OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 2 — Feb. 1, 1999
  • pp: 305–315

Obliquely incident wave coupling on finite-aperture waveguide gratings

Nahum Izhaky and Amos Hardy  »View Author Affiliations


JOSA A, Vol. 16, Issue 2, pp. 305-315 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000305


View Full Text Article

Acrobat PDF (773 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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 (TE+, TE, TM+, and TM) by means of Bragg diffraction at oblique incidence. The grating’s geometry and boundary conditions are properly accounted for, and the problem is solved numerically by a finite-difference method. Near-field and far-field distributions, as well as reflection and transmission (power) coefficients (as functions of the plane-wave incidence angle), are calculated. The model is compared with the degenerate case of two-wave coupling that considers interaction only between pairs (e.g., TE+↔TE), and significant differences may be observed. Compatibility and differences between the 2D-CMT and the one-dimensional CMT (grooves with infinite length) are also presented, in addition to the influence of the beam width and the groove length on the emerging waves. The analysis is general and can be performed on many kinds of realistic beams, grating shapes, and applications.

© 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

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


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1991).
  2. A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991).
  3. H. Kogelnik, “Theory of optical waveguides,” in Guided Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1990).
  4. D. G. Hall, “Optical waveguide diffraction gratings: coupling between guided modes,” Prog. Opt. 29, 1–63 (1991).
  5. K. M. Dzurko, A. Hardy, D. R. Scifres, D. F. Welch, R. G. Waarts, and 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).
  6. S. D. DeMars, K. M. Dzurko, R. J. Lang, D. F. Welch, D. R. Scifres, and A. Hardy, “Angled grating distributed feedback laser with 1 Wcw 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.
  7. A. Schoenfelder, S. D. DeMars, K. M. Dzurko, R. J. Lang, D. F. Welch, D. R. Scifres, and 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.
  8. L. A. Weller-Brophy and D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” J. Lightwave Technol. 6, 1069–1082 (1988).
  9. K. Wagatsuma, H. Sakaki, and S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979).
  10. J. Van Roey and P. E. Lagasse, “Coupled wave analysis of obliquely incident waves in thin film gratings,” Appl. Opt. 20, 423–429 (1981).
  11. A. A. Oliner and S. T. Peng, “New physical effects on periodically grooved optical planar waveguides,” Appl. Sci. Res. 41, 271–274 (1984).
  12. N. Izhaky and 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).
  13. N. Ramanujam, J. J. Burke, and 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.
  14. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Bragg diffraction of finite beams by thick gratings,” J. Opt. Soc. Am. 70, 300–304 (1980).
  15. L. Solimar, “A general two-dimensional theory for volume holograms,” Appl. Phys. Lett. 31, 820–822 (1977).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  17. W. R. Klein and B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
  18. A. Korpel, “Acousto-optics—a review of fundamentals,” Proc. IEEE 69, 48–53 (1981).
  19. H. Kogelnik, “Coupled wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  20. M. G. Moharam and L. Young, “Criterion for Bragg and Raman–Nath diffraction regimes,” Appl. Opt. 17, 1757–1759 (1978).
  21. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
  22. G. Weitman and A. Hardy, “Reduction of coupling coefficients for distributed Bragg reflection in corrugated narrow-rib waveguides,” IEE Proc.: Optoelectron. 144, 101–103 (1997).
  23. R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II.
  24. C. R. Chester, Techniques in Partial Differential Equations (McGraw-Hill, New York, 1971).
  25. W. Press, B. Flannery, S. Teudolsky, and W. Vetterling, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge U. Press, New York, 1986).
  26. W. F. Ames, Numerical Methods for Partial Differential Equations, 3rd ed. (Academic, New York, 1992).
  27. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed. (Wiley, New York, 1967).
  28. R. S. Chu and T. Tamir, “Bragg diffraction of Gaussian beams by periodically modulated media,” J. Opt. Soc. Am. 66, 220–226 (1976).
  29. S. Zhang and T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989).
  30. M. R. Wang, “Analysis and observation of finite beam Bragg diffraction by a thick planar phase grating,” Appl. Opt. 35, 582–592 (1996).
  31. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  32. C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited