Abstract

The propagation of Dyakonov waves guided by the planar interface of a columnar thin film and a topological insulator was investigated by numerically solving the associated canonical boundary-value problem. The topological insulator was modeled as an isotropic dielectric material endowed with a nonzero surface admittance. The propagation directions for the Dyakonov waves, as well as the decay constants and phase speeds of the waves, were significantly modulated by varying the magnitude of the surface admittance. Most significantly, a Dyakonov wave propagating along the direction of a vector u_ has a different phase speed and different decay constants as compared with the Dyakonov wave which propagates along the direction of u_. This nonreciprocity, with respect to interchanging the direction of Dyakonov-wave propagation, is not exhibited when the topological insulator is replaced by an isotropic dielectric material of the same refractive index but with a nonzero surface conductivity instead of a surface admittance.

© 2016 Optical Society of America

1. INTRODUCTION

The discovery of topological insulators [1], such as the chalcogenides Bi2Se3, Bi2Te3, and Sb2Te3, has prompted a flurry of research activity, much of which has been directed toward revealing their optical properties [24]. To this end, the theory underpinning optical scattering from spheres made of topological insulators was recently developed [5]. Classically, a topological insulator may be modeled as an achiral biisotropic material whose nonreciprocity is captured by a magnetoelectric pseudoscalar γ [6]. Alternatively, a topological insulator may be regarded as an isotropic dielectric–magnetic material whose surface is endowed with a surface admittance γ. These two different models give rise to identical results in terms of optical scattering [7]. Macroscopically, topological insulation is a surface phenomenon manifesting as protected conducting states that exist at the surface, but not in the bulk, of a topological insulator [1,2]. Therefore, we adopted the latter model in this paper.

Electromagnetic plane waves bound to the surface of a topological insulator are investigated here. Previous studies in this area have focused upon surface-plasmon-polariton waves [812]. In contrast, we investigate Dyakonov waves guided by the planar interface of a topological insulator and an anisotropic dielectric material [13,14]. While Dyakonov-wave propagation guided by the planar interface of two homogeneous dielectric materials, one isotropic and the other anisotropic, is possible only for a very small range of propagation directions, these surface waves offer considerable potential for long-range on-chip communication [15]. Parenthetically, let us note the dramatic enlargement of the range of propagation directions if the anisotropic partnering material is either a hyperbolic material [16,17] or a periodically nonhomogeneous material [18], but the range-enlargement issue lies outside the scope of this paper.

The anisotropic dielectric material is taken to be a columnar thin film (CTF) [19,20] here. CTFs may be effectively regarded as orthorhombic biaxial materials for optical purposes. Their optical properties and porosity may be engineered through judicious control of the vapor deposition technique used for their fabrication. Dyakonov waves are studied by solving the corresponding canonical boundary-value problem [21] in which the topological insulator occupies the half-space z<0 while the CTF occupies the half-space z>0. We contrast the characteristics of Dyakonov waves at the CTF/topological insulator interface with the characteristics of Dyakonov waves at the interface of a CTF and an isotropic dielectric material whose bulk properties are the same as the topological insulator but whose surface is endowed by a surface conductivity σ˜ [22] instead of the surface admittance γ.

2. BOUNDARY-VALUE PROBLEM FOR DYAKONOV-WAVE PROPAGATION

A schematic diagram illustrating the growth of a CTF by vapor deposition is provided in Fig. 1. The parallel columns grow on a substrate that is oriented parallel to the xy plane. The angle between the growing columns and the substrate plane is χ, while the angle between the incident vapor flux and the xy plane is χvχ. Without loss of generality, Dyakonov-wave propagation parallel to the x axis in the xy plane is considered. The orientation of the CTF’s morphologically significant plane relative to the direction of Dyakonov-wave propagation is specified by the angle ψ, as is schematically illustrated in Fig. 2. Accordingly, the relative permittivity dyadic of the CTF is expressed as

ε__CTF=na2u^_nu^_n+nb2u^_τu^_τ+nc2u^_bu^_b,
wherein na,b,c are the principal refractive indexes, and the unit vectors
u^_n=(u^_xcosψ+u^_ysinψ)sinχ+u^_zcosχu^_τ=(u^_xcosψ+u^_ysinψ)cosχ+u^_zsinχu^_b=u^_xsinψu^_ycosψ}
are expressed in terms of the standard Cartesian unit basis vectors {u^_x,u^_y,u^_z}. The substrate is an isotropic dielectric material specified by the refractive index ns.

 figure: Fig. 1.

