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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6339–6347
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Dyakonov surface wave resonant transmission

Osamu Takayama, Alexey Yu Nikitin, Luis Martin-Moreno, Lluis Torner, and David Artigas  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6339-6347 (2011)
http://dx.doi.org/10.1364/OE.19.006339


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Abstract

The role of Dyakonov surface waves in the transmission through structures composed of birefringent media is theoretically explored. In the case of structures using prisms, unexpected high transmission above the critical angle due to resonant excitation of Dyakonov surface waves is predicted. This transmission is produced only when TE polarized incident wave reaches the interface supporting the surface waves within a narrow interval of angles, for both the angle of incidence and the angle with respect to the optic axis of the birefringent media. As a result, over 90% transmission for a single and isolated peak confined in the two transversal directions, with hybrid TE and TM polarization, can be obtained.

© 2011 OSA

1. Introduction

Light transmission trough a multilayer structure is dictated by the interferences resulting from the multiple reflections at interfaces. Transmission is governed by Fresnel relations in the simplest case of one interface, and by resonant Fabry-Perot (FP) modes in the case of two interfaces [1

1. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988).

]. Guided modes existing in the structure are not usually excited and do not play an important role in the transmission. An exception occurs when the wave vector component parallel to the interfaces of the incident field equals that of the waveguide-mode propagation constant in the structure, resulting in mode excitation. Various methods exist to excite desired modes, such as prism coupling (Otto or Kretschmann configurations) or grating coupling, among others. The effect of the mode excitation is better observed in reflection where for the proper angle of incidence or light wavelength, a dip in the reflected pattern is observed. In the case of transmission using grating coupling, an interesting effect referred to as extraordinary transmission, which involve the excitation of Surface Plasmons Polaritons (SPP) in metallic films, has been reported [2

2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

,3

3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

]. Here, light transmission through the structure normalized to the photon flux incident on the open subwavelength aperture can be several times larger than unity. In addition, by properly engineering the grating around a single aperture, the induced coupling between SPPs and radiation modes can be used to either enhance the total transmission or shape the transmitted beam [3

3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

,4

4. F. J. García-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

].

Among the different types of surface waves [5

5. J. A. Polo Jr and A. Lakhtakia, “Surface electromagnetic waves: a review,” Laser Photonics Rev. 5(2), 234–246 (2011). [CrossRef]

], a special case of surface waves (SWs), referred to as Dyakonov SWs, is supported at the interfaces between an anisotropic cladding and an isotropic medium with refractive index n c [6

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

10

10. O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28(3), 126–145 (2008). [CrossRef]

]. Such SWs form when the anisotropic cladding is (i) a positive uniaxial birefringent medium with the ordinary n o and extraordinary n e, refractive indices satisfying the relation n o < n c < n e [6

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

]; (ii) a biaxial anisotropic medium with refractive indices nx, ny, and nz, fulfilling the condition n1 > nc > n2 > n3, where n1 = max(nx, ny, nz) and n3 = min(nx, ny, nz) [7

7. D. B. Walker, E. N. Glytsis, and T. K. Gaylord, “Surface mode at isotropic-uniaxial and isotropic-biaxial interfaces,” J. Opt. Soc. Am. A 15(1), 248–260 (1998). [CrossRef]

]; (iii) at the interface between two birefringent media, either uniaxial [8

8. N. S. Averkiev and M. I. D’yakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653–655 (1990).

] or biaxial [9

9. S. R. Nelatury, J. A. Polo Jr, and A. Lakhtakia, “Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24(3), 856–865 (2007). [CrossRef]

]. They are lossless, hybrid (TE-dominant) polarized waves, very directional (since they only propagate in a narrow angular range with respect to the optical axis) and weakly localized compared with SPPs (see Ref. [10

10. O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28(3), 126–145 (2008). [CrossRef]

] for a review on these SWs). The difficulty to find natural materials fulfilling the relation among refractive indices described above and the narrow resonant dip obtained in Otto-Kretschmann excitation configuration (three orders of magnitude narrower than in standard SPPs excitation) made the experimental demonstration challenging. Recently, by using the polarization conversion effect [11

11. A. Yu. Nikitin, D. Artigas, L. Torner, F. J. García-Vidal, and L. Martín-Moreno, “Polarization conversion spectroscopy of hybrid modes,” Opt. Lett. 34(24), 3911–3913 (2009). [CrossRef] [PubMed]

], Dyakonov SWs were observed in an Otto–Kretschmann configuration [12

12. O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102(4), 043903 (2009). [CrossRef] [PubMed]

].

