Triangular Lattice Photonic Crystal Research Articles

Anomalous transparency in photonic crystals and its application to point-by-point grating inscription in photonic crystal fibers

It is common belief that photonic crystals behave similarly to isotropic and transparent media only when their feature sizes are much smaller than the wavelength of light. Here, we counter that belief and we report on photonic crystals that are transparent for anomalously high normalized frequencies up to 0.9, where the crystal’s feature sizes are comparable with the free space wavelength. Using traditional photonic band theory, we demonstrate that the isofrequency curves can be circular in the region above the first stop band for triangular lattice photonic crystals. In addition, by simulating how efficiently a tightly focused Gaussian beam propagates through the photonic crystal slab, we judge on the photonic crystal’s transparency rather than on isotropy only. Using this approach, we identified a wide range of photonic crystal parameters that provide anomalous transparency. Our findings indicate the possibility to scale up the features of photonic crystals and to extend their operational wavelength range for applications including optical cloaking and graded index guiding. We applied our result in the domain of femtosecond laser micromachining, by demonstrating what we believe to be the first point-by-point grating inscribed in a multi-ring photonic crystal fiber.

Low Input Power an All Optical 4 × 2 Encoder based on Triangular Lattice Shape Photonic Crystal

AbstractAn all optical encoder based triangular lattice shape photonic crystal (PC) is proposed. The device is composed of two ring resonator waveguides and two OR gate with four input ports waveguides and two output ports waveguides in triangular lattice shape PC. The band diagram of base PC structure calculated by plane wave expansion (PWE) method. Also, transmission and distribution of electrical field behaviors of the proposed device are verified by two dimensional finite difference time domain (2D-FDTD) method. The proposed 4 × 2 encoder can operate at third communication window range, considering definitions of logic 0 and 1 being the normalized transmission as less than 3% and greater than 95% respectively. Despite the nonlinear encoders, in our case, due to the non-use of non-linear effects such as Kerr effect, low input power required for encoder.

Transmission characteristics of Y‐type optical distributor in triangular lattice photonic crystals with Al2O3 rods

AbstractIn this work, a Y‐type optical distributor formed by triangular lattice photonic crystals is numerically and experimentally investigated. The crystals are formed by cylindrical Al2O3 rods array in the air. The band gaps of TE modes for the photonic crystals are calculated by plane wave expansion method. Three photonic band gaps appear numerically within the normalized frequency range 0∼0.8 in the triangular lattice photonic crystals. Based on a Y‐type defect structure, an equal optical distributor is realized within the first photonic band gap of 0.2380 ∼0.2823 . The transmission characteristic of the distributor is calculated by finite element method. To validate the numerical results, experiments were performed in the microwave regime. An Agilent E8361C vector network analyzer was used. The measured reflection and transmission characteristics of the photonic crystals sample agree with the numerical results between 9.77 and 9.91 GHz in the first photonic band gap. At the frequency of 9.86 GHz, the isolation of the photonic crystals reaches −39.02 dB and about 95.72% energy reflecting back to the input port. Furthermore, the equal optical distributor is also validated by making a comparison between the numerical and experimental results.

A Tunable Eight-Wavelength Terahertz Modulator Based on Photonic Crystals

We propose a tunable eight-wavelength terahertz modulator based on a structure of triple triangular lattice photonic crystals by using photonic crystals in the terahertz regime. The triple triangular lattice was formed by nesting circular, square, and triangular dielectric cylinders. Three square point defects were introduced into the perfect photonic crystal to produce eight defect modes. GaAs was used as the point defects to realize tunability. We used a structure with a reflecting barrier to achieve modulation at high transmission rate. The insertion loss and extinction ratio were 0.122 and 38.54 dB, respectively. The modulation rate was 0.788 dB. The performance of the eightwavelength terahertz modulator showed great potential for use in future terahertz communication systems.

Fiber optic mechanical deformation sensors employing perpendicular photonic crystals.

Existing fiber optics (FOs)-based sensors, including mechanical deformation ones rely on structures embedded along the length of the FO. In this paper, we introduce and evaluate photonic crystals (PCs) embedded into FO cores acting as mechanical deformation sensors which are departing from this classical approach as the PCs are perpendicular to the length of the FO. Another noteworthy difference from classical FO-PC based sensors is that while classical ones rely on amplitude variations, the ones presented here use the phase variations of the electromagnetic components for assessing mechanical deformations. We start with a straightforward rectangular-lattice PC while also exploring a triangular-lattice PC. Light transmission simulations through the proposed FO-PC mechanical deformation sensors were performed using EM Explorer, and revealed their behaviors under small mechanical deformations. These simulations (of the rectangular-lattice and triangular-lattice PCs) show that these two FO-PC mechanical deformation sensors have roughly the same sensitivities while the triangular-lattice PC triggers at a lower threshold than the rectangular-lattice PC.

Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining

We demonstrate an electrically pumped, single-mode, large area, edge-emitting InGaAsP/InP two-dimensional photonic crystal (PC) Bragg laser with triangular lattice. The laser operates in the single transverse and longitudinal modes with a single lobe, near-diffraction-limited far field. We compare the performance of the triangular-lattice PC Bragg laser with the rectangular-lattice PC Bragg laser fabricated from the same wafer and find that their performances are comparable. Then, we combine two single triangular-lattice PC Bragg lasers that tilt to opposite directions by taking advantage of the symmetry of the single emitter cavity mode. The measurement results show that the combined PC Bragg lasers provide the near-diffraction-limited output beam, and the single wavelength operation is also maintained in the coherently combined broad-area PC Bragg lasers.

Cylindrical vector resonant modes achieved in planar photonic crystal cavities with enlarged air-holes.

We reveal a triangular-lattice planar photonic crystal supports Bloch modes with radially and azimuthally symmetric electric field distributions at the top band-edge of the first photonic band. Bifurcated from the corresponding Bloch modes, two cylindrical vector resonant modes are achieved by simply enlarging the central air-hole of the planar photonic crystal, which have high quality factors around 3,000 and small mode volume of (λ/n)3. The far-field radiations of the two resonant modes present high-quality cylindrical vector beam profiles. The resonant modes could be optimized by modifying the six nearest neighboring air-holes around the central defect. The cylindrically symmetric characteristics of the resonant mode's near- and far-fields might provide a new view to investigate light-matter interactions and device developments in planar photonic crystal cavities.

All-optical photonic-crystal encoder capable of operating at multiple wavelengths

An all-optical photonic-crystal-based encoder is proposed. The device is composed of two ring resonator waveguides with three input-port waveguides and two output-port waveguides in triangular-lattice photonic crystals. Transmission behaviors of the proposed device are verified by two-dimensional finite difference time domain method. The encoder can operate at various wavelengths such as 1.31, 1.49 and 1.55μm, considering definitions of logic 0 and 1 being the normalized transmission as less than 5% and greater than 80%, respectively.

Cascaded photonic crystals in Ti-diffused LiNbO3 strip waveguide

By using focused ion beam (FIB) technique, we have fabricated two air-hole-type triangular-lattice photonic crystals (PhCs) cascaded in a Ti-diffused LiNbO3 strip waveguide. To ease the problem that the FIB-milled air-holes are not sufficiently deep, which results in that the holes cannot overlap most of optical mode and hence no evident stop-band feature is observed, two measures have been taken: a 0.75-μm-deep shallow trench was milled on the waveguide surface prior to the air-holes, and a scheme of two PhCs cascaded in the same waveguide was adopted. The cascaded two PhCs have the same air-hole array of 15×15 with a lattice constant 376.57nm and an air-hole radius 150nm. Transmission spectrum of the cascaded PhCs was measured, and a stop-band with a contrast ∼10dB and a 3dB bandwidth of ∼200nm is observed in the spectral region 1.0–1.2μm, in good agreement with the simulated result. Present work opens up the possibility of implementing desired PhC functions for various photonic applications by cascading multi-PhCs with different structure parameters.

Transmission Spectral Characteristics of Photonic Crystals Milled in Annealed Proton-Exchange LiNbO3 Waveguide**Supported by the National Natural Science Foundation of China under Grant Nos 50872089, 61077039 and 61377060, the Research Grants Council of the Hong Kong Special Administrative Region of China under Grant No 11211014, the Key Program for Research on Fundamental to Application and Leading Technology of Tianjin Science and

Transmission spectra of triangular lattice photonic crystals milled in the top surface of an annealed proton-exchange waveguide are numerically simulated. The effects of the finite depth, conical shape, trapezoidal shape and hybrid shape of holes are theoretically analyzed. Due to the difficulty of milling high aspect-ratio cylindrical holes in lithium niobate (LiNbO3), a compromised solution is proposed to improve the overlap between shallow holes and the waveguide mode, and useful transmission spectra with strong contrast and sharp band edges are achieved.

