Photonic Crystal Lens Research Articles

Improving the imaging intensity of a photonic crystal flat lens by an antireflection method

In this paper, a two-dimensional photonic crystal (PC) consisting of a triangular lattice of silicon rods in air is studied theoretically. Equal-frequency contours (EFCs) analysis shows that this PC structure exhibits an effective refractive index n eff = −1 at a normalized frequency ω = 0.30 × 2 π c / a . A superlens effect is demonstrated using this PC structure by the finite-difference time-domain (FDTD) simulation. An antireflection layer (ARL) is introduced into the PC slab surface in order to achieve a high-intensity image. Two point sources imaging process is also simulated both in the case of a perfect PC structure and in the case of a PC structure with an ARL. The results show that the method of introducing the ARL into the PC surface is effectual for improving both the intensity of the image and the capability of the super-resolution of two sources, which are in accord with the coupled-mode theory analysis. Theoretical study implies that the surface defect modes play an important role in enhancing the transmitted intensity of energy flow.

Focusing effect of a graded index photonic crystal lens

We present a new graded-index photonic crystal (GRIN PhC) structure which can be made by laser interference lithography (LIL). It can be applied as miniaturized focusing lens. Numerical simulations are carried out on the structures with different widths, lengths, and modulations. In the qualitative analysis of the focal length, focusing of a GRIN PhC was proved to originate from both the graded sizes of the rods and multimode interference. Multimode interference dominates the focusing effect when a GRIN PhC has a small length or a small difference in the rod sizes. Intensity distributions in different cases were given to support the conclusion.

Influence of source displacement on the features of subwavelength imaging of a photoniccrystal slab

In this paper we study the characteristics of subwavelength imaging of a photonic crystal(PhC) superlens under the influence of source displacement. For square and triangularlattice photonic crystal lenses, we investigate the influence of changing the lateral positionof a single point source on imaging uniformity and stability. We also study the effectof changing the geometrical center of a pair of sources on the resolution of thedouble image. Both properties are found to be sensitive to the displacement,which implies that a PhC slab cannot be treated seriously as a flat lens. We alsoshow that by introducing material absorption into the dielectric cylinders of thePhC slab and widening the lateral width of the slab, the imaging uniformity andstability can be substantially improved. This study helps us to clarify the underlyingmechanisms of some recently found phenomena concerning imaging instability.

Mechanically Tunable Negative-Index Photonic Crystal Lens

We report the microelectromechanical systems (MEMS)-enabled mechanically tunable negative-index photonic crystal lens, which was comprised of 2-D photonic crystal and symmetrical electro-thermal actuators. The 2-D photonic crystal was made of a honeycomb lattice of silicon rods embedded in an SU-8 membrane. A silicon input waveguide and deflection block were also fabricated for light in-coupling and monitoring of focused spot size, respectively. When actuated, the electro-thermal actuators stretched the photonic crystal and consequently modified the photonic band structure. This, in turn, modified the focal length of the photonic crystal lens. The fabricated device was fully characterized using a tunable laser and an infrared camera while being actuated with a constant current source. The intensity and lateral spot size observed at the deflection block gradually increased as the applied current increased from 0 to 0.3 A. The observed behavior was in excellent agreement with finite-difference time-domain (FDTD) simulations, confirming the mechanical tuning of negative-index imaging.

Subwavelength focusing with a Mikaelian planar lens

We show that an arbitrary TE-polarized light field propagating in a Mikaelian secant (MS) planar lens can be decomposed into modes described by the Jacobi polynomials. This light field will be periodically repeated at the Talbot length and focused with a half-Talbot length period. An analytical expression for the width of the focal spot has been obtained. The MS lens allows obtaining a focal spot of width equal to the diffraction limit in the medium. The MS lens has been fabricated as a planar photonic crystal lens in a silicon film for wavelength 1.55 μm, and its focusing properties have been demonstrated by visible light (532 nm) interference fringes.

Interface engineering for improved light transmittance through photonic crystal flat lenses

In this paper, we present photonic crystal flat lenses with interfaces engineered to improve the light transmittance thanks to a broad angles impedance matching. The interface engineering consists in the realization of antireflection gratings on the edges of the lenses which are designed to reduce the propagative waves reflectivity over a wide range of incident angles. The fabricated structures were measured in optical near-field and a four times enhancement of the light transmission efficiency is reported.