Fig. 1. Schematic representation of the growth of a CTF.

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 figure: Fig. 2.

Fig. 2. Orientation of the CTF’s morphologically significant plane.

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Let E_ and H_ denote the (complex-valued) electric and magnetic field phasors, respectively, of angular frequency ω, with =c for the region z>0 and =s for the region z<0. According to the Maxwell curl postulates, the phasors satisfy

k_c×E_c=ωμ0H_ck_c×H_c=ωε0ε__CTFE_c}
in the region z>0, where ε0 and μ0 are the free-space permittivity and permeability, respectively. The wave vector
k_c=k0(ϰu^_x+iqcu^_z),
wherein k0=ωε0μ0 is the free-space wavenumber. The propagation constant ϰ>0 for Dyakonov-wave propagation directed along the positive x axis, whereas ϰ<0 for Dyakonov-wave propagation directed along the negative x axis. Furthermore, the real part of the decay constant qc must be positive valued. As described in detail elsewhere [23], the values of qc are determined by combining Eqs. (3) and (4). This provides a system of homogeneous equations that are linear in the six components of E_c and H_c; the determinant of this system delivers a quartic polynomial, the roots of which yield four values of qc. The two roots conforming to Re[qc]>0 are selected and denoted as qc1 and qc2. The two corresponding wave vectors for the region z>0 are denoted as k_c1 and k_c2. Thus, the phasors for z>0 may be expressed as
E_c=Ac1E_c1+Ac2E_c2H_c=1ωμ0(Ac1k_c1×E_c1+Ac2k_c1×E_c2)},
wherein E_c1,c2 arise from Eqs. (3) and (4) as eigenvectors corresponding to k_c1,c2 [23].

According to the Maxwell curl postulates, the phasors satisfy

k_s×E_s=ωμ0H_sk_s×H_s=ωε0ns2E_s}
in the z<0 region, where the wave vector
k_s=k0(ϰu^_xiqsu^_z),
with the decay constant qs=ϰ2ns2 conforming to Re[qs]>0 for Dyakonov-wave propagation. Solutions to Eq. (6) are represented by
E_s=As1u^_y+As2(iqsu^_x+ϰu^_z)H_s=ε0μ0[As1(iqsu^_x+ϰu^_z)As2ns2u^_y]}.
The scalar amplitude coefficients Ac1,c2 and As1,s2 introduced in Eqs. (5) and (8), respectively, are related by the following boundary conditions imposed at the interface z=0. Two cases are considered: in case (i) the substrate possesses topologically insulating surface states characterized by the surface admittance γ [7], while in case (ii) the substrate possesses a surface charge characterized by the surface conductivity σ˜ [22,24,25]. Accordingly, the boundary conditions for case (i) may be formulated as
u^_z×(E_cE_s)=0_u^_z×(H_cH_s)=γu^_z×E_s},
while those for case (ii) may be formulated as
u^_z×(E_cE_s)=0_u^_z×(H_cH_s)=σ˜(u^_xu^_x+u^_yu^_y)E_s}.
Because Eqs. (9) and (10) each yield a system of four homogeneous equations that are linear in the scalar amplitude coefficients Ac1,c2 and As1,s2, each may be expressed conveniently in the matrix-vector form
[M]·[As1As2Ac1Ac2]T=[0000]T.
Thus, the dispersion relations for Dyakonov-wave propagation for cases (i) and (ii) are represented by
det[M]=0,
with [M] being the 4×4 matrix introduced in Eq. (11). The complexity of Eq. (12) is such that an algebraic solution is impractical. Accordingly, recourse was taken to a numerical investigation of Eq. (12).

