Abstract

We investigate the power scaling of optical parametric amplifiers in the high-gain regime. With Gaussian or similarly shaped pump beams, the generated beams tend to become narrower than the pump beam, and backconversion distorts the intense central part of the beams before the peripheral parts of the pump beam are efficiently converted. Good beam quality and high conversion efficiency can nevertheless be combined when diffraction is strong enough to keep the diameter of the generated beams comparable to that of the pump beam. In practice, this requires narrow pump beams and consequently limits the peak power. Recent experiments have already exceeded this limit. As a solution, we find that a two-stage optical parametric amplifier can combine good beam quality and efficiency for much wider beams than a single-stage optical parametric amplifier.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  4. T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Femtosecond fiber-feedback optical parametric oscillator,” Opt. Lett. 26, 304–306 (2001).
    [CrossRef]
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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]
  25. R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani, and R. Righini, “Traveling-wave parametric generation of widely tunable highly coherent femtosecond light pulses,” J. Opt. Soc. Am. B 10, 2222–2232 (1993).
    [CrossRef]

2003 (3)

2002 (2)

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

F. Brunner, T. Südmeyer, E. Innerhofer, F. Morier-Genoud, R. Paschotta, V. E. Kisel, V. G. Shcherbitsky, N. V. Kuleshov, J. Gao, K. Contag, A. Giesen, and U. Keller, “240-fs pulses with 22-W average power from a mode-locked thin-disk Yb:KY(WO4)2 laser,” Opt. Lett. 27, 1162–1164 (2002).
[CrossRef]

2001 (3)

2000 (1)

1999 (2)

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[CrossRef] [PubMed]

G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16, 117–127 (1999).
[CrossRef]

1997 (4)

1996 (2)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profile characteristics of traveling-wave parametric generation in KTiOPO4 crystals,” Opt. Commun. 124, 512–518 (1996).
[CrossRef]

1995 (2)

B. C. Johnson, V. J. Newell, J. B. Clark, and E. S. McPhee, “Narrow-bandwidth low-divergence optical parametric oscillator for nonlinear frequency-conversion applications,” J. Opt. Soc. Am. B 12, 2122–2127 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

1993 (1)

1992 (1)

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

Arbore, M. A.

Arisholm, G.

Aschwanden, A.

Aus der Au, J.

Bäder, U.

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

Banfi, G. P.

R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani, and R. Righini, “Traveling-wave parametric generation of widely tunable highly coherent femtosecond light pulses,” J. Opt. Soc. Am. B 10, 2222–2232 (1993).
[CrossRef]

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

Bowers, M. S.

Brunner, F.

Clark, J. B.

Contag, K.

Danielius, R.

R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani, and R. Righini, “Traveling-wave parametric generation of widely tunable highly coherent femtosecond light pulses,” J. Opt. Soc. Am. B 10, 2222–2232 (1993).
[CrossRef]

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

DeSalvo, R.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Di Trapani, P.

R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani, and R. Righini, “Traveling-wave parametric generation of widely tunable highly coherent femtosecond light pulses,” J. Opt. Soc. Am. B 10, 2222–2232 (1993).
[CrossRef]

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

Dunn, M. H.

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[CrossRef] [PubMed]

Ebrahimzadeh, M.

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[CrossRef] [PubMed]

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

Erhard, S.

Fejer, M. M.

Fermann, M. E.

Fragemann, A.

Galvanauskas, A.

Gao, J.

Giesen, A.

Hagan, D. J.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Hanna, D. C.

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Femtosecond fiber-feedback optical parametric oscillator,” Opt. Lett. 26, 304–306 (2001).
[CrossRef]

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Novel ultrafast parametric systems: high repetition rate single-pass OPG and fibre-feedback OPO,” J. Phys. D 34, 2433–2439 (2001).
[CrossRef]

Häring, R.

Harter, D.

Hönninger, C.

Hövel, R.

Innerhofer, E.

Ito, R.

Johnson, B. C.

Karlsson, G.

Karszewski, M.

Keller, U.

Kisel, V. E.

Kitamoto, A.

Köhler, B.

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

Kondo, T.

Kuleshov, N. V.

Kumkar, M.

Laurell, F.

McPhee, E. S.

Meyn, J. P.

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

Morier-Genoud, F.

Moser, M.

Nebel, A.

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

Newell, V. J.

Nishikawa, T.

T. Nishikawa and N. Uesugi, “Transverse beam profile characteristics of traveling-wave parametric generation in KTiOPO4 crystals,” Opt. Commun. 124, 512–518 (1996).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

Paschotta, R.

Pasiskevicius, V.

Piskarskas, A.

R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani, and R. Righini, “Traveling-wave parametric generation of widely tunable highly coherent femtosecond light pulses,” J. Opt. Soc. Am. B 10, 2222–2232 (1993).
[CrossRef]

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

Podenas, D.