Photonic crystal frequency band selecting and power splitting devices based on the energy coupling effect between waveguides

The photonic crystal power splitter based on the energy coupling effect between waveguides has the advantages of compact structure, wide bandwidth, low bending loss, large angle of separation, and no external electromagnetic interference. In this paper, the power splitting characteristics of two-dimensional triangular-lattice photonic crystal coupled waveguide are theoretically studied by using the finite-difference time-domain method, and a functional device is designed in order to achieve different output power ratios within different frequency ranges.In the two-dimensional photonic crystal structure with triangular lattice, we set two adjacent straight waveguides and the light beam is introduced from one of them. Because of the energy coupling effect between the two line defects, the light energy propagates alternately in them. Based on this principle, structures of different coupling lengths are simulated and the interference effect of each surface is considered. The device with the best coupling length is achieved for three different output energy propagating characteristics at different frequencies, which include three-division, two-division and single output cases. That is to say, the incident light beam within a frequency band travels through a particular waveguide; light in another frequency band only flows through the other two output waveguides; light in the third frequency band is assigned to all the three output waveguides equally. However, the frequency band width for the high-quality light beam splitting area as well as the transmittance contrast of the other two functional band areas are not very ideal.Based on the above numerical results, two transmission modes in the coupling waveguides are achieved by changing the cross section shape of the dielectric column in the coupling region and also by changing the connecting position between the output branch waveguide and the energy-coupling waveguide. Through the above change, the splitting performance is further optimized.By detecting and analyzing the relative intensity of the three output waveguides, we can determine the range of the incident light beam. Furthermore, the frequency ranges of the three different light output characteristics can be adjusted flexibly by changing the cross section shape of the dielectric column in the coupling region or by changing the connecting position of output waveguides. The functional device proposed in this paper has a high transmittance contrast ratio and a compact structure, which will promote the practical application of the all-optical functional devices in the fields of large-scale all-optical complex integration.

Half-disordered photonic crystal slabs.

Optical transmission spectra of finite-thickness slabs of two-dimensional triangular-lattice photonic crystals of air holes in a dielectric matrix with various concentrations of randomly located vacancies (absent air holes) are studied. We focus on structures in which only one half of the structure-the incidence or transmission side-is disordered. We find vacancy-induced scattering gives rise to a strong difference in the two cases; for light incident on the disordered side, high transmission within the photonic pseudogap at normal incidence is predicted, in strong contrast to the opposite case, where low transmission is predicted throughout the pseudogap, as is observed in the case of an ideal structure with no defects.

Exploration of photonic crystal circulator based on gyromagnetic properties and scaling of ferrite materials

Three port optical circulators are designed predicated on two dimensional triangular lattice photonic crystals and examined with different size of regular (circular) and irregular (triangular) ferrite posts, through the structure optimization and exploration of defect mode coupling. Ferrite, a special type of highly permeable and low-loss magnetic material, which is anisotropic when biased by a much larger static magnetic field is modeled and the gyromagnetic property of the same is investigated. According to theoretical analysis, the optimized geometry structure can make the non-reciprocal transmission of electromagnetic waves accompanying a high caliber isolation and low insertion loss with the avail of ferrite post inserted at the center of the joint. In order to minimize the reflections in the isolated port at the nominal frequencies, the scaling of ferrite post is implemented by defining S parameter. The structural optimization and the calculation of tensor elements of the anisotropic medium is executed by the finite element method. Moreover, the further study shows the importance of scaling the magneto-photonic material and the way it affects the transmission and isolation of the structured contrivance. Numerical simulations are performed to manifest the attainability and the characteristics of the designed circulators. Finally the triangular ferrite post with the scale of 0.518 makes the non-reciprocal transmission of electromagnetic waves with the minimum insertion loss at the normalized frequency range of 191.6GHz which benefits from a broad operational bandwidth. This optimized device can realize the operations of splitting, routing and isolation and have good technological compatibility for chip level integration into Photonic Integrated Circuits.

Polarization-independent waveguides in air holes photonic crystals and its slow light

A line-defect waveguide in a triangular lattice photonic crystal (PC) made of air holes in dielectric is demonstrated to support transverse magnetic (TM) as well as transverse electric (TE) guided modes simultaneously. A group of suitable geometric parameters were found to make the guided bands overlapped by means of Genetic Algorithm. The optimized waveguide realizes a polarization-independent single-mode transmission and wide operating bandwidth which reaches 0.012Δωa/(2πc). Moreover, the guided modes are shown to exhibit a wide-bandwidth slow light and an extremely low group velocity dispersion in most frequency range.

Light trapping at Dirac point in 2D triangular Archimedean-like lattice photonic crystal.

