Abstract

We discuss the trapping features of cholesteric liquid crystal as a self-organized photonic crystal and suggest it for absorption improvement. The imperfection of the absorbing surface is manifested by the reflection originating from the indispensable impedance mismatch. The reflection can be suppressed by an additional surface coating to reflect the light back to the absorber once again. In the simple consideration this reflection loop is possible only twice. For a right-handed CLC coating, the boundary reflection switches the light polarization from left to right circular in the first loop and it switches in the second loop back to the left circular polarization before the emerging light finally escapes from the absorbing process. The enhancement of light absorption is possible in the frequency range as large as the photonic bang gap of the cholesteric layer, which can be adjusted as desired.

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References

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2012 (1)

2011 (3)

V. A. Belyakov and S. V. Semenov, “Optical defect modes in chiral liquid crystals,” Sov. Phys. JETP112(4), 694–710 (2011).
[CrossRef]

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectrosc.110(6), 952–960 (2011).
[CrossRef]

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp.54(1), 53–63 (2011).
[CrossRef]

2010 (3)

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp.53(3), 243–256 (2010).
[CrossRef]

V. Ya. Zyryanov, S. A. Myslivets, V. A. Gunyakov, A. M. Parshin, V. G. Arkhipkin, V. F. Shabanov, and W. Lee, “Magnetic-field tunable defect modes in a photonic-crystal/liquid-crystal cell,” Opt. Express18(2), 1283–1288 (2010).
[CrossRef] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

2001 (1)

S. P. Palto, “An algorithm for solving the optical problem for stratified anisotropic media,” Sov. Phys. JETP92(4), 552–560 (2001).
[CrossRef]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
[CrossRef]

1979 (1)

1977 (1)

1972 (1)

Abdulhalim, I.

Arkhipkin, V. G.

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

Belyakov, V. A.

V. A. Belyakov and S. V. Semenov, “Optical defect modes in chiral liquid crystals,” Sov. Phys. JETP112(4), 694–710 (2011).
[CrossRef]

Berreman, D. W.

Dorofeenko, A. V.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp.53(3), 243–256 (2010).
[CrossRef]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
[CrossRef]

Gevorgyan, A. H.

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectrosc.110(6), 952–960 (2011).
[CrossRef]

Gunyakov, V. A.

Hong, C.-S.

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Ishikawa, K.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Kallos, E.

Kildishev, A. V.

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp.54(1), 53–63 (2011).
[CrossRef]

Lee, W.

Lisyansky, A. A.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp.53(3), 243–256 (2010).
[CrossRef]

Merzlikin, A. M.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp.53(3), 243–256 (2010).
[CrossRef]

Myslivets, S. A.

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Oganesyan, K. B.

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectrosc.110(6), 952–960 (2011).
[CrossRef]

Palto, S. P.

S. P. Palto, “An algorithm for solving the optical problem for stratified anisotropic media,” Sov. Phys. JETP92(4), 552–560 (2001).
[CrossRef]

Park, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Parshin, A. M.

Photinos, D. J.

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

Semenov, S. V.

V. A. Belyakov and S. V. Semenov, “Optical defect modes in chiral liquid crystals,” Sov. Phys. JETP112(4), 694–710 (2011).
[CrossRef]

Shabanov, V. F.

Shalaev, V. M.

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp.54(1), 53–63 (2011).
[CrossRef]

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Vinogradov, A. P.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp.53(3), 243–256 (2010).
[CrossRef]

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Yannopapas, V.

Yariv, A.

Yeh, P.

Zyryanov, V. Ya.

