Abstract

We describe a femtosecond optical parametric oscillator based on periodically poled lithium niobate and pumped by a self-mode-locked Ti:sapphire laser. Signal and idler outputs almost continuously tunable from 975 nm to 4.55 μm were generated by a combination of grating tuning and cavity-length tuning, and an explanation of the tuning properties is given in terms of the gain bandwidth. A threshold of 45 mW was measured and, in the absence of optimized output coupling, signal powers of 90 mW and idler powers of 70 mW were obtained, with 140 mW of green light at 540 nm generated by phase-matched frequency doubling of the signal. Dispersion compensation produced near-transform-limited signal pulses of duration 140 fs. Observations regarding temperature tuning and pump depletion are also presented.

© 1998 Optical Society of America

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  1. A. Feisst and P. Koidl, “Current induced periodic ferroelectric domain structures in LiNbO3 applied for efficient nonlinear optical frequency mixing,” Appl. Phys. Lett. 47, 1125–1127 (1985).
    [CrossRef]
  2. M. Asobe, I. Yokohama, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
    [CrossRef] [PubMed]
  3. L. Goldberg, W. K. Burns, and R. W. McElhanon, “Difference-frequency generation of tunable mid-infrared radiation in bulk periodically poled LiNbO3,” Opt. Lett. 20, 1280–1282 (1995).
    [CrossRef] [PubMed]
  4. M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30, 34–35 (1994).
    [CrossRef]
  5. A. Galvanauskas, M. A. Arbore, M. M. Fejer, M. E. Fermann, and D. Harter, “Fiber-laser-based femtosecond parametric generation in bulk periodically poled LiNbO3,” Opt. Lett. 22, 105–107 (1997).
    [CrossRef] [PubMed]
  6. D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
    [CrossRef]
  7. J. J. Zayhowski, “Periodically poled lithium niobate optical parametric amplifiers pumped by high-power passively Q-switched microchip lasers,” Opt. Lett. 22, 169–171 (1997).
    [CrossRef] [PubMed]
  8. M. A. Arbore and M. M. Fejer, “Singly resonant optical parametric oscillation in periodically poled lithium niobate waveguides,” Opt. Lett. 22, 151–153 (1997).
    [CrossRef] [PubMed]
  9. S. D. Butterworth, V. Pruneri, and D. C. Hanna, “Optical parametric oscillation in periodically poled lithium niobate based on continuous-wave synchronous pumping at 1.047 μm,” Opt. Lett. 21, 1345–1347 (1996).
    [CrossRef] [PubMed]
  10. S. D. Butterworth, P. G. R. Smith, and D. C. Hanna, “Picosecond Ti:sapphire pumped optical parametric oscillator based on periodically poled LiNbO3,” Opt. Lett. 22, 618–620 (1997).
    [CrossRef] [PubMed]
  11. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
    [CrossRef]
  12. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
    [CrossRef]
  13. Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
    [CrossRef]
  14. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
    [CrossRef]
  15. D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, Opt. Lett. 22, 1397–1399 (1997).
    [CrossRef]
  16. Z. E. Penman, P. Loza-Alvarez, D. T. Reid, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “All-solid-state mid-infrared femtosecond optical parametric oscillator based on periodically-poled lithium niobate,” Opt. Commun. (to be published).
  17. J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
    [CrossRef]
  18. W. S. Pelouch, P. E. Powers, and C. L. Tang, “Ti:sapphire-pumped, high-repetition-rate femtosecond optical parametric oscillator,” Opt. Lett. 17, 1070–1072 (1992).
    [CrossRef] [PubMed]
  19. T. Kartaloglu, K. G. Köprülü, and O. Aytür, “Phase-matched self-doubling optical parametric oscillator,” Opt. Lett. 22, 280–282 (1997).
    [CrossRef]

1997 (8)

D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
[CrossRef]

A. Galvanauskas, M. A. Arbore, M. M. Fejer, M. E. Fermann, and D. Harter, “Fiber-laser-based femtosecond parametric generation in bulk periodically poled LiNbO3,” Opt. Lett. 22, 105–107 (1997).
[CrossRef] [PubMed]

M. A. Arbore and M. M. Fejer, “Singly resonant optical parametric oscillation in periodically poled lithium niobate waveguides,” Opt. Lett. 22, 151–153 (1997).
[CrossRef] [PubMed]

J. J. Zayhowski, “Periodically poled lithium niobate optical parametric amplifiers pumped by high-power passively Q-switched microchip lasers,” Opt. Lett. 22, 169–171 (1997).
[CrossRef] [PubMed]

M. Asobe, I. Yokohama, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
[CrossRef] [PubMed]

T. Kartaloglu, K. G. Köprülü, and O. Aytür, “Phase-matched self-doubling optical parametric oscillator,” Opt. Lett. 22, 280–282 (1997).
[CrossRef]

