Abstract

A universal model about the sufficient condition of stable single-longitudinal-mode (SLM) operation is established and applied to the theoretical analysis of a high power unidirectional ring Nd:YVO4 laser at 1342 nm with energy transfer upconversion and excited stimulated absorption taken into account. A stable continuous-wave SLM laser with 1342 nm power of 11.3 W and 671 nm power of 0.3 W is fabricated by optimizing the transmission of output coupler and the temperature of LiB3O5 crystal. Mode-hopping-free laser operation with a power stability better than ± 0.5% and a frequency fluctuation less than ± 88 MHz is achieved during a given three hours.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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2017 (1)

2016 (3)

I. E. Olivares and I. A. González, “Diode laser absorption spectroscopy of lithium isotopes,” Appl. Phys. B 122(10), 252 (2016).
[Crossref]

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

M. R. Huo, J. L. Qin, Z. Yan, X. Jia, and K. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016).
[Crossref]

2014 (2)

J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, “Magneto-optical trapping of a diatomic molecule,” Nature 512(7514), 286–289 (2014).
[Crossref] [PubMed]

H. Lu, J. Su, Y. Zheng, and K. Peng, “Physical conditions of single-longitudinal-mode operation for high-power all-solid-state lasers,” Opt. Lett. 39(5), 1117–1120 (2014).
[Crossref] [PubMed]

2012 (1)

Y. H. Zheng, Y. J. Wang, C. D. Xie, and K. C. Peng, “Single-frequency Nd:YVO4 laser at 671 nm with high-output power of 2.8 W,” IEEE J. Quantum Electron. 48(1), 67–72 (2012).
[Crossref]

2011 (2)

X. Délen, F. Balembois, O. Musset, and P. Georges, “Characteristics of laser operation at 1064 nm in Nd:YVO4 under diode pumping at 808 and 914 nm,” J. Opt. Soc. Am. B 28(1), 52–57 (2011).
[Crossref]

The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011).
[Crossref]

2010 (1)

F. A. Camargo, T. Z. Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency NdYVO4 BiB3O6 ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010).
[Crossref]

2009 (1)

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

2008 (1)

R. Sarrouf, T. Badr, and J. J. Zondy, “Intracavity second-harmonic generation of diode-pumped continuous-wave, single-frequency 1.3 μm Nd:YLiF4 lasers,” J. Opt. A, Pure Appl. Opt. 10(10), 104011 (2008).
[Crossref]

2005 (3)

S. Greenstein and M. Rosenbluh, “The influence of nonlinear spectral bandwidth on single longitudinal mode intra-cavity second harmonic generation,” Opt. Commun. 248(1–3), 241–248 (2005).
[Crossref]

M. Okida, M. Itoh, T. Yatagai, H. Ogilvy, J. Piper, and T. Omatsu, “Heat generation in Nd doped vanadate crystals with 1.34 µm laser action,” Opt. Express 13(13), 4909–4915 (2005).
[Crossref] [PubMed]

A. Miffre, M. Jacquey, M. Büchner, G. Trénec, and J. Vigué, “Lithium atom interferometer using laser diffraction: description and experiments,” Eur. Phys. J. D 33(1), 99–112 (2005).
[Crossref]

1999 (1)

Y. F. Chen, L. J. Lee, T. M. Huang, and C. L. Wang, “Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 μm: influence of Auger upconversion,” Opt. Commun. 163(4–6), 198–202 (1999).
[Crossref]

1998 (1)

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

1997 (1)

1994 (1)

Badr, T.

F. A. Camargo, T. Z. Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency NdYVO4 BiB3O6 ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010).
[Crossref]

R. Sarrouf, T. Badr, and J. J. Zondy, “Intracavity second-harmonic generation of diode-pumped continuous-wave, single-frequency 1.3 μm Nd:YLiF4 lasers,” J. Opt. A, Pure Appl. Opt. 10(10), 104011 (2008).
[Crossref]

Balembois, F.

Barry, J. F.

J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, “Magneto-optical trapping of a diatomic molecule,” Nature 512(7514), 286–289 (2014).
[Crossref] [PubMed]

Baxter, G. W.

Booth, D. J.

Bowkett, G. C.