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

Righini, R.

Ross, G. W.

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Novel ultrafast parametric systems: high repetition rate single-pass OPG and fibre-feedback OPO,” J. Phys. D 34, 2433–2439 (2001).
[CrossRef]

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Femtosecond fiber-feedback optical parametric oscillator,” Opt. Lett. 26, 304–306 (2001).
[CrossRef]

Said, A. A.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Shcherbitsky, V. G.

Sheik-Bahae, M.

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Shirane, M.

Shoji, I.

Smith, A. V.

Smith, P. G. R.

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Femtosecond fiber-feedback optical parametric oscillator,” Opt. Lett. 26, 304–306 (2001).
[CrossRef]

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Novel ultrafast parametric systems: high repetition rate single-pass OPG and fibre-feedback OPO,” J. Phys. D 34, 2433–2439 (2001).
[CrossRef]

Spühler, G. J.

Stabinis, A.

Südmeyer, T.

Uesugi, N.

T. Nishikawa and N. Uesugi, “Transverse beam profile characteristics of traveling-wave parametric generation in KTiOPO4 crystals,” Opt. Commun. 124, 512–518 (1996).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

van Stryland, E. W.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Varanavicius, A.

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

Wallenstein, R.

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

Appl. Phys. B (1)

B. Köhler, U. Bäder, A. Nebel, J. P. Meyn, and R. Wallenstein, “A 9.5 Watt, 82 MHz-repetition-rate picosecond optical parametric generator with cw diode laser injection seeding,” Appl. Phys. B 75, 31–34 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorbtion and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

J. Appl. Phys. (1)

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

J. Opt. Soc. Am. B (6)

J. Phys. D (1)

T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Novel ultrafast parametric systems: high repetition rate single-pass OPG and fibre-feedback OPO,” J. Phys. D 34, 2433–2439 (2001).
[CrossRef]

Opt. Commun. (3)

T. Nishikawa and N. Uesugi, “Transverse beam profile characteristics of traveling-wave parametric generation in KTiOPO4 crystals,” Opt. Commun. 124, 512–518 (1996).
[CrossRef]

R. Danielius, A. Piskarskas, D. Podenas, P. Di Trapani, A. Varanavicius, and G. P. Banfi, “High power, subpicosecond, 750–1770 nm tunable pulses from travelling wave parametric generator,” Opt. Commun. 87, 23–27 (1992).
[CrossRef]

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Opt. Photon. News (1)

R. Paschotta and U. Keller, “Ever higher power from mode-locked lasers,” Opt. Photon. News 14, 50–54 (2003).
[CrossRef]

Science (1)

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[CrossRef] [PubMed]

Other (4)

T. Südmeyer, E. Innerhofer, F. Brunner, R. Paschotta, U. Keller, T. Usami, H. Ito, M. Nakamura, K. Kitamura, and D. C. Hanna, “Femtosecond fiber-feedback OPO with 15.5 W average power based on periodically poled stoichiometric LiTaO3,” in Advanced Solid-State Photonics, J. J. Zayhowski, ed., Vol. 83 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 77–81.

A. Dubois, T. Lepine, P. Georges, and A. Brun, “OPO radiance optimization using a numerical model,” in Advanced Solid-State Lasers, C. R. Pollock and W. R. Bosenberg, eds., Vol. 10 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 394–396.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University, New York, 1997).

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chap. 4.

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Figures (14)

Fig. 1
Fig. 1

Evolution of the signal beam profile along the crystal for two different seed powers. For clarity, the profile at each position is normalized to unit peak intensity, although the real intensity changes by several orders of magnitude along the crystal. (a) Negligible pump depletion. Seed power Ps=16 µW, η=5×10-4, Ms2=1.01. The gain was 66 dB, and the signal beam was narrowed from 100 µm to 38 µm radius. (b) Strong pump depletion. Ps=0.79 W, η=0.45, Ms2=1.7.

Fig. 2
Fig. 2

Conversion efficiency (a) and signal beam quality (b) as functions of seed power. The seed power was normalized relative to the level that gave 5% total conversion efficiency. The legend shows the pump waist radii, in micrometers, for the different graphs.

Fig. 3
Fig. 3

Beam quality of signal (solid) and idler (dashed) versus conversion efficiency. The legend shows the pump beam radius in micrometers. Each graph corresponds to increasing seed power (from lower left to upper right).

Fig. 4
Fig. 4

Signal beam quality versus total conversion efficiency in a 3-mm-long crystal. The pump beam waist radius was 200 µm, and the seed beam radius (in micrometers) is shown in the legend. Each graph corresponds to increasing seed power. The small-signal gain was ∼18 dB.

