Abstract

The beam propagation behavior of a quasi-stadium laser diode is theoretically investigated. The resonator that we analyzed consists of one flat end-mirror, one convex curved end-mirror and two straight side wall mirrors. The cavity dimension is much larger than the oscillation wavelength. We derived one-dimensional Huygen’s integral equations for this laser cavity and carried out eigenmode calculations using the Fox and Li mode calculation method taking into account the effect of the side wall reflections and visualized the propagation beams. Unique beam propagation behaviors were obtained. These results well agree with our previous experimental results.

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References

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  1. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York Inc., 1990)
  2. E. J. Heller, "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits," Phys. Rev. Lett. 53, 1515 (1984)
    [CrossRef]
  3. E. J. Heller and S. Tomsovic, "Postmodern Quantum Mechanics," Phys. Today 46, 38 (1993)
    [CrossRef]
  4. S. W. McDonald and A. N. Kaufman, "Wave Chaos in the Stadium: Statistical Properties of Short-Wave Solutions of the Helmholts Equation," Phys. Rev. A 37, 3067 (1988)
    [CrossRef] [PubMed]
  5. S. Tomsovic and E. J. Heller, "Semiclassical Dynamics of Chaotic Motion: Unexpected Long-Time Accuracy," Phys. Rev. Lett. 67, 664 (1991)
    [CrossRef] [PubMed]
  6. S. A. Biellak, "Reactive Ion Etched Unstable and Stable Semiconductor Diode Lasers," Ph.D. thesis, Stanford University (1995)
  7. S. A. Biellak, C. G. Fanning, Y. Sun, S. S. Wong, and A. E. Siegman, "High Power Diffraction Limited Reactive-Ion-Etched Unstable Resonator Diode Lasers," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 4.
  8. Y. Sun, "Lateral Mode Control of Semiconductor Lasers," Ph.D. thesis, Stanford University (1995)
  9. T. Fukushima, S. A. Biellak, Y. Sun, C. G. Fanning, Y. Cheng, S. S. Wong, and A. E. Siegman, "Lasing Characteristics of a Quasi-Stadium Laser Diode," in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 227.
  10. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986)

Other

M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York Inc., 1990)

E. J. Heller, "Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits," Phys. Rev. Lett. 53, 1515 (1984)
[CrossRef]

E. J. Heller and S. Tomsovic, "Postmodern Quantum Mechanics," Phys. Today 46, 38 (1993)
[CrossRef]

S. W. McDonald and A. N. Kaufman, "Wave Chaos in the Stadium: Statistical Properties of Short-Wave Solutions of the Helmholts Equation," Phys. Rev. A 37, 3067 (1988)
[CrossRef] [PubMed]

S. Tomsovic and E. J. Heller, "Semiclassical Dynamics of Chaotic Motion: Unexpected Long-Time Accuracy," Phys. Rev. Lett. 67, 664 (1991)
[CrossRef] [PubMed]

S. A. Biellak, "Reactive Ion Etched Unstable and Stable Semiconductor Diode Lasers," Ph.D. thesis, Stanford University (1995)

S. A. Biellak, C. G. Fanning, Y. Sun, S. S. Wong, and A. E. Siegman, "High Power Diffraction Limited Reactive-Ion-Etched Unstable Resonator Diode Lasers," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 4.

Y. Sun, "Lateral Mode Control of Semiconductor Lasers," Ph.D. thesis, Stanford University (1995)

T. Fukushima, S. A. Biellak, Y. Sun, C. G. Fanning, Y. Cheng, S. S. Wong, and A. E. Siegman, "Lasing Characteristics of a Quasi-Stadium Laser Diode," in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 227.

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

Supplementary Material (2)

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Figures (5)

Fig. 1.
Fig. 1.

Structure of the quasi-stadium laser diode.

Fig. 2.
Fig. 2.

Theoretical model for the analysis of eigenmode. (a) Virtual images of flat end-mirror, (b) virtual images of curved end-mirror.

Fig. 3.
Fig. 3.

Spectrum of round-trip eigenvalue.

Fig. 4.
Fig. 4.

Click in the space to start the animations that show the variations of output beam patterns versus the distance (a) from the flat end-mirror and (b) from the curved end-mirror, respectively. [Media 1] [Media 2]

Fig. 5.
Fig. 5.

Beam propagation behavior inside the laser cavity, (a) forward propagation and (b) backward propagation.

Equations (5)

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E c ( x c , z c ) = j λ exp [ jk ( z c z f ) ] n flat E f ( x f , z f )
× z c z f ( x c x f ) 2 + ( z c z f ) 2 exp [ jk ( x c x f ) 2 2 ( z c z f ) ] cos θd x f .
E f ( x f , z f ) = j λ n curve E c ( x c , z c ) z c z f ( x c x f ) 2 + ( z c z f ) 2
× exp [ jk ( z c z f ) jk ( x c x f ) 2 2 ( z c z f ) ] cos θdr .
γ = lim m E f m + 1 ( x f , z f ) 2 E f m ( x f , z f ) 2 .

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