3. NUMERICAL STUDIES

For our computations, the CTF was taken to be made from titanium dioxide. The following are experimentally determined values of the principal refractive indexes for such a CTF at a free-space wavelength of 633 nm [19]:

na=1.0443+2.7394(2χv/π)1.3697(2χv/π)2nb=1.6765+1.5649(2χv/π)0.7825(2χv/π)2nc=1.3586+2.1109(2χv/π)1.0554(2χv/π)2},
with tanχ=2.8818tanχv, where the columnar inclination angle χ and vapor flux angle χv (see Fig. 1) are given in radians. We fixed the vapor flux angle χv=19.1° and the refractive index of the substrate ns=1.8.

For a given value of γ or σ˜, Eq. (12) was solved to determine the values of ψ for which Dyakonov-wave propagation is possible [23]. In fact, for γ=σ˜=0, four narrow ranges of ψ are found to support Dyakonov-wave propagation: ψ[±ψmΔψ/2,±ψm+Δψ/2] and ψ[180°±ψmΔψ/2,180°±ψm+Δψ/2]. For case (i), we found that the values of ψ for which Dyakonov-wave propagation is possible depend upon the sign of ϰ. In contrast, the values of ψ for which Dyakonov-wave propagation is possible do not depend upon the sign of ϰ for case (ii).

The angle ψm, which represents the midpoint of the ψ range that supports Dyakonov-wave propagation, is plotted against (i) η0γ/α˜ and (ii) η0σ˜/α˜ in Fig. 3. Here, η0=μ0/ε0 is the free-space impedance, while α˜=7.297352566×103 is the fine structure constant [26]. The range of γ values reflects a hopeful future for the presently infant field of topological insulators that could grow to encompass mixed materials and new material compositions. For case (i), the midpoint angle ψm increases uniformly as γ increases for ϰ>0 whereas ψm decreases uniformly as γ increases for ϰ<0. For case (ii), the midpoint angle ψm increases uniformly as σ˜ increases, at a substantially faster rate than the corresponding rate of increase for the topological insulator case with ϰ>0. The value of ψm for γ=0, regardless of the sign of ϰ, is the same as it is for σ˜=0, as may be anticipated from Eqs. (9) and (10).

 figure: Fig. 3.

Fig. 3. ψm (deg) plotted against η0γ/α˜ for ϰ>0 (solid, red curve) and ϰ<0 (dashed, green curve), and against η0σ˜/α˜ (broken dashed, blue curve).

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The extent of the angular range for which Dyakonov-wave propagation is possible, namely, Δψ, is plotted against (i) η0γ/α˜ and (ii) η0σ˜/α˜ in Fig. 4. For case (i), the magnitude of Δψ increases uniformly as γ increases for ϰ>0 whereas Δψ decreases uniformly as γ increases for ϰ<0. For case (ii), the magnitude of Δψ decreases uniformly as σ˜ increases, at a substantially faster rate than the corresponding rate of decrease for the topological insulator case with ϰ<0.

 figure: Fig. 4.

Fig. 4. As Fig. 3 but with Δψ (deg) on the vertical axis.

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Let k0m be the wavenumber for plane-wave propagation in the bulk CTF. In general, two distinct values of m are possible, which arise as roots of the equation [23,27]

nb2cos2χcos2ψm2nb2+nc2sin2ψm2nc2+na2sin2χcos2ψm2na2=0.
Let mmax denote the larger of these two roots. Then, the magnitude of the Dyakonov wave’s phase speed relative to the lower in magnitude of the two phase speeds in the bulk CTF is provided by v¯=mmax/ϰ. Furthermore, let v¯ave represent the average of the two values of v¯ at ψ=ψm±Δψ. The scaled logarithm of v¯ave is plotted against (i) η0γ/α˜ and (ii) η0σ˜/α˜ in Fig. 5. For case (i), v¯ave increases uniformly as γ increases for ϰ>0 whereas v¯ave decreases uniformly as γ increases for ϰ<0. For case (ii), v¯ave increases uniformly as σ˜ increases, at a substantially faster rate than the corresponding rate of increase for the topological insulator case with ϰ>0. Notice that v¯ave<1 for all values of γ and σ˜.

 figure: Fig. 5.

Fig. 5. As Fig. 3 but with 1000log(v¯ave) on the vertical axes.

