Abstract

In this manuscript, the multi-wavelength active coherent polarization beam combining (CPBC) system is investigated theoretically and experimentally. The relationship between the combining efficiency and the optical path difference (OPD), wavelength number, and the spectral density of power of the amplifier chains is analyzed and validated by establishing a two-channel multi-wavelength CPBC system. Further, the relationship between the combining efficiency and the voltage signal of the photo-detector is developed and validated experimentally. Finally, the feasibility of the active CPBC technique with complex spectral structures is verified and as high as 96% combining efficiency is obtained based on all fiber delay lines to compensate the OPD between different channels, which is crucial for further power scaling of the CPBC system. Our theoretical analysis offers a useful approach to estimate the influence of OPDs, wavelength number, and the spectral density of power of the amplifier chains on multi-wavelength active CPBC system.

© 2014 Optical Society of America

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2014 (1)

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B116, 115–119 (2014).

2013 (5)

2012 (5)

2011 (6)

2010 (6)

2009 (2)

2008 (2)

2007 (2)

M. Khajavikhan and J. R. Leger, “Modal Analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE J. Sel. Top. Quantum Electron.13, 460–472 (2007).

J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett.32(13), 1842–1844 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett.86, 201118 (2005).

2002 (1)

Akbulut, M.

D. Engin, W. Lu, M. Akbulut, B. McIntosh, H. Verdun, and S. Gupta, “1 kW cw Yb-fiber-amplifier with <0.5 GHz linewidth and near-diffraction limited beam quality, for coherent combining application,” Proc. SPIE7, 1407 (2011).

Alley, T. G.

Augst, S. J.

Baker, J. T.

Barthelemy, A.

Barty, C. P. J.

Beach, R. J.

Bellanger, C.

Benham, V.

Bourderionnet, J.

Bratcher, A.

Breitkopf, S.

Brignon, A.

Chang, W. Z.

Chen, D. D.

Christensen, S.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Corcoran, C. J.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett.86, 201118 (2005).

Culpepper, M. A.

Dai, S. J.

Dajani, I.

A. Flores, C. Lu, C. Robin, S. Naderi, C. Vergien, and I. Dajani, “Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers,” Proc. SPIE8381, 83811B (2012).
[CrossRef]

Dawson, J. W.

Desfarges-Berthelemot, A.

Dong, X.

Du, W.

Durville, F.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett.86, 201118 (2005).

Eidam, T.

Engin, D.

D. Engin, W. Lu, M. Akbulut, B. McIntosh, H. Verdun, and S. Gupta, “1 kW cw Yb-fiber-amplifier with <0.5 GHz linewidth and near-diffraction limited beam quality, for coherent combining application,” Proc. SPIE7, 1407 (2011).

Fan, T. Y.

Farley, K.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Flores, A.

A. Flores, C. Lu, C. Robin, S. Naderi, C. Vergien, and I. Dajani, “Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers,” Proc. SPIE8381, 83811B (2012).
[CrossRef]

Flores, A. S.

Galipeau, J.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Galvanauskas, A.

Goldizen, K. C.

Goodno, G. D.

Gottschall, T.

Gupta, S.

D. Engin, W. Lu, M. Akbulut, B. McIntosh, H. Verdun, and S. Gupta, “1 kW cw Yb-fiber-amplifier with <0.5 GHz linewidth and near-diffraction limited beam quality, for coherent combining application,” Proc. SPIE7, 1407 (2011).

Hädrich, S.

He, B.

Heebner, J. E.

Hu, M.

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics7(11), 861–867 (2013).
[CrossRef]

Kai, H.

Kermene, V.

Khajavikhan, M.

M. Khajavikhan and J. R. Leger, “Modal Analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE J. Sel. Top. Quantum Electron.13, 460–472 (2007).

Khitrov, V.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Kienel, M.

Klenke, A.

Lachinova, S. L.

Leger, J. R.

M. Khajavikhan and J. R. Leger, “Modal Analysis of path length sensitivity in superposition architectures for coherent laser beam combining,” IEEE J. Sel. Top. Quantum Electron.13, 460–472 (2007).

Leng, J.

Leng, J. Y.

Leveille, R.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Lhermite, J.

Limpert, J.

Liu, H. K.

Liu, Z.

Liu, Z. J.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
[CrossRef]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett.9(6), 456–458 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

Lou, Q. H.

Lu, C.

A. Flores, C. Lu, C. Robin, S. Naderi, C. Vergien, and I. Dajani, “Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers,” Proc. SPIE8381, 83811B (2012).
[CrossRef]

Lu, C. A.

Lu, W.

D. Engin, W. Lu, M. Akbulut, B. McIntosh, H. Verdun, and S. Gupta, “1 kW cw Yb-fiber-amplifier with <0.5 GHz linewidth and near-diffraction limited beam quality, for coherent combining application,” Proc. SPIE7, 1407 (2011).

Ma, H.

Ma, P.

Ma, P. F.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
[CrossRef]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett.9(6), 456–458 (2012).
[CrossRef]

Ma, Y.

