Abstract

It has been found that in the media where the dielectric permittivity ε or the magnetic permeability μ is near zero and in transition metamaterials where ε or μ changes from positive to negative values, there occur a strong absorption or amplification of the electromagnetic wave energy in the presence of an infinitesimally small damping or gain and a strong enhancement of the electromagnetic fields. We attribute these phenomena to the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations and its inverse process. In this paper, we study analogous phenomena occurring in chiral media theoretically using the invariant imbedding method. In uniform isotropic chiral media, right-circularly-polarized and left-circularly-polarized waves are the eigen-modes of propagation with different effective refractive indices n+ and n, whereas in the chiral media with a nonuniform impedance variation, they are no longer the eigenmodes and are coupled to each other. We find that both in uniform chiral slabs where either n+ or n is near zero and in chiral transition metamaterials where n+ or n changes from positive to negative values, a strong absorption or amplification of circularly-polarized waves occurs in the presence of an infinitesimally small damping or gain. We present detailed calculations of the mode conversion coefficient, which measures the fraction of the electromagnetic wave energy absorbed into the medium, for various configurations of ε and μ with an emphasis on the influence of a nonuniform impedance. We propose possible applications of these phenomena to linear and nonlinear optical devices that react selectively to the helicity of the circular polarization.

© 2016 Optical Society of America

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References

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2015 (2)

J. Sun, X. Liu, J. Zhou, Z. Kudyshev, and N. M. Litchinitser, “Experimental demonstration of anomalous field enhancement in all-dielectric transition magnetic metamaterials,” Sci. Rep. 5, 16154 (2015).
[Crossref] [PubMed]

J. Yoon, M. Zhou, M. A. Badsha, T. Y. Kim, Y. C. Jun, and C. K. Hwangbo, “Broadband epsilon-near-zero perfect absorption in the near-infrared,” Sci. Rep. 5, 12788 (2015).
[Crossref] [PubMed]

2014 (5)

Y. Cao and J. Li, “Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality,” Phys. Rev. B 89, 115420 (2014).
[Crossref]

I. D. Rukhlenko, “Optical propagation through graded-index metamaterials in the presence of gain,” Plasmonics 9, 1257–1263 (2014).
[Crossref]

Z. A. Kudyshev, I. R Gabitov, A. I. Maimistov, R. Z Sagdeev, and N. M. Litchinitser, “Second harmonic generation in transition metamaterials,” J. Opt. 16, 114011 (2014).
[Crossref]

K. Halterman and J. M. Elson, “Near-perfect absorption in epsilon-near-zero structures with hyperbolic dispersion,” Opt. Express 22, 7337–7348 (2014).
[Crossref] [PubMed]

K. J. Lee, J. W. Wu, and K. Kim, “Defect modes in a one-dimensional photonic crystal with a chiral defect layer,” Opt. Mater. Express 4, 2542–2550 (2014).
[Crossref]

2013 (8)

P. Ginzburg, F. J. Rodríguez Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21, 14907–14917 (2013).
[Crossref] [PubMed]

Y. S. Ding, C. T. Chan, and R. P. Wang, “Optical waves in a gradient negative-index lens of a half-infinite length,” Sci. Rep. 3, 2954 (2013).
[Crossref] [PubMed]

D. J. Yu, K. Kim, and D.-H. Lee, “Temperature dependence of mode conversion in warm, unmagnetized plasmas with a linear density profile,” Phys. Plasmas 20, 062109 (2013).
[Crossref]

D. J. Yu and K. Kim, “Effects of a random spatial variation of the plasma density on the mode conversion in cold, unmagnetized, and stratified plasmas,” Phys. Plasmas 20, 122104 (2013).
[Crossref]

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in ε-near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87, 035120 (2013).
[Crossref]

S. Zhong and S. He, “Ultrathin and lightweight microwave absorbers made of mu-near-zero metamaterials,” Sci. Rep. 3, 2083 (2013).
[Crossref] [PubMed]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87, 155140 (2013).
[Crossref]

Z. Li, M. Mutlu, and E. Ozbay, “Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission,” J. Opt. 15, 023001 (2013).
[Crossref]

