Band-structure determination for finite 3-D photonic crystals

The partial band structure from a finite photonic crystal is determined using a model based on light diffraction and the transfer-matrix formalism. The predictions from such a model are compared to an experimental measurement of the bands in the LU direction of a face centered cubic colloidal crystal. Then, both the theoretical predictions and the experimental measurements are compared with the usual band-structure calculation based on a plane-wave expansion with perfectly periodic boundary conditions. As in measurements performed in the past, discrepancies between the predictions of this later model and the experimentally determined bands are observed. On the contrary, using the model presented based on light propagation through a finite crystal, where no periodicity is imposed in the direction perpendicular to any of the set of planes considered to determine a specific branch of the band structure, we found a very good agreement between the experimentally determined and the predicted bandwidths.     

Photonic band gap properties of GaP opals with a new topology

In this paper, we propose that the “anomalous” optical response exhibited by GaP and InP infiltrated opals is due to the peculiar morphology shown by these materials when grown within the pores. In order to account for their optical response, we propose a new structural model consisting of a network of high dielectric spheres located in the pores of the bare opal, interconnected by cylinders of the same material. A fair agreement between the theoretical predictions using this model and the experimental measurements has been found. We also show that the inverse structure presents very interesting optical properties.     

Photonic band gap effect in one-dimensional plasma dielectric photonic crystals

Propagation of electromagnetic waves in one-dimensional plasma dielectric photonic crystals, the superlattice structure consisting of alternating plasma and dielectric materials, is studied theoretically using transfer matrix method. Numerical calculation is presented for plasma-air finite and infinite periodic structures. The results of photonic band gap characteristics are discussed in terms of plasma density, plasma width, and number of unit cells (N).     

Enlargement of complete two-dimensional band gap by using photonic crystal heterostructure

A two-dimensional photonic crystal heterostructure, which consists of two photonic crystals of a square lattice of circular columns with reverse dielectric configurations, is proposed. Photonic band gap properties are calculated using a plane-wave method and the transmission spectra are obtained. After optimization, the relative width of the complete band gap reached 13.8% based on the simple unit-cell shape and crystal lattice. The photonic crystal heterostructure opens up new ways of engineering photonic band gap materials and designing photonic crystal devices.     

Experimental determination of the band structure of photonic crystals of colloidal silica spheres

A photonic band structure of colloidal crystals of silica spheres is analytically determined by a band model with three fitting parameters: the sphere size, the effective refractive index, and the band-gap. Optical properties of the crystals annealed at various temperatures were characterized by a procedure similar to X-ray diffraction technique, and the width of photonic band-gap measured from the transmission spectra experimentally servers as an additional check on the validation of the model. The photonic band structures defined by the band-gap, the refractive index, and the Brillouin zone are obviously superior to the use of the Bragg's expression involving simple zone folding.     

Optical properties and photonic bands of GaAs photonic crystal waveguides with tilted square lattice

Reflectance measurements at variable angle of incidence are performed on GaAs photonic crystal waveguides with unconventional square lattices. The technique yields the dispersion of photonic bands for the investigated lattices, as first shown by Astratov et al. [Phys. Rev. B 60, R16225 (1999)]. A sample with a square lattice of air rings and small air fraction yields narrow resonant structures and a dispersion of photonic modes close to that of free photons. Another sample with a square lattice of dielectric squares and large air fraction leads to broader structures and to a dispersion of photonic modes which differs strongly for the two polarizations of light: this sample has a pseudo-gap around 1 micron wavelength. The experimental results are in good agreement with theoretical calculations of the reflectance and of the photonic mode dispersion in the photonic crystal slabs. Received 16 January 2002     

Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure

It has recently been predicted that a conical singularity (=Dirac point) in the band structure of a photonic crystal produces an unusual 1/L scaling of the photon flux transmitted through a slab of thickness L. This inverse-linear scaling is unusual, because it is characteristic of radiative transport via diffusion modes through a disordered medium - while here it appears for propagation of Bloch modes in an ideal crystal without any disorder. We present a quantitative numerical test of the predicted scaling, by calculating the scattering of transverse-electric (TE) modes by a two-dimensional triangular lattice of dielectric rods in air. We verify the 1/L scaling and show that the slope differs by less than 10% from the value predicted for maximal coupling of the Bloch modes in the photonic crystal to the plane waves in free space.     

Effective dielectric constant of two-dimensional photonic crystals in optical bands

By using the Fourier expansion method, we have developed an approach to calculate the effective dielectric index of a two-dimensional photonic crystal. The approach is very general: it can take into account various Bravais lattice structure as well as arbitrary spatial variation of the dielectric index. It has been found that near a nondegenerate frequency ω_n(Γ) at Γ point, the transverse magnetic (TM) mode is ordinary, as it is independent of the propagation direction, whereas in general the transverse electric (TE) mode depends on the propagation direction, it is extraordinary. Therefore, a two-dimensional photonic crystal can always be described by an effective dielectric index for TM mode near the nondegenerate frequency ω_n(Γ). However, the TE mode is much more complicated unless the lattice structure is highly symmetric. Moreover, a two-dimensional square photonic crystal has been identified as an effective birefringent crystal having two negative refractive indexes from the perspective of Snell's law.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

A new anti-reflection surface structure for photonic crystal slab lens

An optimized surface modification structure for suppressing the reflections at the surfaces of photonic crystal slab lens is reported in this paper. The total reflection of the slab lens with proposed anti-reflection surface structure is reduced to below 0.3% for the incident angle of light less than 48 degrees. The image efficiency of the slab lens for the normal incident Gaussian beam with waist width equal to the wavelength is near 99%.     

