## Obliquely incident wave coupling on finite-aperture waveguide gratings

JOSA A, Vol. 16, Issue 2, pp. 305-315 (1999)

http://dx.doi.org/10.1364/JOSAA.16.000305

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### Abstract

The problem of oblique incidence of plane waves and Gaussian beams on finite-aperture gratings (the number of grooves and their length and depth are all finite) in slab waveguides is analyzed by means of a four-wave two-dimensional coupled-mode theory (2D-CMT). This model considers the finite aperture of the gratings and the correct simultaneous interaction among all four relevant waves

© 1999 Optical Society of America

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(050.2770) Diffraction and gratings : Gratings

(130.2790) Integrated optics : Guided waves

(230.7390) Optical devices : Waveguides, planar

(350.5500) Other areas of optics : Propagation

**History**

Original Manuscript: May 20, 1998

Revised Manuscript: September 23, 1998

Manuscript Accepted: September 29, 1998

Published: February 1, 1999

**Citation**

Nahum Izhaky and Amos Hardy, "Obliquely incident wave coupling on finite-aperture waveguide gratings," J. Opt. Soc. Am. A **16**, 305-315 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-2-305

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### References

- D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1991).
- A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991).
- H. Kogelnik, “Theory of optical waveguides,” in Guided Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1990).
- D. G. Hall, “Optical waveguide diffraction gratings: coupling between guided modes,” Prog. Opt. 29, 1–63 (1991). [CrossRef]
- K. M. Dzurko, A. Hardy, D. R. Scifres, D. F. Welch, R. G. Waarts, R. J. Lang, “Distributed Bragg reflector ring oscillators: a large aperture source of high single-mode optical power,” IEEE J. Quantum Electron. 29, 1895–1905 (1993). [CrossRef]
- S. D. DeMars, K. M. Dzurko, R. J. Lang, D. F. Welch, D. R. Scifres, A. Hardy, “Angled grating distributed feedback laser with 1 W cw single-mode, diffraction-limited output at 980 nm,” in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CTuC2, pp. 77–78.
- A. Schoenfelder, S. D. DeMars, K. M. Dzurko, R. J. Lang, D. F. Welch, D. R. Scifres, A. Hardy, “Ultrahigh brightness, high power broad area laser diode arrays,” in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper 7.
- L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” J. Lightwave Technol. 6, 1069–1082 (1988). [CrossRef]
- K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979). [CrossRef]
- J. Van Roey, P. E. Lagasse, “Coupled wave analysis of obliquely incident waves in thin film gratings,” Appl. Opt. 20, 423–429 (1981). [CrossRef] [PubMed]
- A. A. Oliner, S. T. Peng, “New physical effects on periodically grooved optical planar waveguides,” Appl. Sci. Res. 41, 271–274 (1984). [CrossRef]
- N. Izhaky, A. Hardy, “Four wave CMT of obliquely incident plane waves on waveguide diffraction gratings,” J. Opt. Soc. Am. A 15, 473–479 (1998); “Oblique incidence of Gaussian beams on waveguide gratings with the four-wave CMT,” Appl. Opt. 37, 5806–5815 (1998). [CrossRef]
- N. Ramanujam, J. J. Burke, L. Li, “Guided wave deflectors using gratings with slowly-varying groove depth for beam shaping,” in Guided Wave Optoelectronics, T. Tamir, ed. (Plenum, New York, 1995), pp. 321–332.
- M. G. Moharam, T. K. Gaylord, R. Magnusson, “Bragg diffraction of finite beams by thick gratings,” J. Opt. Soc. Am. 70, 300–304 (1980). [CrossRef]
- L. Solimar, “A general two-dimensional theory for volume holograms,” Appl. Phys. Lett. 31, 820–822 (1977). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
- W. R. Klein, B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967). [CrossRef]
- A. Korpel, “Acousto-optics—a review of fundamentals,” Proc. IEEE 69, 48–53 (1981). [CrossRef]
- H. Kogelnik, “Coupled wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969). [CrossRef]
- M. G. Moharam, L. Young, “Criterion for Bragg and Raman–Nath diffraction regimes,” Appl. Opt. 17, 1757–1759 (1978). [CrossRef] [PubMed]
- M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980). [CrossRef]
- G. Weitman, A. Hardy, “Reduction of coupling coefficients for distributed Bragg reflection in corrugated narrow-rib waveguides,” IEE Proc.: Optoelectron. 144, 101–103 (1997).
- R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II.
- C. R. Chester, Techniques in Partial Differential Equations (McGraw-Hill, New York, 1971).
- W. Press, B. Flannery, S. Teudolsky, W. Vetterling, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).
- W. F. Ames, Numerical Methods for Partial Differential Equations, 3rd ed. (Academic, New York, 1992).
- R. D. Richtmyer, K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed. (Wiley, New York, 1967).
- R. S. Chu, T. Tamir, “Bragg diffraction of Gaussian beams by periodically modulated media,” J. Opt. Soc. Am. 66, 220–226 (1976). [CrossRef]
- S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989). [CrossRef]
- M. R. Wang, “Analysis and observation of finite beam Bragg diffraction by a thick planar phase grating,” Appl. Opt. 35, 582–592 (1996). [CrossRef] [PubMed]
- P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
- C. Itzykson, J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).

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