Büchner, M.

A. Miffre, M. Jacquey, M. Büchner, G. Trénec, and J. Vigué, “Lithium atom interferometer using laser diffraction: description and experiments,” Eur. Phys. J. D 33(1), 99–112 (2005).
[Crossref]

Camargo, F. A.

F. A. Camargo, T. Z. Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency NdYVO4 BiB3O6 ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010).
[Crossref]

Chai, B. H. T.

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

Chen, Y. F.

Y. F. Chen, L. J. Lee, T. M. Huang, and C. L. Wang, “Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 μm: influence of Auger upconversion,” Opt. Commun. 163(4–6), 198–202 (1999).
[Crossref]

Chevy, F.

Clarkson, W. A.

Délen, X.

DeMille, D.

J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, “Magneto-optical trapping of a diatomic molecule,” Nature 512(7514), 286–289 (2014).
[Crossref] [PubMed]

Deng, X.

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

Eismann, U.

Fornasiero, L.

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

Georges, P.

González, I. A.

I. E. Olivares and I. A. González, “Diode laser absorption spectroscopy of lithium isotopes,” Appl. Phys. B 122(10), 252 (2016).
[Crossref]

Greenstein, S.

S. Greenstein and M. Rosenbluh, “The influence of nonlinear spectral bandwidth on single longitudinal mode intra-cavity second harmonic generation,” Opt. Commun. 248(1–3), 241–248 (2005).
[Crossref]

Hanna, D. C.

He, J.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Huang, T. M.

Y. F. Chen, L. J. Lee, T. M. Huang, and C. L. Wang, “Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 μm: influence of Auger upconversion,” Opt. Commun. 163(4–6), 198–202 (1999).
[Crossref]

Huber, G.

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

Huo, M. R.

M. R. Huo, J. L. Qin, Z. Yan, X. Jia, and K. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016).
[Crossref]

Itoh, M.

Jacquey, M.

A. Miffre, M. Jacquey, M. Büchner, G. Trénec, and J. Vigué, “Lithium atom interferometer using laser diffraction: description and experiments,” Eur. Phys. J. D 33(1), 99–112 (2005).
[Crossref]

Jensen, T.

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

Jia, X.

M. R. Huo, J. L. Qin, Z. Yan, X. Jia, and K. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016).
[Crossref]

Kobayashi, T.

Kretzschmar, N.

Kück, S.

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

Lee, L. J.

Y. F. Chen, L. J. Lee, T. M. Huang, and C. L. Wang, “Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 μm: influence of Auger upconversion,” Opt. Commun. 163(4–6), 198–202 (1999).
[Crossref]

Li, J.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Li, Q.

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

Liu, Y.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Lu, H.

Martin, K. I.

McCarron, D. J.

J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, “Magneto-optical trapping of a diatomic molecule,” Nature 512(7514), 286–289 (2014).
[Crossref] [PubMed]

Miffre, A.

A. Miffre, M. Jacquey, M. Büchner, G. Trénec, and J. Vigué, “Lithium atom interferometer using laser diffraction: description and experiments,” Eur. Phys. J. D 33(1), 99–112 (2005).
[Crossref]

Musset, O.

Norrgard, E. B.

J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, “Magneto-optical trapping of a diatomic molecule,” Nature 512(7514), 286–289 (2014).
[Crossref] [PubMed]

Ogilvy, H.

Okida, M.

Olivares, I. E.

I. E. Olivares and I. A. González, “Diode laser absorption spectroscopy of lithium isotopes,” Appl. Phys. B 122(10), 252 (2016).
[Crossref]

Omatsu, T.

Peng, K.

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

M. R. Huo, J. L. Qin, Z. Yan, X. Jia, and K. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016).
[Crossref]

H. Lu, J. Su, Y. Zheng, and K. Peng, “Physical conditions of single-longitudinal-mode operation for high-power all-solid-state lasers,” Opt. Lett. 39(5), 1117–1120 (2014).
[Crossref] [PubMed]

Peng, K. C.

Y. H. Zheng, Y. J. Wang, C. D. Xie, and K. C. Peng, “Single-frequency Nd:YVO4 laser at 671 nm with high-output power of 2.8 W,” IEEE J. Quantum Electron. 48(1), 67–72 (2012).
[Crossref]

Piper, J.

