Abstract

Diffractive optical elements are used as end mirrors and internal phase plates in an optical resonator. A single diffractive end mirror is used to produce an arbitrary real-mode profile, and two diffractive mirrors are used to produce complex profiles. Diffractive mirror feature size and phase quantization are shown to affect the shape of the fundamental mode, the fundamental-mode loss, and the discrimination against higher-order modes. Additional transparent phase plates are shown to enhance the modal discrimination of the resonator at the cost of reduced fabrication tolerances of the diffractive optics. A 10-cm-long diffractive resonator design is shown that supports an 8.5-mm-wide fundamental mode with a theoretical second-order mode discrimination of 25% and a negligible loss to the fundamental mode.

© 1995 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  27. J. R. Leger, G. Mowry, X. Li, “Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors,” Appl. Opt. (to be published).
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    [CrossRef]
  30. J. R. Leger, D. Chen, K. Dai, “High modal discrimination in a Nd:YAG Laser resonator using internal phase gratings,” Opt. Lett. 19, 1976–1978 (1994).
    [CrossRef] [PubMed]
  31. D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot cavity semiconductor lasers,” Opt. Lett. 16, 823–885 (1991).
    [CrossRef] [PubMed]
  32. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
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    [CrossRef]

1995

G. Mowry, J. R. Leger, “Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output,” Appl. Phys. Lett. 66, 1614–1616 (1995).
[CrossRef]

1994

1993

J. R. Leger, G. Mowry, “External diode-laser array cavity with mode selecting mirror,” Appl. Phys. Lett. 63, 2884–2886 (1993).
[CrossRef]

1992

1991

1990

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

E. Ho, F. Koyama, K. Iga, “Effective reflectivity from self-imaging in a Talbot cavity and its effect on the threshold of a finite 2-D surface emitting laser array,” Appl. Opt. 29, 5080–5085 (1990).
[CrossRef] [PubMed]

1989

A. Parent, P. Lavigne, “Variable reflectivity unstable resonators for coherent laser radar emitters,” Appl. Opt. 28, 901–903 (1989).
[CrossRef] [PubMed]

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

F. X. D’Amato, E. T. Sievert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

1988

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

1987

A. A. Golubentsev, V. V. Likhanskiĭ, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Sov. Phys. JETP 66, 676–682 (1987).

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, “Radially variable reflectivity output coupler of novel design for unstable resonators,” Opt. Lett. 12, 84–86 (1987).
[CrossRef] [PubMed]

1986

1985

P. Lavigne, N. McCarthy, J.-G. Demers, “Design and characterization of complementary Gaussian reflectivity mirrors,” Appl. Opt. 24, 2581–2586 (1985).
[CrossRef] [PubMed]

R. H. Rediker, R. P. Schloss, L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[CrossRef]

1982

1980

1975

E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
[CrossRef]

1972

Y. A. Anan’ev, “Unstable resonators and their applications,” Sov. J. Quantum Electron. 1, 565–586 (1972).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1965

A. E. Siegman, “Unstable optical resonators for laser applications,” Proc. IEEE 53, 277–287 (1965).
[CrossRef]

Anan’ev, Y. A.

Y. A. Anan’ev, “Unstable resonators and their applications,” Sov. J. Quantum Electron. 1, 565–586 (1972).
[CrossRef]

Bélanger, P.-A.

Botez, D.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Byer, R. L.

Bystrom, K. J.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Cassarly, W.

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Caunt, J. W.

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

Cerullo, G.

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

Chen, D.

Colombeau, B.

D’Amato, F. X.

F. X. D’Amato, E. T. Sievert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Dai, K.

De Silvestri, S.

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, “Radially variable reflectivity output coupler of novel design for unstable resonators,” Opt. Lett. 12, 84–86 (1987).
[CrossRef] [PubMed]

Demers, J.-G.

Diadiuk, V.

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

Ehlert, J. C.

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Finlan, J. M.

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Flood, K. M.

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Froehly, C.

Gaylord, T. K.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Giuliani, G.

Golubentsev, A. A.

A. A. Golubentsev, V. V. Likhanskiĭ, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Sov. Phys. JETP 66, 676–682 (1987).

Harter, D. J.

Ho, E.

Iga, K.

Jansen, M.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Kermene, V.

Koyama, F.

Lachance, R. L.

Laporta, P.