2012 (2)

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

S. Vassant, A. Archambault, F. Marquier, F. Pardo, U. Gennser, A. Cavanna, J. L. Pelouard, and J. J. Greffet, “Epsilon-near-zero mode for active optoelectronic devices,” Phys. Rev. Lett. 109, 237401 (2012).
[Crossref]

2011 (3)

2010 (3)

I. Mozjerin, E. A. Gibson, E. P. Furlani, I. R. Gabitov, and N. M. Litchinitser, “Electromagnetic enhancement in lossy optical transition metamaterials,” Opt. Lett. 35, 3240–3242 (2010).
[Crossref] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, “Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity,” Phys. Rev. A 81, 043839 (2010).
[Crossref]

D. J. Yu, K. Kim, and D.-H. Lee, “Resonant enhancement of mode conversion in unmagnetized plasmas due to a periodic density modulation superimposed on a linear electron density profile,” Phys. Plasmas 17, 102110 (2010).
[Crossref]

2009 (3)

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
[Crossref]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[Crossref] [PubMed]

2008 (5)

2007 (1)

E.-H. Kim, I. H. Cairns, and P. A. Robinson, “Extraordinary-mode radiation produced by linear-mode conversion of Langmuir waves,” Phys. Rev. Lett. 99, 015003 (2007).
[Crossref] [PubMed]

2006 (3)

K. Kim and D.-H. Lee, “Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity,” Phys. Plasmas 13, 042103 (2006).
[Crossref]

K. Kim, H. Yoo, and H. Lim, “Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals,” Waves Random Complex Media 16, 75–84 (2006).
[Crossref]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref]

2005 (2)

K. Kim and D.-H. Lee, “Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas,” Phys. Plasmas 12, 062101 (2005).
[Crossref]

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” EPL 69, 207–213 (2005).
[Crossref]

2004 (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

2002 (1)

N. Garcia, E. V. Ponizovskaya, and John Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
[Crossref]

2001 (1)

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

1996 (1)

J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[Crossref]

1994 (1)

V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994).
[Crossref]

1992 (1)

D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, “Analytic expressions for mode conversion in a plasma with a linear density profile,” Phys. Fluids B 4, 559–575 (1992).
[Crossref]

1990 (1)

E. Mjølhus, “On linear conversion in a magnetized plasma,” Radio Sci. 25, 1321–1339 (1990).
[Crossref]

Ankonina, G.

Archambault, A.

S. Vassant, A. Archambault, F. Marquier, F. Pardo, U. Gennser, A. Cavanna, J. L. Pelouard, and J. J. Greffet, “Epsilon-near-zero mode for active optoelectronic devices,” Phys. Rev. Lett. 109, 237401 (2012).
[Crossref]

Atrashchenko, A.

Badsha, M. A.

J. Yoon, M. Zhou, M. A. Badsha, T. Y. Kim, Y. C. Jun, and C. K. Hwangbo, “Broadband epsilon-near-zero perfect absorption in the near-infrared,” Sci. Rep. 5, 12788 (2015).
[Crossref] [PubMed]

Belov, P. A.

Budden, K. G.

K. G. Budden, The Propagation of Radio Waves (Cambridge University Press, 1985).
[Crossref]

Cairns, I. H.

E.-H. Kim, I. H. Cairns, and P. A. Robinson, “Extraordinary-mode radiation produced by linear-mode conversion of Langmuir waves,” Phys. Rev. Lett. 99, 015003 (2007).
[Crossref] [PubMed]

Campione, S.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87, 155140 (2013).
[Crossref]

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in ε-near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87, 035120 (2013).
[Crossref]

Cao, Y.

Y. Cao and J. Li, “Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality,” Phys. Rev. B 89, 115420 (2014).
[Crossref]

Capolino, F.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87, 155140 (2013).
[Crossref]

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in ε-near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87, 035120 (2013).
[Crossref]

Cavanna, A.

S. Vassant, A. Archambault, F. Marquier, F. Pardo, U. Gennser, A. Cavanna, J. L. Pelouard, and J. J. Greffet, “Epsilon-near-zero mode for active optoelectronic devices,” Phys. Rev. Lett. 109, 237401 (2012).
[Crossref]

Chan, C. T.