Qin, J. L.

M. R. Huo, J. L. Qin, Z. Yan, X. Jia, and K. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016).
[Crossref]

Rosenbluh, M.

S. Greenstein and M. Rosenbluh, “The influence of nonlinear spectral bandwidth on single longitudinal mode intra-cavity second harmonic generation,” Opt. Commun. 248(1–3), 241–248 (2005).
[Crossref]

Salomon, C.

Sarrouf, R.

R. Sarrouf, T. Badr, and J. J. Zondy, “Intracavity second-harmonic generation of diode-pumped continuous-wave, single-frequency 1.3 μm Nd:YLiF4 lasers,” J. Opt. A, Pure Appl. Opt. 10(10), 104011 (2008).
[Crossref]

Sha, P.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Sievers, F.

Steinecker, M. H.

J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, “Magneto-optical trapping of a diatomic molecule,” Nature 512(7514), 286–289 (2014).
[Crossref] [PubMed]

Su, J.

Su, X.

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

Taira, T.

Teranishi, H.

Tian, C.

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

Trénec, G.

A. Miffre, M. Jacquey, M. Büchner, G. Trénec, and J. Vigué, “Lithium atom interferometer using laser diffraction: description and experiments,” Eur. Phys. J. D 33(1), 99–112 (2005).
[Crossref]

Vigué, J.

A. Miffre, M. Jacquey, M. Büchner, G. Trénec, and J. Vigué, “Lithium atom interferometer using laser diffraction: description and experiments,” Eur. Phys. J. D 33(1), 99–112 (2005).
[Crossref]

Wang, C. L.

Y. F. Chen, L. J. Lee, T. M. Huang, and C. L. Wang, “Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 μm: influence of Auger upconversion,” Opt. Commun. 163(4–6), 198–202 (1999).
[Crossref]

Wang, Y. J.

Y. H. Zheng, Y. J. Wang, C. D. Xie, and K. C. Peng, “Single-frequency Nd:YVO4 laser at 671 nm with high-output power of 2.8 W,” IEEE J. Quantum Electron. 48(1), 67–72 (2012).
[Crossref]

Wetter, N. U.

F. A. Camargo, T. Z. Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency NdYVO4 BiB3O6 ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010).
[Crossref]

Willette, T. Z.

F. A. Camargo, T. Z. Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency NdYVO4 BiB3O6 ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010).
[Crossref]

Xie, C.

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref] [PubMed]

Xie, C. D.

Y. H. Zheng, Y. J. Wang, C. D. Xie, and K. C. Peng, “Single-frequency Nd:YVO4 laser at 671 nm with high-output power of 2.8 W,” IEEE J. Quantum Electron. 48(1), 67–72 (2012).
[Crossref]

Xin, J.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Yan, Y.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Yan, Z.

M. R. Huo, J. L. Qin, Z. Yan, X. Jia, and K. Peng, “Generation of two types of nonclassical optical states using an optical parametric oscillator with a PPKTP crystal,” Appl. Phys. Lett. 109(22), 221101 (2016).
[Crossref]

Yatagai, T.

Zhang, H.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Zhang, H. L.

Y. Yan, H. L. Zhang, Y. Liu, J. Li, P. Sha, J. He, H. Zhang, and J. Xin, “End-pumped 20.2-W Nd:YVO4 cw slab laser at 1342 nm with a hybrid resonator,” Opt. Commun. 282(15), 3124–3126 (2009).
[Crossref]

Zheng, Y.

Zheng, Y. H.

Y. H. Zheng, Y. J. Wang, C. D. Xie, and K. C. Peng, “Single-frequency Nd:YVO4 laser at 671 nm with high-output power of 2.8 W,” IEEE J. Quantum Electron. 48(1), 67–72 (2012).
[Crossref]

Zondy, J. J.

