Abstract

We predict and investigate ultrafast optical phase conjugation generated by the spatiospectral mixing of two picosecond light pulses in the active area of a broad-area laser. The microscopic internal processes linked to these phenomena are described on the basis of multiwave Maxwell–Bloch equations and include, in particular, the dynamic interactions of the counterpropagating light fields self-consistently with the dynamics of the active nonlinear charge-carrier plasma within the laser amplifier. Microscopic simulations demonstrate the spatiotemporal dynamics of the fields and reveal the underlying physical processes of the ultrafast refractive-index grating formation: dynamic spatiospectral hole burning, carrier heating, and coupled diffraction and interference of the light beams by means of the nonlinear induced changes in the spatiospectral carrier and refractive-index distribution.

© 2001 Optical Society of America

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  1. S. Diez, A. Mecozzi, and J. Mørk, “Bit rate and pulse width dependence of four-wave mixing of short optical pulses in semiconductor optical amplifiers,” Opt. Lett. 24, 1675–1677 (1999).
    [CrossRef]
  2. H. Shi, I. Nitta, A. Schober, P. J. Delfyett, G. Alphonse, and J. Connolly, “Demonstration of phase correlation in multiwavelength mode-locked semiconductor diode lasers,” Opt. Lett. 24, 238–240 (1999).
    [CrossRef]
  3. J. M. Tang and K. A. Shore, “Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 35, 1032–1040 (1999).
    [CrossRef]
  4. P. Kürz, R. Nager, and T. Mukai, “Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode,” Appl. Phys. Lett. 68, 1180–1182 (1996).
    [CrossRef]
  5. P. Kürz and T. Mukai, “Frequency stabilization of a semiconductor laser by external phase-conjugate feedback,” Opt. Lett. 21, 1369–1371 (1996).
    [CrossRef] [PubMed]
  6. P. P. Vasil’ev and I. H. White, “Phase-conjugation broad area twin-contact semiconductor laser,” Appl. Phys. Lett. 71, 40–42 (1997).
    [CrossRef]
  7. I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
    [CrossRef]
  8. E. Gehrig, O. Hess, and R. Wallenstein, “Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. 35, 320–331 (1999).
    [CrossRef]
  9. E. Gehrig and O. Hess, “Pulse trapping and nonequilibrium spatiotemporal wave mixing in broad-area semiconductor lasers,” J. Opt. Soc. Am. B 15, 2861–2867 (1998).
    [CrossRef]
  10. O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical description,” Phys. Rev. A 54, 3347–3359 (1996).
    [CrossRef] [PubMed]
  11. E. Gehrig and O. Hess, “Nonequilibrium spatiotemporal dynamics of the Wigner distributions in broad-area semiconductor lasers,” Phys. Rev. A 57, 2150–2163 (1998).
    [CrossRef]
  12. E. Gehrig and O. Hess, “Microscopic theory of spatiotemporal multiwave mixing in broad-area semiconductor laser amplifiers,” Phys. Rev. A 60, 5035–5045 (1999).
    [CrossRef]

1999 (5)

J. M. Tang and K. A. Shore, “Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 35, 1032–1040 (1999).
[CrossRef]

E. Gehrig and O. Hess, “Microscopic theory of spatiotemporal multiwave mixing in broad-area semiconductor laser amplifiers,” Phys. Rev. A 60, 5035–5045 (1999).
[CrossRef]

H. Shi, I. Nitta, A. Schober, P. J. Delfyett, G. Alphonse, and J. Connolly, “Demonstration of phase correlation in multiwavelength mode-locked semiconductor diode lasers,” Opt. Lett. 24, 238–240 (1999).
[CrossRef]

S. Diez, A. Mecozzi, and J. Mørk, “Bit rate and pulse width dependence of four-wave mixing of short optical pulses in semiconductor optical amplifiers,” Opt. Lett. 24, 1675–1677 (1999).
[CrossRef]

E. Gehrig, O. Hess, and R. Wallenstein, “Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. 35, 320–331 (1999).
[CrossRef]

1998 (2)