Silicon-Based Thermo-Optically Tunable Photonic Crystal Lens

We report an extremely compact (30 ?m × 7 ?m) silicon-based 2-D thermo-optically tunable photonic crystal (PhC) lens operated at around telecommunication wavelength (1.55 ?m ) with transverse-magnetic-like polarization light. A honeycomb lattice array of high index silicon rods with 340 nm in thickness, 234 nm in diameter, and 338 nm in lattice constant were embedded in 3-?m-thick low index silicon dioxide. A 150-nm-thick NiCr micro-heater was placed directly on top of the PhC structure to provide localized heating to the silicon rod array. The localized heating causes refractive index change in silicon due to thermo-optic effect which results in change of the focal length of the PhC lens. The device was characterized with a tunable laser light source in the wavelength range of 1500 ~ 1580 nm. Tuning of focal length in this device was experimentally demonstrated by applying different current through the heater. Such experimental results showed good agreement with the simulation results.

Defect assisted subwavelength resolution in III–V semiconductor photonic crystal flat lenses with n = −1

We propose a III–V semiconductor photonic crystal slab designed to operate as a n = −1 superlens at λ 0 = 1.55 μm. The structure consists of air holes arranged in a two-dimensional triangular lattice, of period a, nanopatterned in an InP/InGaAsP/InP slab. Exploiting the second pass-band regime ( a/ λ 0 ∼ 0.31), subwavelength resolutions as low as 0.38 λ 0 for planar lenses have been obtained by the insertion of hexagonal nanocavities within the crystal.

Photonic crystal lens for coupling two waveguides

We report the design, fabrication, and characterization of a new nanophotonic device comprising a two-dimensional photonic crystal (PhC) lens of size 3x4 microm fabricated in silicon-on-insulator. The PhC lens is put at the output of a planar waveguide of width 4.5 microm to couple light into a planar waveguide of width 1 microm, with two waveguides being of length 5 mm. A 1 microm off-axis displacement of the smaller waveguide leads to an 8-fold reduction of output light intensity, which means that the focal spot size at output of the PhC lens in silicon is less than 1 microm. The simulation has shown that the PhC lens has maximal transmittance at 1.55 microm, with the coupling efficiency being 73%. The focal spot size of the lens in air calculated at the FWHM is 0.32lambda (where lambda is the wavelength).

Focusing property of two-dimensional photonic crystals with ring-shaped air holes

Imaging properties of two-dimensional photonic crystal slab lens consisting of a triangular lattice of ring-shaped air holes in a high-refraction-index dielectric medium have been studied. The results calculated by the plane wave expansion method （PWE） and the finite-difference time-domain method （FDTD） show that the effective index n=-1 can be realized in this structure. A perfect image can be obtained by increasing the inner radius of ring-shaped holes from 0 to 0.13a with the outer radius 0.4a at the normalized frequency 0.3（a/λ）. Based on the result of normalized frequency with effective refraction index -1 versus inner radius of ring-shaped holes we theoretically analyzed the effects of structure parameters to equifrequency contours of respective normalized frequency and imaging properties.

Direct characterization of focusing light by negative refraction in a photonic crystal flat lens

We report experimental measurements of the field distribution of the light spot focused by a two-dimensional photonic crystal flat lens at wavelengths 1.51–1.58 μm. The photonic crystal slab is fabricated on a silicon-on-insulator substrate by focused-ion-beam direct milling. We confirm the light focusing by the photonic crystal slab through direct observation of the light spot entering into free space at the end facet of the slab lens. The beam profiles as the function of lateral position are measured and the minimal full width half maximum of the beam at 1.2 μm (0.77λ) is obtained.

Graded negative index lens by photonic crystals

Numerical studies on a graded negative index lens made by a slab of graded photonic crystal (PC) are reported. The graded negative index lens is capable of focusing plane waves and can also be made highly insensitive to frequency, enabling broadband negative index imaging. We provide a simple model for the graded PC lens and predict its superior focusing properties such as low chromatic aberrations and broadband operation. Those properties were also confirmed and analyzed by the finite-difference time-domain simulations. We believe the negative index graded PCs will expand the utility of PC lenses and enable new applications in optoelectronic systems.