Similar to SPPs, Dyakonov SWs can play an important role in the transmission through resonances in structures formed by birefringent media. Transmission through multilayer birefringent structures has been studied in the past (See, for example Refs. [1

1. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988).

,13

13. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Reflection and transmission of plane-waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38(4), 649–657 (1991). [CrossRef]

15

15. I. J. Hodgkinson, S. Kassam, and Q. H. Wu, “Eigenequations and compact algorithms for bulk and layered anisotropic optical media: reflection and refraction at a crystal-crystal interface,” J. Comput. Phys. 133(1), 75–83 (1997). [CrossRef]

].). However, to the best of our knowledge, geometries supporting Dyakonov SWs have not been addressed. The objective of the present work is to numerically explore and illustrate the transmission characteristics caused by the excitation of Dyakonov SWs.

2. Structure geometry and analysis

The excitation of Dyakonov surface waves can either be performed using grating or prisms. In the first case the simplest structure is two layers with a grating written at the interface (see Fig. 1(a)
Fig. 1 Structures under consideration showing Dyakonov SW resonant transmission. (a) Grating coupling. (b) Prism-Isotropic-Uniaxial-Isotropic-Prism. The refractive index of the isotropic media must fulfill n o < n c < n e. The order of the sandwiched layers can be exchanged. (c) Lateral view of the structure analyzed in this work: Prism-Uniaxial-Uniaxial-Prism. (d) top view (coordinate system) associated to (c).
). However, in this case transmission through the structure is the superposition of both Dyakonov SW and FP modes, hiding the characteristics of the former [16

16. S. G. Rodrigo, A. Yu. Nikitin, F. J. García-Vidal, L. Martin-Moreno, O. Takayama, L. Torner and D. Artigas, “Extraordinary optical transmission through a slit array in a biaxial dielectric film” (to be published).

]. Excitation using prisms have the advantage that the two kinds of modes are spectrally separated: Dyakonov SWs are excited above and FP modes below the incident critical angle [12

