Finite One-dimensional Photonic Crystal Research Articles

Novel biosensors based on Weyl semimetals

We introduce two novel optical biosensors based on the combination of a Weyl semimetal and a finite one-dimensional photonic crystal to diagnose different analytes such as Jurkat cancer cells. Weyl semimetals are new emerging topological materials recently purposed for employment in optical devices due to their intriguing properties. We demonstrate that hybrid Tamm and surface plasmon polaritons can be excited in these structures under the circumstance of attenuated total reflection. In particular, we find that adjusting parameters of the first biosensor to excite Tamm plasmon polaritons leads to higher sensing performance, while in the second biosensor excitation of the surface plasmon polaritons provides higher functionality of this biosensor. According to our results, biosensors based on the Weyl semimetals can be used for sensitive and accurate recognition of different analytes, and they may form a new platform for high-performance biosensors.

Energy flux optimization in 1D multiperiodic four-component photonic crystals

The results of theoretical and numerical studies of finite one-dimensional (1D) three-periodic photonic crystals of the structure [(ab)3(cd)3]3, consisting of four different materials (dielectric oxides Al2O3, SiO 2, TiO 2, and ZrO 2) are presented. We study the transmittivity spectra and partial energy fluxes of the TE- and TM-modes in the range of 1–5 μm in the vicinity of the first photonic bandgap depending on the incidence angle and frequency of light. The obtained results can be used to create precise polarization-sensitive devices for an input–output of the radiation into an optical fiber. The optimization of the considered multiperiodic structures has been achieved at the telecommunication wavelength 1.55 μm both by changing incidence angle and adjusting the topology (i.e. thicknesses of the constituent layers). We discuss a principle of a new type of polarization splitter on the basis of three-periodic photonic crystal.

Nonspecular Effects That Occur as a Quasi-Plane Wave Passes through a Finite Photonic Crystal with an Asymmetric Polariton Spectrum

First-order nonspecular effects emerge in the plane of layers for both reflected and transmitted waves (particularly the spatial and angular Goos–Hanchen effect) for a quasi-plane of the TM (or TE) type normally incident from outside on a finite one-dimensional magnetic photonic crystal with a spectrum of normal magnetic polaritons, asymmetrical with respect to the inversion of the direction of wave propagation.

Electromagnetic density of modes in one-dimensional photonic crystals containing dispersive metamaterials

The electromagnetic density of modes (DOM) in a finite one-dimensional photonic crystal containing dispersive metamaterials is computed using Wigner’s time approach. The expression of DOM is derived using the transfer matrix method. Different structural parameters, such as relative thickness, incident angle, and total number of unit cells are varied and their effects are investigated. It is observed that relative thickness, angle of incidence, and total number of unit cells all play an important role in determining the properties of DOM depending on the frequency regime under consideration.

Peculiarities of electromagnetic field distribution in a finite one-dimensional photonic crystal at oblique incidence of radiation

The effect of increasing an electric field E is investigated for oblique incidence of radiation on a finite one-dimensional photonic crystal. The peculiarities in the field distribution in the structure E(x) are found to be due to the interference of counterpropagating Bloch waves; therefore, the conditions for increasing the field to a maximum value |E|max coincide with those for achieving the maximum band gap Eg of an infinite crystal. It is shown that a significant (several times for structures with 30 periods) growth of |E|max is observed with increasing angle of incidence θ for wavelengths λ, which correspond to transmission maxima T nearest to the band gap boundaries. The increased interference of the counterpropagating Bloch modes is caused by an enhancement of the x-component contrast (perpendicular to the planes of the layers) of the wave numbers k1x/k2x in the structure layers. Along with this, there also arise characteristic features in the distribution of E(x) associated with the vanishing of the forbidden band width. In this case, the field distribution in all periods is the same. Two types of such features are observed in the case of oblique incidence. The former takes place for p-polarisation at an angle of incidence θ, which is an analogue of the Brewster angle. The latter corresponds to the situation when the length of each structure layer is equal to an integer of half-waves. This occurs simultaneously for s- and p-polarisations and is observed in a limited range of layer widths only for the second and highest forbidden bands.

Electromagnetic-field amplification in finite one-dimensional photonic crystals

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.

Phase retarder based on one-dimensional photonic crystals composed of plasma and mu-negative materials

By using transfer matrix method, a systematic study on the properties of the reflection phase shifts and the reflection phase difference between TE and TM waves in a finite one-dimensional (1D) photonic crystal containing plasma and mu-negative materials is presented. It is found that the reflection phase difference between the two polarizations remains constant in a rather wide frequency range for a given incident angle. More specifically, the reflection phase difference increases gradually from 0 to π rad with the increase of the incident angle. That is to say, the finite 1D structure can serve as a broadband phase retarder. It is also evident that the working frequency range of the phase retarder can be adjusted by altering the plasma frequency and the thickness of the plasma layers without changing the structure of the photonic crystal.

