Abstract

An electromagnetic method based on rigorous diffraction theory of gratings is introduced to analyze the modal structure of semiconductor laser cavities. The approach is based on the use of the Fourier Modal Method, the S-matrix algorithm, and the formulation of an eigenvalue problem from which the wave forms and eigenvalues of the modes can be determined numerically. The method is completely rigorous for infinitely periodic laser arrays and is applicable to individual laser resonators with the introduction of imaginary absorbing regions.

© 2005 Optical Society of America

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References

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2004 ICO International Conference Optics (1)

M. G. Moharam and A. Greenwell, �??Integrated Output Grating Coupler in Semiconductor Lasers,�?? in 2004 ICO International Conference Optics & Photonics in Technology Frontier, pp. 543�??544 (ICO, Tokyo, 2004).

Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, �??Resonant modes in a maser interferometer,�?? Bell Syst. Tech. J. 40, 453�??458 (1961).

J. Opt. Soc. Am. (1)

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

Mathematical Modeling in Optical Science (1)

L. Li, �??Mathematical Reflections on the Fourier modal method in Grating Theory,�?? in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, and W. Masters, eds., pp. 111�??139 (SIAM, Philadelphia, 2001).
[CrossRef]

Micro-Optics: Elements, Systems, and App (1)

J. Turunen, �??Diffraction theory of microrelief gratings,�?? in Micro-Optics: Elements, Systems, and Applications, H. P. Herzig, ed., chap. 2 (Taylor & Francis, London, 1997).

Opt. Commun. (2)

P. Vahimaa, M. Kuittinen, J. Turunen, J. Saarinen, R.-P. Salmio, E. Lopez Lago, and J. Liñares, �??Guided-mode propagation through an ion-exchanged graded-index boundary,�?? Opt. Commun. 14, 247�??253 (1998).
[CrossRef]

J. Tervo, M. Kuittinen, P. Vahimaa, J. Turunen, T. Aalto, P. Heimala, and M. Leppihalme, �??Efficient Bragg waveguide-grating analysis by quasi-rigorous approach based on Redheffer�??s star product,�?? Opt. Commun. 198, 265�??272 (2001).
[CrossRef]

Opt. Lett. (1)

Other (4)

M. Mansuripur, Classical Optics and its Applications (Cambridge University Press, Cambridge, 2002).

A. Taflove and S. C. Hagness, Computational Electrodymanics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000).

A. Yariv, Optical Electronics, 3rd ed. (College Publishing, Holt, 1985).

A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).

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Figures (3)

Fig. 1.
Fig. 1.

A general y-invariant periodic resonator structure with imaginary absorption layers inserted at the boundaries of the periods to decouple the interactions between the adjacent resonators in the array.

Fig. 2.
Fig. 2.

Cavity surrounded by dielectric mirrors.

Fig. 3.
Fig. 3.

Time average of electric energy density distribution 〈w e(x)〉 of the resonating mode of the structure of Fig. 2 at z = -1 μm (dashed line) and in the middle of the resonator, i.e. z = (z 5 + z 6)/2 (solid line).

Equations (3)

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E j y x z = m { A j m exp [ i β j m ( z z j ) ] + β j m exp [ i β j m ( z z j + 1 ) ] } X j m ( x ) ,
[ A j + 1 B j ] = [ T u u j j + 1 R u d j j + 1 R d u j j + 1 T d d j j + 1 ] [ A j B j + 1 ]
A R Γ = M 0 j J A R ,

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