Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

Using penetration depth for phase matching in photonic crystal waveguides

S. Y. Goldin, G. Meliach, Y. Arieli, B. Sfez


A new method of design for the phase-matching in waveguides is suggested. The approach is based on utilizing the concept of the penetration depth of light into the waveguide walls. The lateral components of wavevectors are employed to adjust the phase-matching condition in the propagation direction. The method is demonstrated in two systems: one using single and the other using double photonic-crystal mirrors.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2011.11018]

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J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric" Phys. Rev. 127, 1918-1939 (1962).

J. A. Giordmaine, "Mixing of light beams in crystals" Phys. Rev. Lett. 8, 19-20 (1962).

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, "Effects of dispersion and focusing on the production of optical harmonics" Phys. Rev. Lett. 8, 21-22 (1962).

P. A. Franken, and J. F. Ward, "Optical harmonics and nonlinear phenomena" Rev. Mod. Phys. 35, 23-39 (1963).

A. Yariv, and P. Yeh, "Electromagnetic propagation in periodic stratified media. II. Birefringence, phase matching, and x-ray la- sers" J. Opt. Soc. Am. 67, 438-447 (1977).

V. Berger, "Nonlinear photonic crystals" Phys. Rev. Lett. 81, 4136 -4138 (1998).

G. E. Smith, "Phase matching in four-layer optical waveguides" IEEE J. Quantum Electron., 288-289 (1968)

P. K. Tien, "Light waves in thin films and integrated optics" Appl. Opt. 10, 2395-2413 (1971).

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, "Phase-matched three -wave mixing in silica fiber optical waveguides" Appl. Phys. Lett. 24, 308-310 (1974).

K. Jain and G. H. Hewig, "Phase-matched second-harmonic gener- ation at 440 nm in a LiNbO3-Gd3Ga5O12 waveguide with a tuna- ble stimulated Raman source" Opt. Commun. 36, 483-486 (1981).

K. O. Hill, D. C. Johnson, and B. S. Kawasaki, "Efficient conversion of light over a wide spectral range by four-photon mixing in a multimode graded-index fiber" Appl. Opt. 20, 1075-1079 (1981)

T. L. Penner, H. R. Motschmann, N. J. Armstrong, M. C. Ezenyilim- ba and D. J. Williams, "Efficient phase-matched second-harmonic generation of blue light in an organic waveguide" Nature 367, 49- 51 (1994).

T. Watanabe, V. Edel, X. T. Tao, S. Shimoda, and S. Miyata, "A polymeric five-layer nonlinear optical waveguide with a large dimension tolerance and large overlap integral for mode conver- sion phase-matching" Opt. Commun. 123, 76-82 (1996).

B. Oster, and H. Fouckhardt, "M-waveguide structures for direct phase matching in AlGaAs" Appl. Phys. B 73, 535-540 (2001).

K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calli- garo, V. Ortiz, and V. Berger, "Second-harmonic generation through optimized modal phase matching in semiconductor waveguides" Appl. Phys. Lett. 83, 620-622 (2003).

A.S. Helmy, "Phase matching using Bragg reflection waveguides for monolithic nonlinear optics applications" Opt. Express 14, 1243-1252 (2006).

L. Xiao, C. Lin, W. Zhang, Y. Huang, and J. Peng, "Modal phase- matching second harmonic generation in Bragg fiber" Opt. Com- mun. 281, 2614-2617 (2008).

B. Bijlani, P. Abolghasem, and A.S. Helmy, "Second harmonic generation in ridge Bragg reflection waveguides" Appl. Phys. Lett. 92, 101124 (2008).

G. P. Agrawal, Nonlinear fiber optics (3rd Edition, Academic Press, San Diego, 2001).

P. K. Tien, R. Ulrich, and R. J. Martin, "Optical second harmonic generation in form of coherent Cerenkov radiation from a thin- film waveguide" Appl. Phys. Lett. 17, 447-450 (1970).

H. Ito, N. Uesugi, and H. Inaba, "Phase-matched guided optical second harmonic wave generation in oriented ZnS polycrystalline thin-film waveguides" Appl. Phys. Lett. 25, 385-387 (1974).

H. P. Wagner, M. Kuhnelt, W. Langbein, and J. M. Hvam, "Dispersion of the second-order nonlinear susceptibility in ZnTe, ZnSe, and ZnS" Phys. Rev. B 58, 10494-10501 (1998).

H.-Y. Leea, and T. Yao, "Design and evaluation of omnidirectional one-dimensional photonic crystals" J. Appl. Phys. 93, 819-830 (2003).

P. Yeh, A. Yariv, and C. Hong, "Electromagnetic propagation in periodic stratified media. I. General theory", J. Opt. Soc. Am. 67, 423-438 (1977).

P. Yeh, Optical Waves in Layered Media (2nd Edition, Wiley- Interscience, New York, 2005).