Properties Of Photonic Crystal Slabs Research Articles

Cross-polarization mode coupling and exceptional points in photonic crystal slabs

We study exceptional points that occur in photonic crystal slabs due to cross-polarization (TE-TM) mode coupling. To do this, we develop spatiotemporal coupled-mode theory that describes optical properties of photonic crystal slabs supporting TE and TM modes in the case of conical mount. The developed theory suggests that by tuning the in-plane wave numbers of the incident light one can make two modes of the structure coalesce, which results in an exceptional point. The developed theory provides simple analytical expressions for the exceptional point position and the line shape of the corresponding resonance. The parameters of the proposed model can be rigorously estimated by a numerical calculation of the S-matrix poles of the structure. We show that the proposed analytical model with the estimated parameters is in good agreement with the presented full-wave simulations.

ω−kxFano line shape in photonic crystal slabs

We study the resonant properties of photonic crystal slabs theoretically. An $\omega{\rm-}k_x$ Fano line shape that approximates the transmission (reflection) spectrum is obtained. This approximation, being a function of light's frequency and in-plane wave vector, generalizes the conventional Fano line shape. Two particular approximations, parabolic and hyperbolic, are obtained and investigated in detail, taking into account the symmetry of the structure, the reciprocity, and the energy conservation. The parabolic approximation considers a single resonance at normal incidence, while the hyperbolic one takes into account two modes, the symmetric and the antisymmetric. Using rigorous simulations based on the Fourier modal method we show that the hyperbolic line shape provides a better approximation of the transmission spectrum. By deriving the causality conditions for both approximations, we show that only the hyperbolic one provides causality in a relativistic sense.

Plane-wave scattering by a photonic crystal slab: Multipole modal formulation and accuracy

The optical properties of photonic crystal slabs are often simulated with general three-dimensional methods such as finite-difference time-domain. Here we develop a multipole modal method, which is specialized to exploit two symmetries of the photonic crystal slab: the slab's vertically invariant nature allows the field to be expressed in Bloch modes, while the cylindrical inclusions allow the Bloch modes themselves to be expressed in the multipole basis. We find the multipole method to be fast and efficient in finding the Bloch modes, with convergence approaching the numerical accuracy possible. By matching the Bloch modes to plane waves at the top and bottom interfaces of the photonic crystal, the field scattered by the slab is calculated. Values of transmittance and reflectance accurate to 2–3 digits are easily and quickly achieved, whereas 5–6 digits are possible with greater numbers of modes and plane waves in field expansions. Higher accuracy is limited by Gibbs-related phenomena arising from the matching at the interface of necessarily discontinuous Bloch modes to necessarily continuous plane waves. We believe this limit may be present in all modal methods that use Bloch modes to expand the field within the photonic crystal.

Optimized focusing properties of photonic crystal slabs

We propose an optimization procedure for focusing operation in finite two dimensional photonic crystal slabs. The device consists of a triangular lattice air holes etched in a semiconductor matrix at a nanometer scale to operate at 1.55 μm. To reach simultaneously an effective refractive index equal to −1 along with a very high transmission coefficient whatever optical wave incidence, the parameters as the lattice period and/or filling factor are precisely adjusted depending on the slab thickness. The method relies on Fabry–Perot resonances engineering in the air/crystal/air cavity constituting the lens.

Focusing properties of a photonic crystal slab with multiple mechanisms in addition to negative refraction

A brief review of imaging by a photonic crystal (PC) slab with negative refraction is given. The focusing properties of the PC with multiple mechanisms in addition to negative refraction are studied by the finite-difference time-domain method. In addition to the effect of negative refraction, there are multiple mechanisms that are all attributed to the PC focusing properties, including Bragg diffraction, excitation of the surface mode, and self-collimation. The resulting field pattern is the total result of these factors. Bragg diffraction occurs in the high-frequency domain and mainly influences the quality of focusing in the optical axis direction. The excitation of the surface mode improves the resolution of focusing. Self-collimation makes the focusing position deviate from Snell's law.

The imaging properties of photonic crystal slabs with effective negative refraction indexes

The imaging properties of photonic crystals (PCs) with effective negative refraction indexes are studied by the finite-difference time-domain (FDTD) method. The images resulting from a PC are the results of the interaction of multiple mechanisms. The superlens phenomena are restricted within some special conditions, such as low source frequency, excitation of surface mode and little effect of Bragg diffraction.

Optical properties of photonic crystal slabs with an asymmetrical unit cell

Using the unitarity and reciprocity properties of the scattering matrix, we analyse the symmetry and resonant optical properties of the photonic crystal slabs (PCS) with complicated unit cell. We show that the reflectivity is not changed upon the 180deg-rotation of the sample around the normal axis, even in PCS with asymmetrical unit cell. Whereas the transmissivity becomes asymmetrical if the diffraction or absorption are present. The PCS reflectivity peaks to unity near the quasiguided mode resonance for normal light incidence in the absence of diffraction, depolarisation, and absorptive losses. For the oblique incidence the full reflectivity is reached only in symmetrical PCS.

Fundamental optical properties of photonic crystal slabs in the strong coupling regime

We report on the transmission and photoluminescence (PL) properties of semiconductor-imbedded photonic crystal slabs where the photon mode is strongly mixed with the exciton mode. The samples are prepared by incorporating PbI-based inorganic–organic layered perovskites with the large oscillator strength of excitons into periodically arranged square holes on a quartz substrate. In transmission spectra, well-pronounced dips due to the excitation of quasi-guided modes are observed, when a polystyrene layer is overcoated with an appropriate thickness on the substrate. The quasi-guided and exciton modes exhibit an anticrossing with large Rabi splitting of over 100 meV, which demonstrates the formation of polaritons via the strong coupling between these two modes. In PL spectra, we found that the polariton PL is significantly enhanced where the polariton has the largest population. Thus, the optical properties of excitons can be controlled by the electromagnetic periodic boundary condition via strong coupling with a quasi-guided mode in a photonic crystal slab.

Quasiguided modes and optical properties of photonic crystal slabs

We formulate a scattering-matrix-based numerical method to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensionally periodic photonic crystal slab (PCS) of finite thickness. The square symmetry (point group C4v) is taken for the illustration of the method, but it is quite general and works for any point group symmetry for one-dimensional (1D) and 2D PCS’s. We show that the appearance of well-pronounced dips in the transmission spectra of a PCS is due to the interaction with resonant waveguide eigenmodes in the slab. The energy position and width of the dips in transmission provide information on the frequency and inverse radiative lifetime of the quasiguided eigenmodes. We calculate the energies, linewidths, and electromagnetic fields of such quasiguided eigenmodes, and analyze their symmetry and optical activity. The electromagnetic field in such modes is resonantly enhanced, which opens possibilities for use in creating resonant enhancement of different nonlinear effects.