Optical cavities and waveguides are critical parts of modern optical devices. Traditionally, optical cavities and waveguides rely on photonic bandgaps, or total internal reflection, to achieve light trapping. It has been reported that a novel light trapping, which exists in triangular and honeycomb lattices, is attributed to the so-called Dirac point. Our analysis reveals that 2D triangular Archimedean-like lattice photonic crystals also can support this Dirac mode with similar characteristics. This is a new type of localized mode with a different algebraic field profile at a different specified Dirac frequency, which is also beyond any complete photonic bandgap. The new wave localization has different features and can be applied to the design of new optical devices.

Low-loss Y-junction two-dimensional magneto-photonic crystals circulator using a ferrite cylinder

A new defect structure of two-dimensional magnetic-photonic crystal is given and a new three-port Y-junction circulator using a ferrite cylinder is proposed in this short paper. Based on the agreements between the resonance frequency of micro-cavity constructed by a point defect in the 2D triangular lattice photonic crystal with those numerical results of corresponding literatures, external characteristics of the circulator were calculated by the plane wave expansion method and finite element method. According to the scaling theory of Maxwell's equations, a 3cm Y-junction 2D MPCs circulator is developed by scaling the radius of the center ferrite cylinder. The results show that there is a significant improvement for insertion loss 0.062dB and isolation 26.2dB compared with those in literatures.

All-optical AND, XOR, and NOT logic gates based on Y -branch photonic crystal waveguide

This paper presents all-optical AND, XOR, and NOT logic gates based on the light beam interference effect. Each logic gate is simply composed of a Y-branch waveguide with two input ports and one output port in the two-dimensional triangular-lattice photonic crystals. The designed logic gates are analyzed and simulated by the plane wave expansion and finite difference time-domain method. Simulation results show that the proposed all-optical structures really function as AND, XOR, and NOT logic gates, possess a small size of less than 11.6 μm×13.8 μm and low power consumption. The contrast ratio of the proposed devices reaches 5.4 dB for the AND gate, 33 dB for the XOR and NOT gates, respectively, by precisely controlling the phase differences and properly choosing the size of the scattering rods.

Mode division multiplexing of two-dimensional triangular lattice photonic crystal based on magneto-optical effect

With the rapid development of all-optical communication, the wavelength division multiplexing transmission system cannot meet the requirements of high capacity in optical networks, while mode division multiplexing uses the limited stability modes as independent channels to transmit information, improving the system capacity and spectrum efficiency, which is one of the key technologies in the construction of future optical network. In this paper, a mode division multiplexer of two-dimensional triangular lattice photonic crystal in 1.55 μm band based on the magneto-optic effect of Bi-doped compound rare earth iron garnet bulk single crystal is proposed. The defects of TbYbBiIG medium are introduced as mode splitting waveguides in photonic crystal, of which the permeability changes with the applied magnetic field in different polarization modes. Therefore, mode division multiplexing in 1.55 μm band can be achieved by controlling the propagations of TE and TM mode. The band and transmission characteristics of this device can be analyzed by using the plane wave expansion and finite difference time domain method. The results show that the transmission rates of TE and TM modes both exceed 92% and channel segregation degrees reach 19.7 dB and 42.1 dB respectively. These features indicate the important application prospect in the future high-capacity optical transmission system.

光子晶体理论应用于二元溶液浓度测量的研究

The application of photonic crystal in the solution concentration detection is investigated by using plane wave expansion method. A two-dimensional triangular lattice photonic crystal(Si and Ge) is chosen as the substrate,filling the air hole with different percentage concentration of mixed binary solution materials which will be measured,and the photonic band gap of the photonic crystal filled with binary solution under different polarization modes is obtained. The results show that when the binary solution is used as the dielectric material in the air hole, the photonic band gap(PBG) changes with the different percentage concentrations of the solution quality. This has a certain guiding function in solution mass percentage concentration detection applications.

Channel drop filter using photonic crystal ring resonators for CWDM communication systems

In this paper, a new optical channel drop filter (CDF) using photonic crystal ring resonators (PCRRs) is presented. Using the two-dimensional (2D) finite-difference time-domain (FDTD) method in triangular lattice photonic crystal (PC) silicon rods, 100% forward dropping efficiency and a quality factor of more than 1000 can be achieved in third communication window while the resonant wavelength is 1550nm. Through this novel (CDF), a multi-CDF operation with 100% drop efficiencies across all channels can be obtained. The proposed device could be used in future coarse wavelength division multiplexing (CWDM) communication systems.