Abstract

We have made a feasibility study on how to use transversely pumped counterpropagating optical parametric amplification to amplify short laser pulses. To achieve a large amplification factor, one should use long laser pulses for pumping. Because of its counterpropagating nature, our geometry can lead to much larger broadening for the parametric pulses. We have studied the temporal behaviors of amplified pulses and output pulses at difference frequency as a function of the pump power and the pulse width of the input beam. One can see that the temporal behaviors are quite sensitive to the pump power close to the threshold for cw parametric oscillation.

© 2000 Optical Society of America

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References

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  1. See, e.g., C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahimzdeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
    [CrossRef]
  2. R. Normandin, R. L. Williams, and F. Chatenaud, “Enhanced surface emitting waveguides for visible, monolithic semiconductor laser sources,” Electron. Lett. 26, 2088–2089 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, and G. N. S. Chu, “Blue-green surface-emitting second-harmonic generators on (111)B GaAs,” Appl. Phys. Lett. 59, 896–898 (1991).
    [CrossRef]
  3. X. Gu, Y. J. Ding, W. S. Rabinovich, D. S. Katzer, and J. B. Khurgin, “First observation of high-order quasi-phase-matched second-harmonic generation in semiconductor multilayers in reflection geometry,” in Quantum Electronics and Laser Science Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 243–244.
  4. J. Khurgin, “Large-scale quantum well domain structures,” J. Appl. Phys. 64, 5026–5029 (1988); S. Janz, F. Chatenoud, and R. Normandin, “Quasi-phase-matched second-harmonic generation from asymmetric coupled quantum wells,” Opt. Lett. 19, 622–624 (1994).
    [CrossRef] [PubMed]
  5. J. B. Khurgin, “Second-order nonlinear effects in asymmetric quantum-well structures,” Phys. Rev. B 38, 4056–4066 (1988).
    [CrossRef]
  6. R. Lodenkamper, M. L. Bortz, M. M. Fejer, K. Bacher, and J. S. Harris, Jr., “Surface-emitting second-harmonic generation in a semiconductor vertical resonator,” Opt. Lett. 18, 1798–1800 (1993).
    [CrossRef] [PubMed]
  7. Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995).
    [CrossRef] [PubMed]
  8. Y. J. Ding, J. B. Khurgin, and S. J. Lee, “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995).
    [CrossRef]
  9. Y. J. Ding and J. B. Khurgin, “Transversely pumped counterpropagating optical parametric amplification and difference-frequency generation,” J. Opt. Soc. Am. B 14, 2161–2166 (1997).
    [CrossRef]
  10. S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
    [CrossRef]
  11. A. Picozzi and M. Haelterman, “Spontaneous formation of symbiotic solitary waves in a backward quasi-phase-matched parametric oscillator,” Opt. Lett. 23, 1808–1810 (1998).
    [CrossRef]
  12. P. M. Lushnikov, P. Lodahl, and M. Saffman, “Transverse modulational instability of counterpropagating quasi-phase-matched beams in a quadratically nonlinear medium,” Opt. Lett. 23, 1650–1652 (1998).
    [CrossRef]
  13. J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic, San Diego, 1996), pp. 10–31.
  14. S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
    [CrossRef]
  15. The extra 286-ML AlAs layer can be used to maximize the modal overlap among the waves.
  16. J. B. Khurgin and Y. J. Ding, “Resonant cascaded surface-emitting second-harmonic generation: a strong third-order nonlinear process,” Opt. Lett. 19, 1016–1018 (1994).
    [CrossRef] [PubMed]
  17. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
    [CrossRef] [PubMed]

1998

1997

1995

Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995).
[CrossRef] [PubMed]

Y. J. Ding, J. B. Khurgin, and S. J. Lee, “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995).
[CrossRef]

1994

1993

1992

1988

J. B. Khurgin, “Second-order nonlinear effects in asymmetric quantum-well structures,” Phys. Rev. B 38, 4056–4066 (1988).
[CrossRef]

1985

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

1966

S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
[CrossRef]

Adachi, S.

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

Bacher, K.

Bortz, M. L.

DeSalvo, R.

Ding, Y. J.

Y. J. Ding and J. B. Khurgin, “Transversely pumped counterpropagating optical parametric amplification and difference-frequency generation,” J. Opt. Soc. Am. B 14, 2161–2166 (1997).
[CrossRef]

Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995).
[CrossRef] [PubMed]

Y. J. Ding, J. B. Khurgin, and S. J. Lee, “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995).
[CrossRef]

J. B. Khurgin and Y. J. Ding, “Resonant cascaded surface-emitting second-harmonic generation: a strong third-order nonlinear process,” Opt. Lett. 19, 1016–1018 (1994).
[CrossRef] [PubMed]

Ebrahimzdeh, M.

