Decay distribution of spontaneous emission from atoms in one-dimensional photonic crystal

Spontaneous emission behavior from atoms (or molecules) in one-dimensional photonic crystal with a defect is investigated. Taken all the TE and TM modes into account, the normalized spontaneous emission rate of the atom is calculated as a function of the position of the atom in the crystal. Results for both nonabsorbing dielectric structure and absorbing dielectric structure are presented. With the increase of the thickness of the defect in which the atoms are embedded, the oscillations of the spontaneous emission rate versus the position of the atom become dense and the lifetime distribution becomes narrow and sharp. The PC effect may lead to the coexistence of both accelerated and inhibited decay processes.     

Synthesis and photonic band gap characterization of high quality photonic crystal heterostructures

High quality photonic crystal heterostructures with a thin titania planar defect layer between its two constitutional photonic crystals were fabricated and their structural and optical properties were analyzed. The results suggest that the thin planar defect layer is beneficial to separate the two constitutional photonic crystals from each other and to reduce the roughness of the interface. The quality of the resulting photonic crystal heterostructures is improved largely and the main features of the photonic band gaps of the two constitutional photonic crystals are inherited. The predominant optical quality of these heterostructures (e.g. deep double photonic band gaps and steep photonic band edges) may afford new flexibility and functionality for engineered photonic behavior in practical devices such as late-model light-operated switches.     

Light propagation in photonic crystal with gain: Applicability of the negative loss approximation

The applicability of the concept of permittivity with Im ?_gain < 0 to describe the light propagation in a metamaterial system with gain is discussed using the example of a 1D photonic crystal containing gain layers. It is shown that this approach is in agreement with the principle of causality, unless lasing is present. Though the lasing process itself requires nonlinear analysis, the lasing threshold can be determined by linear (negative loss) approximation. Connecting the onset of lasing with the passage of the transfer function pole into the upper half-plane of the complex frequency, we show that (i) if the pump frequency lies in a pass band then an increase in the number N of elementary cells will sooner or later lead to lasing; (ii) if the frequency of the pump lies in the band gap, then lasing at band gap frequencies may occur in a sample with a low N before the band gap has been formed. Nevertheless, lasing will be necessarily suppressed by a further increase in N. In any case, for sufficiently large number of layers due to a finite line width of ?_gain(ω), lasing appears in the pass band even if the pump frequency is in the band gap.     

Fine structural adjustment of lasing wavelengths in photonic crystal waveguide laser arrays

We propose new and simple designs that allow one to adjust the relative frequency of photonic crystal waveguide lasers included in a laser array. Using numerical simulations, we demonstrate that wavelength shifts smaller than 2 nm can be achieved while remaining compatible with common lithographic precision. Specific details of the implemented methods allow to deal with relative shifts as small as ≈2×10⁻⁴.     

Entanglement of a two-level atom and its spontaneous emission near the edge of a photonic band gap

The entanglement of a two-level atom and its radiation field near the edge of a photonic band gap is studied by using the quantum entropy. Unlike the free space case, there is a steady-state entanglement between the atom and its spontaneous emission field even when the atomic transition frequency lies outside the band gap. Moreover, the degree of entanglement, which is due to the formation of atom–photon bound dressed state, depends on the detuning of the atomic transition frequency from the photonic band edge and can be controlled by a controllable photonic band gap crystal.     

Physics and applications of photonic crystals

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.     

Low threshold laser cavities of two-dimensional photonic crystal line defect mode

Two-dimensional (2D) rod-type photonic crystal (PC) line defect waveguide (LDW) laser cavities based on three types of line defect modes with zero group velocity are studied by using finite-difference time-domain (FDTD) method. These laser cavities have high quality (Q) factor, better localization of light, non-uniform gain distribution and small overlap between gain medium and light field. Therefore, they have the advantages over conventional and air-bridge PC cavities with uniform gain, such as low threshold, single mode lasing and effectively avoiding thermal effect. From their comparison, one can find the mode at middle Brillouin zones (BZ) is the best one to be used as lasing mode. Its dynamic lasing process and lasing features are demonstrated by the numerical experiment where the FDTD method coupling Maxwell's equations with the rate equations of electronic population is used.     

Large range of omni-directional reflection in 1D photonic crystal heterostructures

A simple design of one-dimensional omni-directional reflector based on photonic crystal heterostructures structure has been proposed. The proposed structure consists of a periodic array of alternate layers of SiO₂ and Te as the materials of low and high refractive indices, respectively. The structure considered here has three stacks of periodic structures having five layers each. The lattice period of successive stack is increased by a certain multiple (say gradual constant, δ) of the lattice period of the just preceding stack. For numerical computation, the method of transfer matrix method (TMM) has been employed. It is found that such a structure has wider reflection bands in comparison to a conventional dielectric PC structure and the width of the omni-directional reflection (ODR) bands can be enlarged by increasing the value of the gradual constant δ.     

Silicon-based two-dimensional photonic crystal waveguides

A review of the properties of silicon-based two-dimensional (2D) photonic crystals is given, essentially infinite 2D photonic crystals made from macroporous silicon and photonic crystal slabs based on silicon-on-insulator basis. We discuss the bulk photonic crystal properties with particular attention to the light cone and its impact on the band structure. The application for wave guiding is discussed for both material systems, and compared to classical waveguides based on index-guiding. Losses of resonant waveguide modes above the light line are discussed in detail.     

