Tamm Waves Research Articles

Multiple compound Tamm waves with Uller–Zenneck wave characteristics guided by dissipative dielectric defect in periodic multilayered isotropic dielectric material

A canonical problem configured in three different arrangements of periodic multilayered isotropic dielectric material layers with a dissipative dielectric defect, to guide multiple compound Tamm waves with Uller–Zenneck wave characteristics, was formulated and solved. The numerical solutions showed multiple Tamm waves guided at a fixed wavelength along the dissipative defect with same polarization state. These waves propagate with different phase speeds, different propagation distances, different field localizations, and different field profiles. The results identified excitation of symmetric and anti-symmetric solutions of p-polarized Tamm waves and p- and s-polarized waveguide modes. The high phase speed solutions ceased to exist beyond a certain limit of dissipative dielectric defect thickness, but the low phase speed solutions were computed for a wide range of dissipative dielectric defect thickness. The Tamm waves were compounded when the thickness of defect is very small and transmuted into waveguide modes for increasing thickness of dissipative dielectric defect because most of the energy is then strongly confined to the dissipative dielectric defect. The excitation of multiple Tamm waves and waveguide modes at a given dissipative dielectric defect thickness and fixed wavelength can be considered for multi-channel optical communication and sensing applications.

Effect of chemical potential on Dyakonov–Tamm waves guided by a graphene-coated structurally chiral medium

We numerically investigated the effect of chemical potential on Dyakonov–Tamm waves (DTWs) guided by a graphene-coated structurally chiral medium in the terahertz and the visible spectral regimes. Only one DTW can propagate in a specific direction in wide angular sectors, but multiple DTWs can propagate in a specific direction in narrow angular sectors, in both spectral regimes. Although the phase speed of a DTW depends weakly on the chemical potential in both spectral regimes, the propagation distance can be strongly dependent on the chemical potential in the terahertz regime but not in the visible regime. This difference can be attributed to the real part of the surface conductivity of graphene, which varies significantly with the chemical potential in the terahertz regime but not in the visible regime.

Dyakonov–Tamm waves guided by the planar surface of a chiral sculptured thin film: erratum

Dyakonov–Tamm waves guided by the planar surface of a chiral sculptured thin film: erratum

Analysis of Bloch Surface Waves at the Interface Between Two Semi-infinite Rugate Filters with Symmetric Refractive Index Profiles

Surface electromagnetic waves are representation of Maxwell’s frequency domain equations at the interface of two dissimilar materials. In this article, two canonical boundary value problems have been formulated to analyze the multiplicity of electromagnetic surface waves at the interface between two dissimilar materials. In the first problem, interface between two semi-infinite rugate filters having symmetric refractive index profiles is considered and in the second problem, to enhance the multiplicity of surface electromagnetic waves, a homogeneous dielectric slab is included between two semi-infinite symmetric rugate filters. Multiplicity has been observed by varying the size of dielectric material from 0 to 1000 nm. Numerical results show that the number of Tamm waves of different phase speeds, different polarization states, different degrees of localization, and different field profiles that are being propagated at interface between two semi-infinite rugate filters having symmetric refractive profile is almost twice as when asymmetric refractive index profile is used. Having two interfaces when a homogeneous dielectric layer is placed between two semi-infinite rugate filters has increased the multiplicity of electromagnetic surface waves.

Signatures of thermal hysteresis in Tamm-wave propagation

We numerically solved the boundary-value problem for Tamm waves (which may also be classified as Uller-Zenneck waves here) guided by the planar interface of a homogeneous isotropic dissipative dielectric (HIDD) material and a periodically multilayered isotropic dielectric material. The HIDD material was chosen to be VO${}_2$ which, at optical wavelengths, has a temperature-dependent refractive index with a hysteresis feature, i.e., the temperature-dependence of its refractive index varies depending upon whether the temperature is increasing or decreasing. A numerical code was implemented to extract solutions of the dispersion equation at a fixed wavelength for both $p$- and $s$-polarization states over the temperature range [50,80] degrees. A multitude of Tamm waves of both linear polarization states were found, demonstrating a clear demarcation of the heating and cooling phases in terms of wavenumbers and propagation distances. Thereby, the signatures of thermal hysteresis in Tamm-wave propagation were revealed.

