Abstract

A resonator structure in which one reflector is replaced by a biprismlike reflecting surface is investigated theoretically. It is shown that such a modification leads to two regions of parameters, each with different regimes of mode selection. The first region has an improved laser power output because of the nearly flat-top mode shape. In the second region the biprism is inverted, with the result that the main oscillating mode can be the first odd mode. The line singularity contained in such a mode is one example of singular beams that are employed in various fields, such as micromanipulators and advanced high-resolution metrology.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2004 (5)

1999 (1)

1996 (2)

1992 (1)

1980 (1)

A. P. Kol'chenko, A. G. Nikitenko, Yu Troitskij, “Control of the structure of transverse modes by phase-shifting masks,” Sov. J. Quantum Electron. 10, 1013–1016 (1980).
[CrossRef]

1975 (2)

1969 (1)

Adam, J. F.

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

Ananev, Yu.

Yu. Ananev, Laser Resonators and the Beam Divergence Problem, Adam Hilger Series on Optics and Optoelectronics (Adam Hilger, Bristol, 1992).

Anisimova, O. V.

Yu. N. Parkhomenko, O. V. Anisimova, O. N. Galkin, “Lasers with fast electronic synthesis of spectral line shape,” in Advances in Laser and Optic Research (Nova Science, New York, 2002), Vol. 1, pp. 128–161.

Berlanger, P. A.

Brunfeld, A.

B. Spektor, G. Toker, J. Shamir, M. Friedman, A. Brunfeld, “High-resolution surface evaluation using multiwavelength optical transforms,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 345–351 (July2002).

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

Crabtree, K.

Cromwell, E. F.

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

Davidson, N.

G. Machavariani, A. A. Ishaaya, L. Shimshi, N. Davidson, A. A. Friesem, E. Hasman, “Efficient mode transformations of degenerate Laguerre–Gaussian beams,” Appl. Opt. 43, 2561–2567 (2004).
[CrossRef] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 2001), Vol. 42, pp. 325–386.
[CrossRef]

Davis, J. A.

Endo, M.

Friedman, M.

B. Spektor, G. Toker, J. Shamir, M. Friedman, A. Brunfeld, “High-resolution surface evaluation using multiwavelength optical transforms,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 345–351 (July2002).

Friedmann, M.

M. Friedmann, E. Paquet, J. Shamir, “Surface feature reconstruction using scanning beams,” in Lasers and Electro-optics Europe, 1996 (Optical Society of America, Washington, D.C., 1996), p. 30.

Friesem, A. A.

G. Machavariani, A. A. Ishaaya, L. Shimshi, N. Davidson, A. A. Friesem, E. Hasman, “Efficient mode transformations of degenerate Laguerre–Gaussian beams,” Appl. Opt. 43, 2561–2567 (2004).
[CrossRef] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 2001), Vol. 42, pp. 325–386.
[CrossRef]

Fujii, M.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Fukuchi, N.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Galkin, O. N.

Yu. N. Parkhomenko, O. V. Anisimova, O. N. Galkin, “Lasers with fast electronic synthesis of spectral line shape,” in Advances in Laser and Optic Research (Nova Science, New York, 2002), Vol. 1, pp. 128–161.

Greninger, C. E.

Hasman, E.

G. Machavariani, A. A. Ishaaya, L. Shimshi, N. Davidson, A. A. Friesem, E. Hasman, “Efficient mode transformations of degenerate Laguerre–Gaussian beams,” Appl. Opt. 43, 2561–2567 (2004).
[CrossRef] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 2001), Vol. 42, pp. 325–386.
[CrossRef]

Hill, W. T.

Igasaki, Y.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Iketaki, Y.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Ishaaya, A. A.

Ishiuchi, S.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Kol'chenko, A. P.

A. P. Kol'chenko, A. G. Nikitenko, Yu Troitskij, “Control of the structure of transverse modes by phase-shifting masks,” Sov. J. Quantum Electron. 10, 1013–1016 (1980).
[CrossRef]

Lachnce, R. L.

Lax, M.

Lousell, W. H.

Machavariani, G.

McKnight, W. B.

Milan, D.

Moreno, I.

Nikitenko, A. G.

A. P. Kol'chenko, A. G. Nikitenko, Yu Troitskij, “Control of the structure of transverse modes by phase-shifting masks,” Sov. J. Quantum Electron. 10, 1013–1016 (1980).
[CrossRef]

Omatsu, T.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 2001), Vol. 42, pp. 325–386.
[CrossRef]

Paquet, E.