Local density of optical states in the band gap of a finite one-dimensional photonic crystal

We study the local density of states (LDOS) in a finite photonic crystal, in particular in the frequency range of the band gap. We propose an original point of view on the band gap, which we consider to be the result of vacuum fluctuations in free space that tunnel in the forbidden range in the crystal. As a result, we arrive at a model for the LDOS that is in two major items modified compared to the well-known expression for infinite crystals. First, we modify the Dirac $\ensuremath{\delta}$ functions to become Lorentzian with a width set by the crystal size. Second, building on characterization of the fields versus frequency and position we calculated the fields in the band gap. We start from the fields at the band edges, interpolated in space and position, and incorporating the exponential damping in the band gap. We compare our proposed model to exact calculations in one dimension using the transfer matrix method and find very good agreement. Notably, we find that in finite crystals, the LDOS inside the band gap depends on frequency, on position, and on crystal size, in contrast to the well-known results for infinite crystals where the LDOS is zero, independent of frequency and position.

Modification of the radiation of a luminescent dye embedded in a finite one-dimensional photonic crystal

A numerical modeling of the radiation emitted from a Luminescent dye embedded in a finite one-dimensional photonic crystal is presented. The Photonic Band Structure and the Photonic Density of States are derived using classical electromagnetic approach, and the Finite Difference Time-Domain formalism is used to calculate the electromagnetic field distribution. It is found that the periodic modulation provides an effective way to control the Spontaneous Emission under certain circumstances. We find the conditions where a large amount of light can be enhanced on the vicinity of a photonic band edge due to the presence of a high density of states. This phenomena opens the possibility to design new Lasers sources.

Properties of the dispersion relation in finite one-dimensional photonic crystals

Using the transfer-matrix method we have expressed the dispersion relation of a finite, N-period, one-dimensional photonic crystal in terms of a frequency dependent function g(ω) determining important features of the band structure. We have then investigated the similarities and differences between the dispersion relation of a N-period crystal and that of an infinite one for finite and large values of the number N of unit cells. It is shown that in the frequency range where the infinite crystal has a bandgap, the dispersion relation of the finite crystal exhibits a bandgap of zero width for any value of N. The frequency ωC at which the null gap occurs corresponds to a zero of g(ω) and is independent of N. Around ωC and for sufficiently large values of N, the group velocity attains superluminal values. These results are general enough and were used to investigate the effects of finite crystal size on the properties of the zero-n− gap in photonic crystals consisting of alternating layers of right- and left-handed materials. In this case, the frequency at which the null gap occurs is insensitive to geometrical scaling of the structure.

Calculation of atomic spontaneous emission rate in 1D finite photonic crystal with defects

Abstract We derive an expression for the spontaneous-emission rate in finite one-dimensional photonic crystals with arbitrary defects, using the effective resonator model to describe electromagnetic field distributions in the structure. We obtain explicit formulae for contributions from different modes, i.e. radiation, substrate and guided modes. Formal calculations are illustrated by a few numerical examples, which demonstrate that application of the effective resonator model simplifies the interpretation of results.

Modeling of the propagation of single photons in finite one-dimensional photonic crystals

A model of the propagation of a quantized electromagnetic field in a one-dimensional photonic crystal that contains two-level atoms that interact with the field is proposed. The model separately considers the interaction of the quantized radiation with the quantum system and with the photonic crystal. The use of the model is exemplified by its application to the study of the decay of excited states of one- and two-level atoms placed in the photonic crystal. The possibility of the transformation of the front of a single photon by a finite dielectric is demonstrated.

Optic Tamm states: The Bloch-wave-expansion method

Optic Tamm states (OTSs) in one-dimensional photonic crystal (PhC) heterostructures are studied via a Bloch-wave-expansion method (BWEM). We show that by considering both the periodicity and the finiteness, the propagation of electromagnetic wave in a finite one-dimensional PhC can be characterized by three parameters---two Bloch impedances and the Bloch-wave vector---in the framework of the BWEM. Applying the BWEM, we give a criterion of optic Tamm states at the interfaces inside finite heterostructures. It is demonstrated that the criterion is applicable for the OTSs at the interface inside both finite PhC-PhC heterostructures and PhC-metal heterostructures. In addition, we also discuss the importance of the number and the element order of the unit cells in the occurrence of optic Tamm states.

Coupled optical defect microcavities in one-dimensional photonic crystals and quasi-normal modes

We analyze coupled optical defect cavities realized in finite one-dimensional photonic crystals (PC). Viewing these as open systems, where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and quasi-normal modes (QNM) (eigenfunctions). Single-defect structures (PC atoms) can be viewed as elementary building blocks for multiple-defect structures (PC molecules) with more complex functionality. The QNM description links the resonant behavior of individual PC atoms to the properties of the PC molecules via eigenfrequency splitting. A variational principle for QNMs permits one to predict the eigenfield and the complex eigenvalues in PC molecules, starting with a field template incorporating the relevant QNMs of the PC atoms. Furthermore both the field representation and the resonant spectral transmission close to these resonances are obtained from a variational formulation of the transmittance problem using a template with the most relevant QNMs. The method applies to both symmetric and nonsymmetric single and multiple-cavity structures with weak or strong coupling between the defects.

