Square Lattice Of Dielectric Rods Research Articles

Generalized scheme for coupling length reduction in photonic crystal based directional coupler designed with square lattice of dielectric rods in air background

A general technique is proposed to reduce coupling length of optical couplers embedded in square latticed photonic crystals. In this approach, reduction in coupling length is achieved by engineering dispersion characteristics of coupled waveguide system with the introduction of an additional mode associated with special type of line defect. Two such line defects, namely type-I and type-II, are investigated and both the co-directional and contra-directional propagations are realized. The smallest coupling length achieved using the type-I is 2.05a, while that obtained using the type-II is 2.47a in contrast with the existing value of 28a for square lattice and 3.83a in the case of triangular lattice. Greater control over the resulting coupling length of a system is also attained. Frequency responses of the proposed couplers are finally verified using FDTD method.

All-Optical XOR, XNOR, NAND and OR Logic Gates Based on Photonic Crystal 3-DB Coupler for BPSK Signals

Abstract We propose a very compact structure for all-optical XOR, XNOR, NAND and OR logic gates based on photonic crystal 3-dB coupler in binary-phase-shift-keyed (BPSK) signals. The square lattice of dielectric rods in SiO2 background has been considered for photonic crystal structure. The photonic band gap (PBG) and light propagation simulations of proposed logic structure have been accomplished by plane wave expansion and finite difference time domain methods. The proposed structure can achieve logical function when the refractive index of all rods and substrate is fabricated with relaxed error tolerance within −0.005 to 0.005 from designed parameters. The proposed logic functions may potentially be used as key components in all-optical information networks for processing the BPSK signals.

All-optical half adder based on photonic crystals for BPSK signals

We propose a very compact structure for all-optical half adder based on photonic crystal in binary-phase-shift-keyed signals. The square lattice of dielectric rods in SiO2 background has been considered for photonic crystal structure. The photonic band gap and light propagation of proposed logic structure have been accomplished by plane wave expansion and finite difference time domain methods. The proposed structure can achieve logical function when the refractive index and radius of all rods are fabricated with relaxed error tolerance within − 0.005 to 0.005 and − 3 to 3 nm, respectively.

Normal-mode splitting induced by homogeneous electromagnetic fields in cavities filled with effective zero-index metamaterials

In cavity quantum electrodynamics (cQED), how an atom behaves in a cavity is what people care about. The coupling strength (g) between cavity field and atoms plays a fundamental role in various QED effects including Rabi splitting. In the solid-state case, when an atomic-like two-level system such as a single quantum dot (QD) is placed into a cavity, Rabi splitting would occur if g is strong enough. In the classical limit, when a QD in a cavity changes into a classical oscillator, the normal-mode splitting would also take place. It is known that g relies on the local fields at the places of the QDs or classical oscillators inside the cavity. However, for both cases, the traditional cavity modes involved are all in the form of standing waves and the localized fields are position-dependent. To ensure strong coupling between QDs or classical oscillators and photons, they should be placed right at the place where the cavity field is maximum, which is very challenging. How is the positional uncertainty overcome? Recently, the peculiar behaviors of electromagnetic (EM) fields inside zero-index metamaterial (ZIM) in which permittivity and/or permeability are zero have aroused considerable interest. In ZIMs the propagating phase everywhere is the same and the effective wavelength is infinite, which strongly changes the scattering and mode properties of the EM waves. In addition to the above characteristics, the fields in ZIM could be homogeneous as required by Maxwell equations. While the special properties of ZIMs are investigated, the fabrication of ZIMs is widely studied. It is found that a two dimensional (2D) photonic crystal consisting of a square lattice of dielectric rods with accidental degeneracy can behave as a loss-free ZIM at Dirac point. To overcome the positional uncertainty, in this paper we propose a cavity filled with effective zero-index metamaterial (ZIM). When the ZIM is embedded in a cavity, the enhanced homogeneous fields can occur under the resonance condition. Finally, experimental verification in microwave regime is conducted. In the experiments, we utilize a composite right/left-handed transmission line with deep subwavelength unit cell to mimic a ZIM and use a metallic split ring resonator (SRR) as a magnetic resonator whose resonance frequency is determined by structural parameters. The experimental results that in general agree well with the simulations demonstrate nearly position-independent normal-mode splitting.

Tunable plasmon lensing in graphene-based structure exhibiting negative refraction

We propose a novel method to achieve tunable plasmon focusing in graphene/photonic-crystal hybrid structure exhibiting all-angle negative refraction at terahertz frequencies. A two-dimensional photonic crystal composed of a square lattice of dielectric rods is constructed on the substrate of a graphene sheet to provide the hyperbolic dispersion relations of the graphene plasmon, giving rise to the all-angle plasmonic negative refraction. Plasmon lensing induced from the negative refraction is observed. We show that the ultracompact graphene-based system can produce sub-diffraction-limited images with the resolution significant smaller than the wavelength of the incident terahertz wave. Moreover, by adjusting the Fermi energy of the graphene, the imaging performance of the proposed system can remain almost invariant for different frequencies. Our results may find applications in diverse fields such as subwavelength spatial light manipulation, biological imaging, and so forth.

