Abstract

We report a low-voltage and fast-response polymer network liquid crystal (PNLC) infrared phase modulator. To optimize device performance, we propose a physical model to understand the curing temperature effect on average domain size. Good agreement between model and experiment is obtained. By optimizing the UV curing temperature and employing a large dielectric anisotropy LC host, we have lowered the 2π phase change voltage to 22.8V at 1.55μm wavelength while keeping response time at about 1 ms. Widespread application of such a PNLC integrated into a high resolution liquid-crystal-on-silicon (LCoS) for infrared spatial light modulator is foreseeable.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  21. D.-K. Yang, Y. Cui, H. Nemati, X. Zhou, and A. Moheghi, “Modeling aligning effect of polymer network in polymer stabilized nematic liquid crystals,” J. Appl. Phys. 114(24), 243515 (2013).
    [Crossref]
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    [Crossref] [PubMed]
  23. H. Kneppe, F. Schneider, and N. K. Sharma, “Rotational viscosity γ1 of nematic liquid crystals,” J. Chem. Phys. 77(6), 3203–3208 (1982).
    [Crossref]
  24. H. Chen, F. Peng, Z. Luo, D. Xu, S.-T. Wu, M.-C. Li, S.-L. Lee, and W.-C. Tsai, “High performance liquid crystal displays with a low dielectric constant material,” Opt. Mater. Express 4(11), 2262–2273 (2014).
    [Crossref]
  25. S.-T. Wu, A. M. Lackner, and U. Efron, “Optimal operation temperature of liquid crystal modulators,” Appl. Opt. 26(16), 3441–3445 (1987).
    [Crossref] [PubMed]
  26. J. Yan, Y. Chen, S.-T. Wu, and X. Song, “Figure of merit of polymer-stabilized blue phase liquid crystals,” J. Disp. Technol. 9(1), 24–29 (2013).
    [Crossref]

2015 (1)

2014 (5)

H. Chen, F. Peng, Z. Luo, D. Xu, S.-T. Wu, M.-C. Li, S.-L. Lee, and W.-C. Tsai, “High performance liquid crystal displays with a low dielectric constant material,” Opt. Mater. Express 4(11), 2262–2273 (2014).
[Crossref]

J. Sun, S.-T. Wu, and Y. Haseba, “A low voltage submillisecond-response polymer network liquid crystal spatial light modulator,” Appl. Phys. Lett. 104(2), 023305 (2014).
[Crossref]

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci., Part B, Polym. Phys. 52(3), 183–192 (2014).
[Crossref]

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S.-T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

F. Peng, Y. Chen, S.-T. Wu, S. Tripathi, and R. J. Twieg, “Low loss liquid crystals for infrared applications,” Liq. Cryst. 41(11), 1545–1552 (2014).
[Crossref]

2013 (5)

2012 (2)

J. Sun, Y. Chen, and S.-T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[PubMed]

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

2004 (1)

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

2003 (3)

S. A. Serati, X. Xia, O. Mughal, and A. Linnenberger, “High-resolution phase-only spatial light modulators with submillisecond response,” Proc. SPIE 5106, 138–145 (2003).
[Crossref]

F. Du, S. Gauza, and S.-T. Wu, “Influence of curing temperature and high birefringence on the properties of polymerstabilized liquid crystals,” Opt. Express 11(22), 2891–2896 (2003).
[Crossref] [PubMed]

F. Du and S.-T. Wu, “Curing temperature effects on liquid crystal gels,” Appl. Phys. Lett. 83(7), 1310–1312 (2003).
[Crossref]

2000 (1)

I. Dierking, “Polymer network–stabilized liquid crystals,” Adv. Mater. 12(3), 167–181 (2000).
[Crossref]

1993 (1)

B. M. Moslehi, K. K. Chau, and J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processors,” Opt. Eng. 32(5), 974–981 (1993).
[Crossref]

1992 (1)

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

1990 (1)

S.-T. Wu and C.-S. Wu, “Experimental confirmation of the Osipov-Terentjev theory on the viscosity of nematic liquid crystals,” Phys. Rev. A 42(4), 2219–2227 (1990).
[Crossref] [PubMed]

1987 (1)

1986 (1)

S.-T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33(2), 1270–1274 (1986).
[Crossref] [PubMed]

1982 (1)

H. Kneppe, F. Schneider, and N. K. Sharma, “Rotational viscosity γ1 of nematic liquid crystals,” J. Chem. Phys. 77(6), 3203–3208 (1982).
[Crossref]

Au, A.