Maximum-Exponent Scaling Behavior of Optical Second-Harmonic Generation in Finite Multilayer Photonic Crystals

Scaling laws of second-harmonic generation (SHG) in nonlinear Bragg stacks (or finite one-dimensional photonic crystals) as a function of the number N of periods are explored. While it is known that SHG scales like the sixth power of N when phase matching is achieved, we find maximal scaling like the eighth power of N under appropriate non-phase-matching conditions with the pump and harmonic waves being resonant with band-edge states. In this framework we introduce the concept of self-adaptive coherence length that scales with the system length. An analytical treatment based on coupled-mode equations clarifies the conditions for obtaining different scaling laws as a function of filling factor in the photonic gap map.

Surface wave effect on light scattering from one-dimensional photonic crystals

Light scattering and reflection measurements using attenuated total reflection technique for s polarization of the incident light on a finite one-dimensional photonic crystal are reported. Angular specular reflection was measured experimentally to determine, the optimum thickness, the angular position of the surface mode, and the number of bi-layers of the system. It was demonstrated that the position of the surface mode inside the last film is close to the asymptotic value when the number of periods is increased. Spectral reflection measurements were made to determine experimentally the band gap width and measure the dispersion relation of the surface mode inside this band. The corresponding field amplitude was calculated (∣E∣ 2) showing that in resonant conditions it has a maximum near the surface. The angular dependence of the scattered light measured displays a peak caused by singles cattering and located approximately at the excitation angle of the surface electromagnetic mode. When the incident light is in resonance with the surface electromagnetic wave, it is found experimentally that the scattering of light is enhanced overall by approximately one order of magnitude in comparison with the off-resonance case.

Frequency bands of negative refraction in finite one-dimensional photonic crystals

We have discussed theoretically the negative refraction in finite one-dimensional (1D) photonic crystals (PCs) composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs, which is analysed in detail.

Single-Frequency Refractive Index Sensor Based on a Finite One-Dimensional Photonic Crystals with Two Defects

A numerical analysis by means of transfer matrix method has been performed on finite one-dimensional photonic crystals consisting of two-layer repeated cells and two non-identical defect cells for the normal incident transverse electric (TE) wave. The study reveals a remarkable new feature showing that the variation of a photonic pass-band transmittance can be induced by varying the refractive index of one of the defect layer at practically the same peak frequency, which offers the potential application for single frequency sensing. The result further demonstrates the flexibility of tailoring the system parameters for application in the desired range of refractive index at the required sensitivity. It is also shown that the photonic pass-band (PPB) peak transmittance is generally less than unity in the index range considered, except for the case with the grating segment lengths (M,N,L) satisfying the condition N=M+L. This peculiar feature is explained qualitatively in this work.

Optical band gaps as a result of destructive superposition of scattered waves

Light transmission through a finite one-dimensional photonic crystal is formulated using the theory of multiple scattering. It is shown that optical band gaps of the crystal are created by destructive superposition of waves multiply scattered from the dielectric slabs that constitute the crystal. The effects of the number of slabs and the lattice constant on the band gaps are also studied.

Modified phase matching conditions for second harmonic generation in a finite one-dimensional photonic crystal near the bragg condition: Weak and strong diffraction

Enhanced noncollinear second harmonic generation in a finite one-dimensional photonic crystal is analyzed theoretically under conditions of pump field localization near the Bragg reflection. It is shown numerically that phase-matched second-harmonic generation can be implemented in a finite one-dimensional photonic crystal that does not satisfy the conventional phase-matching conditions calculated for effective Bloch modes with narrow spectral lines. The intensity of the generated second-harmonic signal exceeds the second-harmonic intensity attained under the conventional phase-matching conditions by more than an order of magnitude. This phenomenon is explained by interference between Bloch modes having similar amplitudes, wavenumbers, and spectral widths. Since the spatial spectra of waves propagating in a bounded medium have finite widths, the broadened spectral lines of proximate effective Bloch modes resulting from Bragg diffraction of waves tuned to the first transmission resonances near the photonic bandgap edge overlap, merging into a spectral profile with center shifted relative to the original effective Bloch wavevectors. This effect leads to modified phase matching conditions for second harmonic generation in a finite photonic crystal, which are written for the centers of the spectral profiles resulting from modal overlap, rather than for individual effective wavevectors. Substantially different phase matching conditions are obtained for weakly and strongly diffracted beams, whereas conventional phase matching conditions hold only for transmitted signals in the case of weak diffraction.