Abstract

We propose a novel scheme of achromatic phase matching for second-harmonic generation (SHG) in tilted quasi-phase matching gratings. The spectral angular dispersion is introduced in fundamental waves such that each frequency component satisfies the two-dimensional quasi-phase matched condition. This is equivalent to simultaneous quasi-phase- and group-velocity-matched SHG for ultrashort pulses. Equations to describe achromatic conditions are derived and applied specifically to periodically poled lithium niobate (PPLN). The phase-matching bandwidth for 10 mm-long PPLN increases by factors of 110 and 32 at wavelengths of 0.8 and 1.55 μm, respectively, compared with those for the conventional quasi-phase matching.

© 2003 Optical Society of America

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References

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    [CrossRef]
  3. B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “All-prism achromatic phase matching for tunable second-harmonic generation,” Appl. Opt. 38, 3316–3323 (1999).
    [CrossRef]
  4. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  5. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
    [CrossRef]
  6. N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, “Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communication band,” Opt. Lett. 27, 1046–1048 (2002).
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2002 (2)

2000 (1)

1999 (1)

1998 (1)

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

1997 (1)

1995 (1)

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1989 (1)

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

Arbore, M. A.

Ashihara, S.

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

Bisson, S. E.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Cha, M.

Chou, M. H.

Dienes, A.

Fejer, M. M.

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Galvanauskas, A.

Harter, D.

Jacobson, A.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kivshar, Y. S.

Knoesen, A.

Kurimura, S.

Kuroda, K.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Martinez, O. E.

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

Nishina, J.

Richman, B. A.

Ro, J. H.

Saltiel, S.

Shimura, T.

Sidick, E.

Taira, T.

Trebino, R.

Yu, N. E.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

Other (1)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, “Handbook of Nonlinear Optical Crystals,” 3rd ed. (Springer, New York, 1999).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of 2D SHG interactions in tilted QPM structures. (b) Wave-vector diagram of the 2D QPM interaction. Dashed curves, arcs with radii of 2k1 (inner) and k2 (outer).

Fig. 2
Fig. 2

Phase-matching angles α in noncollinear geometry near 1.55-μm wavelength. The curves correspond to three normalized grating periods R.

Fig. 3
Fig. 3

Calculated values of α, β, , and at 1.55-μm wavelength as a function of normalized grating period R.

Fig. 4
Fig. 4

Calculated values of α, β, , and as functions of wavelength. Normalized grating period R was set to be 0.5 at each wavelength.

Fig. 5
Fig. 5

Calculated values of (a) (Δλ)L for 1D QPM and (b) (Δλ)2L for 2D QPM with the appropriate spectral angular dispersion plotted as a function of operation wavelength, where (Δλ) is the phase-matching bandwidth for interaction length L.

Equations (8)

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Δk=-2k1cos(ζ-α)-K cos ζ+{k22-[2k1sin(ζ-α)+K sin ζ]2}1/2.
Δk(λ0+Δλ)=Δk(λ0)+dΔkdλλ0Δλ+12d2Δkdλ2λ0(Δλ)2+,
cos α=-K2+4k12-k224Kk1,
cos β=4k12+k22-K24k1k2.
=dαdλλ0=14k1K sin α4(2k1+K cos α) dkdλλ0-k2dkdλλ0/2,
=dγdλλ0/2=1k2K sin γ8k1dkdλλ0+(K cos γ-k2) dkdλλ0/2,
ΔλL=0.886πd(Δk)dλλ0-1.
(Δλ)2L=1.772πd2(Δk)dλ2λ0-1.

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