12. O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102(4), 043903 (2009). [CrossRef] [PubMed]

]. Therefore, the properties of the Dyakonov SW resonant transmissions are better described in this second excitation configuration. Here, to decouple the SW allowing for the transmission, an additional output prism is required, resulting in a two layer structure (with the interface supporting the Dyakonov SWs) sandwiched between two prisms. Figures 1(b) and 1(c) show the different and simplest possible configurations (more layers can be added). In this paper, for simplicity and without loss of generality, we focus on the configuration described in Fig. 1(c). This figure corresponds to two identical uniaxial birefringent media with the optic axis parallel to the interface. The two optic axes form an angle Θ between them. The coordinate system is taken so that the SW propagates along the x axis, which is contained in the interface and forms an angle θ with respect to the optic axis (OA1) of the top layer. The z axis is orthogonal to the interface, directed to the bottom output prism. The y axis is also contained in the interface as shown in Fig. 1(d). The angle of incidence φi is measured from the normal to the interface in the coupling prism (negative z axis). In this geometry, Dyakonov SWs propagates only within a range of existence angles Δθ centered at the bisector angle θ = Θ/2 (measured from the optic axis at the upper layer), as Fig. 1(d) shows.The electric field amplitude in the prism coupler, assuming harmonic dependence exp=[i(Nk0xωt)], with k 0 the free space wave number, np the refractive index in the prism, and γp=np2N2, with N=npsinϕbeing the effective refractive index, can be written in compact form in terms of the incident and reflected TE and TM wave as,
Ep1(x,z)=[0γp100N][ATEiexp[ik0γpz]ATMiexp[ikoγpz]]+[0γp100N][ATERexp[ik0γpz]ATMRexp[ikoγpz]]
(1)
This equation is also valid for the bottom output coupler substitutingATE,TMiATE,TMT, ATE,TMR0, and zzd1d2. For the geometry considered here, the relative permittivity tensor for the birefringent layer is symmetric. This tensor for the top layer has the form:
[ε1]=(εosin2θ+εecos2θ(εeεo)sinθcosθ0(εeεo)sinθcosθεocos2θ+εesin2θ000εo),
(2)
where εe=ne2 and εo=no2 are the relative permittivities of the ordinary and extraordinary waves, respectively. Since the considered structure supports SWs, we chose to express the field in both birefringent media as a superposition of evanescent ordinary and extraordinary waves, which are truncated by the presence of the prism. The field amplitude in the top layer can be written as
Eb1(x,z)=[γotanθγo2γono2tanθiNtanθiNγe][Ao1+exp[k0γoz]Ae1+exp[koγe1z]]+[γotanθγo2γono2tanθiNtanθiNγe][Ao1exp[k0γoz]Ae1exp[koγe1z]],
(3)
where γo and γe are the ordinary and extraordinary decaying constants. From the wave equation one gets
γo=N2no2 and γe=nene(θ)N2ne2(θ),
(4)
with
1ne2(θ)=cos2θno2+sin2θne2,
(5)
n e(θ) being the refractive index of the extraordinary wave propagating in an unbounded uniaxial crystal. Equations (2) to (5) are also valid for the bottom birefringent layer by substitutingθ(90ºθ) and zzd1.

By imposing boundary conditions at the different layers, the eigenvalue relations can be found. To solve the transmission and reflection problem through the structure, a practical procedure is to use a matrix formalism such as the one developed by Hodgkinson et. al. [15

15. I. J. Hodgkinson, S. Kassam, and Q. H. Wu, “Eigenequations and compact algorithms for bulk and layered anisotropic optical media: reflection and refraction at a crystal-crystal interface,” J. Comput. Phys. 133(1), 75–83 (1997). [CrossRef]

]. This formalism can efficiently deal with multilayer structures formed by birefringent media, providing the reflectance and transmittance (irradiance) coefficients. By varying the angle of incidence φi and propagation angle θ, reflectance and transmittance spectra can be obtained. As a reference in spectra in Figs. 2
Fig. 2 Reflectance and transmittance spectra for a Prism-Uniaxial-Uniaxial-Prism configuration. The two prisms and uniaxial layers are identical with n p = 1.77862, n o = 1.520, n e = 1.725, d b = 4λ. θ, is the angle between the top uniaxial optical axis OA1 and the in-plane component of the incident wavevector. The angle between optical axes is Θ = 90°. Reflection for (a) TEin-TEout, (b) TMin-TMout, and (c) TEin-TMout = TMin-TEout, input-output polarizations. Transmission for (d) TEin-TMout = TMin-TEout, (e) TEin-TEout, and (f) TMin-TMout input-output polarizations. Magnification of red rectangle in (e) is shown in Fig. 3(a). The green (blue) line shows the critical angles for the extraordinary refractive index ne(θ) for the top (bottom) birefringent layer.
to 4
Fig. 4 (a) Transmission spectra (TEin−TEout) for a Prism-Uniaxial-Uniaxial-Prism configuration when the thicknesses of the two uniaxial layers are different. db1 = 6λ and db2 = 3λ. The rest of the parameters are same as Fig. 2. (b) Magnification of the transmission spectrum associated with Dyakonov SWs. The red vertical lines represent the angular existence domain for semi-infinite layers of two uniaxial media. (c) Transmission in terms of θ when the angle of incidence is fixed at φ = 65.185° (red line in (b)). (d) Transmission in terms of φ when the angle of incidence is fixed at θ = 45.5° (blue line in (b)).
, the critical angles for the extraordinary refractive index n e(θ) are denoted as a green line in the top layer given by ϕic=sin1(np/ne(θ)) and as a blue line for the bottom layer, obtained substituting θ(90ºθ).

