Abstract

We theoretically study third harmonic generation in silica microfiber loop resonators wherein the large resonant field strength is exploited to increase the efficiency and reduce the required pump power, with a focus on the influence of loop parameters such as loss and coupling. For a 3 mm length loop, the conversion can reach several percent, that is, 640 times greater than an equivalent straight microfiber, for input powers as low as 100 W. The harmonic signal can be toggled between a high- and low-output state due to hysteresis at higher powers, and the efficiency can be further enhanced if the harmonic light is recirculated and coresonant with the pump.

© 2013 Optical Society of America

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2012 (3)

2011 (4)

2010 (4)

2009 (1)

2008 (1)

2007 (3)

Z. Yang, P. Chak, A. D. Bristow, H. M. van Driel, R. Iyer, J. S. Aitchison, A. L. Smirl, and J. E. Sipe, “Enhanced second-harmonic generation in AlGaAs microring resonators,” Opt. Lett. 32, 826–828 (2007).
[CrossRef]

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
[CrossRef]

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274, 447–450 (2007).
[CrossRef]

2006 (3)

2005 (1)

2004 (3)

2003 (2)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

1989 (1)

C. Caspar and E. J. Bachus, “Fibre-optic micro-ring-resonator with 2 mm diameter,” Electron. Lett. 25, 1506–1508 (1989).
[CrossRef]

Afshar, S.

Afshar V., S.

N. G. R. Broderick, M. A. Lohe, T. Lee, and S. Afshar V., “Analytic theory of two wave interactions in a waveguide with a χ(3)nonlinearity,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), p. I366.

Ahmad, H.

Aitchison, J. S.

Akimov, D.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Alfimov, M.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Alt, W.

Ashcom, J. B.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Azizur Rahman, B. M.

Bachus, E. J.

C. Caspar and E. J. Bachus, “Fibre-optic micro-ring-resonator with 2 mm diameter,” Electron. Lett. 25, 1506–1508 (1989).
[CrossRef]

Belal, M.

R. Ismaeel, T. Lee, M. Ding, M. Belal, and G. Brambilla, “Optical microfiber passive components,” Laser Photon. Rev. (to be published).
[CrossRef]

Bi, Z.

Birks, T.

S. Leon-Saval, T. Birks, W. Wadsworth, P. St. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004).
[CrossRef]

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Brambilla, G.

Bristow, A. D.

Broderick, N. G. R.

T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express 20, 8503–8511 (2012).
[CrossRef]

N. G. R. Broderick, M. A. Lohe, T. Lee, and S. Afshar V., “Analytic theory of two wave interactions in a waveguide with a χ(3)nonlinearity,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), p. I366.

Carmon, T.

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
[CrossRef]

Caspar, C.

C. Caspar and E. J. Bachus, “Fibre-optic micro-ring-resonator with 2 mm diameter,” Electron. Lett. 25, 1506–1508 (1989).
[CrossRef]

Chak, P.

Codemard, C. A.

Coillet, A.

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285, 3493–3497 (2012).
[CrossRef]

A. Coillet, G. Vienne, and P. Grelu, “Potentialities of glass air-clad micro-and nanofibers for nonlinear optics,” J. Opt. Soc. Am. B 27, 394–401 (2010).
[CrossRef]

Corona, M.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84, 033823 (2011).
[CrossRef]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36, 190–192 (2011).
[CrossRef]

Damanhuri, S. S. A.

Dan, C.

DiGiovanni, D.

Ding, M.

T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express 20, 8503–8511 (2012).
[CrossRef]

R. Ismaeel, T. Lee, M. Ding, M. Belal, and G. Brambilla, “Optical microfiber passive components,” Laser Photon. Rev. (to be published).
[CrossRef]

Duchesne, D.

Dulashko, Y.

Feinberg, J.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274, 447–450 (2007).
[CrossRef]

Finazzi, V.

Fini, J.

Foster, M. A.

Gaeta, A. L.

Garay-Palmett, K.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36, 190–192 (2011).
[CrossRef]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84, 033823 (2011).
[CrossRef]

Gattass, R. R.

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Grelu, P.

Grubsky, V.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274, 447–450 (2007).
[CrossRef]

V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13, 6798–6806 (2005).
[CrossRef]

Guo, X.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Hale, A.

Harun, S. W.

Hashemi, H.

He, S.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Irsen, S.

Ismaeel, R.

R. Ismaeel, T. Lee, M. Ding, M. Belal, and G. Brambilla, “Optical microfiber passive components,” Laser Photon. Rev. (to be published).
[CrossRef]

Ivanov, A.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Iyer, R.

Jasim, A. A.

Jiang, X.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Johnson, S. G.

Jung, Y.

Karapetyan, K.

Kolevatova, O.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Lægsgaard, J.

Lee, T.

T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express 20, 8503–8511 (2012).
[CrossRef]

R. Ismaeel, T. Lee, M. Ding, M. Belal, and G. Brambilla, “Optical microfiber passive components,” Laser Photon. Rev. (to be published).
[CrossRef]

N. G. R. Broderick, M. A. Lohe, T. Lee, and S. Afshar V., “Analytic theory of two wave interactions in a waveguide with a χ(3)nonlinearity,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), p. I366.

Leon-Saval, S.

Levy, J. S.

Li, Y.

Lim, K. S.

Lipson, M.

Lohe, M. A.

N. G. R. Broderick, M. A. Lohe, T. Lee, and S. Afshar V., “Analytic theory of two wave interactions in a waveguide with a χ(3)nonlinearity,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), p. I366.