S. D. Butterworth, P. G. R. Smith, and D. C. Hanna, “Picosecond Ti:sapphire pumped optical parametric oscillator based on periodically poled LiNbO3,” Opt. Lett. 22, 618–620 (1997).
[CrossRef] [PubMed]

D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, Opt. Lett. 22, 1397–1399 (1997).
[CrossRef]

1996 (1)

1995 (2)

1994 (2)

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30, 34–35 (1994).
[CrossRef]

J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

1992 (1)

1985 (1)

A. Feisst and P. Koidl, “Current induced periodic ferroelectric domain structures in LiNbO3 applied for efficient nonlinear optical frequency mixing,” Appl. Phys. Lett. 47, 1125–1127 (1985).
[CrossRef]

1984 (1)

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

1969 (1)

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Arbore, M. A.

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Asobe, M.

Aytür, O.

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Bortz, M. L.

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30, 34–35 (1994).
[CrossRef]

Bosenberg, W. R.

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Burns, W. K.

Butterworth, S. D.

Byer, R. L.

Dudley, J. M.

J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Ebrahimzadeh, M.

D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
[CrossRef]

D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, Opt. Lett. 22, 1397–1399 (1997).
[CrossRef]

J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Eckardt, R. C.

Edwards, G. J.

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

Feisst, A.

A. Feisst and P. Koidl, “Current induced periodic ferroelectric domain structures in LiNbO3 applied for efficient nonlinear optical frequency mixing,” Appl. Phys. Lett. 47, 1125–1127 (1985).
[CrossRef]

Fejer, M. M.

Fermann, M. E.

Fujimura, M.

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30, 34–35 (1994).
[CrossRef]

Galvanauskas, A.

Goldberg, L.

Hanna, D. C.

Harter, D.

Itoh, H.

Kaino, T.

Karlsson, H.

Kartaloglu, T.

Kim, Y. S.

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

Koidl, P.

A. Feisst and P. Koidl, “Current induced periodic ferroelectric domain structures in LiNbO3 applied for efficient nonlinear optical frequency mixing,” Appl. Phys. Lett. 47, 1125–1127 (1985).
[CrossRef]

Köprülü, K. G.

Laurell, F.

Lawrence, M.

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

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

McElhanon, R. W.

McGowan, C.

D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
[CrossRef]

Myers, L. E.

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Pelouch, W. S.

Penman, Z.

Pierce, J. W.

Powers, P. E.

Pruneri, V.

Reid, D. T.

D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, Opt. Lett. 22, 1397–1399 (1997).
[CrossRef]

D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
[CrossRef]

J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Sibbett, W.

D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
[CrossRef]

D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, Opt. Lett. 22, 1397–1399 (1997).
[CrossRef]

J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Smith, P. G. R.

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Smith, R. T.

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

Tang, C. L.

Yokohama, I.

Zayhowski, J. J.

Appl. Phys. Lett. (2)

A. Feisst and P. Koidl, “Current induced periodic ferroelectric domain structures in LiNbO3 applied for efficient nonlinear optical frequency mixing,” Appl. Phys. Lett. 47, 1125–1127 (1985).
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Electron. Lett. (1)

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30, 34–35 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. T. Reid, C. McGowan, M. Ebrahimzadeh, and W. Sibbett, “Characterization and modeling of a noncollinearly phase-matched femtosecond optical parametric oscillator based on KTA and operating to beyond 4 μm,” IEEE J. Quantum Electron. 33, 1–9 (1997).
[CrossRef]

J. Appl. Phys. (1)

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

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

Opt. Commun. (1)

J. M. Dudley, D. T. Reid, M. Ebrahimzadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti-sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Opt. Lett. (10)

W. S. Pelouch, P. E. Powers, and C. L. Tang, “Ti:sapphire-pumped, high-repetition-rate femtosecond optical parametric oscillator,” Opt. Lett. 17, 1070–1072 (1992).
[CrossRef] [PubMed]

L. Goldberg, W. K. Burns, and R. W. McElhanon, “Difference-frequency generation of tunable mid-infrared radiation in bulk periodically poled LiNbO3,” Opt. Lett. 20, 1280–1282 (1995).
[CrossRef] [PubMed]

A. Galvanauskas, M. A. Arbore, M. M. Fejer, M. E. Fermann, and D. Harter, “Fiber-laser-based femtosecond parametric generation in bulk periodically poled LiNbO3,” Opt. Lett. 22, 105–107 (1997).
[CrossRef] [PubMed]

M. A. Arbore and M. M. Fejer, “Singly resonant optical parametric oscillation in periodically poled lithium niobate waveguides,” Opt. Lett. 22, 151–153 (1997).
[CrossRef] [PubMed]

