Abstract

The parasitic oscillations in a disk gain medium are refined by a rigorous electrodynamics study. The boundary conditions of an electromagnetic field decide not only the spatial distribution of the field (transverse eigenmodes) but also the spectrum of the field (longitudinal eigenmodes) due to the higher geometric symmetry of the disk. The novel dispersion relations only allow a few longitudinal eigenmodes. Because stable parasitic modes possess a larger spatial volume, in quasi-cw operating high-average-power solid-state lasers the longitudinal eigenmodes play a more important role than transverse ones in mode competition with the main laser. Furthermore, the polarizations are also selected by the boundary conditions, and a given eigenmode cannot possess radial polarization and azimuthal polarization components simultaneously.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2009

2008

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

2004

2003

J. Vetrovec, R. Shah, T. Endo, and A. Koumavakalis, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54-64 (2003).
[CrossRef]

2000

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

1999

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

N. P. Barnes and B. M. Walsh, “Amplified spontaneous emission-application to Nd:YAG lasers,” IEEE J. Quantum Electron. 35, 101-110 (1999).
[CrossRef]

1987

J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

1978

1973

1969

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

1954

R. N. Dieke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Baird, E. D.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

Barnes, N. P.

N. P. Barnes and B. M. Walsh, “Amplified spontaneous emission-application to Nd:YAG lasers,” IEEE J. Quantum Electron. 35, 101-110 (1999).
[CrossRef]

Brown, D. C.

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 1995).

Cao, H.

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Dane, C. B.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Dieke, R. N.

R. N. Dieke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Emmett, J.

J. M. McMahon, J. Emmett, J. Holzrichter, and J. B. Trenholme, “A glass-disk-laser amplifier,” IEEE J. Quantum Electron. 9, 992-999 (1973).
[CrossRef]

Endo, T.

J. Vetrovec, R. Shah, T. Endo, and A. Koumavakalis, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54-64 (2003).
[CrossRef]

Goldman, L. M.

Gonzales, S. A.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Holzrichter, J.

J. M. McMahon, J. Emmett, J. Holzrichter, and J. B. Trenholme, “A glass-disk-laser amplifier,” IEEE J. Quantum Electron. 9, 992-999 (1973).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Jacobs, S. D.

Kidder, R. E.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

Koumavakalis, A.

J. Vetrovec, R. Shah, T. Endo, and A. Koumavakalis, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54-64 (2003).
[CrossRef]

Li, Z. G.

Loth, B.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

Lubin, M. J.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

McMahon, J. M.

J. M. McMahon, J. Emmett, J. Holzrichter, and J. B. Trenholme, “A glass-disk-laser amplifier,” IEEE J. Quantum Electron. 9, 992-999 (1973).
[CrossRef]

Merrill, R. D.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Miceli, J. J.

J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Mitchell, S. C.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Moors, N.

Nee, N.

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Noda, S.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Parks, C. W.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Pettipiece, K.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

Rainer, F.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

Rotter, M. D.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Shah, R.

J. Vetrovec, R. Shah, T. Endo, and A. Koumavakalis, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54-64 (2003).
[CrossRef]

Soures, J. M.

Speiser, J.

Swain, J. E.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

Trenholme, J. B.

J. M. McMahon, J. Emmett, J. Holzrichter, and J. B. Trenholme, “A glass-disk-laser amplifier,” IEEE J. Quantum Electron. 9, 992-999 (1973).
[CrossRef]

J. B. Trenholme, “Flurescence amplification and parastic oscillation limitations in disc lasers,” Naval Research Labs, Memo. Rept. 2480 (1972).

Vetrovec, J.

J. Vetrovec, R. Shah, T. Endo, and A. Koumavakalis, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54-64 (2003).
[CrossRef]

Walsh, B. M.

N. P. Barnes and B. M. Walsh, “Amplified spontaneous emission-application to Nd:YAG lasers,” IEEE J. Quantum Electron. 35, 101-110 (1999).
[CrossRef]

Wu, X.

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

Xiong, Z. J.

Yamamoto, R. M.

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

Appl. Opt.

IEEE J. Quantum Electron.

J. M. McMahon, J. Emmett, J. Holzrichter, and J. B. Trenholme, “A glass-disk-laser amplifier,” IEEE J. Quantum Electron. 9, 992-999 (1973).
[CrossRef]

N. P. Barnes and B. M. Walsh, “Amplified spontaneous emission-application to Nd:YAG lasers,” IEEE J. Quantum Electron. 35, 101-110 (1999).
[CrossRef]

J. Appl. Phys.

J. E. Swain, R. E. Kidder, K. Pettipiece, F. Rainer, E. D. Baird, and B. Loth, “Large-aperture glass disk laser system,” J. Appl. Phys. 40, 3973-3977 (1969).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Nature

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Phys. Rev.

R. N. Dieke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Phys. Rev. A

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

Phys. Rev. Lett.

J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Proc. SPIE

J. Vetrovec, R. Shah, T. Endo, and A. Koumavakalis, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54-64 (2003).
[CrossRef]

Other

M. D. Rotter, C. B. Dane, S. A. Gonzales, R. D. Merrill, S. C. Mitchell, C. W. Parks, and R. M. Yamamoto, “The solid-state heat-capacity laser,” in Advanced Solid-State Photonics (TOPS), G.Quarles, ed. Vol. 94 of 2004 OSA Trends in Optics and Photonics (Optical Society of America, 2004), paper 278.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 1995).

