Substantial gain enhancement for optical parametric amplification and oscillation in two-dimensional χ^{(2)} nonlinear photonic crystals
Optics Express, Vol. 16, Issue 13, pp. 9714-9725 (2008)
http://dx.doi.org/10.1364/OE.16.009714
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Abstract
We have analyzed optical parametric interaction in a 2D NPC. While in general the nonlinear coefficient is small compared to a 1D NPC, we show that at numerous orientations a multitude of reciprocal vectors contribute additively to enhance the gain in optical parametric amplification and oscillation in a 2D patterned crystal. In particular, we have derived the effective nonlinear coefficients for common-signal amplification and common-idler amplification for a tetragonal inverted domain pattern. We show that in the specific case of signal amplification with QPM by both G _{10} and G _{11} , symmetry of the crystal results in coupled interaction with the corresponding signal amplification by G _{10} and G _{1,-1} . As a consequence, this coupled utilization of all three reciprocal vectors leads to a substantial increase in parametric gain. Using PPLN we demonstrate numerically that a gain that comes close to that of a 1D QPM crystal could be realized in a 2D NPC with an inverted tetragonal domain pattern. This special mechanism produces two pairs of identical signal and idler beams propagating in mirror-imaged forward directions. In conjunction with this gain enhancement and multiple beams output we predict that there is a large pulling effect on the output wavelength due to dynamic signal build-up in the intrinsic noncollinear geometry of a 2D NPC OPO.
© 2008 Optical Society of America
1. Introduction
1. V. Berger, “Nonlinear photonic crystals”, Phys. Rev. Lett. 81, No. 19, 4136–4139 (1998). [CrossRef]
2. N. G. R. Broderick, G.W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal”, Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed]
3. L.-H. Peng, C.-C. Hsu, Jimmy Ng, and A. H. Kung, “Wavelength tunability of second-harmonic generation from two-dimensional χ^{(2)} nonlinear photonic crystals with a tetragonal lattice structure”, Appl. Phys. Lett. 84, 3250–3252 (2004). [CrossRef]
4. M. Seiter and M. W. Sigrist, “On-line multicomponent trace-gas analysis with a broadly tunable pulsed difference-frequency laser spectrometer,” Appl. Opt. 38, 4691–4698 (1999). [CrossRef]
5. M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO_{3} waveguides,” IEEE Photonics Technology Lett. 12, 82–84 (2000). [CrossRef]
6. L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched 1.064 micron-pumped optical parametric oscillator in bulk periodically poled LiNbO_{3}”, Opt. Lett. 20, 52–54 (1995). [CrossRef] [PubMed]
1. V. Berger, “Nonlinear photonic crystals”, Phys. Rev. Lett. 81, No. 19, 4136–4139 (1998). [CrossRef]
7. A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in 2D nonlinear photonic crystals”, Opt. Quantum Electron. 39, 361 (2007). [CrossRef]
2. Parametric interaction in 2D NPC
3. Theoretical derivation of the parametric gain
1. V. Berger, “Nonlinear photonic crystals”, Phys. Rev. Lett. 81, No. 19, 4136–4139 (1998). [CrossRef]
3. L.-H. Peng, C.-C. Hsu, Jimmy Ng, and A. H. Kung, “Wavelength tunability of second-harmonic generation from two-dimensional χ^{(2)} nonlinear photonic crystals with a tetragonal lattice structure”, Appl. Phys. Lett. 84, 3250–3252 (2004). [CrossRef]
7. A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in 2D nonlinear photonic crystals”, Opt. Quantum Electron. 39, 361 (2007). [CrossRef]
4. Numerical simulation
10. L.-H. Peng, C.-C. Hsu, and Y.-C. Shih, “Second-harmonic green generation from two-dimensional χ^{(2)} nonlinear photonic crystal with orthorhombic lattice structure”, Appl. Phys. Lett. 83, 3447 (2003). [CrossRef]
5. Conclusion
References and links
1. | V. Berger, “Nonlinear photonic crystals”, Phys. Rev. Lett. 81, No. 19, 4136–4139 (1998). [CrossRef] |