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

Chau, K. K.

B. M. Moslehi, K. K. Chau, and J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processors,” Opt. Eng. 32(5), 974–981 (1993).
[Crossref]

Chen, H.

Chen, Y.

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S.-T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

F. Peng, Y. Chen, S.-T. Wu, S. Tripathi, and R. J. Twieg, “Low loss liquid crystals for infrared applications,” Liq. Cryst. 41(11), 1545–1552 (2014).
[Crossref]

J. Yan, Y. Chen, S.-T. Wu, and X. Song, “Figure of merit of polymer-stabilized blue phase liquid crystals,” J. Disp. Technol. 9(1), 24–29 (2013).
[Crossref]

J. Sun, Y. Chen, and S.-T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[PubMed]

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

Cheng, K.-L.

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

Cui, Y.

D.-K. Yang, Y. Cui, H. Nemati, X. Zhou, and A. Moheghi, “Modeling aligning effect of polymer network in polymer stabilized nematic liquid crystals,” J. Appl. Phys. 114(24), 243515 (2013).
[Crossref]

Dierking, I.

I. Dierking, “Polymer network–stabilized liquid crystals,” Adv. Mater. 12(3), 167–181 (2000).
[Crossref]

Du, F.

Efron, U.

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

S.-T. Wu, A. M. Lackner, and U. Efron, “Optimal operation temperature of liquid crystal modulators,” Appl. Opt. 26(16), 3441–3445 (1987).
[Crossref] [PubMed]

Fan, Y.-H.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Feng, F.

Forber, R. A.

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

Gauza, S.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

F. Du, S. Gauza, and S.-T. Wu, “Influence of curing temperature and high birefringence on the properties of polymerstabilized liquid crystals,” Opt. Express 11(22), 2891–2896 (2003).
[Crossref] [PubMed]

Goldsmith, G. C.

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

Goodman, J. W.

B. M. Moslehi, K. K. Chau, and J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processors,” Opt. Eng. 32(5), 974–981 (1993).
[Crossref]

Haseba, Y.

J. Sun, S.-T. Wu, and Y. Haseba, “A low voltage submillisecond-response polymer network liquid crystal spatial light modulator,” Appl. Phys. Lett. 104(2), 023305 (2014).
[Crossref]

Hu, W.

Huang, Z. D.

Kneppe, H.

H. Kneppe, F. Schneider, and N. K. Sharma, “Rotational viscosity γ1 of nematic liquid crystals,” J. Chem. Phys. 77(6), 3203–3208 (1982).
[Crossref]

Lackner, A. M.

Lee, S.-L.

Li, M.-C.

Lin, X. W.

Lin, Y.-H.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Linnenberger, A.

S. A. Serati, X. Xia, O. Mughal, and A. Linnenberger, “High-resolution phase-only spatial light modulators with submillisecond response,” Proc. SPIE 5106, 138–145 (2003).
[Crossref]

Liu, S.-H.

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

Lu, Y. Q.

Luo, Z.

Moheghi, A.

D.-K. Yang, Y. Cui, H. Nemati, X. Zhou, and A. Moheghi, “Modeling aligning effect of polymer network in polymer stabilized nematic liquid crystals,” J. Appl. Phys. 114(24), 243515 (2013).
[Crossref]

Moslehi, B. M.

B. M. Moslehi, K. K. Chau, and J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processors,” Opt. Eng. 32(5), 974–981 (1993).
[Crossref]

Mughal, O.

S. A. Serati, X. Xia, O. Mughal, and A. Linnenberger, “High-resolution phase-only spatial light modulators with submillisecond response,” Proc. SPIE 5106, 138–145 (2003).
[Crossref]

Nemati, H.

D.-K. Yang, Y. Cui, H. Nemati, X. Zhou, and A. Moheghi, “Modeling aligning effect of polymer network in polymer stabilized nematic liquid crystals,” J. Appl. Phys. 114(24), 243515 (2013).
[Crossref]

Peng, F.

F. Peng, H. Chen, S. Tripathi, R. J. Twieg, and S.-T. Wu, “Fast-response infrared phase modulator based on polymer network liquid crystal,” Opt. Mater. Express 5(2), 265–273 (2015).
[Crossref]

H. Chen, F. Peng, Z. Luo, D. Xu, S.-T. Wu, M.-C. Li, S.-L. Lee, and W.-C. Tsai, “High performance liquid crystal displays with a low dielectric constant material,” Opt. Mater. Express 4(11), 2262–2273 (2014).
[Crossref]

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S.-T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

F. Peng, Y. Chen, S.-T. Wu, S. Tripathi, and R. J. Twieg, “Low loss liquid crystals for infrared applications,” Liq. Cryst. 41(11), 1545–1552 (2014).
[Crossref]

Peterka, D. S.