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The extent to which Dyakonov waves are bound to the CTF/substrate interface is gauged by the real parts of the decay constants qs and qc1,c2. In the region z<0, the decay constant qs is real valued. Whereas qs0 as ψψmΔψ/2, the maximum value qs,max of qs is attained in the limit ψψm+Δψ/2. In Fig. 6, qs,max is plotted against (i) η0γ/α˜ and (ii) η0σ˜/α˜. For case (i), qs,max for ϰ>0 increases uniformly as γ increases, whereas qs,max decreases uniformly as γ increases for ϰ<0. For case (ii), qs,max decreases uniformly as σ˜ increases, at a noticeably slower rate than the corresponding rate of decrease for the topological insulator case with ϰ<0.

 figure: Fig. 6.

Fig. 6. As Fig. 3 but with qs,max on the vertical axis.

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In the region z>0, the decay constants qc1,c2 are complex valued. Whereas Re[qc1]0 as ψψm+Δψ/2, the maximum value Re[qc1]max of Re[qc1] is attained in the limit ψψmΔψ/2. In Fig. 7, Re[qc1]max is plotted against (i) η0γ/α˜ and (ii) η0σ˜/α˜. For case (i), Re[qc1]max is independent of γ regardless of the sign of ϰ. For case (ii), Re[qc1]max decreases uniformly as σ˜ increases.

 figure: Fig. 7.

Fig. 7. As Fig. 3 but with Re[qc1]max on the vertical axis.

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Unlike the behavior of Re[qc1], there is little variation in the magnitude of Re[qc2] across the ψ range for Dyakonov-wave propagation. Let Re[qc2]ave denote the average of the two values of Re[qc2] at ψ=ψm±Δψ. In Fig. 8, Re[qc2]ave is plotted against (i) η0γ/α˜ and (ii) η0σ˜/α˜. For case (i), Re[qc2]ave for ϰ>0 increases uniformly as γ increases whereas Re[qc2]ave decreases uniformly as γ increases for ϰ<0. For case (ii), Re[qc2]ave decreases uniformly as σ˜ increases, at a substantially faster rate than the corresponding rate of decrease for the topological insulator case with ϰ<0.

 figure: Fig. 8.

Fig. 8. As Fig. 3 but with Re[qc2]ave on the vertical axis.

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4. CLOSING REMARKS

In conclusion, the directions along which Dyakonov waves propagate at the planar interface of a CTF and a topological insulator are significantly modulated by varying the magnitude of the topological insulator’s surface admittance γ; so too are the decay constants and phase speeds of these Dyakonov waves. Values of γη0/α˜ other than ±1 require the use of magnetic coatings and/or immersion in a magnetostatic field [6]. Most importantly, a Dyakonov wave propagating along the direction of a vector u_ has a different phase speed and different decay constants as compared with the Dyakonov wave which propagates along the direction of u_. This nonreciprocity, with respect to interchanging the direction of Dyakonov-wave propagation, is not exhibited when the topological insulator is replaced by an isotropic dielectric material of the same refractive index but with a surface conductivity σ˜ instead of a surface admittance γ. Dyakonov-wave propagation thus provides a way to distinguish between topologically insulating surface states and conducting surface states.

Funding

Engineering and Physical Sciences Research Council (EPSRC) (EP/M018075/1); Charles Godfrey Binder Endowment.

REFERENCES

1. M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010). [CrossRef]  

2. M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009). [CrossRef]  

3. F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).

4. F. Liu, J. Xu, and Y. Yang, “Polarization conversion of reflected electromagnetic wave from topological insulator,” J. Opt. Soc. Am. B 31, 735–741 (2014). [CrossRef]  

5. A. Lakhtakia and T. G. Mackay, “Electromagnetic scattering by homogeneous, isotropic, dielectric-magnetic sphere with topologically insulating surface states,” J. Opt. Soc. Am. B 33, 603–609 (2016). [CrossRef]  

6. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008). [CrossRef]  

7. A. Lakhtakia and T. G. Mackay, “Classical electromagnetic model of surface states in topological insulators,” J. Nanophoton. 10, 033004 (2016). [CrossRef]  

8. M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015). [CrossRef]  

9. J. C. Granada E and D. F. Rojas, “Local excitations in thin metal films bounded by topological insulators,” Physica B 455, 82–84 (2014). [CrossRef]  

10. A. Karch, “Surface plasmons and topological insulators,” Phys. Rev. B 83, 245432 (2011). [CrossRef]  

11. Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012). [CrossRef]  