Ma, Y. X.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
[CrossRef]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett.9(6), 456–458 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

Majid, I.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

McComb, T. S.

McIntosh, B.

D. Engin, W. Lu, M. Akbulut, B. McIntosh, H. Verdun, and S. Gupta, “1 kW cw Yb-fiber-amplifier with <0.5 GHz linewidth and near-diffraction limited beam quality, for coherent combining application,” Proc. SPIE7, 1407 (2011).

McNaught, S. J.

Messerly, M. J.

Mies, E.

Minden, M.

Murphy, D. V.

Naderi, S.

A. Flores, C. Lu, C. Robin, S. Naderi, C. Vergien, and I. Dajani, “Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers,” Proc. SPIE8381, 83811B (2012).
[CrossRef]

Nelson, D. J.

Pax, P. H.

Peng, M. Y.

Pilkington, D.

Primot, J.

Pulford, B.

Qian, Q.

Qiu, J. R.

Redmond, S. M.

Ripin, D. J.

Robin, C.

A. Flores, C. Lu, C. Robin, S. Naderi, C. Vergien, and I. Dajani, “Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers,” Proc. SPIE8381, 83811B (2012).
[CrossRef]

Rothenberg, J. E.

Rothhardt, J.

Saitou, T.

Samson, B.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Sanchez, A.

Sanchez, A. D.

Sekiguchi, T.

Shay, T. M.

Shen, S. X.

Shih, C. C.

Shirakawa, A.

Shverdin, M. Y.

Si, L.

Siders, C. W.

Siiman, L. A.

Spring, J.

Sridharan, A. K.

Stappaerts, E. A.

Su, R.

Su, R. T.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
[CrossRef]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett.9(6), 456–458 (2012).
[CrossRef]

Tankala, K.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE7686, 76860A (2010).
[CrossRef]

Tao, R.

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B116, 115–119 (2014).

Thielen, P. A.

Tiemann, B. G.

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron.46, 1191–1196 (2010).
[CrossRef] [PubMed]

Tünnermann, A.

Uberna, R.

Ueda, K.

Verdun, H.

D. Engin, W. Lu, M. Akbulut, B. McIntosh, H. Verdun, and S. Gupta, “1 kW cw Yb-fiber-amplifier with <0.5 GHz linewidth and near-diffraction limited beam quality, for coherent combining application,” Proc. SPIE7, 1407 (2011).

Vergien, C.

A. Flores, C. Lu, C. Robin, S. Naderi, C. Vergien, and I. Dajani, “Experimental and theoretical studies of phase modulation in Yb-doped fiber amplifiers,” Proc. SPIE8381, 83811B (2012).
[CrossRef]

Vorontsov, M. A.

Wang, B. S.

Wang, X.

Wang, X. L.

Ward, B.

Weber, M. E.

Wei, X. M.

Wei, Y. R.

Wickham, M. G.

Xiao, H.

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
[CrossRef]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett.36(6), 951–953 (2011).
[CrossRef] [PubMed]

Xiaojun, X.

Xu, S. H.

Xu, X.

Xu, X. J.

Yang, Y. F.

Yang, Z. M.

Yu, C. X.

Zejin, L.

Zhang, Q. Y.

Zhang, W. N.

Zhao, Y.

Zhou, J.

Zhou, P.

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B116, 115–119 (2014).

P. Ma, P. Zhou, X. Wang, Y. Ma, R. Su, and Z. Liu, “Influence of perturbative phase noise on active coherent polarization beam combining system,” Opt. Express21(24), 29666–29678 (2013).
[CrossRef] [PubMed]

P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
[CrossRef]

P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett.9(6), 456–458 (2012).
[CrossRef]

Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett.36(6), 951–953 (2011).
[CrossRef] [PubMed]

X. L. Wang, P. Zhou, Y. X. Ma, J. Y. Leng, X. J. Xu, and Z. J. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett.35(9), 1308–1310 (2010).
[CrossRef] [PubMed]

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett.34(19), 2939–2941 (2009).
[CrossRef] [PubMed]

Zhou, T.

Zhu, J.

Appl. Opt. (1)

Appl. Phys. B (1)

R. Tao, X. Wang, P. Zhou, L. Si, and Z. Liu, “Widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth,” Appl. Phys. B116, 115–119 (2014).

Appl. Phys. Lett. (1)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett.86, 201118 (2005).

IEEE J. Quantum Electron. (1)

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron.46, 1191–1196 (2010).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

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P. F. Ma, P. Zhou, H. Xiao, Y. X. Ma, R. T. Su, and Z. J. Liu, “Generation of a 481 W single frequency and linearly polarized beam by coherent polarization locking,” IEEE Photon. Technol. Lett.25(19), 1936–1938 (2013).
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P. F. Ma, P. Zhou, R. T. Su, Y. X. Ma, and Z. J. Liu, “Coherent polarization beam combining of eight fiber lasers using single-frequency dithering technique,” Laser Phys. Lett.9(6), 456–458 (2012).
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C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics7(11), 861–867 (2013).
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T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
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J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express19(18), 17053–17058 (2011).
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R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, A. S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express18(13), 13547–13553 (2010).
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Proc. SPIE (3)

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Other (1)

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in Conference on Laser and Electro-Optics (CLEO):Laser Applications to Photonic Applications, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.
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Figures (12)

Fig. 1
Fig. 1

The schematic of the polarization beam combination process for (a) without phase controlling and (b) phase controlling.