Quirin, S.

Ren, H.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Sayyah, K.

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

Schneider, F.

H. Kneppe, F. Schneider, and N. K. Sharma, “Rotational viscosity γ1 of nematic liquid crystals,” J. Chem. Phys. 77(6), 3203–3208 (1982).
[Crossref]

Serati, S. A.

S. A. Serati, X. Xia, O. Mughal, and A. Linnenberger, “High-resolution phase-only spatial light modulators with submillisecond response,” Proc. SPIE 5106, 138–145 (2003).
[Crossref]

Sharma, N. K.

H. Kneppe, F. Schneider, and N. K. Sharma, “Rotational viscosity γ1 of nematic liquid crystals,” J. Chem. Phys. 77(6), 3203–3208 (1982).
[Crossref]

Shi, L. Y.

Shiu, J.-W.

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

Song, X.

J. Yan, Y. Chen, S.-T. Wu, and X. Song, “Figure of merit of polymer-stabilized blue phase liquid crystals,” J. Disp. Technol. 9(1), 24–29 (2013).
[Crossref]

Sun, J.

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci., Part B, Polym. Phys. 52(3), 183–192 (2014).
[Crossref]

J. Sun, S.-T. Wu, and Y. Haseba, “A low voltage submillisecond-response polymer network liquid crystal spatial light modulator,” Appl. Phys. Lett. 104(2), 023305 (2014).
[Crossref]

J. Sun, Y. Chen, and S.-T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[PubMed]

Tripathi, S.

F. Peng, H. Chen, S. Tripathi, R. J. Twieg, and S.-T. Wu, “Fast-response infrared phase modulator based on polymer network liquid crystal,” Opt. Mater. Express 5(2), 265–273 (2015).
[Crossref]

F. Peng, Y. Chen, S.-T. Wu, S. Tripathi, and R. J. Twieg, “Low loss liquid crystals for infrared applications,” Liq. Cryst. 41(11), 1545–1552 (2014).
[Crossref]

Tsai, W.-C.

Twieg, R. J.

F. Peng, H. Chen, S. Tripathi, R. J. Twieg, and S.-T. Wu, “Fast-response infrared phase modulator based on polymer network liquid crystal,” Opt. Mater. Express 5(2), 265–273 (2015).
[Crossref]

F. Peng, Y. Chen, S.-T. Wu, S. Tripathi, and R. J. Twieg, “Low loss liquid crystals for infrared applications,” Liq. Cryst. 41(11), 1545–1552 (2014).
[Crossref]

Wei, B. Y.

White, I. H.

Wilkinson, T. D.

Wu, C.-S.

S.-T. Wu and C.-S. Wu, “Experimental confirmation of the Osipov-Terentjev theory on the viscosity of nematic liquid crystals,” Phys. Rev. A 42(4), 2219–2227 (1990).
[Crossref] [PubMed]

Wu, S. T.

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci., Part B, Polym. Phys. 52(3), 183–192 (2014).
[Crossref]

R. A. Forber, A. Au, U. Efron, K. Sayyah, S. T. Wu, and G. C. Goldsmith, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” Proc. SPIE 1665, 259–273 (1992).
[Crossref]

Wu, S.-T.

F. Peng, H. Chen, S. Tripathi, R. J. Twieg, and S.-T. Wu, “Fast-response infrared phase modulator based on polymer network liquid crystal,” Opt. Mater. Express 5(2), 265–273 (2015).
[Crossref]

H. Chen, F. Peng, Z. Luo, D. Xu, S.-T. Wu, M.-C. Li, S.-L. Lee, and W.-C. Tsai, “High performance liquid crystal displays with a low dielectric constant material,” Opt. Mater. Express 4(11), 2262–2273 (2014).
[Crossref]

J. Sun, S.-T. Wu, and Y. Haseba, “A low voltage submillisecond-response polymer network liquid crystal spatial light modulator,” Appl. Phys. Lett. 104(2), 023305 (2014).
[Crossref]

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S.-T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

