 2 ] 1 / 2 .
β ¨ = - λ 2 2 π c 1 L d τ d λ = - λ 2 2 π c D .
λ ( t ) = n ( t ) n 0 λ 0 ,
n ( t ) = n 0 - A N ( t ) ,
λ ( t ) = λ 0 - A λ 0 n 0 N ( t ) .

Metrics