Fig. 2
Fig. 2

The simplified schematic of the unit of CPBC system.

Fig. 3
Fig. 3

Experimental setup of the two-channel multi-wavelength CPBC system. CO1-CO2: collimators; HWP: half wavelength plate; M1: all- reflected mirror; PBC1-PBC2: polarization beam combiners; M2: high-reflected mirror; PD-photo-detector; P1-P3: Power meters.

Fig. 4
Fig. 4

The time dependent signals and spectral density of energy collected in the PD in open loop and closed loop. (a) Time dependent signals. (b) Spectral density of phase noise.

Fig. 5
Fig. 5

The relative spectral density of power and discrete frequencies with different modulation frequencies and voltages.

Fig. 6
Fig. 6

The theoretical and experimentally measured combining efficiencies of the representative twelve different spectral structures.

Fig. 7
Fig. 7

The change of the normalized voltage signals along with the modulation frequencies with the modulation voltage of 10 V.

Fig. 8
Fig. 8

The compared results of estimated combining efficiencies and the measured combining efficiencies with different modulation frequencies (modulation voltage-10V).

Fig. 9
Fig. 9

The change of the normalized voltage signals along with the modulation voltages (d) with the modulation frequency of 100 MHz.

Fig. 10
Fig. 10

The compared results of estimated combining efficiencies and the measured combining efficiencies with different modulation voltages (modulation frequency-100 MHz).

Fig. 11
Fig. 11

The modulated spectral structures of each seed laser ((a)-(c)) and the optical spectrum measured by a spectrum analyzer (d).

Fig. 12
Fig. 12

The voltage signals in the PD when the OPD is carefully compensated.

Equations (16)

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η=P/ P 0
E i = n=1 N E i, v n exp(j2π v n t i ) ( i=1, 2)
E i, v n = 2 P i, v n π . 1 w .exp[ ( x 2 + y 2 ) w 2 ]exp(j ϕ i )
P i, v n = | E i, v n | 2 dxdy
t i = l i c
E (1) =[ n=1 N E 1, v n exp(j2π v n t 1 ) m=1 N E 2, v m exp(j2π v m t 2 ) ]
I 1 =[ n=1 N E 1, v n exp(j2π v n t 1 ) ][ p=1 N E * 1, v p exp(j2π v p t 1 ) ]+[ m=1 N E 2, v m exp(j2π v m t 2 ) ][ q=1 N E * 2, v q exp(j2π v q t 2 ) ] = n=1 N p=1 N E 1, v n E * 1, v p exp[j2π( v n v p ) t 1 ] + m=1 N q=1 N E 2, v m E * 2, v q exp[j2π( v m v q ) t 2 ] = n=1 N | E 1, v n | 2 + n=1 N p=1 pn N E 1, v n E * 1, v p exp[j2π( v n v p ) t 1 ] + m=1 N | E 2, v m | 2 + m=1 N q=1 qm N E 2, v m E * 2, v q exp[j2π( v m v q ) t 2 ]
P PBC1 = n=1 N P 1, v n + n=1 N P 2, v n
J HWP =[ cos(2α) sin(2α) sin(2α) cos(2α) ]
E ' =[ cos(2α) n=1 N E 1, v n exp(j2π v n t 1 )+sin(2α) m=1 N E 2, v m exp(j2π v m t 2 ) sin(2α) n=1 N E 1, v n exp(j2π v n t 1 )cos(2α) m=1 N E 2, v m exp(j2π v m t 2 ) ]
P y = 1 2 n=1 N P 1, v n [1cos(4α)]+ 1 2 n=1 N P 2, v n [1+cos(4α)] sin(4α) n=1 N P 1, v n P 2, v n cos[ ϕ 1 ϕ 2 + 2π v n ( l 1 l 2 ) c ]
P y = 1 2 n=1 N P 1, v n [1cos(4α)]+ 1 2 n=1 N P 2, v n [1+cos(4α)] sin(4α) n=1 N P 1, v n P 2, v n cos[ ϕ 1 ϕ 2 + 2π v n ( l 1 l 2 ) c +δ(t)]
P ' y = 1 2 n=1 N P 1, v n + 1 2 n=1 N P 2, v n 1 2 4 { n=1 N P 1, v n P 2, v n cos[ ϕ 1 ϕ 2 + 2π v n ( l 1 l 2 ) c +δ(t)] } 2 + ( n=1 N P 1, v n n=1 N P 2, v n ) 2
η=1 P ' y t n=1 N P 1, v n + n=1 N P 2, v n
η a = P p2 P p1 + P p2 + P p3
η=1 1 N i=1 N V(i) V m

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