Photonic band gap failure in photonic crystal devices

The photonic crystal is an artificial material with periodic dielectric constant and the key factor to preserve their band features is its periodicity. When the number of periods of photonic crystal is decreased the photonic band gap cannot prevent the light of the corresponding frequencies from propagating in photonic crystal, in another word, photonic band gap will be failure. The minimum periods of photonic crystal device which can keep photonic band gap effective in miniaturization process is analyzed, the transmittance spectrum is calculated by the Finite-difference time-domain algorithm (FDTD) [1], the minimum periods is got in the simulation and the reason which affects the minimum periods is analyzed in this paper.     

Switchable photonic crystal for polymer dispersed liquid crystal

Single-prism systems are used to fabricate electrically switchable Photonic Crystal (PhC) structures in Polymer Dispersed Liquid Crystal (PDLC) films. The optical configuration is simple, stable and repeatable. A good agreement between theoretical and experimental results is obtained for the PhC structures. Hexagonal far-field diffraction patterns and electrical switching characteristics are also investigated. The smallest droplets of liquid crystals are 10 nm in diameter. The switching voltage can be decreased to 13.3 V/μm.     

Near-field optics and control of photonic crystals

We discuss recent progress and the exciting potential of scanning probe microscopy methods for the characterization and control of photonic crystals. We demonstrate that scanning near-field optical microscopy can be used to characterize the performance of photonic crystal device components on the sub-wavelength scale. In addition, we propose scanning probe techniques for realizing local, low-loss tuning of photonic crystal resonances, based on the frequency shifts that high-index nanoscopic probes can induce. Finally, we discuss prospects for on-demand spontaneous emission control. We demonstrate theoretically that photonic crystal membranes induce large variations in spontaneous emission rate over length scales of 50 nm that can be probed by single light sources, or nanoscopic ensembles of light sources attached to the end of a scanning probe.     

A 2D rods-in-air square-lattice photonic crystal optical switch

A 2D photonic crystal optical switch is proposed based on a rods-in-air square-lattice photonic crystal by removing two cross-lines of rods from a 2D square-lattice photonic crystal to form four optical channels. The simulation results show that, when inserting a single rod along the diagonal line of the intersection area of two removed cross-lines of rods, the position of the single inserted rod determines how much incident energy goes into different channels. In the case of transverse magnetic (TM) Gaussian point source, time domain simulation shows that up to 87.3% of the incident energy can be switched into a channel, which is vertical to the source channel. Because there are two diagonal lines in the intersection area of two removed cross-lines of rods, the optical switch feature is achieved by shifting the inserted rod between two diagonal lines. It is also found that the magnitude of the reflected wave in the source channel varies greatly with spatial position of the single inserted rod. The larger the magnitude of the reflected wave in the source channel, the less the energy that goes into the switched channel. The time delay between the incident wave and the reflected wave in the source channel is also related to the position of the single inserted rod. In addition, the large time delay between the incident wave and the reflected wave in the source channel shows that the reflected wave encounters many reflections with the walls of the source channel, instead of waves reflected back from the single inserted rod.     

Graphene based photonic crystal optical filter: Design and exploration of the tunability

Optical characteristics of two new graphene based photonic crystals are studied in detail. A structure containing alternating layers of graphene and SiO₂ slabs is considered as the ideal crystal. The dependency of the photonic band gaps (PBGs) to the dielectric layer thickness and the period number is explored at first step. Potential of the proposed crystal to be used as an optical filter is then investigated. Adding a nonlinear electro-optic polymer as a defect layer, the alterations of the optical features are inspected. Results show that the defect layer insertion causes a resonant mode inside the PBGs. However, the location of the defect layer inside the crystal is very effective on both the frequency and width of the resonant mode. Tunability of the optical features is probed by taking into account of the dependencies to the wave incident angle, graphene chemical potential and the applied external voltage to the defect layer.     

Analytical evaluation of bending loss oscillations in photonic crystal fibers

In this paper we present an analytical formula for bending loss oscillations in photonic crystal fibers (PCFs). We follow the approach originally adopted for conventional double-clad fibers and show that it can be applied to PCFs by substituting the structural parameters of the conventional fiber by their PCF counterparts. We then examine the spectral dependence of the critical bending radius and the position of the first order loss peak as a function of structural parameters of the PCF cladding such as the fill factor and the number of hole rings. Finally, we evaluate the precision of the analytical model by comparing the results to finite element calculations for a selection of PCF geometries.     

Selective modes excitation in multimode photonic crystal waveguides

We investigate modes excitation with the input field of different positions in two-dimensional multimode photonic crystal waveguides. Odd modes can be selectively excited by the input field of odd symmetry. The input field with different positions can excite different modes due to the field intensity distribution of modes. When the input field locates at the position of the zero field, intensity of waveguide modes is zero and the modes are not excited. The finite-difference time-domain method is used to obtain the excited field distributions.     

Lateral shifting in one dimensional chiral photonic crystal

We report the lateral shifts of the transmitted waves in a one dimensional chiral photonic crystal by using the stationary-phase approach. It is revealed that two kinds of lateral shifts are observed due to the existence of cross coupling in chiral materials, which is different from what has been observed in previous non-chiral photonic crystals. Unlike the chiral slab, the positions of lateral shift peaks are closely related to the band edges of band gap characteristics of periodic structure and lateral shifts can be positive as well as negative. Besides, the lateral shifts show a strong dependence on the chiral factor, which varies the lateral shift peaks in both magnitudes and positions. These features are desirable for future device applications.     

Contra-directional coupling between two-dimensional photonic crystal waveguides

The contra-directional coupling between two photonic crystal (PC) waveguides is studied, using the finite-difference time-domain (FDTD) method. A design of contra-directional coupler is presented and its transmission properties are investigated. The device can be used as an add/drop filter. It is also shown that the coupled mode theory is suitable to study the photonic crystal waveguide coupler.