12. J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014). [CrossRef]  

13. M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. J. Exp. Theor. Phys. 67, 714–716 (1988).

14. O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008). [CrossRef]  

15. O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012). [CrossRef]  

16. S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012). [CrossRef]  

17. Y.-L. Zhang, Q. Zhang, and X.-Z. Wang, “Extraordinary surface polaritons in obliquely truncated dielectric/metal metamaterials,” J. Opt. Soc. Am. B 33, 543–547 (2016). [CrossRef]  

18. A. Lakhtakia and J. A. Polo Jr., “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. 2, 07021 (2007). [CrossRef]  

19. I. Hodgkinson, Q. h. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998). [CrossRef]  

20. A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005), Chap. 7.

21. J. A. Polo Jr., T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013), Chap. 4.

22. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55, 1930–1935 (1977).

23. J. A. Polo Jr., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007). [CrossRef]  

24. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009). [CrossRef]  

25. A. M. Nemilentsau, “Linear surface conductivity of an achiral single-wall carbon nanotube,” J. Nanophoton. 5, 050401 (2011). [CrossRef]  

26. R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011). [CrossRef]  

27. M. Born and E. Wolf, Principles of Optics, 7th ed. (CUP, 1999), Chap. 15.

References

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  1. M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
    [Crossref]
  2. M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
    [Crossref]
  3. F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).
  4. F. Liu, J. Xu, and Y. Yang, “Polarization conversion of reflected electromagnetic wave from topological insulator,” J. Opt. Soc. Am. B 31, 735–741 (2014).
    [Crossref]
  5. A. Lakhtakia and T. G. Mackay, “Electromagnetic scattering by homogeneous, isotropic, dielectric-magnetic sphere with topologically insulating surface states,” J. Opt. Soc. Am. B 33, 603–609 (2016).
    [Crossref]
  6. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
    [Crossref]
  7. A. Lakhtakia and T. G. Mackay, “Classical electromagnetic model of surface states in topological insulators,” J. Nanophoton. 10, 033004 (2016).
    [Crossref]
  8. M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
    [Crossref]
  9. J. C. Granada E and D. F. Rojas, “Local excitations in thin metal films bounded by topological insulators,” Physica B 455, 82–84 (2014).
    [Crossref]
  10. A. Karch, “Surface plasmons and topological insulators,” Phys. Rev. B 83, 245432 (2011).
    [Crossref]
  11. Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
    [Crossref]
  12. J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014).
    [Crossref]
  13. M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. J. Exp. Theor. Phys. 67, 714–716 (1988).
  14. O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
    [Crossref]
  15. O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
    [Crossref]
  16. S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
    [Crossref]
  17. Y.-L. Zhang, Q. Zhang, and X.-Z. Wang, “Extraordinary surface polaritons in obliquely truncated dielectric/metal metamaterials,” J. Opt. Soc. Am. B 33, 543–547 (2016).
    [Crossref]
  18. A. Lakhtakia and J. A. Polo, “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. 2, 07021 (2007).
    [Crossref]
  19. I. Hodgkinson, Q. h. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998).
    [Crossref]
  20. A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005), Chap. 7.
  21. J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013), Chap. 4.
  22. C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55, 1930–1935 (1977).
  23. J. A. Polo, S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007).
    [Crossref]
  24. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
    [Crossref]
  25. A. M. Nemilentsau, “Linear surface conductivity of an achiral single-wall carbon nanotube,” J. Nanophoton. 5, 050401 (2011).
    [Crossref]
  26. R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
    [Crossref]
  27. M. Born and E. Wolf, Principles of Optics, 7th ed. (CUP, 1999), Chap. 15.

2016 (3)

2015 (1)

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

2014 (3)

F. Liu, J. Xu, and Y. Yang, “Polarization conversion of reflected electromagnetic wave from topological insulator,” J. Opt. Soc. Am. B 31, 735–741 (2014).
[Crossref]

J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014).
[Crossref]

J. C. Granada E and D. F. Rojas, “Local excitations in thin metal films bounded by topological insulators,” Physica B 455, 82–84 (2014).
[Crossref]

2013 (1)

F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).