Fejer, M. M.

Haelterman, M.

Hagan, D. J.

Harris, S. E.

S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
[CrossRef]

Harris Jr., J. S.

Jundt, D. H.

Khurgin, J. B.

Y. J. Ding and J. B. Khurgin, “Transversely pumped counterpropagating optical parametric amplification and difference-frequency generation,” J. Opt. Soc. Am. B 14, 2161–2166 (1997).
[CrossRef]

Y. J. Ding, J. B. Khurgin, and S. J. Lee, “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995).
[CrossRef]

Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995).
[CrossRef] [PubMed]

J. B. Khurgin and Y. J. Ding, “Resonant cascaded surface-emitting second-harmonic generation: a strong third-order nonlinear process,” Opt. Lett. 19, 1016–1018 (1994).
[CrossRef] [PubMed]

J. B. Khurgin, “Second-order nonlinear effects in asymmetric quantum-well structures,” Phys. Rev. B 38, 4056–4066 (1988).
[CrossRef]

Lee, S. J.

Y. J. Ding, J. B. Khurgin, and S. J. Lee, “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995).
[CrossRef]

Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995).
[CrossRef] [PubMed]

Lodahl, P.

Lodenkamper, R.

Lushnikov, P. M.

McGowan, C.

Penman, Z. E.

Picozzi, A.

Reid, D. T.

Saffman, M.

Sheik-Bahae, M.

Sibbett, W.

Stegeman, G. I.

Van Stryland, E. W.

Vanherzeele, H.

Appl. Phys. Lett.

S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
[CrossRef]

IEEE J. Quantum Electron.

Y. J. Ding, J. B. Khurgin, and S. J. Lee, “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995).
[CrossRef]

J. Appl. Phys.

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. B

J. B. Khurgin, “Second-order nonlinear effects in asymmetric quantum-well structures,” Phys. Rev. B 38, 4056–4066 (1988).
[CrossRef]

Phys. Rev. Lett.

Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995).
[CrossRef] [PubMed]

Other

R. Normandin, R. L. Williams, and F. Chatenaud, “Enhanced surface emitting waveguides for visible, monolithic semiconductor laser sources,” Electron. Lett. 26, 2088–2089 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, and G. N. S. Chu, “Blue-green surface-emitting second-harmonic generators on (111)B GaAs,” Appl. Phys. Lett. 59, 896–898 (1991).
[CrossRef]

X. Gu, Y. J. Ding, W. S. Rabinovich, D. S. Katzer, and J. B. Khurgin, “First observation of high-order quasi-phase-matched second-harmonic generation in semiconductor multilayers in reflection geometry,” in Quantum Electronics and Laser Science Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 243–244.

J. Khurgin, “Large-scale quantum well domain structures,” J. Appl. Phys. 64, 5026–5029 (1988); S. Janz, F. Chatenoud, and R. Normandin, “Quasi-phase-matched second-harmonic generation from asymmetric coupled quantum wells,” Opt. Lett. 19, 622–624 (1994).
[CrossRef] [PubMed]

J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic, San Diego, 1996), pp. 10–31.

The extra 286-ML AlAs layer can be used to maximize the modal overlap among the waves.

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Figures (8)

Fig. 1
Fig. 1

Wave-propagation configuration for a TPCOPA or a difference-frequency generation for a pulsed input.

Fig. 2
Fig. 2

For β1.8×103, L1 cm and dl2.5×10-7, the normalized output intensity for (a) the amplified signal defined by Eq. (28) and (b) phase are plotted against normalized or origin-shifted time or both: τr=β(τ-1) and τr=βτ (solid curves). In (a) the temporal profile for the normalized input intensity defined by Eq. (28) is plotted for comparison (dotted curve).

Fig. 3
Fig. 3

For a3=0.05(P3/Pth=2.5×10-3) and β=0.1, the normalized output intensity for the amplified pulse defined by Eq. (28) (solid curve) and at difference frequency (solid curve) is plotted. For comparison, the temporal profile for the input pulse is plotted (dashed curve).

Fig. 4
Fig. 4

For a3=0.05(P3/Pth=2.5×10-3) and β=10, the normalized output intensity for amplified pulse (solid curve) and at difference frequency (solid curve) is plotted. For comparison, the temporal profile for the input pulse is plotted (dashed curve).

Fig. 5
Fig. 5

For a3=0.05(P3/Pth=2.5×10-3) and β=1, the normalized output intensity for amplified pulse (solid curve) and at difference frequency (solid curve) is plotted. For comparison, the temporal profile for the input pulse is plotted (dashed curve).