3. Results

As a model structure we consider a SF11 prisms with refractive index n p = 1.77862. The two uniaxial layers are considered identical with refractive index no = 1.520 and ne = 1.725, corresponding to a E7 liquid crystal. The angle between optical axes of the two birefringent layers is chosen to be Θ = 90°. The thickness of the two layers are considered equal, d1 = d2 = 4λ, where λ is the wavelength of the incident field. The resulting reflection and transmission spectra are shown in Fig. 2.

The reflection spectra maintaining the polarization are composed of dark regions or dips of low reflection (Figs. 2(a) and 2(b)). These dips in reflectance are caused by the coupling to FP modes (below the green and blue lines showing the critical angles) and the excitation of other modes supported by the structure, namely leaky guided modes supported by the top birefringent layer (dips above the blue critical angle line) and Dyakonov SWs (dips above both, the green and blue critical angle lines). Note that since this structure supports TE dominant hybrid modes, TE input results in a more efficient excitation of all the existing modes (lower reflection for the corresponding dip) than TM input. Interestingly, excitation of birefringent layers results in a polarization conversion effect (Fig. 2(c)) [17

17. F. Yang and J. R. Sambles, “Critical angles for reflectivity at an isotropic-anisotropic boundary,” J. Mod. Opt. 40(6), 1131–1142 (1993). [CrossRef]

,18

18. Y. J. Jen, C. Y. Peng, and H. H. Chang, “Optical constant determination of an anisotropic thin film via polarization conversion,” Opt. Express 15(8), 4445–4451 (2007). [CrossRef] [PubMed]

]. This conversion appears as peaks in the intensity of reflected light and is identical for both input polarization but stronger for propagating modes (leaky or Dyakonov) than for FP modes. This effect was used to demonstrate the existence of Dyakonov SWs [12

12. O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102(4), 043903 (2009). [CrossRef] [PubMed]

] and has extensively been discussed in Ref. [11

11. A. Yu. Nikitin, D. Artigas, L. Torner, F. J. García-Vidal, and L. Martín-Moreno, “Polarization conversion spectroscopy of hybrid modes,” Opt. Lett. 34(24), 3911–3913 (2009). [CrossRef] [PubMed]

].

The Dyakonov SW resonant transmission is a localized resonance in both, the angle θ with respect to the optical axis and the angle of incidence. In order to better understand this localization, we show slices of Fig. 3(a) maintaining one of the two angles fixed. In the first case, the angle of incidence is fixed at φ = 65.147°. Here, only one transmission peak is obtained, with the maximum at θ = 45° (corresponding to the center of the existence domain of Dyakonov SW), with a TE and converted TM transmission of ~80% and ~10%, respectively (~90% of total transmission), and a width of Δθp = 0.4°. This situation corresponds to the broadest peak in θ. For higher angles of incidence, the peak splits into two narrower peaks with lower transmission coefficient. In the second slice, the angle with respect to the optical axis is fixed at θ = 45°. In Fig. 3(c), the resonance peaks are shown in an extended range φi considered in Fig. 2. This clearly shows the difference between the FP resonances (broad peaks with a background-to-peak ratio higher that 20% in all cases) and the Dyakonov SW resonant transmission (much narrower and with no surrounding background). Figure 3(d) shows a magnification of the Dyakonov peak, whose main difference with respect to Fig. 3(b) is that in this case the peak width is much narrower, of Δφ p = 0.006°. Such a narrow peak could seem extremely hard to experimentally detect. However, peaks of similar width were detected by the polarization conversion method used to observe Dyakonov SWs [12

12. O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102(4), 043903 (2009). [CrossRef] [PubMed]

]. As in that experiment, the key point is that the null background surrounding the peak offers enough contrast for the peak detection. Therefore, the resulting narrow peak implies a high sensitivity to parameters variations in the structure.