M. Friedmann, E. Paquet, J. Shamir, “Surface feature reconstruction using scanning beams,” in Lasers and Electro-optics Europe, 1996 (Optical Society of America, Washington, D.C., 1996), p. 30.

Pare, C.

Parkhomenko, Y.

B. Spektor, Y. Parkhomenko, J. Shamir, “Intracavity beam shaping for nanoscale surface metrology,” in Optical Measurement Systems for Industrial Inspection III, W. Osten, M. Kujawinska, K. Creath, SPIE5144, 17–25 (June2003).
[CrossRef]

Parkhomenko, Yu. N.

Yu. N. Parkhomenko, O. V. Anisimova, O. N. Galkin, “Lasers with fast electronic synthesis of spectral line shape,” in Advances in Laser and Optic Research (Nova Science, New York, 2002), Vol. 1, pp. 128–161.

Pasqualetty, F.

Piestun, R.

Ronchi, L.

Sakai, M.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Sanderson, R. L.

Shamir, J.

R. Piestun, B. Spektor, J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

B. Spektor, R. Piestun, J. Shamir, “Dark beams with a constant notch,” Opt. Lett. 21, 456–458 (1996).
[CrossRef] [PubMed]

B. Spektor, Y. Parkhomenko, J. Shamir, “Intracavity beam shaping for nanoscale surface metrology,” in Optical Measurement Systems for Industrial Inspection III, W. Osten, M. Kujawinska, K. Creath, SPIE5144, 17–25 (June2003).
[CrossRef]

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

M. Friedmann, E. Paquet, J. Shamir, “Surface feature reconstruction using scanning beams,” in Lasers and Electro-optics Europe, 1996 (Optical Society of America, Washington, D.C., 1996), p. 30.

B. Spektor, G. Toker, J. Shamir, M. Friedman, A. Brunfeld, “High-resolution surface evaluation using multiwavelength optical transforms,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 345–351 (July2002).

Shimshi, L.

Shum, P.

Song, Y.

Spektor, B.

R. Piestun, B. Spektor, J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

B. Spektor, R. Piestun, J. Shamir, “Dark beams with a constant notch,” Opt. Lett. 21, 456–458 (1996).
[CrossRef] [PubMed]

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

B. Spektor, Y. Parkhomenko, J. Shamir, “Intracavity beam shaping for nanoscale surface metrology,” in Optical Measurement Systems for Industrial Inspection III, W. Osten, M. Kujawinska, K. Creath, SPIE5144, 17–25 (June2003).
[CrossRef]

B. Spektor, G. Toker, J. Shamir, M. Friedman, A. Brunfeld, “High-resolution surface evaluation using multiwavelength optical transforms,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 345–351 (July2002).

Streifer, W.

Sun, X. W.

Toker, G.

B. Spektor, G. Toker, J. Shamir, M. Friedman, A. Brunfeld, “High-resolution surface evaluation using multiwavelength optical transforms,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 345–351 (July2002).

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

Troitskij, Yu

A. P. Kol'chenko, A. G. Nikitenko, Yu Troitskij, “Control of the structure of transverse modes by phase-shifting masks,” Sov. J. Quantum Electron. 10, 1013–1016 (1980).
[CrossRef]

Wang, Q.

Watanabe, T.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Yamamoto, K.

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

T. Watanabe, Y. Igasaki, N. Fukuchi, M. Sakai, S. Ishiuchi, M. Fujii, T. Omatsu, K. Yamamoto, Y. Iketaki, “Formation of a doughnut laser beam for super-resolving microscopy using a phase spatial light modulator,” Opt. Eng. 43, 1136–1143 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Sov. J. Quantum Electron. (1)

A. P. Kol'chenko, A. G. Nikitenko, Yu Troitskij, “Control of the structure of transverse modes by phase-shifting masks,” Sov. J. Quantum Electron. 10, 1013–1016 (1980).
[CrossRef]

Other (7)

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 2001), Vol. 42, pp. 325–386.
[CrossRef]

B. Spektor, Y. Parkhomenko, J. Shamir, “Intracavity beam shaping for nanoscale surface metrology,” in Optical Measurement Systems for Industrial Inspection III, W. Osten, M. Kujawinska, K. Creath, SPIE5144, 17–25 (June2003).
[CrossRef]

Yu. N. Parkhomenko, O. V. Anisimova, O. N. Galkin, “Lasers with fast electronic synthesis of spectral line shape,” in Advances in Laser and Optic Research (Nova Science, New York, 2002), Vol. 1, pp. 128–161.