Analysis of photonic band gaps in a two-dimensional photonic crystal with centrifugal core-shell rods

The absolute photonic band gap (PBG) in two-dimensional (2D) photonic crystal with excentric core-shell rods is studied in this paper. The core rod shifts away from the core-shell rod center, and its position is decided by two new introduced parameters — the shift angle θ and the offset ρ. We use the FDTD algorithm to calculate the photonic bands of the photonic crystal, and analyze how the offset and shift angle affect the photonic bang gap of excentric core-shell photonic crystal for different core rod size. It has been shown that the variation of the photonic band gap is quite peculiar.     

Influence of Kerr nonlinearity on the band structures of two-dimensional photonic crystals

Dynamic modifications of the band structures of two-dimensional photonic crystals composed of Kerr-nonlinear dielectric rods in air forming hexagonal, square and honeycomb lattices are investigated. Calculations are carried out by the method based on the finite-difference time-domain (FDTD) technique for both TM and TE polarizations. The bands in all cases are observed to red-shift with the introduction of nonlinearity. Inspection of the variation of the mid-gap frequencies with source intensity reveals that the red-shift increases as gap number increases, in a manner proportional to the mid-gap frequency in linear regime. The red-shift of mid-gap frequencies is also found to follow the adopted saturable model for the change of relative permittivity with source intensity. Either the so-called dielectric or the air band edges of the gaps are found to be more sensitive to nonlinearity resulting in broadening or shrinking of the gaps. Possible utilizations of the present observations for all-optical device applications, such as wavelength multiplexing, are discussed.     

Applications of the expanded basis method to study the behavior of light in a two-dimensional photonic crystal slab

We apply the expanded basis method (EBM) to investigate the behavior of light in a two-dimensional photonic crystal (PC) slab. This method is based on expanded completeness bases, including both the propagation and evanescence modes. We calculate the reflected and transmitted coefficients and the corresponding field distributions in the case of multiple mode transportation. We also show the related phases which exhibit oscillations with the frequency of the incident light.     

Holographic design of hexagonal photonic crystals of irregular columns with large full band gap

The shape and size of the dielectric columns or particles (“atoms”) of photonic crystals (PhCs) formed by holographic lithography are determined by the isointensity surfaces of the interference field; consequently the PhCs’ photonic band gap (PBG) properties are closely related to their fabrication design. Here we have proposed a new structure of two-dimensional (2-D) hexagonal lattice with irregular columns, which can yield a 2-D complete relative band gap of 24.0% in case of the dielectric columns of ε = 13.6 in air, about 27% increase compared with that of the same lattice with regular triangular columns. This band gap size is among the largest for all the possible 2-D PhCs reported until now. The relationship between band gap properties of resultant structure and the specific fabrication conditions such as structure design and the choice of optimum intensity threshold and filling ratio are systematically discussed. The optical design for making this structure by two exposures is explained. This work may demonstrate the unique feature and advantages of photonic crystals made by holographic method and provide a guideline for their design and experimental fabrication.     

The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals

The photonic band structures of two-dimensional (2D) photonic crystals with etched interfacial layers between air rods and the background dielectric is studied theoretically. The effect of etching interfacial layers on absolute photonic band gap (PBG) is analyzed quantitatively. Numerical calculations are carried out based on Maxwell's equations and the plane-wave expansion method. It is shown that the physical property of interfacial layers influence the absolute PBG, and the existence of interfacial layers cannot enlarge the largest absolute PBG of an ideal case without interfacial layers.     

Angular tuning of defect modes spectrum in the one-dimensional photonic crystal with liquid-crystal layer

A one-dimensional ZrO₂/SiO₂ photonic crystal with a 4-n -pentyl-4' -cyanobiphenyl (5CB) nematic defect layer was used to investigate the transmission spectra of light polarized parallel and perpendicular to the liquid-crystal director at different angles of incidence. The spectra of the photonic crystal were shown to split into four polarized components T_ij at oblique incidence. When the incident angle increased, the bandgap edges and the defect modes shifted towards short wavelengths, while the amplitudes of the defect modes increased for the transverse magnetic polarization and decreased for the transverse electric polarization. The observed discrepancy between the defect mode amplitudes in the center and near the edges of the photonic bandgap was found to be related to the radiation losses inside the defect layer of a non-ideal photonic crystal. The simulated transmission spectra obtained using recurrence relations and taking into account the decay of defect modes are in good agreement with the experimental data.     

Study on composite photonic crystal patch antenna

The paper investigated a composite photonic crystal patch antenna by using the method of finite difference time domain (FDTD). The results show that there exists a wave resonance state at 2.635 GHz, where the real part of the permittivity and permeability are all negative; its refraction index is –1. The effect has largely enhanced the electromagnetic wave’s resonance intensity, and has improved the localized extent of electromagnetic energy obviously in such photonic crystal structure (PBG), resulting in a higher antenna gain, a lower return loss, and a better improvement of the antenna’s characteristics. Due to such the advantages, the use of patch antennas can be extended to such fields as mobile communication, satellite communication, aviation, etc.     

Quantitative analysis of subdiffractive light propagation in photonic crystals

We present a qualitative study of the subdiffractive light beam propagation in photonic crystals, based on the theoretical analysis of full Maxwell equation system beyond the slowly varying envelope and paraxial approximations. We calculate the zero diffraction curve in the parameter space, we calculate the weak asymptotical broadening (spreading in transverse direction), and we also analyze the dependence of subdiffractive propagation on the polarization orientation (both for TM and TE polarization).     

Bose-Einstein condensates in optical lattices: Spontaneous emission in the presence of photonic band gaps

An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of 10¹⁴ cm^-3. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics. Received 27 March 2000     

Roughness losses and volume-current methods in photonic-crystal waveguides

We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green’s functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.