For practical purposes, transmission control by changing the angle with respect to the optic axis θ (which can be performed by rotating the structure while maintaining the output beam direction) can be more convenient than changing the angle of incidence φi (which results in the change of the transmitted direction). However, as discussed above, the structure analyzed in Fig. 3 does not offer a high sensitivity (Δθ p = 0.4°) and in addition it can result in two transmission peaks. This can be solved by using an asymmetrical structure, for example, by using different thicknesses for the two birefringent layers. The results considering d1 = 6λ and d2 = 3λ, and maintaining the same value for all the other parameters, are shown in Fig. 4. In this case, the different layer thickness breaks the symmetry of the transmission spectrum with respect to the angle θ, as can be seen by comparing Fig. 2(e) and Fig. 4(a). The increase in the top layer thickness moves the Dyakonov SWs cutoff (by radiation to the coupling prism) to higher angles θ. In a similar way, the cutoff by radiation to the output prism moves to higher angles θ by the decrease in the bottom layer thickness (compare Fig. 3(a) and 4(b)). As a result, the transmission can be engineered to obtain a narrow transmission peak in the angle θ. For the particular case analyzed here, the transmission is maintained up to 80% for TEin – TEout and 10% for TEin – TMout polarization conversion. The maximum transmission is translated to higher values of θ, in this case around θ = 45.5° with a width one order of magnitude narrower, Δθ p = 0.04° (compare Fig. 3(b) and 4(c)), while the width for the angle φi remain in the same order, Δφ p = 0.005° (compare Fig. 3(d) and 4(d)).

The results reported here correspond to a specific structure, however there is room for optimization and engineering for a given particular purpose. In general the total transmission depends on the range of existence of the Dyakonov SWs and the polarization conversion on its degree of hybridity. For example, by increasing the angle between the two optic axis to Θ = 120°, the range of existence of Dyakonov SWs increases, resulting in a higher TE output transmission (90%) and a lower TM output transmission (6%).

4. Conclusion and discussion

We have theoretically studied the effect of Dyakonov SWs in the transmission through dielectric structures. We have shown that it is possible to obtain high transmission for TE excitation, resulting in ~80% for TE output and a small polarization conversion, i.e., ~10% for TM output. However, transmission maintaining the polarization by TM excitation is marginal, only resulting in polarization conversion. Such transmission is produced only in a certain range of excitation angles in the two transversal directions, namely angle of incidence φi and angle with respect the optic axis θ. The range of transmission angles are Δφ p = 0.006° and Δθ p = 0.4° for a typical symmetric structure, while in an asymmetrical structure the range in θ can be reduced by one order of magnitude to Δθ p = 0.04°.

Potential applications of the effect reported here include directional spatial filters and sensing applications. In the first case the structure considered here is the most suitable, since it shows very well defined transmission characteristics. In the second case, a structure formed by a birefringent and an isotropic layer (instead of two birefringent layers) is more adequate since the isotropic layer could be easily substituted by the medium to be sensed. In this last situation, when compared with sensors based on surface plasmons polaritons (SPP), the low localization of the Dyakonov SW at the surface decreases the its sensitivity, however, this can be compensated to some extent by the narrower peak showed by the Dyakonov SW resonant transmission, which is two orders of magnitude narrower than the typical resonance dip in SPP.

The transmission in general can be engineered by changing the different parameters, such as the birefringent layer thicknesses, the angle Θ between optical axes or the prism refractive index. In addition, new opportunities appear in combination with other material and geometrical properties, such as nanostructured materials exhibiting tunable form-birefringence [19

19. D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94(1), 013901 (2005). [CrossRef] [PubMed]

], magnetic materials [20

20. L. C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30(22), 3075–3077 (2005). [CrossRef] [PubMed]

], thin films [21

21. L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13(10), 2027–2033 (1995). [CrossRef]

], nonlinear media [22

22. L. Tomer, J. P. Torres, F. Lederer, D. Mihalache, D. M. Baboiu, and M. Ciumac, “Nonlinear hybrid waves guided by birefringent interfaces,” Electron. Lett. 29(13), 1186–1188 (1993). [CrossRef]