J. J. Zayhowski, “Periodically poled lithium niobate optical parametric amplifiers pumped by high-power passively Q-switched microchip lasers,” Opt. Lett. 22, 169–171 (1997).
[CrossRef] [PubMed]

M. Asobe, I. Yokohama, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
[CrossRef] [PubMed]

T. Kartaloglu, K. G. Köprülü, and O. Aytür, “Phase-matched self-doubling optical parametric oscillator,” Opt. Lett. 22, 280–282 (1997).
[CrossRef]

S. D. Butterworth, P. G. R. Smith, and D. C. Hanna, “Picosecond Ti:sapphire pumped optical parametric oscillator based on periodically poled LiNbO3,” Opt. Lett. 22, 618–620 (1997).
[CrossRef] [PubMed]

D. T. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, Opt. Lett. 22, 1397–1399 (1997).
[CrossRef]

S. D. Butterworth, V. Pruneri, and D. C. Hanna, “Optical parametric oscillation in periodically poled lithium niobate based on continuous-wave synchronous pumping at 1.047 μm,” Opt. Lett. 21, 1345–1347 (1996).
[CrossRef] [PubMed]

Opt. Quantum Electron. (1)

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

Other (1)

Z. E. Penman, P. Loza-Alvarez, D. T. Reid, M. Ebrahimzadeh, W. Sibbett, and D. H. Jundt, “All-solid-state mid-infrared femtosecond optical parametric oscillator based on periodically-poled lithium niobate,” Opt. Commun. (to be published).

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Figures (12)

Fig. 1
Fig. 1

Theoretical phase-matching curve showing the grating tuning available from PPLN at a temperature of 24 °C for pumping at typical Ti:sapphire wavelengths of 790 nm, 800 nm, and 810 nm.

Fig. 2
Fig. 2

OPO cavity configuration. Inset shows the prism arrangement used for intracavity dispersion compensation.

Fig. 3
Fig. 3

Experimental grating and cavity-length tuning data (points). Idler data are inferred from measured signal data. The different symbols indicate different mirror sets. Shown for comparison is a theoretical tuning curve calculated for a pump wavelength of 803 nm and a crystal temperature of 24 °C.

Fig. 4
Fig. 4

Variation of the magnitude of the normalized gain coefficient, sinc2(ΔkL/2), across the OPO tuning range for a pump wavelength of 803 nm. Perfect phase matching (ΔkL=0), where the normalized gain is unity, is shown in black, while a gain of zero (ΔkL equals an integer multiple of 2π) is shown in white. Experimental data points recorded for a pump wavelength of 803 nm are shown in white.

Fig. 5
Fig. 5

Experimental temperature tuning results (circles), showing the signal wavelengths obtained by cavity-length tuning at 24 °C, 60 °C, and 100 °C, with a pump wavelength of 798 nm and a grating period of 20.71 μm. The curve is the tuning predicted from Sellmeier equations.12

Fig. 6
Fig. 6

Variation with wavelength of signal power extracted from the uncompensated cavity via a 1% output coupler, at a crystal temperature of 100 °C, with 1.35 W of pump power at 803 nm. The signal wavelength was varied by cavity-length tuning. The pump pulses were transform limited with a duration of 100 fs.

Fig. 7
Fig. 7

Depleted pump spectra for a range of successive signal wavelengths obtained by cavity-length tuning. The dotted curve in each case indicates the spectrum of the undepleted pump.

Fig. 8
Fig. 8

(a)–(c) Interferometric autocorrelations of signal pulses from the uncompensated cavity, at increasingly longer wavelengths, with (d)–(f) corresponding spectra. The pulse durations were 335 fs (a), 346 fs (b), and 548 fs (c). The signal wavelength was varied by cavity-length tuning.

Fig. 9
Fig. 9

(a) Interferometric autocorrelation of signal pulses from the compensated cavity, with (b) corresponding spectrum. The pulse duration was 140 fs and the spectral bandwidth was 10.3 nm, giving a time–bandwidth product of 0.35.

Fig. 10
Fig. 10

Variation with wavelength of signal power extracted via a 1% output coupler from the compensated cavity, at a crystal temperature of 100 °C, with 1.35 W of pump power. The signal wavelength was varied by cavity-length tuning.

Fig. 11
Fig. 11

Phase-matching curve for third-order SHG in PPLN. Circles are experimental data points.

Fig. 12
Fig. 12

Variation of relative power of the second harmonic with signal wavelength (circles), compared with theoretical SHG efficiency (curve).

Equations (3)

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Δk=kp-ks-ki-km,
Λ=mλω2(n2ω-nω),
ηsin(Δkl/2)Δkl/22.

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