2. | N. G. R. Broderick, G.W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal”, Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed] |
3. | L.-H. Peng, C.-C. Hsu, Jimmy Ng, and A. H. Kung, “Wavelength tunability of second-harmonic generation from two-dimensional χ^{(2)} nonlinear photonic crystals with a tetragonal lattice structure”, Appl. Phys. Lett. 84, 3250–3252 (2004). [CrossRef] |
4. | M. Seiter and M. W. Sigrist, “On-line multicomponent trace-gas analysis with a broadly tunable pulsed difference-frequency laser spectrometer,” Appl. Opt. 38, 4691–4698 (1999). [CrossRef] |
5. | M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO_{3} waveguides,” IEEE Photonics Technology Lett. 12, 82–84 (2000). [CrossRef] |
6. | L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched 1.064 micron-pumped optical parametric oscillator in bulk periodically poled LiNbO_{3}”, Opt. Lett. 20, 52–54 (1995). [CrossRef] [PubMed] |
7. | A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in 2D nonlinear photonic crystals”, Opt. Quantum Electron. 39, 361 (2007). [CrossRef] |
8. | D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n_{e}, in congruent lithium niobate”, Opt. Lett. 22, 1553 (1997). [CrossRef] |
9. | R. W. Boyd, Nonlinear Optics, 2nd Ed. Chap. 2 (Academic Press, 2003). |
10. | L.-H. Peng, C.-C. Hsu, and Y.-C. Shih, “Second-harmonic green generation from two-dimensional χ^{(2)} nonlinear photonic crystal with orthorhombic lattice structure”, Appl. Phys. Lett. 83, 3447 (2003). [CrossRef] |
11. | A. E. Siegman, Lasers, pg 1169, Chapter 29 (University Science Books, 1986). |
OCIS Codes
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(160.5298) Materials : Photonic crystals
ToC Category:
Nonlinear Optics
History
Original Manuscript: April 7, 2008
Revised Manuscript: June 2, 2008
Manuscript Accepted: June 12, 2008
Published: June 17, 2008
Citation
Hsi-Chun Liu and A. H. Kung, "Substantial gain enhancement for optical parametric amplification and oscillation in two-dimensional χ^{(2)} nonlinear photonic crystals," Opt. Express 16, 9714-9725 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9714
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References
- V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998). [CrossRef]
- N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, "Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal," Phys. Rev. Lett. 84, 4345-4348 (2000). [CrossRef] [PubMed]
- L.-H. Peng, C.-C. Hsu, J. Ng, and A. H. Kung, "Wavelength tunability of second-harmonic generation from two-dimensional ?(2) nonlinear photonic crystals with a tetragonal lattice structure," Appl. Phys. Lett. 84, 3250-3252 (2004). [CrossRef]
- M. Seiter and M. W. Sigrist, "On-line multicomponent trace-gas analysis with a broadly tunable pulsed difference-frequency laser spectrometer," Appl. Opt. 38, 4691-4698 (1999). [CrossRef]
- M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, "Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides," IEEE Photonics Technology Lett. 12, 82-84 (2000). [CrossRef]
- L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, and R. L. Byer, "Quasi-phase-matched 1.064 micron-pumped optical parametric oscillator in bulk periodically poled LiNbO3," Opt. Lett. 20, 52-54 (1995). [CrossRef] [PubMed]
- A. Arie, N. Habshoosh, and A. Bahabad, "Quasi phase matching in 2D nonlinear photonic crystals," Opt. Quantum Electron. 39, 361 (2007). [CrossRef]
- D. H. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate," Opt. Lett. 22, 1553 (1997). [CrossRef]
- R. W. Boyd, Nonlinear Optics, 2nd Ed. (Academic Press, 2003) Chap. 2.
- L.-H. Peng, C.-C. Hsu, and Y.-C. Shih, "Second-harmonic green generation from two-dimensional ?^{(2)} nonlinear photonic crystal with orthorhombic lattice structure," Appl. Phys. Lett. 83, 3447 (2003). [CrossRef]
- A. E. Siegman, Lasers, (University Science Books, 1986) Chap. 29, pp. 1169.
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