Abstract

Tunable second- and fourth-harmonic radiation was generated in a single 1-cm-long lithium niobate (LiNbO3) crystal with the Mark III infrared free electron laser at Duke University. The fundamental laser radiation was tuned from 2 to 2.5 μm, yielding 1–1.25-μm radiation (second harmonic) and 0.5–0.625-μm radiation (fourth harmonic). A fundamental–second-harmonic energy conversion efficiency of 66% and a fundamental–fourth-harmonic energy conversion efficiency of 3.3 × 10−6 were measured. The maximum energy in the fourth harmonic was 3.3 nJ.

© 1994 Optical Society of America

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  1. S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).
  2. S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
    [CrossRef]
  3. B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
    [CrossRef]
  4. B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
    [CrossRef]
  5. B. Hooper, S. Benson, J. M. J. Madey, “Conversion efficiency optimization of free electron laser light,” Nucl. Instrum. Methods A 331, 93–97 (1993).
    [CrossRef]
  6. V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).
  7. G. P. A. Malcolm, M. A. Persaud, A. I. Ferguson, “Resonant frequency quadrupling of a mode-locked diode-pumped Nd:YLF laser,” Opt. Lett. 16, 983–985 (1991).
    [CrossRef] [PubMed]
  8. S. C. Tidwell, J. F. Seamans, D. D. Lowenthal, G. Matone, G. Giordano, “Efficient high-power UV generation by use of a resonant ring driven by a cw mode-locked IR laser,” Opt. Lett. 18, 1517–1519 (1993).
    [CrossRef] [PubMed]
  9. D. Eimerl, “Quadrature frequency conversion,” IEEE J. Quantum Electron. QE-28, 1361–1371 (1987).
    [CrossRef]
  10. D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” IEEE J. Quantum Electron. QE-2, 338–379 (1966).
  11. imsl version 2.0, routine divpag, Visual Numerics, Houston, Tex.
  12. G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
    [CrossRef]

1993 (2)

1991 (1)

1990 (2)

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
[CrossRef]

1988 (1)

B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
[CrossRef]

1987 (1)

D. Eimerl, “Quadrature frequency conversion,” IEEE J. Quantum Electron. QE-28, 1361–1371 (1987).
[CrossRef]

1984 (1)

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

1975 (1)

V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).

1974 (1)

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

1966 (1)

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” IEEE J. Quantum Electron. QE-2, 338–379 (1966).

Akhmanov, S. A.

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

Ashkin, A.

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” IEEE J. Quantum Electron. QE-2, 338–379 (1966).

Benson, S.

B. Hooper, S. Benson, J. M. J. Madey, “Conversion efficiency optimization of free electron laser light,” Nucl. Instrum. Methods A 331, 93–97 (1993).
[CrossRef]

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
[CrossRef]

B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
[CrossRef]

Boyd, G. D.

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” IEEE J. Quantum Electron. QE-2, 338–379 (1966).

Cutolo, A.

B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
[CrossRef]

Dubovik, A. N.

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

Edwards, G. J.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Eimerl, D.

D. Eimerl, “Quadrature frequency conversion,” IEEE J. Quantum Electron. QE-28, 1361–1371 (1987).
[CrossRef]

Fann, W.

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

Ferguson, A. I.

Giordano, G.

Hooper, B.

B. Hooper, S. Benson, J. M. J. Madey, “Conversion efficiency optimization of free electron laser light,” Nucl. Instrum. Methods A 331, 93–97 (1993).
[CrossRef]

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
[CrossRef]

B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
[CrossRef]

Kleinman, D. A.

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” IEEE J. Quantum Electron. QE-2, 338–379 (1966).

Kornienko, N. E.

V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).

Krylov, V. N.

V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).

Lawrence, M.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Lowenthal, D. D.

Madey, J.

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

Madey, J. M. J.

B. Hooper, S. Benson, J. M. J. Madey, “Conversion efficiency optimization of free electron laser light,” Nucl. Instrum. Methods A 331, 93–97 (1993).
[CrossRef]

B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
[CrossRef]

B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
[CrossRef]

Malcolm, G. P. A.

Matone, G.

Persaud, M. A.

Richman, B.

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

Saltiel, S. M.

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

Seamans, J. F.