2012 (3)

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref]

S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
[Crossref]

2011 (3)

A. M. Nemilentsau, “Linear surface conductivity of an achiral single-wall carbon nanotube,” J. Nanophoton. 5, 050401 (2011).
[Crossref]

A. Karch, “Surface plasmons and topological insulators,” Phys. Rev. B 83, 245432 (2011).
[Crossref]

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

2010 (1)

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[Crossref]

2009 (2)

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

2008 (2)

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[Crossref]

2007 (2)

J. A. Polo, S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007).
[Crossref]

A. Lakhtakia and J. A. Polo, “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. 2, 07021 (2007).
[Crossref]

1998 (1)

1988 (1)

M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. J. Exp. Theor. Phys. 67, 714–716 (1988).

1977 (1)

C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55, 1930–1935 (1977).

Artigas, D.

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref]

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Autore, M.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Bie, Y.-Q.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Biraben, F.

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Bohren, C. F.

C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55, 1930–1935 (1977).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (CUP, 1999), Chap. 15.

Bouchendira, R.

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Bozhko, S. I.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Brahlek, M.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Chang, M.-C.

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[Crossref]

Cladé, P.

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Crasovan, L.-C.

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

D’Apuzzo, F.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

D’yakonov, M. I.

M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. J. Exp. Theor. Phys. 67, 714–716 (1988).

Di Gaspare, A.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Fleischer, K.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

García de Abajo, F. J.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Giliberti, V.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Granada E, J. C.

J. C. Granada E and D. F. Rojas, “Local excitations in thin metal films bounded by topological insulators,” Physica B 455, 82–84 (2014).
[Crossref]

Guellati-Khélifa, S.

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Han, B.-H.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Hasan, M. Z.

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[Crossref]

Hazel, J.

Hodgkinson, I.

Hughes, T. L.

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[Crossref]

Hunt, A. J.

C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55, 1930–1935 (1977).

Jakšic, Z.

S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
[Crossref]

Johansen, S. K.

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Kane, C. L.

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[Crossref]

Karch, A.

A. Karch, “Surface plasmons and topological insulators,” Phys. Rev. B 83, 245432 (2011).
[Crossref]

Koirala, N.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Lakhtakia, A.

A. Lakhtakia and T. G. Mackay, “Classical electromagnetic model of surface states in topological insulators,” J. Nanophoton. 10, 033004 (2016).
[Crossref]

A. Lakhtakia and T. G. Mackay, “Electromagnetic scattering by homogeneous, isotropic, dielectric-magnetic sphere with topologically insulating surface states,” J. Opt. Soc. Am. B 33, 603–609 (2016).
[Crossref]

A. Lakhtakia and J. A. Polo, “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. 2, 07021 (2007).
[Crossref]

J. A. Polo, S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007).
[Crossref]

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013), Chap. 4.

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005), Chap. 7.

Liao, Z.-M.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Limaj, O.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Liu, F.

F. Liu, J. Xu, and Y. Yang, “Polarization conversion of reflected electromagnetic wave from topological insulator,” J. Opt. Soc. Am. B 31, 735–741 (2014).
[Crossref]

F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).

Liu, H.

J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014).
[Crossref]

Lupi, S.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Mackay, T. G.

A. Lakhtakia and T. G. Mackay, “Electromagnetic scattering by homogeneous, isotropic, dielectric-magnetic sphere with topologically insulating surface states,” J. Opt. Soc. Am. B 33, 603–609 (2016).
[Crossref]

A. Lakhtakia and T. G. Mackay, “Classical electromagnetic model of surface states in topological insulators,” J. Nanophoton. 10, 033004 (2016).
[Crossref]

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013), Chap. 4.

Messier, R.

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005), Chap. 7.

Mihalache, D.

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Miret, J. J.

S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
[Crossref]

Nelatury, S. R.

J. A. Polo, S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007).
[Crossref]

Nemilentsau, A. M.

A. M. Nemilentsau, “Linear surface conductivity of an achiral single-wall carbon nanotube,” J. Nanophoton. 5, 050401 (2011).
[Crossref]

Nez, F.

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Oh, S.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Polo, J. A.

J. A. Polo, S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007).
[Crossref]

A. Lakhtakia and J. A. Polo, “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. 2, 07021 (2007).
[Crossref]

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013), Chap. 4.

