Abstract

Laterally periodic resonators, which can be constructed by use of transversely periodic phase- or amplitude-modulating elements in a cavity, are proposed for stabilization and generation of transversely coherent output from large-area gain. Lasers with periodic resonators have the combined features of conventional cavities and laser arrays. Significant low-order transverse modes and mode discrimination of a sample resonator with intracavity periodic phase elements are investigated numerically by the iteration method. Wave-propagation calculations are carried out by use of a fast Fourier transform, and a modified Prony method is used to evaluate wave functions and losses of transverse modes. Results of numerical calculations are consistent with expectations.

© 2002 Optical Society of America

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References

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Appl. Opt. (3)

Appl. Phys. Lett. (3)

J. K. Butler, D. E. Ackley, and D. Botez, �??Coupled-mode analysis of phase-locked injection laser arrays,�?? Appl. Phys. Lett. 44, 293-295 (1984); Appl. Phys. Lett. 44, 935 (erratum) (1984).
[CrossRef]

M. Cronin-Golomb, A. Yariv, and I. Ury, �??Coherent coupling of diode lasers by phase conjugation,�?? Appl. Phys. Lett. 48, 1240-1242 (1986).
[CrossRef]

K. M. Abramski, A. D. Colley, H. J. Baker, and D. R. Hall, �??Phase-locked CO2 laser array using diagonal coupling of waveguide channels,�?? Appl. Phys. Lett. 60, 530-532 (1992).
[CrossRef]

Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, �??Resonant modes in a maser interferometer,�?? Bell Syst. Tech. J. 40, 453-488 (1961).

Electron. Lett. (1)

B. Mroziewicz, �??Broad-area semiconductor lasers with spatially modulated reflectivity of mirrors,�?? Electron. Lett. 32, 329-330 (1996).
[CrossRef]

IEEE J. Quantum Electron. (5)

Y. Kono, M. Takeoka, K. Uto, A. Uchida, and F. Kannari, �??A coherent all-solid-state laser array using the Talbot effect in a three-mirror cavity,�?? IEEE J. Quantum Electron. 36, 607-614 (2000).
[CrossRef]

M. Oka, H. Masuda, Y. Kaneda, and S. Kubota, �??Laser-diode-pumped phase-locked Nd:YAG laser arrays,�?? IEEE J. Quantum Electron. 28, 1142-1147 (1992).
[CrossRef]

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, �??Theory of grating-confined broad-area lasers,�?? IEEE J. Quantum Electron. 34, 2196-2210 (1998).
[CrossRef]

M. Szymanski, J. M. Kubica, P. Szczepanski, �??Theoretical analysis of lateral modes in broad-area semiconductor lasers with profiled reflectivity output facets,�?? IEEE J. Quantum Electron. 37, 430-438 (2001
[CrossRef]

J. R. Marciante and G. P. Agrawal, �??Lateral spatial effects of feedback in gain-guided and broad-area semiconductor lasers,�?? IEEE J. Quantum Electron. 32, 1630-1635 (1996).
[CrossRef]

IEEE. J. Sel. Top. Quantum Electron. (2)

R. J. Pierre, G.W. Holleman, M. Valley, H. Injeyan, J. G. Berg, G. M. Harpole, R. C. Hilyard, M. Mitchell, M. E. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, �??Active tracked laser (ATLAS),�?? IEEE. J. Sel. Top. Quantum Electron. 3, 64-70 (1997).
[CrossRef]

R. J. Pierre, D.W. Mordaunt, H. Injeyan, J. G. Berg, R. C. Hilyard, M. E.Weber, M. G.Wickham, G. M. Harpole, and R. Senn, �??Diode array pumped kilowatt laser,�?? IEEE. J. Sel. Top. Quantum Electron. 3, 53-58 (1997).
[CrossRef]

J. Mod. Opt. (1)

M. V. Berry, and S. Klein, �??Integer, fractional and fractal Talbot effects,�?? J. Mod. Opt. 43, 2139-2164 (1996).
[CrossRef]

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

Opt. Commun. (1)

A. Desfarges-Berthelemot, B. Colombeau, M. Vampouille, P. J. Devilder, C. Froehly, and S. Monneret, �??Adjustable phase-locking of two Nd:Glass ring laser beams,�?? Opt. Commun. 141, 123-126 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Proc. IEEE (1)

E. A. Sziklas and A. E. Siegman, �??Diffraction calculations using fast Fourier transform methods,�?? Proc. IEEE 62, 410-412 (1974).
[CrossRef]

Proc. SPIE (1)

V. I. Yukalov, �??Optical turbulent structures,�?? in High-Power Laser Ablation III, C. R. Phipps, ed., Proc. SPIE 4065, 237-244 (2001).
[CrossRef]

Other (3)

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, �??Transverse mode shaping and selection in laser resonators,�?? in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 2001), Vol. II.

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge U. Press, Cambridge, UK, 1994), Chap. 1
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 22 and 23.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the introductory resonator configuration used in numerical investigation. Ml , Mr , and P are left end mirror, right end mirror, and periodic phase plate, respectively. L is cavity length; d and λ m are modulation depth and spatial period of P, respectively. u(x,y) is the optical field oscillating in the cavity.

Fig. 2.
Fig. 2.

Left, fundamental mode patterns for resonators with modulation d=π/8 and cavity length L=0.125, 0.250, …, 1.25 from top to bottom, respectively. Right, corresponding far-field patterns.

Fig. 3.
Fig. 3.

Left, near-field amplitude profiles of the five lowest-order modes at d=π/8, L=0.625 m. Right, corresponding far-field intensity patterns.

Fig. 4.
Fig. 4.

Round-trip losses of three lowest-order modes for different cavity lengths L and phasemodulation depths d.

Equations (1)

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u ( x , y ) = u ( x , y ) exp [ j 2 d cos ( 2 π x 2 + y 2 λ m ) ] ,

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