Tamm-Langmuir surface waves

In this work we develop a theory of surface electromagnetic waves localized at the interface of periodic metal-dielectric structures. We have shown that the anisotropy of plasma frequency in metal layers lifts the degeneracy of plasma oscillations and opens a series of photonic band gaps. This results in appearance of surface waves with singular density of states - we refer to them as Tamm-Langmuir waves. Such naming is natural since we have found that their properties are very similar to the properties of both bulk Langmuir and surface Tamm waves. Depending on the anisotropy parameters, Tamm-Langmuir waves can be either forward or backward waves. Singular density of states and high sensitivity of the dispersion to the anisotropy of the structure makes Tamm-Langmuir waves very promising for potential applications in nanophotonics and biosensing.

Left/right asymmetry in Dyakonov–Tamm-wave propagation guided by a topological insulator and a structurally chiral material

The propagation of Dyakonov–Tamm waves guided by the planar interface of an isotropic topological insulator and a structurally chiral material, both assumed to be nonmagnetic, was investigated by numerically solving the associated canonical boundary-value problem. The topologically insulating surface states of the topological insulator were quantitated via a surface admittance , which significantly affects the phase speeds and the spatial profiles of the Dyakonov–Tamm waves. Most significantly, it is possible that a Dyakonov–Tamm wave propagates co-parallel to a vector in the interface plane, but no Dyakonov–Tamm wave propagates anti-parallel to . The left/right asymmetry, which vanishes for , is highly attractive for one-way on-chip optical communication.

Compound guided waves that mix characteristics of surface-plasmon-polariton, Tamm, Dyakonov–Tamm, and Uller–Zenneck waves

Solutions of the boundary-value problem for electromagnetic waves guided by a layer of a homogeneous and isotropic (metal or dielectric) material sandwiched between a structurally chiral material (SCM) and a periodically multi-layered isotropic dielectric (PMLID) material were numerically obtained and analyzed. If the sandwiched layer is sufficiently thick, the two bimaterial interfaces decouple from each other, and each interface may guide one or more electromagnetic surface waves (ESWs) by itself. Depending on the constitution of the two materials that partner to form an interface, the ESWs can be classified as surface-plasmon-polarition (SPP) waves, Tamm waves, Dyakonov-Tamm waves, or Uller-Zenneck waves. When the sandwiched layer is sufficiently thin, the ESWs for single bimaterial interfaces coalesce to form compound guided waves (CGWs). The phase speeds, propagation distances, and spatial profiles of the electromagnetic fields of CGWs are different from those of the ESWs. The energy of a CGW is distributed in both the SCM and the PMLID material, if the sandwiched layer is sufficiently thin. Some CGWs require the sandwiched layer to have a minimum thickness. Indeed, the coupling between the two faces of the sandwiched layer is affected by the ratio of the thickness of the sandwiched layer to the skin depth in that material and the rates at which the fields of the ESWs guided individually by the two interfaces decay away from their respective guiding interfaces.

Dyakonov–Tamm waves guided by the planar interface of a rugate filter and a columnar thin film

Dyakonov–Tamm waves guided by a planar interface of an anisotropic, homogeneous dielectric material, and an isotropic, periodically nonhomogeneous dielectric material was investigated in a canonical boundary-value problem. The former material was taken to be a columnar thin film (CTF) and the latter was a rugate filter. Dyakonov–Tamm waves are surface electromagnetic waves that have negligible propagation losses. In the chosen setup, multiple Dyakonov–Tamm waves of different phase speeds, degrees of localization, and spatial field profiles, but of the same frequency were found to exist. The effect of direction of propagation with respect to the morphologically significant plane of the CTF, the phase and the amplitude of modulation of the rugate filter was investigated. The number of Dyakonov–Tamm waves depends on the direction of propagation with respect to the morphologically significant plane of the CTF. The relative wavenumber and the degree of localization of the Dyakonov–Tamm waves increase with an increase in the amplitude of modulation of the rugate filter.