F. A. Camargo, T. Z. Willette, T. Badr, N. U. Wetter, and J. J. Zondy, “Tunable single-frequency NdYVO4 BiB3O6 ring laser at 671 nm,” IEEE J. Quantum Electron. 46(5), 804–809 (2010).
[Crossref]

R. Sarrouf, T. Badr, and J. J. Zondy, “Intracavity second-harmonic generation of diode-pumped continuous-wave, single-frequency 1.3 μm Nd:YLiF4 lasers,” J. Opt. A, Pure Appl. Opt. 10(10), 104011 (2008).
[Crossref]

Appl. Phys. B (2)

I. E. Olivares and I. A. González, “Diode laser absorption spectroscopy of lithium isotopes,” Appl. Phys. B 122(10), 252 (2016).
[Crossref]

L. Fornasiero, S. Kück, T. Jensen, G. Huber, and B. H. T. Chai, “Excited state absorption and stimulated emission of Nd3+ in crystals. Part 2: YVO4, GdVO4, and Sr5(PO4)3F,” Appl. Phys. B 67(5), 549–553 (1998).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Critical value of nonlinear conversion coefficient as a function of output transmission for the sufficient condition of stable SLM operation for a high-power cw laser at 1342 nm
Fig. 2
Fig. 2 Experimental setup of a LD-pumped cw SLM Nd:YVO4 laser at 1342 nm.
Fig. 3
Fig. 3 Output powers of 1342 nm and 671 nm laser versus the temperature of LBO.
Fig. 4
Fig. 4 Transmitted intensity of the scanned F-P interferometer at an output transmission of 7% and different LBO temperatures (a) 39.5 °C, (b) 32.5 °C and (c) 29.04 °C.
Fig. 5
Fig. 5 Output powers of 1342 nm and 671 nm lasers versus transmission of output coupler.
Fig. 6
Fig. 6 Measured fluctuations of the power and frequency of the 1342 nm laser.
Fig. 7
Fig. 7 Measured beam quality of the 1342 nm laser.

Equations (13)

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g 0 ( q )= g 0 max /[ 1+ ( qΔω Δ ω g /2 ) 2 ],
2K( ω 0 , ω 1 ,Δ ω NL )I( ω 1 )+K( ω 0 , ω 0 ,Δ ω NL )I( ω 0 )+ δ 0 + T oc = g 0 max l 0 1+ I( ω 0 ) I 0 ( ω 0 ) + I( ω 1 ) I 0 ( ω 1 ) ,
[ g 0 max g 0 ( 1 )] l 0 /(1+ I( ω 0 ) I 0 ( ω 0 ) + I( ω 1 ) I 0 ( ω 1 ) ])[2K( ω 0 , ω 1 ,Δ ω NL )I( ω 1 )+K( ω 0 , ω 0 ,Δ ω NL )I( ω 0 ) 2K( ω 0 , ω 1 ,Δ ω NL )I( ω 0 )K( ω 1 , ω 1 ,Δ ω NL )I( ω 1 )]>ΔG(m),
K( ω i , ω j ,Δ ω NL )=Ksin c 2 ( 1.39 ω i + ω j 2 ω 0 Δ ω NL ),
I 0 ( ω i )= I 0 ( 1+ ( iΔω Δ ω g /2 ) 2 ),
AK I 2 ( ω 0 )+AK I 0 I( ω 0 )B g 0 max l 0 I( ω 0 )>C I 0 g 0 max l 0 ,
A=2sin c 2 ( 1.39 Δω Δ ω NL )1; B= ( mΔω ) 2 ( Δ ω g /2 ) 2 + ( mΔω ) 2 ; C= ( m 2 1 )Δ ω 2 ( Δ ω g /2 ) 2 ( ( Δ ω g /2 ) 2 +Δ ω 2 )( ( Δ ω g /2 ) 2 + m 2 Δ ω 2 ) .
P f = T oc SI( ω 0 ),
P sh = K 0 S I 2 ( ω 0 ),
( g 0 max l 0 ) etu&esa =( σ e σ esa l ) 0 l 0 n etu&esa ( z ) dz,
( g 0 max l 0 ) no etu&esa = σ e 0 l 0 n no etu&esa ( z ) dz,
n etu&esa = 1+4γ τ 2 P in αexp(αz)/( h ν p π w pa 2 ) 1 2γτ ,
n no etu&esa = P in ταexp(αz)/( h ν p π w pa 2 ),

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