E. Gehrig and O. Hess, “Nonequilibrium spatiotemporal dynamics of the Wigner distributions in broad-area semiconductor lasers,” Phys. Rev. A 57, 2150–2163 (1998).
[CrossRef]

E. Gehrig and O. Hess, “Pulse trapping and nonequilibrium spatiotemporal wave mixing in broad-area semiconductor lasers,” J. Opt. Soc. Am. B 15, 2861–2867 (1998).
[CrossRef]

1997 (1)

P. P. Vasil’ev and I. H. White, “Phase-conjugation broad area twin-contact semiconductor laser,” Appl. Phys. Lett. 71, 40–42 (1997).
[CrossRef]

1996 (4)

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
[CrossRef]

P. Kürz, R. Nager, and T. Mukai, “Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode,” Appl. Phys. Lett. 68, 1180–1182 (1996).
[CrossRef]

P. Kürz and T. Mukai, “Frequency stabilization of a semiconductor laser by external phase-conjugate feedback,” Opt. Lett. 21, 1369–1371 (1996).
[CrossRef] [PubMed]

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical description,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

Alphonse, G.

Connolly, J.

Delfyett, P. J.

Diez, S.

Elsässer, W.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
[CrossRef]

Fischer, I.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
[CrossRef]

Gehrig, E.

E. Gehrig and O. Hess, “Microscopic theory of spatiotemporal multiwave mixing in broad-area semiconductor laser amplifiers,” Phys. Rev. A 60, 5035–5045 (1999).
[CrossRef]

E. Gehrig, O. Hess, and R. Wallenstein, “Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. 35, 320–331 (1999).
[CrossRef]

E. Gehrig and O. Hess, “Pulse trapping and nonequilibrium spatiotemporal wave mixing in broad-area semiconductor lasers,” J. Opt. Soc. Am. B 15, 2861–2867 (1998).
[CrossRef]

E. Gehrig and O. Hess, “Nonequilibrium spatiotemporal dynamics of the Wigner distributions in broad-area semiconductor lasers,” Phys. Rev. A 57, 2150–2163 (1998).
[CrossRef]

Göbel, E.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
[CrossRef]

Hess, O.

E. Gehrig, O. Hess, and R. Wallenstein, “Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. 35, 320–331 (1999).
[CrossRef]

E. Gehrig and O. Hess, “Microscopic theory of spatiotemporal multiwave mixing in broad-area semiconductor laser amplifiers,” Phys. Rev. A 60, 5035–5045 (1999).
[CrossRef]

E. Gehrig and O. Hess, “Nonequilibrium spatiotemporal dynamics of the Wigner distributions in broad-area semiconductor lasers,” Phys. Rev. A 57, 2150–2163 (1998).
[CrossRef]

E. Gehrig and O. Hess, “Pulse trapping and nonequilibrium spatiotemporal wave mixing in broad-area semiconductor lasers,” J. Opt. Soc. Am. B 15, 2861–2867 (1998).
[CrossRef]

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
[CrossRef]

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical description,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

Kuhn, T.

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical description,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

Kürz, P.

P. Kürz, R. Nager, and T. Mukai, “Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode,” Appl. Phys. Lett. 68, 1180–1182 (1996).
[CrossRef]

P. Kürz and T. Mukai, “Frequency stabilization of a semiconductor laser by external phase-conjugate feedback,” Opt. Lett. 21, 1369–1371 (1996).
[CrossRef] [PubMed]

Mecozzi, A.

Mørk, J.

Mukai, T.

P. Kürz and T. Mukai, “Frequency stabilization of a semiconductor laser by external phase-conjugate feedback,” Opt. Lett. 21, 1369–1371 (1996).
[CrossRef] [PubMed]

P. Kürz, R. Nager, and T. Mukai, “Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode,” Appl. Phys. Lett. 68, 1180–1182 (1996).
[CrossRef]

Nager, R.

P. Kürz, R. Nager, and T. Mukai, “Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode,” Appl. Phys. Lett. 68, 1180–1182 (1996).
[CrossRef]

Nitta, I.

Schober, A.

Shi, H.

Shore, K. A.