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, “Radially variable reflectivity output coupler of novel design for unstable resonators,” Opt. Lett. 12, 84–86 (1987).
[CrossRef] [PubMed]

Lavigne, P.

Leger, J. R.

G. Mowry, J. R. Leger, “Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output,” Appl. Phys. Lett. 66, 1614–1616 (1995).
[CrossRef]

J. R. Leger, D. Chen, Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG Laser,” Opt. Lett. 19, 108–110 (1994).
[CrossRef] [PubMed]

J. R. Leger, D. Chen, K. Dai, “High modal discrimination in a Nd:YAG Laser resonator using internal phase gratings,” Opt. Lett. 19, 1976–1978 (1994).
[CrossRef] [PubMed]

J. R. Leger, G. Mowry, “External diode-laser array cavity with mode selecting mirror,” Appl. Phys. Lett. 63, 2884–2886 (1993).
[CrossRef]

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

G. Mowry, J. R. Leger, “Large-area, single-tranverse-mode semiconductor laser with near diffraction limited super-Gaussian output,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 2–3.

J. R. Leger, G. Mowry, X. Li, “Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors,” Appl. Opt. (to be published).

Li, X.

J. R. Leger, G. Mowry, X. Li, “Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors,” Appl. Opt. (to be published).

Liau, Z. L.

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

Likhanskii, V. V.

A. A. Golubentsev, V. V. Likhanskiĭ, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Sov. Phys. JETP 66, 676–682 (1987).

Magni, V.

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, “Radially variable reflectivity output coupler of novel design for unstable resonators,” Opt. Lett. 12, 84–86 (1987).
[CrossRef] [PubMed]

Majocchi, B.

Mawst, L. J.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

McCarthy, N.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

P. Lavigne, N. McCarthy, J.-G. Demers, “Design and characterization of complementary Gaussian reflectivity mirrors,” Appl. Opt. 24, 2581–2586 (1985).
[CrossRef] [PubMed]

Mehuys, D.

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot cavity semiconductor lasers,” Opt. Lett. 16, 823–885 (1991).
[CrossRef] [PubMed]

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Moharam, M. G.

Mooradian, A.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Mowry, G.

G. Mowry, J. R. Leger, “Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output,” Appl. Phys. Lett. 66, 1614–1616 (1995).
[CrossRef]

J. R. Leger, G. Mowry, “External diode-laser array cavity with mode selecting mirror,” Appl. Phys. Lett. 63, 2884–2886 (1993).
[CrossRef]

G. Mowry, J. R. Leger, “Large-area, single-tranverse-mode semiconductor laser with near diffraction limited super-Gaussian output,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 2–3.

J. R. Leger, G. Mowry, X. Li, “Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors,” Appl. Opt. (to be published).

Nam, D.

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

Nam, D. W.

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Napartovich, A. P.

A. A. Golubentsev, V. V. Likhanskiĭ, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Sov. Phys. JETP 66, 676–682 (1987).

Paré, C.

Parent, A.

Park, Y. K.

Peterson, G.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Philipp-Rutz, E. M.

E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
[CrossRef]

Piché, M.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

Rediker, R. H.

R. H. Rediker, R. P. Schloss, L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[CrossRef]

Roth, T. J.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Roychoudhuri, C.

F. X. D’Amato, E. T. Sievert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Saviot, A.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schloss, R. P.

R. H. Rediker, R. P. Schloss, L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[CrossRef]

Scifres, D.

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

Scott, M. L.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Seppala, J.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Sharfin, W. F.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “Unstable optical resonators for laser applications,” Proc. IEEE 53, 277–287 (1965).
[CrossRef]

Sievert, E. T.

F. X. D’Amato, E. T. Sievert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Simmons, W. W.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Snell, K. J.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

Soltz, B. A.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Streifer, W.

D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot cavity semiconductor lasers,” Opt. Lett. 16, 823–885 (1991).
[CrossRef] [PubMed]

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

Svelto, O.

Valentini, G.

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

Vampouille, M.

Van Ruyven, L. J.

R. H. Rediker, R. P. Schloss, L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Vollmer, B. J.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Waarts, R.

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

Waarts, R. G.

D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot cavity semiconductor lasers,” Opt. Lett. 16, 823–885 (1991).
[CrossRef] [PubMed]

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Walling, J. C.

Walpole, J. N.

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

Wang, Z.

Waters, R. G.