A new proposal for eight-channel optical demultiplexer based on photonic crystal resonant cavities

In this paper, we used the novel defective resonant cavities to design an eight-channel photonic crystal demultiplexer. We showed that by choosing appropriate values for the width of the resonant cavity, the desired wavelengths can be separated. The proposed platform has a square lattice of dielectric rods immersed in air. The value of transmission efficiency for channels was obtained in 94$$-$$-99 % range. In addition, the maximum value of crosstalk and average quality factor for channels were calculated ---11.2 dB and 2200, respectively.

Design and Simulation of All-Optical OR Logic Gate based on 2-D Photonic Crystal

this paper, we present the design of All-optical OR logic gate based on 2-D (two dimension) photonic crystals. To realize this, we consider the photonic crystals (PCs) with a square lattice of dielectric rods (refractive index=3.40). These rods are surrounded by air (refractive index=1).First we design the structure using the Finite Difference Time Domain (FDTD) method and in second step, we compute the band gap by plane wave expansion (PWE) method. These methods are kept to analyze the behavior of the structure. Band gap width is 0.2516 and normalized central frequency of band gap is 0.6451. Overall size of the logic gate designed is 13µm * 8µm i.e. 104 µm 2 with the lattice constant 540 nm.

Enhanced energy confinement induced by metallic coating of central rod in square array photonic crystal of dielectric rods for TM light

We study the effects of a defect created by metallic coating of the central rod in a square lattice of dielectric rods for TM polarization lights. A calculation using the Plane Wave Expansion Method (PWE) in the supercell model shows that the photonic band structure and field distribution in the defect area varies with changing metallic layer thickness. The optimal energy localization is explored by varying the thickness of the metal layer. Enhancement of the energy confinement is described by the narrower spatial distribution profile of the energy with thicker metal coating. A more quantitative description, given in terms of confinement quality (CQ) defined by the normalized integrated intensity in the central rod, exhibits monotonous increase of CQ with growing metal layer thickness. The highest CQ value achieved is around 80% for a 3 × 3 supercell, which is considerably higher than the 44% optimal value achievable in the same dielectric PC structure with a defective central rod. Further calculation using the Extended Plane Wave Expansion Method for determining the imaginary part of the Bloch wave vector shows increasing with increasing metal coating thickness. The following analysis explains and corroborates the enhanced energy confinement effect.

All-Optical NOT Logic Gate Based on Photonic Crystals

A novel scheme for implementation of all-optical NOT logic gate based on photonic crystal ring resonator has been proposed. Photonic crystal is comprised of two-dimensional square lattice of dielectric rods in air substrate. Indium phosphide with a refractive index of 3.1 is adopted as the material of the rods. The finite different time domain (FDTD) and plane wave Expansion (PWE) methods are used to analyze the behavior of the structure. The simulation results show that the contrast ratio is 10.97dB for NOT gate. Moreover, the operational wavelength of the input ports is 1.55µm. Since the structure has a simple geometric shape with clear operating principle, it is potentially applicable for photonic integrated circuits. DOI: http://dx.doi.org/10.11591/ijece.v3i4.2909 Full Text: PDF

Tunable anisotropic photonic crystal channel-drop filter

In this numerical study, we present a tunable photonic crystal optical filter designcomposed of anisotropic material. Various tunable optical filters which are composed ofpoint and line defects in a square lattice of dielectric rods, with selective infiltration ofsome of the rods with anisotropic material, are presented. Our numerical simulations withthe finite-difference time-domain (FDTD) technique reveal that defect states originatingfrom the anisotropic material impurities can be effectively tuned. The tunable range of20 nm of the optical channel is obtained. Moreover, we suggest a new tunabletwo-port channel-drop photonic crystal filter based on a Y-splitter and show that, bytuning the characteristics of this structure, total transmission up to 94% and 84%in each output port is achievable. Also, we come to the fact that our proposedstructure, compared to conventional photonic crystal channel-drop filters, hasthe advantages in miniaturizing wavelength-selective filters for WDM systems.

Intersecting veins effects of a two-dimensional photonic crystal with a large two-dimensional complete bandgap

Optimal design of a two-dimensional photonic crystal with a square lattice of dielectric rods with intersecting veins in GaAs is investigated numerically using plane wave expansion method. It is shown how a maximum complete two-dimensional bandgap is obtained by optimally connecting the dielectric rods with intersecting veins. The complete two-dimensional photonic bandgap (PBG) of our optimal design reaches Δ ω = 0.10664(2 πc/ a) (where a is the lattice constant and c is the speed of light in vacuum) when the radius of dielectric rod is 280.1 nm and the half-vein width is 60 nm. Our result shows 40% the width of PBG higher than that obtained from Ref. [M. Qiu, S. He, J. Opt. Soc. Am. B 17 (2000) 1027] (Δ ω = 0.0762(2 πc/ a)). In addition, we found that the complete bandgap can be obtained in a large range of radius R of dielectric rod when the half width of intersecting veins d is larger than 65 nm.