Fig. 5
Fig. 5

Radius of signal beam as function of position z along the crystal. The two graphs are labeled with their respective pump beam waist radii. The seed beams had the same radii as the pump beams. The dashed lines show the theoretical estimate, which is the maximum of Eqs. (4) and (6). That is, Eq. (4) is used for z>zss, and Eq. (6) is used for z<zss, where zss is given by Eq. (7). Equation (6) overestimates the radius for small z because the finite initial radius is not taken into account.

Fig. 6
Fig. 6

Evolution of signal beam radius in a 20-mm-long crystal. Each set of graphs is labeled with the pump beam radius, and for each pump radius, there are graphs for three different seed radii, equal to 0.5, 1, or 2 times the pump radius. The dashed lines show the theoretical estimate, which was explained in Fig. 5.

Fig. 7
Fig. 7

(a) Beam quality versus conversion efficiency for 100-µm pump beam radius and 6-, 10-, or 15-mm crystal lengths. (b) As above, but with 200-µm pump beam radius. (c) Beam quality versus conversion efficiency for 200-µm pump beam radius, 6-mm crystal, and various seed beam radii (on legend). (d) As (c), but for 10-mm crystal.

Fig. 8
Fig. 8

Effect of varying the signal wavelengths for three different pump radii. The signal wavelengths are shown in the legend. The nonlinear coefficient deff was adjusted so that σ was the same for each wavelength.

Fig. 9
Fig. 9

Signal beam quality versus conversion efficiency with super-Gaussian pump beams. The order and waist radii are shown in the legend. The other parameters were as in Section 2. Results for a Gaussian beam (order 2) are shown for comparison.

Fig. 10
Fig. 10

Signal beam quality versus conversion efficiency with phase mismatch. The legend shows (ΔkLc). The pump beam diameter was 70 µm, and the other parameters were as in Section 2.

Fig. 11
Fig. 11

Signal beam quality versus conversion efficiency for two-stage OPAs. The pump beam waist radius was 150 µm. (a) 7-mm crystal, 11-mm gap, 3-mm crystal. (b) 6-mm crystal, 13-mm gap, signal-blocking filter, 4-mm crystal. (c) Single stage with 10-mm crystal for comparison. The position of the pump beam waist in cases (a) and (b) was between the two crystals, but this is not very important because the Rayleigh length is much greater than the length of the crystals and air gap.

Fig. 12
Fig. 12

Signal beam quality (left column) and peak total intensity (right column) versus conversion efficiency for various pump beam waist radii and values of n2. The values of n2, in units of 10-16 cm2/W, are shown in the legend. The pump beam waist radius is shown on each graph.

Fig. 13
Fig. 13

(a) Signal beam quality versus conversion efficiency for 6-ps pump pulses. The legend shows the pump waist radius in micrometers. (b) Analogous graphs for 0.3-ps pump pulse.

Fig. 14
Fig. 14

(a) Signal beam quality versus conversion efficiency for an OPG with 6-ps pump pulses. The legend shows the pump waist radius in micrometers. η was varied by varying the peak pump intensity. (b) Relative standard deviation of the output energy (i.e., standard deviation divided by the mean).

Tables (1)

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Table 1 Scaling Factors under the Invariant Transformation of the Propagation Equations

Equations (22)

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α=α0-12α2r2,
w2=2λπnα21/2,
α(r)=κI3(r)=κa0,3 exp(-r2/w32)=Lg-1 exp(-r2/w32),
w22=w32λLgπn1/2.
a2(r, z)=a2(r, 0)exp[zα(r)]=a2(0, 0)exp(-r2/w22)exp[z/Lg×exp(-r2/w32)],
r2=1w22+zLgw32-1w32Lgz,
zss=w3πnLg2λ1/2.
a1z=-i2k1T2a1+iω1γa3a2*,
a2z=-i2k2T2a2+iω2γa3a1*,
a3z=-i2k3T2a3+iω3γa1a2,
1Lc A1z=-i2βLdT2A1+iβσA3A2*,
1Lc A2z=-i2(1-β)LdT2A2+i(1-β)σA3A1*,
1Lc A3z=-i2LdT2A3+iσA1A2.
κ=γ(ω1ω2)1/2=ω3γβ1/2(1-β)1/2
Lg=1/[σβ1/2(1-β)1/2]=1/(κa0,3),
Ld,max(ηc, Ms,c2, β, σ/s, sLc)
=sLd,max(ηc, Ms,c2, β, σ, Lc).
Ld,max(ηc, Ms,c2, β, σ, Lc)=σ-1D(ηc, Ms,c2, β, Lcσ),
Wmax2=Ld,maxk3=cnω3σD(ηc, Ms,c2, β, Lcσ),
Pmax=Imax π2Wmax2=πcamax2nω32γD(ηc, Ms,c2, β, Lcσ)=πc2amax(2c0n)1/24deffω32D(ηc, Ms,c2, β, Lcσ),
Imax  u2Imax,γ  rγ,n  tn,
B=2πλn20LcI(z)dz,

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