Fig. 6
Fig. 6

For β=0.1, 0.5, and 1.0, the normalized input intensity is plotted versus time. For a3=0.95 [(P3-Pth)/Pth=-0.1], the normalized output intensity for amplified pulse (solid curve) and at difference frequency (dotted curve) is plotted. For comparison, the temporal profiles for the input pulses are plotted: β=0.1 (dotted curve), β=0.5 (dotted–dashed curve), and β=1.0 (solid curve).

Fig. 7
Fig. 7

For different pump powers the normalized output intensity for amplified pulse defined by Eq. (28) is plotted versus normalized time. For comparison, the normalized input intensity defined by Eq. (28) is plotted versus normalized time (bottom).

Fig. 8
Fig. 8

Our preliminary design of a structure for amplifying an input beam at 1.55 µm and generating a tunable output around 2.66 µm in the presence of a cw pump at 980 nm [the layer thicknesses are given by the unit of monolayer (ML)]. More accurate layer thicknesses can be obtained following the first growth and characterization of the structure.

Equations (41)

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2E1-1c22E1t2
=1c22t2[(r1-1)E1]+1c22t2[χ(2)E2(E3+E3)],
2E2-1c22E2t2
=1c22t2[(r2-1)E2]+1c22t2[χ(2)E1(E3+E3)],
2E3-1c22E3t2-(1-R1R2)2d0ct(r3E3)
=1c22t2[(r3-1)E3]+1c22t2(χ(2)E1E2),
E1=A1(z, t)ψ1(x)exp[i(β1z-ω1t)]+c.c.,
E2=A2(z, t)ψ2(x)exp[i(-β2z-ω2t)]+c.c.,
E3=A3(t)ψ3(x)exp[i(β3 sin θz-ω3t)]+c.c.,
E3=A3(t)ψ3(x)exp[i(β3 sin θz-ω3t)]+c.c.,
iA1z+1vgA1t-μ22A1t2=-g(A3+A3)A2*,
i-A2z+1vgA2t-μ22A2t2=g(A3+A3)A1*,
d=[χ0(2)]2-+χ(2)(x)ψ1(x)ψ2(x)ψ3(x)dx2
A3=ig3A1A2,g3=2ω3χ0(2)d0n3cd(1-R1R2).
ξ=zL,τ=tvgL,
a1=-i4d0n1n3L(1-R)1/2 A1Ath,
a2=4d0n2n3L(1-R)1/2 A2*Ath,a3=A3Ath.
a1ξ+a1τ+i dl 2a1τ2=π2a3-π2a1a2*a2,
-a2ξ+a2τ-i dl 2a2τ2=π2a3-π2a1*a2a1,
P1=12|a1|2Pth,P2=12|a2|2Pth,P3=a32Pth,
Pth=n1n2n34η0[χ0(2)]2(1-R) WLdd0,
a2(1, τ)=a0 sech(βτ),
a1ξ+a1τ+i dl 2a1τ2=π2a3a2,
-a2ξ+a2τ-i dl 2a2τ2=π2a3a1.
a¯1(ξ, Ω)=-+a1(ξ,τ)exp(-iΩτ)dτ,
a¯2(ξ, Ω)=-+a2(ξ,τ)exp(-iΩτ)dτ,
a1(1, τ)=12π-f1(Ω) πa0βsechΩπ2β×exp(iΩτ)dΩ,
a2(0, τ)=12π-f2(Ω) πa0βsechΩπ2β×exp(-i dlΩ2)exp(iΩτ)dΩ,
f1(Ω)=(π/2)a3 sinΩ2+(π/2)2a32Ω2+(π/2)2a32 cosΩ2+(π/2)2a32+iΩ sinΩ2+(π/2)2a32,
f2(Ω)=Ω2+(π/2)2a32Ω2+(π/2)2a32 cosΩ2+(π/2)2a32+iΩ sinΩ2+(π/2)2a32.
a2(0, τ)=2 sech[β(τ-1)]×1-cos[π/4+β2(τ-1)2/π] exp(iϕ),
ϕ=tan-12/2-cos[β2(τ-1)2/π]2/2+sin[β2(τ-1)2/π],
|Vr(ξ,τ)|2=2P2(ξ,τ)a02Pth.
a1(1, τ)=a0 tanπ2a3sech(βτ),
a2(0, τ)=a0cosπ2a3sech(βτ).
a1(1, τ)=πa0a32βtan-1sinh βcosh[(τ-1)β],
a2(0, τ)=a0 sech[β(τ-1)].
a1(1, τ)=πa0a32sech[β(τ-1)].
η=π2a324=π24P3Pth.
a1(1, τ)=π4a3πv0βif0τ20otherwise.
τp=2n3 d0c(1-R2).

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