Effective theory of quadratic degeneracies

We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a bandgap or split the degeneracy into a pair of linear degeneracies that are continuable to Dirac points. A degeneracy of this type occurs between the second and third TM bands of a photonic crystal formed by a square lattice of dielectric rods. We show that the theory agrees with numerically computed photonic bandstructures, and discuss the resulting insight into the reflection-free edge modes induced by parity breaking.

Two-Dimensional and Three-Dimensional Analysis of Taper Structures for Coupling into and out of Photonic Crystal Slab Waveguides

The appropriate technique for coupling light efficiently from the conventional silica waveguide (SWG) entrance and exit of a photonic crystal slab waveguide (PCSWG) in a square lattice of dielectric rods is determined by calculation using the two-dimensional (2D) and three-dimensional (3D) finite-difference time-domain method. Four types of taper structure as the interface between SWG and PCSWG have been investigated. Coupling efficiency is found to be highly sensitive to the taper structure, defect rod configuration, and slab thickness. We find that when the type D tapered structure with a pair of larger defect rods, which is more flexible during fabrication, is placed between input/output SWG and PCSWG, if alters the mode properties of the guide mode so that mode matching can be achieved by determining the optimum defect configurations. Also, detailed computations of the 2D device and 3D slab version are given.

Design and analysis of two-dimensional photonic crystals channel filter

A novel three-port channel add/drop filter consisting of two waveguides and two cavities is proposed. One is used for a resonant tunneling-based channel add/drop operation from the bus waveguide to the add/drop waveguide, while the other is used to realize the wavelength-selective reflection feedback in the bus waveguide. By means of coupled mode theory in time, the conditions to achieve 100% add efficiency are derived thoroughly. Based on these theoretical analysis, the channel add filter and some other multi-channel filters are designed in two-dimensional photonic crystals (2D PCs) with square lattice of dielectric rods in air. The numerical results by using the finite-difference time-domain (FDTD) method demonstrate almost complete channel add/drop tunneling at resonance via the three-port systems.

Optical filter based on contra-directional waveguide coupling in a 2D photonic crystal with square lattice of dielectric rods

A coupler-type optical filter in 2D photonic crystal (PhC) with square lattice of dielectric rods in air is presented. The reduced-index and increased-index waveguides of filter have dispersion curves with opposite slopes to realize contra-directional coupling, and the point of anti-crossing is designed below the light line to avoid vertical radiation. The filter has a broad operable bandwidth due to the absence of mini stop bands. The transmission properties are analyzed using coupled modes theory (CMT) and simulated using the finite-difference time-domain (FDTD) method. The results show that a filtering bandwidth of 4 nm can be achieved in the range of 1500~1600 nm, and over 83% drop coefficient is obtained.

Fabrication of photonic crystal waveguides composed of a square lattice of dielectric rods

The use of a negative resist, hydrogen silsesquioxane (HSQ), combined with electron-beam lithography, was found to greatly simplify the fabrication of photonic crystal structures having submicron-sized features. Two methods of fabrication were compared for the creation of photonic crystals; in this example, the structures were composed of a square lattice of dielectric rods. One method utilized positive resist PMMA, whereas another method used a negative resist HSQ. The process sequence using PMMA required a lift-off step and a hard mask in order to convert the hole-patterned PMMA into high-aspect-ratio dielectric rods through reactive ion etching. Alternatively, the electron-beam exposure and development of HSQ resist resulted in the formation of SiO2-like posts which then served as a hard mask for subsequent etches. The use of HSQ eliminated the need for the SiO2 deposition and nickel lift-off, thereby reducing the required number of steps in the process sequence and greatly simplified the fabrication.

Theoretical bandgap modeling of two-dimensional square photonic crystals fabricated by the interference of three noncoplanar laser beams

We have investigated numerically the photonic bandgap (PBG) and spectral properties of two-dimensional (2-D) square structures fabricated by holographic lithography. Based on the block-iterative frequency-domain method and on the nonorthogonal finite-difference time-domain method, we have calculated band structure as a function of intensity threshold and shown that the PBG of 2-D titania arrays opens only for TM polarization and that directional PBGs can be obtained simultaneously for TE- and TM-polarized waves. In addition, we have shown that symmetry reduction of the atom introduced by holographic lithography can lift the band degeneracies and create an absolute PBG for a square lattice of dielectric rods in air.

Microwave measurements of stub tuners in two-dimensional photonic crystal waveguides

The transmission spectra of photonic crystal stub-tuned waveguides created in the microwave region are measured. The photonic crystal is a two-dimensional square lattice of dielectric rods. The waveguides are formed by removing rods along a line or by creating a line of coupled cavities. Additional stub-tuning cavities are formed by removing rods or by replacing them with different diameter rods to stub tune the transmission properties of the waveguides. Depending on the cavity geometry, certain wavelengths can be reflected from the stub tuner creating a notch in the waveguide transmission with measured quality factors as high as 488.