Straight, R.

B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
[CrossRef]

Strizhevskii, V. L.

V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).

Szarmes, E.

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

Tidwell, S. C.

Tomov, I. V.

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

Tunkin, V. G.

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

Vintro, L.

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

Volosov, V. D.

V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).

IEEE J. Quantum Electron. (2)

D. Eimerl, “Quadrature frequency conversion,” IEEE J. Quantum Electron. QE-28, 1361–1371 (1987).
[CrossRef]

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” IEEE J. Quantum Electron. QE-2, 338–379 (1966).

JETP Lett. (1)

S. A. Akhmanov, A. N. Dubovik, S. M. Saltiel, I. V. Tomov, V. G. Tunkin, “Nonlinear optical effects of fourth order in the field in a lithium formiate crystal,” JETP Lett. 20, 117–118 (1974).

Nucl. Instrum. Methods A (4)

S. Benson, W. Fann, B. Hooper, J. Madey, E. Szarmes, B. Richman, L. Vintro, “A review of the Stanford Mark III infrared FEL program,” Nucl. Instrum. Methods A 296, 110–114 (1990).
[CrossRef]

B. Hooper, S. Benson, A. Cutolo, J. M. J. Madey, “Experimental results of two-stage harmonic generation with picosecond pulses on the Stanford Mark III FEL,” Nucl. Instrum. Methods A 272, 96–98 (1988).
[CrossRef]

B. Hooper, S. Benson, R. Straight, J. M. J. Madey, “Applications of harmonic generation of picosecond pulses from a free electron laser,” Nucl. Instrum. Methods A 296, 797–803 (1990).
[CrossRef]

B. Hooper, S. Benson, J. M. J. Madey, “Conversion efficiency optimization of free electron laser light,” Nucl. Instrum. Methods A 331, 93–97 (1993).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

V. D. Volosov, N. E. Kornienko, V. N. Krylov, V. L. Strizhevskii, “Cascade interresonator generation of fourth optical harmonic,” Sov. Tech. Phys. Lett. 1, 483–484 (1975).

Other (1)

imsl version 2.0, routine divpag, Visual Numerics, Houston, Tex.

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Figures (2)

Fig. 1
Fig. 1

Phase mismatch versus angle for FHG by cascaded SHG Δk(——) and by direct FHG Δkω when (a) type I phase matched for SHG (θ = θm) in LiNbO3 at (a) λ = 2.2 μm and (b) type I phase matched for SHG in LiNbO3, at each wavelength shown.

Fig. 2
Fig. 2

(a) Energy conversion efficiencies as a function of crystal length for the fundamental, η1 = 1/1, the SH, η2 = 2/1, and the FH, η4 = 4/1 from an approximate analytical solution (solid curve with x, η1; dashed curve with ○, η2; solid curve, η4) and a numerical simulation (χ, η1, ○, η2; □, η4) of Eqs. (1) in LiNbO3 at 2 μm for the following parameters: Δk = 0 rad/cm, Δk = 12,150 rad/cm, κ1 = 6.8 × 10−6 (Φ = 90°), κ2 = 42.8 × 10−6 and I1(0) = 1.0 GW/cm2. (b) Comparison of the experimentally measured FHG (◆, η4-measured), the numerical simulation of FHG (□, η4-simulation), and the analytically calculated (solid curve, η4-analytic) conversion efficiencies for the FH versus input intensity in 1 cm of LiNbO3 at 2 μm.

Equations (5)

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E 1 z = i κ 1 E 1 * E 2 exp ( i Δ k 2 ω z ) + i κ 4 E 1 * 3 E 4 exp ( i Δ k ω z ) ,
E 2 z = i κ 1 E 1 2 exp ( - i Δ k 2 ω z ) + i κ 2 E 2 * E 4 exp ( i Δ k 4 ω z ) ,
E 4 z = i κ 2 E 2 2 exp ( - i Δ k 4 ω z ) + i κ 4 E 1 4 exp ( - i Δ k ω z ) ,
d eff 1 = d 31 sin θ - d 22 cos θ sin 3 Φ ,
d eff 2 = d 31 cos 2 θ sin θ + d 22 cos 3 θ sin 3 Φ + d 33 sin 3 θ .

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