Focusing properties of two types of diffractive photonic crystal lens

We designed novel two type of binary 2D subwavelength (wavelength was λ= 10 mm) focus diffractive photonic crystal lens and calculated the diffraction of plane TE-wave by use FDTD-method (our program in C++). It has been shown that diffractive photonic crystal lens designs have not an unique solution. It has been also shown the diffractive lens with equal holes in Fresnel zones has better focusing characteristics. Lens diameter was 5 times more than her width and full width half maximum diameter of focal spot was 0.48λ.

Optical Near-Field Microscopy of Light Focusing through a Photonic Crystal Flat Lens

We report here the direct observation by using a scanning near-field microscopy technique of the light focusing through a photonic crystal flat lens designed and fabricated to operate at optical frequencies. The lens is fabricated using a III-V semiconductor slab, and we directly visualize the propagation of the electromagnetic waves by using a scanning near-field optical microscope. We directly evidence spatially, as well as spectrally, the focusing operating regime of the lens. At last, in light of the experimental scanning near-field optical microscope pictures, we discuss the lens ability to focus light at a subwavelength scale.

Aberration reduction and unique light focusing in a photonic crystal negative refractive lens

Light focusing characteristics of a negative refractive lens fabricated out of a silicon-on-insulator photonic crystal (PC) slab are investigated theoretically and experimentally. It focuses in the near infrared, but the focal spot is degraded by a lens aberration. To reduce the aberration, we designed a composite PC that gives rise to a narrower focal spot. In addition, two unique functions of this lens are demonstrated: refocusing outside of the PC and parallel focusing, enabling image transfer and real image formation, respectively. These results prove the feasibility of an in-plane free space optical network based on negative refraction.

A Novel Design of Photonic Crystal Lens Based on Negative Refractive Index

In this study a concave lens based on two dimensional photonic crystal platform with negative refractive index is presented. The proposed lens is employed as a spot-size con- verter to facilitate coupling of the light from a single mode flbre with a large spot-size area into photonic crystal waveguide with a very small spot-size area, even smaller than the operating wavelength. Optimisation of the lens and its integration with the single mode flbre and photonic crystal waveguide into a single optical chip was performed by employing 2D Finite-Difierence Time-Domain (FDTD). A signiflcant reduction of the optical chip dimensions and high cou- pling e-ciency have been achieved by optimizing each device (the lens and the photonic crystal waveguide).

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%.

Negative refraction, subwavelength focusing and beam formation by photonic crystals

We present a review of our experimental and numerical studies on the negative refraction related phenomena in two-dimensional dielectric photonic crystals (PCs). By employing photonic bands with appropriate dispersion, the propagation of the electromagnetic wave through a PC can be controlled to a large extent, and diverse and completely novel electromagnetic phenomena can be generated. We perform the spectral analysis of the negative refraction arising from a convex TM polarized photonic band of a hexagonal PC. As a consequence of negative refraction, we demonstrate a photonic crystal flat lens, which has the ability to focus electromagnetic waves and provide subwavelength resolution laterally. Finally, a photonic crystal with an embedded source is shown to provide a highly directional beam, which can be utilized in certain antenna applications.

Tunable negative refraction by electro-optical control in two-dimensional photonic crystal

We analyze negative refraction in two-dimensional photonic crystals that are made from electro-optical active materials. Application of an electric field to the photonic crystal changes the dielectric constant of the material and consequently modifies the photonic band and dispersion properties. We have investigated focusing properties of the photonic crystal slab lens at different frequencies within the first two bands and under various magnitudes of electric field. The simulation results reveal that one can dynamically tune negative refraction by means of index-tunable photonic crystals.

Antireflection coating for two-dimensional air hole-type photonic crystal negative refraction slab lens

We propose and optimize the antireflection coating composed of a row of tapered dielectric waveguides for two-dimensional air hole-type photonic crystal negative refraction slab lens. The image quality of the lens with the antireflection coating is improved. The simulation result using finite difference time domain method shows, at the working frequency leading to the effective index neff=-1, the reflection rate of the surface of photonic crystal with anti-reflection coating is reduced to below 1% in the range of incident angle less than 23 degrees.