IEEE Trans. Antenn. Propag. (1)

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
[CrossRef]

J. Opt. Soc. Am. (3)

Nat. Mater. (2)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater.4(5), 383–387 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Opt. Mater. Express (1)

Opt. Spectrosc. (1)

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectrosc.110(6), 952–960 (2011).
[CrossRef]

Phys. Usp. (2)

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp.54(1), 53–63 (2011).
[CrossRef]

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp.53(3), 243–256 (2010).
[CrossRef]

Sov. Phys. JETP (2)

S. P. Palto, “An algorithm for solving the optical problem for stratified anisotropic media,” Sov. Phys. JETP92(4), 552–560 (2001).
[CrossRef]

V. A. Belyakov and S. V. Semenov, “Optical defect modes in chiral liquid crystals,” Sov. Phys. JETP112(4), 694–710 (2011).
[CrossRef]

Other (8)

H. K. Pulker, Coatings on Glass, 2nd ed. (Elsevier Science, 1999).

L. M. Blinov, Structure and Properties of Liquid Crystals (Springer, 2011), Chap. 12.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008), pp. 286.

V. F. Shabanov, S. Ya. Vetrov, and A. V. Shabanov, Optics of Real Photonic Crystals: Liquid Crystal Defects, Irregularities (SB RAS Publisher [in Russian], 2005).

S. J. Farlow, Partial Differential Equations for Scientists and Engineers (Dover, 1993), Lesson 7.

L. I. Schiff, Quantum Mechanics (McGraw-Hill College, 1968), Sec. 2.9.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Sec. 3.9.

S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University Press, 1992). Chap. 4.

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Figures (5)

Fig. 1
Fig. 1

(a) Light absorbing layer with a mirror at the back surface. (b) Enhanced light absorption with a CLC layer. (c) and (d) Schematics showing the paths of light and changes of the polarization states in cases (a) and (b), respectively [12]. L: left circularly polarized light; R: right circularly polarized light. The substrate is semi-infinite.

Fig. 2
Fig. 2

Reflectance versus the refractive index n of an absorbing layer with a mirror back surface at L/λ = 1 and n0 = 1. (a) The contour plot and (b) the reflectance as a function of the complex index showing four reflection zeros at n = 0.48 + 0.08i, 0.90 + 0.17i, 1.29 + 0.15i, 1.76 + 0.10i.

Fig. 3
Fig. 3

Calculated reflection spectra in logarithmic scale for the models of Fig. 1(a) (blue dotted curve) and Fig. 1(b) (magenta solid curve) near the PBG of a CLC. The parameters are described in the text. The interference oscillations are due to the additional boundary.

Fig. 4
Fig. 4

Calculated | E | 2 (z) profiles (maximum of oscillating electric strength square) inside the absorber structure without a neighboring CLC (dotted curve) and with a CLC layer (solid curve) schematically given by Figs. 1(a) and 1(b), respectively. It is normalized to an incident vacuum value of | E 0 | 2 =1 . The CLC layer in Fig. 1(b) is situated between z = 1 and 4 μm as shown by schematics (blue sinusoidal lines show the CLC director rotation). The parameters are the same as used to produce Fig. 3. The optical wavelength is at the CLC PBG center: λ=P( n o + n e )/2 = 0.5 μm.

Fig. 5
Fig. 5

Calculated reflectance without CLC (dotted curves) and with a CLC layer (solid curves) for tan δ = 0.03 (blue), 0.06 (green), 0.3 (red). Parameters are the same as used to produce Fig. 3. The middle plot (green) has a condition close to the critical match with reflection zero.

Equations (9)

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[ A B ] mirror =[ 1 1 ],
E=A e iωt+ikz +B e iωtikz ,
P=[ e iϕ 0 0 e iϕ ],
D= D 1 1 D 2 = [ 1 1 1 1 ] 1 [ 1 1 n ˜ n ˜ ]= 1 2 [ 1 1 1 1 ]+ n ˜ 2 [ 1 1 1 1 ],
[ A 0 B 0 ]=[ A 0 r A 0 ]=DP [ A B ] mirror ,
r= n ˜ cos( ϕ )+isin( ϕ ) n ˜ cos( ϕ )isin( ϕ ) .
n ˜ =itan( ϕ 0 n ˜ ),
log R PBG =2logR.
( n e n o ) | n n 0 | <2.

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