Composite surface-plasmon-polariton waves guided by a thin metal layer sandwiched between a homogeneous isotropic dielectric material and a periodically multilayered isotropic dielectric material

Multiple p- and s-polarized compound surface plasmon-polariton (SPP) waves at a fixed frequency can be guided by a structure consisting of a metal layer sandwiched between a homogeneous isotropic dielectric (HID) material and a periodic multilayered isotropic dielectric (PMLID) material. For any thickness of the metal layer, at least one compound SPP wave must exist. It possesses the p-polarization state, is strongly bound to the metal/HID interface when the metal thickness is large but to both metal/dielectric interfaces when the metal thickness is small. When the metal layer vanishes, this compound SPP wave transmutes into a Tamm wave. Additional compound SPP waves exist, depending on the thickness of the metal layer, the relative permittivity of the HID material, and the period and the composition of the PMLID material. Some of these are p polarized, the others being s polarized. All of them differ in phase speed, attenuation rate, and field profile, even though all are excitable at the same frequency. The multiplicity and the dependence of the number of compound SPP waves on the relative permittivity of the HID material when the metal layer is thin could be useful for optical sensing applications.

Dyakonov–Tamm waves-based optical sensing using sculptured nematic thin film

Dyakonov–Tamm (DT) waves are highly sensitive to the constitutive properties of the partnering materials near the interface. DT waves are excited at the interface of two dielectric materials of which at least one is anisotropic and periodically nonhomogeneous normal to their interface. Sculptured nematic thin film (SNTF) is a good candidate for the periodically nonhomogeneous dielectric partner for optical sensing of a fluid due to its porosity. The nanoscale parameters of an uninfiltrated SNTF obtained from the inverse Bruggeman homogenization formalism were used in the forward Bruggeman homogenization formalism to determine the constitutive parameters for the infiltrated SNTF. The sensitivity of DT waves to the refractive index was analyzed for two possible sensing modalities and it was found that the sensitivity was comparable to that of the chiral sculptured thin films (STFs) made of the same material as of the SNTF. This implies that the sensing with DT waves is robust, is independent of the morphology of the partnering nonhomogeneous dielectric material and could make the sensing easier since SNTFs are easier to fabricate than the chiral STFs.

An optical-sensing modality that exploits Dyakonov–Tamm waves

Surface-wave-based optical sensing of an analyte in a fluid relies on the sensitivity of the surface wave to the electromagnetic properties of the analyte-containing fluid in the vicinity of the guiding interface. Surface-plasmon-polariton (SPP) waves are most commonly used for optical sensing because of the ease of the excitation of an SPP wave when the fluid is partnered with a metal. If the fluid is replaced by a porous, anisotropic, and periodically nonhomogeneous solid filled with the fluid, while the metal is replaced by an isotropic homogeneous dielectric material, the surface wave is called a Dyakonov–Tamm (DT) wave. We have theoretically determined that the incorporation of the DT-waveguiding interface in a prism-coupled configuration provides an alternative to the analogous SPP wave-based sensor, with comparable dynamic sensitivity.

Theory of optical sensing with Dyakonov–Tamm waves

An optical modality to sense a fluid by exploiting Dyakonov–Tamm (DT) waves was devised. In the modality, the fluid is present on both sides of the guiding interface. Theoretical analysis indicated that the angular location of the reflectance dip in a practically implementable configuration will shift if the refractive index of the fluid changes. Furthermore, the detection sensitivity will decrease as the refractive index of the fluid increases over a wide range, and should be comparable to that for sensing modalities that exploit surface-plasmon-polariton (SPP) waves. Higher sensitivities are available with DT waves than with SPP waves, and the DT-wave-based sensor should be simpler to fabricate than the SPP-wave-based sensor. Multiple DT waves are excitable at the same frequency, leading to multiple channels for more reliable sensing as well as for sensing multiple analytes simultaneously.

Evolution of surface-plasmon-polariton and Dyakonov–Tamm waves with the ambichirality of a partnering dielectric material

The planar interface of an isotropic homogeneous metal and an ambichiral dielectric material can guide surface-plasmon-polariton waves. The planar interface of an isotropic, homogeneous dielectric material and an ambichiral dielectric material can guide Dyakonov-Tamm waves. In either instance, we found that, as the ambichiral partnering material evolves into a finely chiral material, the solutions of the dispersion equation for surface-wave propagation evince convergence. The convergence is faster for the surface waves with larger phase speeds than for the surface waves with smaller phase speeds.