M. Friedmann, E. Paquet, J. Shamir, “Surface feature reconstruction using scanning beams,” in Lasers and Electro-optics Europe, 1996 (Optical Society of America, Washington, D.C., 1996), p. 30.

G. Toker, A. Brunfeld, J. Shamir, B. Spektor, E. F. Cromwell, J. F. Adam, “In-line optical surface roughness determination by laser scanning,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 323–329 (2002).

B. Spektor, G. Toker, J. Shamir, M. Friedman, A. Brunfeld, “High-resolution surface evaluation using multiwavelength optical transforms,” in Interferometry XI: Techniques and Analysis, K. Creath, J. Schmit, eds., Proc. SPIE4777, 345–351 (July2002).

Yu. Ananev, Laser Resonators and the Beam Divergence Problem, Adam Hilger Series on Optics and Optoelectronics (Adam Hilger, Bristol, 1992).

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Figures (11)

Fig. 1
Fig. 1

(a) Schematic diagram of the cavity with a BPE, M1, and a conventional spherical mirror, M2, with radius of curvature R. L is the distance between mirrors, and β is the prism angle. The figure shows a negative β, corresponding to a concave BPE. (b) Two pairs of possible BPE variants.

Fig. 2
Fig. 2

Intensity distribution, |u00(x1)|2, of the fundamental mode TEM00 over the BPE for g = 0.775, b1 = 3.45, b2 = 10 and several values of α represented by the parameters (a) C and (b) H. α is (C1) 0, (C2) 0.1, (C3) 0.2, (C4) 0.3, (C5) 0.4, (C6) 0.5, (C7) 0.6, (H1) 0.5 (H3) 0.54, (H4) 0.56, (H5) 0.58, (H6) 0.56, (H7) 0.58.

Fig. 3
Fig. 3

Intensity distribution of modes TEM00 and TEM01 in a resonator with g = 0.775, b1 = 3.45, b2 = 10 for α = 0.56 (TEM00, solid curve; TEM01, dashed) and α = 0 (TEM00, dotted curve; TEM01, double dotted dashed).

Fig. 4
Fig. 4

Dependence of the squared eigenvalue, |Λn|2, on angle α for g = 0.775, b1 = 3.45, and b2 = 10. The various lines correspond to modes: TEM00, solid curves; TEM01, dashed curve; and TEM02, dashed–dotted curve.

Fig. 5
Fig. 5

Dependence of the squared eigenvalue, |Λn|2, of modes TEM00, TEM01 and TEM02 on the angle α for g = 0.65, and b2 = 5, (a) b1 = 2.5 and (b) b1 = 2.9.

Fig. 6
Fig. 6

Same as Fig. 4, but with g = 0.75, (a) b1 = 2.9, (b) b1 = 3.

Fig. 7
Fig. 7

Same as Fig. 4, but with g = 0.85, (a) b1 = 2.95, (b) b1 = 3.1. Points D denote intersections of the lines corresponding to TEM00 and TEM01.

Fig. 8
Fig. 8

Shape variation of the fundamental, TEM00, mode for a resonator with g = 0.85, b1 = 2.95, b2 = 5 and convex BPE having −α = (C1 0, (C2) 0.2, (C3) 0.4,(C4) 0.6, (C5) 0.8, (C6) 1, (C7) 1.2.

Fig. 9
Fig. 9

Same as Fig. 7, but for the TEM01 mode.

Fig. 10
Fig. 10

Intensity distribution of the first two modes for the cavity parameters, g = 0.5, b1 = 2.95, b2 = 5, and for α = −0.7 (TEM00, dashed curve; TEM01, solid curve) and α = 0 (TEM00, double dotted–dashed curve; TEM01, dotted curve).

Fig. 11
Fig. 11

Dependence of the TEM00 mode configuration over M1 with the misalignment, αd, changing with the equidistant step from (C1) αd = 0 to (C6) αd = 0.02, for a resonator with g = 0.775, b1 = 3.45, b2 = 10, α = 0.56.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

α = a 1 β / λ ,
γ u 2 ( x 2 ) = a 1 a 1 P 1 ( x 1 ) P 2 ( x 2 ) G ( x 2 , x 1 ) u 1 ( x 1 ) d x 1 , γ u 1 ( x 1 ) = a 1 a 1 P 1 ( x 1 ) P 2 ( x 2 ) G ( x 2 , x 1 ) u 2 ( x 2 ) d x 2 ,
g = 1 L / R ,
b j = [ 2 π a j 2 / ( λ L ) ] 1 / 2 , j = 1 , 2 .
S = | Λ 1 | 2 | Λ 0 | 2 .

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