], or electro-optic effect [23

23. S. R. Nelatury, J. A. Polo Jr, and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic material,” Electromagnetics 28(3), 162–174 (2008). [CrossRef]

], which may afford further control of the transmission characteristics. A special important case is the combination with SPP. Recent works have proposed the use of dielectric layers on top of a thin metal to enhance the TE transmission in structures where the existence of SPP results in TM extraordinary transmission [24

24. M. Guillaumée, A. Yu. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010). [CrossRef] [PubMed]

]. The combination of Dyakonov SWs and SPP opens new opportunities to achieve this objective.

Acknowledgments

This work is supported by the Generalitat de Catalunya (2009-SGR-159) and the Ministry of Science and Innovation, Government of Spain (grant FIS2009-09928).

References and links

1.

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988).

2.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

3.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

4.

F. J. García-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

5.

J. A. Polo Jr and A. Lakhtakia, “Surface electromagnetic waves: a review,” Laser Photonics Rev. 5(2), 234–246 (2011). [CrossRef]

6.

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

7.

D. B. Walker, E. N. Glytsis, and T. K. Gaylord, “Surface mode at isotropic-uniaxial and isotropic-biaxial interfaces,” J. Opt. Soc. Am. A 15(1), 248–260 (1998). [CrossRef]

8.

N. S. Averkiev and M. I. D’yakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653–655 (1990).

9.

S. R. Nelatury, J. A. Polo Jr, and A. Lakhtakia, “Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24(3), 856–865 (2007). [CrossRef]

10.

O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28(3), 126–145 (2008). [CrossRef]

11.

A. Yu. Nikitin, D. Artigas, L. Torner, F. J. García-Vidal, and L. Martín-Moreno, “Polarization conversion spectroscopy of hybrid modes,” Opt. Lett. 34(24), 3911–3913 (2009). [CrossRef] [PubMed]

12.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102(4), 043903 (2009). [CrossRef] [PubMed]

13.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Reflection and transmission of plane-waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38(4), 649–657 (1991). [CrossRef]

14.

G. D. Landry and T. A. Maldonado, “Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media,” J. Opt. Soc. Am. A 12(9), 2048–2063 (1995). [CrossRef]

15.

I. J. Hodgkinson, S. Kassam, and Q. H. Wu, “Eigenequations and compact algorithms for bulk and layered anisotropic optical media: reflection and refraction at a crystal-crystal interface,” J. Comput. Phys. 133(1), 75–83 (1997). [CrossRef]

16.

S. G. Rodrigo, A. Yu. Nikitin, F. J. García-Vidal, L. Martin-Moreno, O. Takayama, L. Torner and D. Artigas, “Extraordinary optical transmission through a slit array in a biaxial dielectric film” (to be published).

17.

F. Yang and J. R. Sambles, “Critical angles for reflectivity at an isotropic-anisotropic boundary,” J. Mod. Opt. 40(6), 1131–1142 (1993). [CrossRef]

18.

Y. J. Jen, C. Y. Peng, and H. H. Chang, “Optical constant determination of an anisotropic thin film via polarization conversion,” Opt. Express 15(8), 4445–4451 (2007). [CrossRef] [PubMed]

19.

D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94(1), 013901 (2005). [CrossRef] [PubMed]

20.

L. C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30(22), 3075–3077 (2005). [CrossRef] [PubMed]

21.

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13(10), 2027–2033 (1995). [CrossRef]

22.

L. Tomer, J. P. Torres, F. Lederer, D. Mihalache, D. M. Baboiu, and M. Ciumac, “Nonlinear hybrid waves guided by birefringent interfaces,” Electron. Lett. 29(13), 1186–1188 (1993). [CrossRef]

23.

S. R. Nelatury, J. A. Polo Jr, and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic material,” Electromagnetics 28(3), 162–174 (2008). [CrossRef]

24.