J. M. Tang and K. A. Shore, “Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 35, 1032–1040 (1999).
[CrossRef]

Tang, J. M.

J. M. Tang and K. A. Shore, “Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 35, 1032–1040 (1999).
[CrossRef]

Vasil’ev, P. P.

P. P. Vasil’ev and I. H. White, “Phase-conjugation broad area twin-contact semiconductor laser,” Appl. Phys. Lett. 71, 40–42 (1997).
[CrossRef]

Wallenstein, R.

E. Gehrig, O. Hess, and R. Wallenstein, “Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. 35, 320–331 (1999).
[CrossRef]

White, I. H.

P. P. Vasil’ev and I. H. White, “Phase-conjugation broad area twin-contact semiconductor laser,” Appl. Phys. Lett. 71, 40–42 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

P. Kürz, R. Nager, and T. Mukai, “Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode,” Appl. Phys. Lett. 68, 1180–1182 (1996).
[CrossRef]

P. P. Vasil’ev and I. H. White, “Phase-conjugation broad area twin-contact semiconductor laser,” Appl. Phys. Lett. 71, 40–42 (1997).
[CrossRef]

Europhys. Lett. (1)

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “Complex spatio-temporal dynamics in the nearfield of a broad-area semiconductor laser,” Europhys. Lett. 35, 579–584 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. Gehrig, O. Hess, and R. Wallenstein, “Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. 35, 320–331 (1999).
[CrossRef]

J. M. Tang and K. A. Shore, “Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 35, 1032–1040 (1999).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. A (3)

O. Hess and T. Kuhn, “Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers. I. Theoretical description,” Phys. Rev. A 54, 3347–3359 (1996).
[CrossRef] [PubMed]

E. Gehrig and O. Hess, “Nonequilibrium spatiotemporal dynamics of the Wigner distributions in broad-area semiconductor lasers,” Phys. Rev. A 57, 2150–2163 (1998).
[CrossRef]

E. Gehrig and O. Hess, “Microscopic theory of spatiotemporal multiwave mixing in broad-area semiconductor laser amplifiers,” Phys. Rev. A 60, 5035–5045 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Snapshots of (left) the intensity and (right) the induced index distribution in the active area of a broad-area amplifier after optical injection of two light pulses with a duration of 4 ps and an input power Pin, which is low compared with the saturation power Ps of the active medium (Pin=0.1Ps). The time distance between successive plots is 3 ps. In the snapshots, light shading corresponds to high local intensity and refractive index.

Fig. 2
Fig. 2

(a) Transverse and (b) longitudinal dependence of the microscopic refractive-index distribution during the molding of the optical pulses. The cuts were taken in the longitudinal and the transverse centers, respectively, of the semiconductor laser (insets).

Fig. 3
Fig. 3

(a) Transverse and (b) longitudinal dependence of the microscopic gain distribution during the molding of the optical pulses. The cuts were taken in the longitudinal and the transverse centers, respectively, of the semiconductor laser (insets).

Fig. 4
Fig. 4

Snapshots of (left) the intensity and (right) the induced index distribution in the active area of a broad-area amplifier after optical injection of two light pulses with a duration of 4 ps and high input power (Pin=0.8Ps). The time distance between successive plots is 3 ps. In the snapshots, light shading corresponds to high local intensity and refractive index.

Fig. 5
Fig. 5

Intensity snapshots of the probe pulse and the respective phase conjugate signal for a typical pump–probe situation (duration of the counterprogating pump pulses, 4 ps; duration of the probe pulse, 2 ps). The time distance between successive plots is 1.5 ps.

Equations (6)

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±zE±+nlc tE±
=i2 1Kz 2x2E±-α2+iηE± i0 ΓKz2nl2P±
tfke,h=gk-γke,h(fke,h-fk,eqe,h)+Λke,h-Γkspfkefkh-γnrfke,h,
tpk±=-(iω¯k+γkp)pk±+1idkE±(fke+fkh).
gkγkpω¯k2+γkp2(|E+|2+|E-|2)(fke+fkh-1),
δnnl ω¯kω¯k2+γkp2(fke+fkh-1)

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