Coupled Tamm waves guided by an isotropic and homogeneous dielectric layer in a rugate filter

The propagation of Tamm waves (also known as Bloch surface waves) guided by a layer of homogeneous dielectric material in a rugate filter was studied theoretically. A canonical boundary-value problem was set up and a dispersion equation was obtained. The solution of the dispersion equation indicated the existence of coupled modes of Tamm waves that were absent when the homogeneous dielectric material was taken to occupy a half space. The spatial profiles of the electric and magnetic fields of Tamm waves showed that Tamm waves propagate localized to either one or both interfaces. Multiple Tamm waves may lead to multi-analyte chemical sensors and multi-channel communication.

Experimental excitation of the Dyakonov–Tamm wave in the grating-coupled configuration

The Dyakonov-Tamm wave was experimentally excited along the periodically corrugated interface of magnesium fluoride as the isotropic homogeneous partnering material and a zinc-selenide chiral sculptured thin film (STF) as the anisotropic and periodically nonhomogeneous partnering material. The total transmittance of a p-polarized 633 nm laser beam was measured as a function of the angle of incidence for several thicknesses of the chiral STF to identify those dips in total transmittance that are indicative of the excitation of a Dyakonov-Tamm wave.

Dyakonov–Tamm waves guided by the planar surface of a chiral sculptured thin film

Propagation of Dyakonov–Tamm waves guided by the interface of air and a chiral sculptured thin film (STF) was investigated theoretically. The solution of the dispersion equation showed that the direction of propagation is either unrestricted or almost unrestricted in the interface plane. For very limited ranges of the direction of propagation, multiple Dyakonov–Tamm waves may even exist. These surface waves were theoretically found to be excitable in the Otto prism-coupled configuration by an incident plane wave of either linear polarization state, thereby lending hope for an easy way to observe Dyakonov–Tamm waves experimentally.

Parametric investigation of prism-coupled excitation of Dyakonov–Tamm waves

In order to pave the way for the yet-to-be reported experimental observation of the Dyakonov–Tamm wave, the excitation of this surface wave in a prism-coupled configuration was theoretically investigated when one partnering dielectric material is isotropic and homogeneous while the other is a chiral sculptured thin film (CSTF). The excitation of a Dyakonov–Tamm wave in the prism-coupled configuration was identified by those peaks in the plots of the absorptance versus the angle of incidence that were independent of the thicknesses of both partnering materials (beyond some thresholds) and the polarization state of the incident plane wave. The results of the prism-coupled configuration were successfully correlated with the underlying canonical boundary-value problem. An increase in either the structural period or the average vapor flux angle of the CSTF results in a larger angle of incidence for experimental excitation, whereas an increase in an offset angle results in a decrease of that angle. An increase in the bulk refractive index of the material from which the CSTF is fabricated is likely to increase the angle of incidence for experimental observation. It is highly preferable for the CSTF to be an integral number of periods in thickness, and that number does not have to be large.

Prism-coupled excitation of multiple Tamm waves

A Tamm wave is guided by the interface of a homogeneous dielectric material and a periodically nonhomogeneous dielectric material, both isotropic. We found theoretically that multiple Tamm waves of different linear polarization states can be guided by such an interface incorporated in a prism-coupled configuration. The Tamm waves have different linear polarization states, phase speeds, and spatial profiles, but the same frequency. The narrow absorptance peaks associated with the excitation of Tamm waves in the prism-coupled configuration offer the application as chemical sensors with very high sensitivity.

Prism-coupled excitation of Dyakonov–Tamm waves

The prism-coupled excitation of Dyakonov–Tamm waves guided by the planar interface of a homogeneous, isotropic dielectric material and a periodically nonhomogeneous sculptured nematic thin film (SNTF) was investigated. The excitation of Dyakonov–Tamm waves was identified by correlating a high-absorptance band in the plots of absorptance vs. the incidence angle and the direction of propagation in the interface plane with the solutions of the underlying canonical boundary–value problem. Dyakonov–Tamm waves were found to have a much wider angular existence domain than Dyakonov waves, and broader absorptance peaks than both the Dyakonov and Tamm waves in the plots of absorptance vs. the incidence angle.