M. Guillaumée, A. Yu. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010). [CrossRef] [PubMed]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(160.1190) Materials : Anisotropic optical materials
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(240.5440) Optics at surfaces : Polarization-selective devices

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 7, 2011
Revised Manuscript: March 9, 2011
Manuscript Accepted: March 9, 2011
Published: March 18, 2011

Citation
Osamu Takayama, Alexey Yu Nikitin, Luis Martin-Moreno, Lluis Torner, and David Artigas, "Dyakonov surface wave resonant transmission," Opt. Express 19, 6339-6347 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6339


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References

  1. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988).
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]
  4. F. J. García-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]
  5. J. A. Polo and A. Lakhtakia, “Surface electromagnetic waves: a review,” Laser Photonics Rev. 5(2), 234–246 (2011). [CrossRef]
  6. M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP 67, 714–716 (1988).
  7. D. B. Walker, E. N. Glytsis, and T. K. Gaylord, “Surface mode at isotropic-uniaxial and isotropic-biaxial interfaces,” J. Opt. Soc. Am. A 15(1), 248–260 (1998). [CrossRef]
  8. N. S. Averkiev and M. I. D’yakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653–655 (1990).
  9. S. R. Nelatury, J. A. Polo, and A. Lakhtakia, “Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24(3), 856–865 (2007). [CrossRef]
  10. O. Takayama, L. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: a review,” Electromagnetics 28(3), 126–145 (2008). [CrossRef]
  11. A. Yu. Nikitin, D. Artigas, L. Torner, F. J. García-Vidal, and L. Martín-Moreno, “Polarization conversion spectroscopy of hybrid modes,” Opt. Lett. 34(24), 3911–3913 (2009). [CrossRef] [PubMed]
  12. O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102(4), 043903 (2009). [CrossRef] [PubMed]
  13. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Reflection and transmission of plane-waves at the planar interface of a general uniaxial medium and free space,” J. Mod. Opt. 38(4), 649–657 (1991). [CrossRef]
  14. G. D. Landry and T. A. Maldonado, “Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media,” J. Opt. Soc. Am. A 12(9), 2048–2063 (1995). [CrossRef]
  15. I. J. Hodgkinson, S. Kassam, and Q. H. Wu, “Eigenequations and compact algorithms for bulk and layered anisotropic optical media: reflection and refraction at a crystal-crystal interface,” J. Comput. Phys. 133(1), 75–83 (1997). [CrossRef]
  16. S. G. Rodrigo, A. Yu. Nikitin, F. J. García-Vidal, L. Martin-Moreno, O. Takayama, L. Torner and D. Artigas, “Extraordinary optical transmission through a slit array in a biaxial dielectric film” (to be published).
  17. F. Yang and J. R. Sambles, “Critical angles for reflectivity at an isotropic-anisotropic boundary,” J. Mod. Opt. 40(6), 1131–1142 (1993). [CrossRef]
  18. Y. J. Jen, C. Y. Peng, and H. H. Chang, “Optical constant determination of an anisotropic thin film via polarization conversion,” Opt. Express 15(8), 4445–4451 (2007). [CrossRef] [PubMed]
  19. D. Artigas and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett. 94(1), 013901 (2005). [CrossRef] [PubMed]
  20. L. C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30(22), 3075–3077 (2005). [CrossRef] [PubMed]
  21. L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13(10), 2027–2033 (1995). [CrossRef]
  22. L. Tomer, J. P. Torres, F. Lederer, D. Mihalache, D. M. Baboiu, and M. Ciumac, “Nonlinear hybrid waves guided by birefringent interfaces,” Electron. Lett. 29(13), 1186–1188 (1993). [CrossRef]
  23. S. R. Nelatury, J. A. Polo, and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic material,” Electromagnetics 28(3), 162–174 (2008). [CrossRef]
  24. M. Guillaumée, A. Yu. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18(9), 9722–9727 (2010). [CrossRef] [PubMed]

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