Qi, J.

J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014).
[Crossref]

Qi, X.-L.

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[Crossref]

Rojas, D. F.

J. C. Granada E and D. F. Rojas, “Local excitations in thin metal films bounded by topological insulators,” Physica B 455, 82–84 (2014).
[Crossref]

Roy, P.

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

Shvets, I. V.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Song, G.

F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).

Takayama, O.

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref]

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Torner, L.

O. Takayama, D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett. 37, 4311–4313 (2012).
[Crossref]

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

Vukovic, S.

S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
[Crossref]

Wang, X.-Z.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (CUP, 1999), Chap. 15.

Wu, H.-C.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Wu, Q. h.

Xie, X. C.

J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014).
[Crossref]

Xu, J.

F. Liu, J. Xu, and Y. Yang, “Polarization conversion of reflected electromagnetic wave from topological insulator,” J. Opt. Soc. Am. B 31, 735–741 (2014).
[Crossref]

F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).

Yan, Y.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Yang, M.-F.

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[Crossref]

Yang, Y.

F. Liu, J. Xu, and Y. Yang, “Polarization conversion of reflected electromagnetic wave from topological insulator,” J. Opt. Soc. Am. B 31, 735–741 (2014).
[Crossref]

F. Liu, J. Xu, G. Song, and Y. Yang, “Goos-Hänchen and Imbert-Fedorov shifts at the interface of ordinary dielectric and topological insulator,” J. Opt. Soc. Am. B 30, 735–741 (2013).

Yashina, L. V.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Yu, D.-P.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Zapata-Rodríguez, C. J.

S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
[Crossref]

Zhang, Q.

Zhang, S.-C.

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[Crossref]

Zhang, Y.-L.

Zhao, Q.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Zhou, Y.-B.

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Adv. Opt. Mater. (1)

M. Autore, F. D’Apuzzo, A. Di Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon-phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3, 1257–1263 (2015).
[Crossref]

AIP Adv. (1)

Z.-M. Liao, B.-H. Han, H.-C. Wu, L. V. Yashina, Y. Yan, Y.-B. Zhou, Y.-Q. Bie, S. I. Bozhko, K. Fleischer, I. V. Shvets, Q. Zhao, and D.-P. Yu, “Surface plasmon on topological insulator/dielectric interface enhanced ZnO ultraviolet photoluminescence,” AIP Adv. 2, 022105 (2012).
[Crossref]

Appl. Opt. (1)

Can. J. Phys. (1)

C. F. Bohren and A. J. Hunt, “Scattering of electromagnetic waves by a charged sphere,” Can. J. Phys. 55, 1930–1935 (1977).

Electromagnetics (1)

O. Takayama, L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28, 126–145 (2008).
[Crossref]

J. Eur. Opt. Soc. (1)

A. Lakhtakia and J. A. Polo, “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. 2, 07021 (2007).
[Crossref]

J. Nanophoton. (3)

A. Lakhtakia and T. G. Mackay, “Classical electromagnetic model of surface states in topological insulators,” J. Nanophoton. 10, 033004 (2016).
[Crossref]

J. A. Polo, S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton. 1, 013501 (2007).
[Crossref]

A. M. Nemilentsau, “Linear surface conductivity of an achiral single-wall carbon nanotube,” J. Nanophoton. 5, 050401 (2011).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Lett. (1)

Phys. Rev. B (4)

A. Karch, “Surface plasmons and topological insulators,” Phys. Rev. B 83, 245432 (2011).
[Crossref]

J. Qi, H. Liu, and X. C. Xie, “Surface plasmon polaritons in topological insulators,” Phys. Rev. B 89, 155420 (2014).
[Crossref]

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[Crossref]

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[Crossref]

Phys. Rev. Lett. (1)

R. Bouchendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Phys. Scripta (1)

S. Vuković, J. J. Miret, C. J. Zapata-Rodríguez, and Z. Jakšić, “Oblique surface waves at an interface between a metal-dielectric superlattice and an isotropic dielectric,” Phys. Scripta T149, 014041 (2012).
[Crossref]

Physica B (1)

J. C. Granada E and D. F. Rojas, “Local excitations in thin metal films bounded by topological insulators,” Physica B 455, 82–84 (2014).
[Crossref]

Rev. Mod. Phys. (2)

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Sov. Phys. J. Exp. Theor. Phys. (1)

M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. J. Exp. Theor. Phys. 67, 714–716 (1988).