J. B. Trenholme, “Flurescence amplification and parastic oscillation limitations in disc lasers,” Naval Research Labs, Memo. Rept. 2480 (1972).

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Figures (4)

Fig. 1
Fig. 1

Spatial regions in which the electromagnetic field takes different asymptotic behaviors.

Fig. 2
Fig. 2

Sketch map on intensity distribution of the face eigenmodes at different axial positions where χ = 10.0 .

Fig. 3
Fig. 3

Lossless r polarization modes distributing during the wavelength 1063.8 1064.2 nm where the radius and thickness of the Nd:YAG disk are 5 cm and 1 cm , respectively. The scattering points denote the eigenmodes in spectrum space. The modes located at a given transverse line or a given longitudinal line have approximately the same values of k or of the wavelength, and three pair of modes marked by different loops have approximately the same transverse mode interval in k space.

Fig. 4
Fig. 4

Part of geometric path of k λ 2 π = 1.14 parasitic mode.

Equations (28)

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E i ( x , t ) = e i u i ( x ) e i ω t + g 0 c t , B i ( x , t ) = e i B i ( x ) e i ω t + g 0 c t ,
u r ± u r , u ϕ ± u ϕ , u z u z .
u r = cos k z { a 0 r ( k ) J 1 ( β k r ) + n 0 e i n ϕ [ a n ( k ) J n + 1 ( β k r ) + b n J n 1 ( β k r ) ] } ,
u ϕ = cos k z { a 0 r ( k ) J 1 ( β k r ) i n 0 e i n ϕ [ a n ( k ) J n + 1 ( β k r ) b n J n 1 ( β k r ) ] } ,
u z = β k k sin k z { a 0 r ( k ) J 0 ( β k r ) + n 0 e i n ϕ ( a n ( k ) b n ( k ) ) J n ( β k r ) } ,
u z = β k k sin k z { a 0 r ( k ) K 0 ( β k r ) + n 0 e i n ϕ ( a n ( k ) + b n ( k ) ) K n ( β k r ) } ,
n ( ϵ 1 E 1 ϵ 2 E 2 ) = 0 ,
n × ( E 1 E 2 ) = 0 ,
× ( E 1 E 2 ) = 0 .
{ tan k l = ξ n r 2 n r 2 1 ξ 2 n r 2 tan ( k d n r 2 ξ 2 1 π 4 ) = n r 2 ξ 2 1 ξ 2 tan ( k d ξ 2 1 π 4 ) } , ( r z polarization )
{ tan k l = n r 2 1 ξ 2 ξ tan ( k d n r 2 ξ 2 1 π 4 ) = n r 2 ξ 2 1 ξ 2 tan ( k d ξ 2 1 π 4 ) } , ( ϕ polarization )
| E | 2 χ 2 z 2 J 0 2 ( χ r ) + J 1 2 ( χ r ) ,
{ a n = b n , k sin k l = k ̃ cos k l , or a n = b n , n r 2 k ̃ sin k l = k cos k l , J n ( β k d ) = J n ( β k d ) or J n ( β k d ) = J n ( β k d ) , }
k ̃ = 4 π 2 λ 2 ( n r 2 1 ) k 2 , β k = 4 π 2 n r 2 λ 2 k 2 ,
β k = 4 π 2 λ 2 k 2 .
λ = 2 d ( n r 1 ) m m , m = m n r ( 1 1 n r ) ( n 2 + 1 4 ) ,
J n ( β k d ) = J n ( β k d ) = 0 .
tan ( 2 π d λ n r 2 ξ 2 π 4 ) = { 1 n r 2 n r 2 ξ 2 ξ 2 1 ( r polarization ) n r 2 ξ 2 ξ 2 1 ( ϕ polarization ) } ,
k = m π 2 l , λ 4 l = n r 2 1 m 2 m 2 , m , m Z .
ξ = n r 2 n r 2 + 1 , λ 2 l = n r 2 1 m n r 2 + 1 , tan ( 2 π n r n r 2 + 1 d λ π 4 ) = 1 n r n r 4 n r 2 1 .
R r amp = R z amp = | m m n r 2 | m + m n r 2 , R ϕ amp = m m m + m .
{ tan k l = ξ n r 2 n r 2 1 ξ 2 tan ( k d n r 2 ξ 2 1 π 4 ) = n r 2 ξ 2 n r 2 ξ 2 1 } , ( r z polarization )
{ tan k l = n r 2 1 ξ 2 ξ tan ( k d n r 2 ξ 2 1 π 4 ) = n r 2 ξ 2 ξ 2 1 } . ( ϕ polarization )
δ λ λ λ 2 d , δ k π l ,
L = n r D 4 π 2 n r 2 k 2 λ 2 .
| u z | | u r | β k = | m 2 n r 2 m 2 | m 2 ( n r 2 1 ) ,
( m n r 2 m ) 2 ( m + n r 2 m ) 2 exp ( 2 g a n r l m m 2 m 2 n r 2 1 ) = 1 .
δ λ k λ 3 4 π l ( n r 2 1 ) .

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