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

Welch, D.

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

Welch, D. F.

D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot cavity semiconductor lasers,” Opt. Lett. 16, 823–885 (1991).
[CrossRef] [PubMed]

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

Wilcox, J. Z.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Williamson, R. C.

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

Yang, J. J.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

E. M. Philipp-Rutz, “Spatially coherent radiation from an array of GaAs lasers,” Appl. Phys. Lett. 26, 475–477 (1975).
[CrossRef]

R. H. Rediker, R. P. Schloss, L. J. Van Ruyven, “Operation of individual diode lasers as a coherent ensemble controlled by a spatial filter within an external cavity,” Appl. Phys. Lett. 46, 133–135 (1985).
[CrossRef]

W. F. Sharfin, J. Seppala, A. Mooradian, B. A. Soltz, R. G. Waters, B. J. Vollmer, K. J. Bystrom, “High-power, diffraction limited, narrow-band, external-cavity diode laser,” Appl. Phys. Lett. 54, 1731–1733 (1989).
[CrossRef]

V. Diadiuk, Z. L. Liau, J. N. Walpole, J. W. Caunt, R. C. Williamson, “External-cavity coherent operation of the In-GaAsP buried-heterostructure laser array,” Appl. Phys. Lett. 55, 2161–2163 (1989).
[CrossRef]

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

F. X. D’Amato, E. T. Sievert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

R. Waarts, D. Mehuys, D. Nam, D. Welch, W. Streifer, D. Scifres, “High-power, cw, diffraction-limited, GaAlAs laser diode array in an external Talbot cavity,” Appl. Phys. Lett. 58, 2586–2588 (1991).
[CrossRef]

J. R. Leger, G. Mowry, “External diode-laser array cavity with mode selecting mirror,” Appl. Phys. Lett. 63, 2884–2886 (1993).
[CrossRef]

G. Mowry, J. R. Leger, “Large-area, single-transverse-mode semiconductor laser with diffraction-limited super-Gaussian output,” Appl. Phys. Lett. 66, 1614–1616 (1995).
[CrossRef]

Electron. Lett.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, “Phase-locked array of antiguided lasers with monolithic spatial filter,” Electron. Lett. 25, 365–366 (1989).
[CrossRef]

IEEE J. Quantum Electron.

C. Paré, P.-A. Bélanger, “Custom laser resonators using graded-phase mirrors,” IEEE J. Quantum Electron. 28, 355–362 (1992).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, “Single transverse mode oscillation from an unstable resonator Nd:YAG laser using a variable reflectivity mirror,” Opt. Commun. 65, 377–382 (1988).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, G. Valentini, G. Cerullo, “Comparative analysis of Nd:YAG unstable resonators with super-Gaussian variable reflectivity mirrors,” Opt. Commun. 77, 179–184 (1990).
[CrossRef]

Opt. Lett.

P.-A. Bélanger, C. Paré, “Optical resonators using graded-phase mirrors,” Opt. Lett. 16, 1057–1059 (1991).
[CrossRef] [PubMed]

P.-A. Bélanger, R. L. Lachance, C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett. 17, 739–741 (1992).
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[CrossRef] [PubMed]

D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot cavity semiconductor lasers,” Opt. Lett. 16, 823–885 (1991).
[CrossRef] [PubMed]

V. Kermene, A. Saviot, M. Vampouille, B. Colombeau, C. Froehly, “Flattening of the spatial laser beam profile with low losses and minimal beam divergence,” Opt. Lett. 17, 859–861 (1992).
[CrossRef] [PubMed]

J. R. Leger, D. Chen, Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG Laser,” Opt. Lett. 19, 108–110 (1994).
[CrossRef] [PubMed]

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Other

R. G. Waarts, D. W. Nam, D. F. Welch, D. Mehuys, W. Cassarly, J. C. Ehlert, J. M. Finlan, K. M. Flood, “Semiconductor laser array in an external Talbot cavity,” in Laser Diode Technology and Applications IV, D. Renner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1634, 288–298 (1992).

J. R. Leger, G. Mowry, X. Li, “Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors,” Appl. Opt. (to be published).

G. Mowry, J. R. Leger, “Large-area, single-tranverse-mode semiconductor laser with near diffraction limited super-Gaussian output,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 2–3.

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Figures (16)

Fig. 1
Fig. 1

General design of a diffractive optical resonator.