Y. S. Ding, C. T. Chan, and R. P. Wang, “Optical waves in a gradient negative-index lens of a half-infinite length,” Sci. Rep. 3, 2954 (2013).
[Crossref] [PubMed]

Cheng, Q.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref] [PubMed]

Ciattoni, A.

M. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second-and third-harmonic generation at ε-near-zero crossing points,” Phys. Rev. A 84, 063826 (2011).
[Crossref]

A. Ciattoni, C. Rizza, and E. Palange, “Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity,” Phys. Rev. A 81, 043839 (2010).
[Crossref]

Cui, T. J.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref] [PubMed]

Cummer, S. A.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref] [PubMed]

de Ceglia, D.

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in ε-near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87, 035120 (2013).
[Crossref]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87, 155140 (2013).
[Crossref]

M. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second-and third-harmonic generation at ε-near-zero crossing points,” Phys. Rev. A 84, 063826 (2011).
[Crossref]

Dickson, W.

Ding, Y. S.

Y. S. Ding, C. T. Chan, and R. P. Wang, “Optical waves in a gradient negative-index lens of a half-infinite length,” Sci. Rep. 3, 2954 (2013).
[Crossref] [PubMed]

Dong, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Dong, W. T.

Elson, J. M.

Engheta, N.

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref]

Fedotov, V. A.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Feng, S.

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

Fried, B. D.

D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, “Analytic expressions for mode conversion in a plasma with a linear density profile,” Phys. Fluids B 4, 559–575 (1992).
[Crossref]

Furlani, E. P.

Gabitov, I. R

Z. A. Kudyshev, I. R Gabitov, A. I. Maimistov, R. Z Sagdeev, and N. M. Litchinitser, “Second harmonic generation in transition metamaterials,” J. Opt. 16, 114011 (2014).
[Crossref]

Gabitov, I. R.

Gao, L.

Garcia, N.

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Appl. Phys. Lett. (1)

N. Garcia, E. V. Ponizovskaya, and John Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
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EPL (1)

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” EPL 69, 207–213 (2005).
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J. Korean Phys. Soc. (1)

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

J. Opt. (2)

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[Crossref]

Z. A. Kudyshev, I. R Gabitov, A. I. Maimistov, R. Z Sagdeev, and N. M. Litchinitser, “Second harmonic generation in transition metamaterials,” J. Opt. 16, 114011 (2014).
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J. Opt. A: Pure Appl. Opt. (1)

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
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Opt. Express (7)

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Opt. Mater. Express (1)

Phys. Fluids B (1)

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[Crossref]

D. J. Yu, K. Kim, and D.-H. Lee, “Resonant enhancement of mode conversion in unmagnetized plasmas due to a periodic density modulation superimposed on a linear electron density profile,” Phys. Plasmas 17, 102110 (2010).
[Crossref]

D. J. Yu, K. Kim, and D.-H. Lee, “Temperature dependence of mode conversion in warm, unmagnetized plasmas with a linear density profile,” Phys. Plasmas 20, 062109 (2013).
[Crossref]

D. J. Yu and K. Kim, “Effects of a random spatial variation of the plasma density on the mode conversion in cold, unmagnetized, and stratified plasmas,” Phys. Plasmas 20, 122104 (2013).
[Crossref]

K. Kim and D.-H. Lee, “Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity,” Phys. Plasmas 13, 042103 (2006).
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Figures (5)