F. Peng, Y. Chen, S.-T. Wu, S. Tripathi, and R. J. Twieg, “Low loss liquid crystals for infrared applications,” Liq. Cryst. 41(11), 1545–1552 (2014).
[Crossref]

J. Yan, Y. Chen, S.-T. Wu, and X. Song, “Figure of merit of polymer-stabilized blue phase liquid crystals,” J. Disp. Technol. 9(1), 24–29 (2013).
[Crossref]

J. Sun, Y. Chen, and S.-T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[PubMed]

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

F. Du, S. Gauza, and S.-T. Wu, “Influence of curing temperature and high birefringence on the properties of polymerstabilized liquid crystals,” Opt. Express 11(22), 2891–2896 (2003).
[Crossref] [PubMed]

F. Du and S.-T. Wu, “Curing temperature effects on liquid crystal gels,” Appl. Phys. Lett. 83(7), 1310–1312 (2003).
[Crossref]

S.-T. Wu and C.-S. Wu, “Experimental confirmation of the Osipov-Terentjev theory on the viscosity of nematic liquid crystals,” Phys. Rev. A 42(4), 2219–2227 (1990).
[Crossref] [PubMed]

S.-T. Wu, A. M. Lackner, and U. Efron, “Optimal operation temperature of liquid crystal modulators,” Appl. Opt. 26(16), 3441–3445 (1987).
[Crossref] [PubMed]

S.-T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33(2), 1270–1274 (1986).
[Crossref] [PubMed]

Xia, X.

S. A. Serati, X. Xia, O. Mughal, and A. Linnenberger, “High-resolution phase-only spatial light modulators with submillisecond response,” Proc. SPIE 5106, 138–145 (2003).
[Crossref]

Xu, D.

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S.-T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

H. Chen, F. Peng, Z. Luo, D. Xu, S.-T. Wu, M.-C. Li, S.-L. Lee, and W.-C. Tsai, “High performance liquid crystal displays with a low dielectric constant material,” Opt. Mater. Express 4(11), 2262–2273 (2014).
[Crossref]

Yan, J.

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S.-T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

J. Yan, Y. Chen, S.-T. Wu, and X. Song, “Figure of merit of polymer-stabilized blue phase liquid crystals,” J. Disp. Technol. 9(1), 24–29 (2013).
[Crossref]

J. Yan, Y. Chen, S.-T. Wu, S.-H. Liu, K.-L. Cheng, and J.-W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012).
[Crossref]

Yang, D.-K.

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Figures (4)

Fig. 1
Fig. 1 Curing temperature dependent threshold voltage of PNLCs: dots stand for measured data and red line for fitting curve with Eq. (9).
Fig. 2
Fig. 2 Curing temperature dependent average domain size of PNLCs: dots stand for the measured data and red line for fitting curve with Eq. (8).
Fig. 3
Fig. 3 (a) Voltage-dependent phase change at λ = 1.55μm for a PNLC cured at 73°C with V = 22.8V. (b) Measured phase decay time of the PNLC sample. Black line is experimental data and red line is fitting result with Eq. (4) and δo = 2π.
Fig. 4
Fig. 4 Temperature dependent FoM1 for JC-BP07N at λ = 633nm: dots stand for the measured data and red line for fitting curve with Eq. (17)

Tables (1)

Tables Icon

Table 1 Physical properties and figure of merits of five LC hosts used in PNLCs.

Equations (19)

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δ=2πdΔn/λ,
V on πd d 1 K 11 ε 0 Δε ,
τ= γ 1 d 1 2 /( K 11 π 2 ),
δ(t)= δ 0 exp(2t/τ).
d 1 2 ~ k B Tt 3πηR ,
η~Sexp( E b / k B T),
S= (1T/ T c ) β ,
d 1 =A Texp( E b / k B T) (1T/ T c ) β ,
V th = B d 1 =B (1T/ T c ) β exp( E b / k B T) T ,
d=λ/Δn.
V 2π ~ λ Δn d 1 K 11 ε 0 Δε .
Fo M 1 =1/( V 2π 2 τ)~ΔεΔ n 2 / γ 1 .
Fo M 2 =1/( V 2π 2 τ)~Δε/ γ 1 .
Δn=Δ n 0 (1T/ T c ) β ,
γ 1 ~Sexp( E b / k B T),
Δε=CSexp(U/ k B T),
Fo M 1 =D (1T/ T c ) 2β exp(( E a U)/ k B T) ,
Fo M 2 ~exp((U E a )/ k B T).
T opt = T c 2β k B T c 2 E a U .

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