Fig. 2
Fig. 2

Threshold gain of fundamental and second-order modes as a function of two cavity Fresnel numbers N 1 and N 2. The DMSM is adjusted to be phase conjugate to a super-Gaussian that is slightly smaller than the output aperture.

Fig. 3
Fig. 3

Threshold gains of the fundamental and the second-order modes as a function of normalized output-mirror-aperture size. Normalization is with respect to the super-Gaussian full width.

Fig. 4
Fig. 4

Fundamental-mode shape as a function of aperture size: (a) aperture is applied to DMSM, and curves correspond to Fresnel numbers N 2 = 4, 8, and 20; (b) aperture is applied to output mirror, normalized to the super-Gaussian full width.

Fig. 5
Fig. 5

Modal threshold gain of second-order mode for an array of eight Gaussian sources: (a) threshold gain as a function of normalized cavity length for an array fill factor of 0.12, (b) threshold gain as a function of the fill factor for a cavity length of z t /2.

Fig. 6
Fig. 6

Threshold gains of super-Gaussian fundamental and second-order modes as functions of minimum DMSM feature size.

Fig. 7
Fig. 7

Threshold gains of Gaussian-array fundamental and second-order modes as functions of minimum DMSM feature size.

Fig. 8
Fig. 8

Effect of phase quantization on laser resonator performance: (a) threshold gain of fundamental and second-order modes as functions of number of phase-quantization levels; (b) mode shapes for 4, 8, and 32 phase-quantization levels.

Fig. 9
Fig. 9

Four mask patterns for fabricating 16-level DMSM. The smallest feature size is 50 μm.

Fig. 10
Fig. 10

Second-order TEM10 modal threshold gain as a function of sinusoidal-grating frequency. The loss to the fundamental mode is less than 0.1%.

Fig. 11
Fig. 11

Second-order TEM10 modal threshold gain for sinusoidal phase grating with different phase shifts.

Fig. 12
Fig. 12

Second-order TEM10 modal threshold gain for a sinusoidal phase grating with different modulation depths.

Fig. 13
Fig. 13

Fundamental and second-order TEM10 modal threshold gains versus feature size for square-wave and sine-wave grating phase plates.

Fig. 14
Fig. 14

Modal threshold gain of second-order mode as a function of bandwidth of a pseudorandom phase plate.

Fig. 15
Fig. 15

Modal threshold gain of fundamental and second-order modes as functions of minimum DMSM feature size when a pseudorandom phase plate is used.

Fig. 16
Fig. 16

Theoretical performance of a 10-cm laser cavity containing a random phase plate: (a) two-dimensional fundamental-mode intensity profile, (b) laser gain required for overcoming the diffractive losses to the second-order mode for various fundamental beam sizes. The result from a conventional Fabry–Perot cavity is shown for comparison.

Equations (19)

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K ( x ¯ , x ¯ ) U ν ( x ¯ ) d 2 x ¯ = γ ν U ν ( x ¯ ) ,
G ν = 1 / γ ν 2 .
A 1 ( x , y ) = exp [ ( x / ω 0 ) 20 ] exp [ ( y / ω 0 ) 20 ] ,
A 2 ( x , y ) = m = M / 2 M / 2 exp [ ( x m a ) 2 + y 2 ω 0 2 ] ,
N i = d i 2 4 λ z ,
Δ y = Δ l λ z
R ( z = z 0 ) = z ( 1 + z 0 2 z 2 ) = 2 z 0 .
d = 2 ω 0 π N 2
f / # = z 0 2 ω 0 π N 2 .
Δ l = 2 λ f / # M = ω 0 M π N 2 ,
Δ y = 1 M N 2 ,
η edge = | sin ( π / M ) π / M | 2 1 1 3 ( π M ) 2 ,
L edge π N 2 3 ( Δ l ω 0 ) 2 .
L edge π 2 N 2 3 Δ y 2 .
G 1 = ( 1 π 2 N 2 3 Δ y 2 ) 1 1 + π 2 N 2 3 Δ y 2 ,
Δ y = Δ l λ z = Δ l a = f Δ l 2 ω 0 .
t ( x , y ) = exp [ j m sin ( 2 π f g x + ϕ ) ] ,
P q = | J q ( m / 2 ) | 2 ,
| J q ( m / 2 ) | 2 1 2 π q ( e m 4 q ) 2 q , q 1 ,

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