Fig. 1
Fig. 1 Mode conversion coefficients A+ and A for RCP and LCP waves incident on a uniform chiral slab of thickness L versus incident angle, when (a) εR = μR = γ = ±2 and (b) εR = μR = −γ = ±2. The other parameters used are k0L = 5π and εI = μI = 10−5. In (a), strong absorption for LCP waves occurs, while A+ for RCP waves vanishes, because nγ = 0. In (b), strong absorption for RCP waves occurs, while A for LCP waves vanishes, because n + γ = 0. The A curve in (a) is identical to the A+ curve in (b).
Fig. 2
Fig. 2 Mode conversion coefficients in the absorbing case, A+ and A, and those in the amplifying case, |A+| and |A|, for RCP and LCP waves incident on a uniform chiral slab of thickness L versus incident angle, when (a), (c) εR = μR = γ = 2 and (b), (d) εR = 4, μR = 1, γ = 2. The parameter k0L is equal to 5π. Strong absorption occurs in (a) and (b), where εI = μI = 10−5, whereas strong amplification occurs in (c) and (d), where εI = μI = −10−5. In (c), A+ is identically zero and is not shown on the logarithmic plot.
Fig. 3
Fig. 3 Mode conversion coefficients in the absorbing case, A+ and A, and those in the amplifying case, |A+| and |A|, for RCP and LCP waves incident on a nonuniform slab, where εR = μR = 2(z/L) − 1 (0 ≤ zL) and γ = 0.8, versus incident angle. Circularly-polarized waves are assumed to be incident from the region where z > L. The parameter k0L is equal to 20π. In (a), εI = μI = 10−8 and in (b), εI = μI = −10−8.
Fig. 4
Fig. 4 Mode conversion coefficients in the absorbing case, A+ and A, and those in the amplifying case, |A+| and |A|, for RCP and LCP waves incident on a nonuniform slab, where εR = μR = z/L (0 ≤ zL) and γ = 0.1, 0.9, versus incident angle. Circularly-polarized waves are assumed to be incident from the region where z > L. The parameter k0L is equal to 20π. In (a), εI = μI = 10−8 and in (b), εI = μI = −10−8. In (b), A+ is identically zero and is not shown on the logarithmic plot.
Fig. 5
Fig. 5 Mode conversion coefficients in the absorbing case, A+ and A, and those in the amplifying case, |A+| and |A|, for RCP and LCP waves incident on a nonuniform slab, where εR = z/L, μR = (z/L)2 and γ = 0.5, versus incident angle. Circularly-polarized waves are assumed to be incident from the region where z > L. The parameter k0L is equal to 20π. In (a), εI = μI = 10−8 and in (b), εI = μI = −10−8.

Equations (10)

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D = ε E + i γ H , B = μ H i γ E .
d 2 ψ d z 2 d d z 1 ( z ) d ψ d z + [ k 0 2 ( z ) ( z ) q 2 I ] ψ = 0 ,
= ( μ i γ i γ ε ) , = ( ε i γ i γ μ ) .
1 i k 0 cos θ d r d l = r + r + 1 2 ( r + I ) [ + tan 2 θ ( 1 ) ] ( r + I ) ,
1 i k 0 cos θ d t d l = t + 1 2 t [ + tan 2 θ ( 1 ) ] ( r + I ) ,
r + + = 1 2 ( r 22 + r 11 ) + i 2 ( r 21 r 12 ) , r + = 1 2 ( r 22 r 11 ) + i 2 ( r 21 + r 12 ) , r + = 1 2 ( r 22 r 11 ) i 2 ( r 21 + r 12 ) , r = 1 2 ( r 22 + r 11 ) i 2 ( r 21 r 12 ) , t + + = 1 2 ( t 22 + t 11 ) + i 2 ( t 21 t 12 ) , t + = 1 2 ( t 22 t 11 ) + i 2 ( t 21 + t 12 ) , t + = 1 2 ( t 22 t 11 ) i 2 ( t 21 + t 12 ) , t = 1 2 ( t 22 + t 11 ) i 2 ( t 21 t 12 ) .
A 1 = 1 | r 11 | 2 | r 21 | 2 | t 11 | 2 | t 21 | 2 , A 2 = 1 | r 12 | 2 | r 22 | 2 | t 12 | 2 | t 22 | 2 , A + = 1 | r + + | 2 | r + | 2 | t + + | 2 | t + | 2 , A = 1 | r + | 2 | r | 2 | t + | 2 | t | 2 .
F ± = E ± i η H , η = μ ε ,
× F ± = ± [ k ± F ± + 1 2 η η × ( F + F ) ] , k ± = n ± k 0 ,
n ± = n ± γ .

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