Loncar, M.

Lou, J.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Mason, M.

Maxwell, I.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Mazur, E.

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Meschede, D.

Monro, T. M.

Naumov, A.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Podshivalov, A.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Pritzkau, D.

Richard, S.

Richardson, D.

Rodriguez, A. W.

Russell, P.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Russell, P. St. J.

Savchenko, A.

Shen, M.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Sipe, J. E.

Smirl, A. L.

Sumetsky, M.

Svacha, G. T.

Tong, L.

G. Vienne, Y. Li, L. Tong, and P. Grelu, “Observation of a nonlinear microfiber resonator,” Opt. Lett. 33, 1500–1502 (2008).
[CrossRef]

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[CrossRef]

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Tsao, A.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

U’Ren, A. B.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36, 190–192 (2011).
[CrossRef]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84, 033823 (2011).
[CrossRef]

Vahala, K. J.

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
[CrossRef]

van Driel, H. M.

Vienne, G.

Wadsworth, W.

S. Leon-Saval, T. Birks, W. Wadsworth, P. St. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004).
[CrossRef]

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Wang, K.

Wiedemann, U.

Yang, D.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Yang, Q.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Yang, Z.

Zheltikov, A.

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

D. Akimov, A. Ivanov, A. Naumov, O. Kolevatova, M. Alfimov, T. Birks, W. Wadsworth, P. Russell, A. Podshivalov, and A. Zheltikov, “Generation of a spectrally asymmetric third harmonic with unamplified 30 fs Cr: Forsterite laser pulses in a tapered fiber,” Appl. Phys. B 76, 515–519 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Electron. Lett. (1)

C. Caspar and E. J. Bachus, “Fibre-optic micro-ring-resonator with 2 mm diameter,” Electron. Lett. 25, 1506–1508 (1989).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Nat. Phys. (1)

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3, 430–435 (2007).
[CrossRef]

Nature (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Opt. Commun. (2)

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274, 447–450 (2007).
[CrossRef]

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285, 3493–3497 (2012).
[CrossRef]

Opt. Express (10)

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the microfiber loop resonator. The amplitudes in the two arms of the coupling region are denoted A1(s) and A2(s), and the amplitudes in the loop are A0(s).

Fig. 2.
Fig. 2.

Pump Pω and third harmonic P3ω output power from a loop resonator when input pump power P0 is (a) 100, (b) 250, and (c) 600 W. The labeled dots indicate the position of the detunings for the transfer characteristics shown in Fig. 3. Parameters: L0=3mm, Lc=50μm, αω,3ω=5m1, κ=8×104m1, and δβ1440m1.

Fig. 3.
Fig. 3.

Transfer characteristics when the pump is detuned from resonance by (a) 50, (b) 96, (c) 100, and (d) 120 pm. Other parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

Enhancement ζ against detuning δλω for different proximities to critical coupling ΔK (equivalent to 6.5×104m1<κω<8.2×104m1. Regions where ζ>1 generate a greater third-harmonic conversion than an equivalent straight microfiber. The dotted line at ΔK=0.71 corresponds to the situation in Fig. 2(a), when κω=8×104m1. P0=100W, and other parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Maximum internal pump power on resonance inside the loop, Pcirc/P0, for different proximities to critical coupling ΔK and loss. P0=100W, and other parameters are the same as in Fig. 2. The inset confirms the cubic pump dependency of the enhancement over the range of values simulated.

Fig. 6.
Fig. 6.

(a) Resonant enhancement factor ζ of the third harmonic power and (b) bandwidth of the enhancement (taken as the full width measured halfway between ζ=1 and maximum ζ) for different proximities to critical coupling ΔK. P0=100W, and other parameters are the same as in Fig. 2.

Fig. 7.
Fig. 7.

Third-harmonic conversion against detuning, when the harmonic light is partially recirculated (i.e., with κ3ω>0m1). P0=100W, and other parameters are the same as in Fig. 2.

Tables (1)

Tables Icon

Table 1. Summary of Parameters Used in the Simulation of the Loop Resonator when Phase-Matching the HE11(ω) Mode with the HE12(3ω) Mode for λω=1.55μm

Equations (12)

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dA0ωds=αωA0ω+in(2)kω[(J1|A0ω|2+2J2|A03ω|2)A0ω+J3(A0ω*)2A03ωeiδβs],
dA03ωds=α3ωA03ω+in(2)kω[(6J2|A0ω|2+3J5|A03ω|2)A03ω+J3*(A0ω)3eiδβs],
dAiωds=αωAiω+iκωAjω+in(2)kω[(J1|Aiω|2+2J2|Ai3ω|2)Aiω+J3(Aiω*)2Ai3ωeiδβs],
dAi3ωds=α3ωAi3ω+iκ3ωAj3ω+in(2)kω[(6J2|Aiω|2+3J5|Ai3ω|2)Ai3ω+J3*(Aiω)3eiδβs].
A0ω,3ω(0)=A1ω,3ω(Lc)exp(iβω,3ωLc),
A2ω,3ω(0)=A0ω,3ω(L0)exp(iβω,3ωL0)
A1ω(0)=P0,
A13ω(0)=0
Pω,3ωP0=|A2ω,3ω(Lc)A1ω(0)exp(iβω,3ωLc)|2.
|T|2=|A2ω(Lc)|2P0=eαωL0+sin(κωLc)1+sin(κωLc)eαωL0
PcircP0=1|T|21exp(2αωL0).
ζ[1sin2(κωLc)(1+sin(κωLc)eαωL0)2]3.

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