Other (3)

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005), Chap. 7.

J. A. Polo, T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013), Chap. 4.

M. Born and E. Wolf, Principles of Optics, 7th ed. (CUP, 1999), Chap. 15.

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Figures (8)

Fig. 1.
Fig. 1. Schematic representation of the growth of a CTF.
Fig. 2.
Fig. 2. Orientation of the CTF’s morphologically significant plane.
Fig. 3.
Fig. 3. ψ m (deg) plotted against η 0 γ / α ˜ for ϰ > 0 (solid, red curve) and ϰ < 0 (dashed, green curve), and against η 0 σ ˜ / α ˜ (broken dashed, blue curve).
Fig. 4.
Fig. 4. As Fig. 3 but with Δ ψ (deg) on the vertical axis.
Fig. 5.
Fig. 5. As Fig. 3 but with 1000 log ( v ¯ ave ) on the vertical axes.
Fig. 6.
Fig. 6. As Fig. 3 but with q s , max on the vertical axis.
Fig. 7.
Fig. 7. As Fig. 3 but with Re [ q c 1 ] max on the vertical axis.
Fig. 8.
Fig. 8. As Fig. 3 but with Re [ q c 2 ] ave on the vertical axis.

Equations (14)

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ε _ _ CTF = n a 2 u ^ _ n u ^ _ n + n b 2 u ^ _ τ u ^ _ τ + n c 2 u ^ _ b u ^ _ b ,
u ^ _ n = ( u ^ _ x cos ψ + u ^ _ y sin ψ ) sin χ + u ^ _ z cos χ u ^ _ τ = ( u ^ _ x cos ψ + u ^ _ y sin ψ ) cos χ + u ^ _ z sin χ u ^ _ b = u ^ _ x sin ψ u ^ _ y cos ψ }
k _ c × E _ c = ω μ 0 H _ c k _ c × H _ c = ω ε 0 ε _ _ CTF E _ c }
k _ c = k 0 ( ϰ u ^ _ x + i q c u ^ _ z ) ,
E _ c = A c 1 E _ c 1 + A c 2 E _ c 2 H _ c = 1 ω μ 0 ( A c 1 k _ c 1 × E _ c 1 + A c 2 k _ c 1 × E _ c 2 ) } ,
k _ s × E _ s = ω μ 0 H _ s k _ s × H _ s = ω ε 0 n s 2 E _ s }
k _ s = k 0 ( ϰ u ^ _ x i q s u ^ _ z ) ,
E _ s = A s 1 u ^ _ y + A s 2 ( i q s u ^ _ x + ϰ u ^ _ z ) H _ s = ε 0 μ 0 [ A s 1 ( i q s u ^ _ x + ϰ u ^ _ z ) A s 2 n s 2 u ^ _ y ] } .
u ^ _ z × ( E _ c E _ s ) = 0 _ u ^ _ z × ( H _ c H _ s ) = γ u ^ _ z × E _ s } ,
u ^ _ z × ( E _ c E _ s ) = 0 _ u ^ _ z × ( H _ c H _ s ) = σ ˜ ( u ^ _ x u ^ _ x + u ^ _ y u ^ _ y ) E _ s } .
[ M ] · [ A s 1 A s 2 A c 1 A c 2 ] T = [ 0 0 0 0 ] T .
det [ M ] = 0 ,
n a = 1.0443 + 2.7394 ( 2 χ v / π ) 1.3697 ( 2 χ v / π ) 2 n b = 1.6765 + 1.5649 ( 2 χ v / π ) 0.7825 ( 2 χ v / π ) 2 n c = 1.3586 + 2.1109 ( 2 χ v / π ) 1.0554 ( 2 χ v / π ) 2 } ,
n b 2 cos 2 χ cos 2 ψ m 2 n b 2 + n c 2 sin 2 ψ m 2 n c 2 + n a 2 sin 2 χ cos 2 ψ m 2 n a 2 = 0 .

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