Three-dimensional Photonic Crystal Waveguides Research Articles

Three-dimensional dielectric photonic crystal structures for laser-driven acceleration

We present the design and simulation of a three-dimensional photonic crystal waveguide for linear laser-driven acceleration in vacuum. The structure confines a synchronous speed-of-light accelerating mode in both transverse dimensions. We report the properties of this mode, including sustainable gradient and optical-to-beam efficiency. We present a novel method for confining a particle beam using optical fields as focusing elements. This technique, combined with careful structure design, is shown to have a large dynamic aperture and minimal emittance growth, even over millions of optical wavelengths.

Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals

The authors present a general procedure that allows the design of single-mode air-core waveguides in three-dimensional photonic crystals. The procedure involves analyzing the modal profile of the band edge mode in the perfect crystal, identifying the regions of maximal electric-field intensity, and placing the air defects to enclose these regions. As an illustration, they present a detailed design of air-core waveguides in a recently proposed silicon body-center-cubic crystal structure that possesses a 25% complete band gap.

Design of compound-defect waveguides in three-dimensional photonic crystals

We designed three-dimensional (3D) photonic crystal (PC) waveguides by simultaneously introducing one acceptor-type and two donor-type line defects. The waveguides have an extremely large singlemode bandwidth, which covers more than 90% of the complete photonic band gap. The relatively large group velocity and the mode-field localization in the air core should prevent unintended nonlinear phenomena for ultra-short pulse propagation. These promising characteristics could only be achieved by using 3D PCs, which have the advantages of complete light confinement and no restrictions of the light cone.

Controlled nonuniformity in macroporous silicon pore growth

Photoelectrochemical etching of uniform prestructured silicon wafers in hydrofluoric acid containing solutions yields periodic structures that can be applied to two- and three-dimensional photonic crystals or microfluidics. Here we demonstrate experimentally macroporous silicon etching initiated by a nonuniform predefined lattice. For conveniently chosen parameters we observe a stable growth of pores whose geometrical appearance depends strongly on the spatially different nucleation conditions. Moreover, we show preliminary results on three-dimensionally shaped pores. This material can be used to realize hybrid photonic crystal structures and incorporate waveguides in three-dimensional photonic crystals.

Design of donor-type line-defect waveguides in three-dimensional photonic crystals

We have theoretically investigated the characteristics of three-dimensional (3D) photonic crystal (PC) waveguides formed by the introduction of dielectric line defects. We show that the guided modes in 3D PC waveguides strongly depend on the volume, position and number of dielectric defects introduced. We have succeeded in designing a waveguide structure with a large single-mode bandwidth of 178 nm (range = 1,466 to 1,644 nm) for wavelengths used in optical communications. Our study indicates that there is great flexibility in the design of 3D PC waveguides and that a variety of desirable properties can be obtained by altering the configuration of the line defects appropriately.

Integrated horns for improved side coupling into in-plane three-dimensional photonic crystal waveguides

We examine the frequency response and radiation patterns for horn antennas constructed into a three-dimensional layer-by-layer photonic crystal. These horns resemble a pyramidal cavity and can be built by omitting material during the construction or by removing material from the finished crystal. The horns can be used to couple electromagnetic waves that are incident on the surface of a photonic crystal into an in-plane waveguide within the crystal. The horns are of a design suitable for use at optical frequencies.

Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides

The plane-wave-based transfer-matrix method (TMM) exhibits a peculiar advantage of being capable of solving eigenmodes involved in an infinite photonic crystal and electromagnetic (EM) wave propagation in finite photonic crystal slabs or even semi-infinite photonic crystal structures within the same theoretical framework. In addition, this theoretical approach can achieve much improved numerical convergency in solution of photonic band structures than the conventional plane-wave expansion method. In this paper we employ this TMM in combination with a supercell technique to handle two important kinds of three-dimensional (3D) photonic crystal waveguide structures. The first one is waveguides created in a 3D layer-by-layer photonic crystal that possesses a complete band gap, the other more popular one is waveguides built in a two-dimensional photonic crystal slab. These waveguides usually have mirror-reflection symmetries in one or two directions perpendicular to their axis. We have taken advantage of these structural symmetries to reduce the numerical burden of the TMM solution of the guided modes. The solution to the EM problems under these mirror-reflection symmetries in both the real space and the plane-wave space is discussed in a systematic way and in great detail. Both the periodic boundary condition and the absorbing boundary condition are employed to investigate structures with or without complete 3D optical confinement. The fact that the EM field components investigated in the TMM are collinear with the symmetric axes of the waveguide brings great convenience and clarity in exploring the eigenmode symmetry in both the real space and the plane-wave space. The classification of symmetry involved in the guided modes can help people to better understand the coupling of the photonic crystal waveguides with external channels such as dielectric slab or wire waveguides.

Propagation loss in three-dimensional photonic crystal waveguides with imperfect confinement

Perfect confinement and efficient propagation of electromagnetic (EM) waves can be realized in waveguides created into a three-dimensional (3D) layer-by-layer photonic crystal that exhibits a complete band gap. However, the difficulty to build very thick 3D photonic crystals in the fundamental optical and infrared regimes by means of current lithography techniques will induce leakage of EM waves away from the waveguide through limited cladding layers. In order to assess the degradation of the optical properties of these photonic crystal waveguides, we build waveguides in a microwave-frequency 3D layer-by-layer photonic crystal and measure the leakage induced propagation loss. We find that this propagation loss exponentially decays with respect to the thickness of the cladding wall of the waveguide. The measurement results can scale to optical and infrared wavelengths and provide useful information for optimal design of photonic crystal structures in these regimes.

Full three-dimensional photonic bandgap crystals at near-infrared wavelengths

An artificial crystal structure has been fabricated exhibiting a full three-dimensional photonic bandgap effect at optical communication wavelengths. The photonic crystal was constructed by stacking 0.7-micrometer period semiconductor stripes with the accuracy of 30 nanometers by advanced wafer-fusion technique. A bandgap effect of more than 40 decibels (which corresponds to 99.99% reflection) was successfully achieved. The result encourages us to create an ultra-small optical integrated circuit including a three-dimensional photonic crystal waveguide with a sharp bend.

Design for Waveguides in Three-Dimensional Photonic Crystals

We present a design for waveguides in three-dimensional photonic crystals. A single-mode three-dimensional photonic crystal waveguide can be created in the stacked-stripe structure by removing one stripe. A method for creating a waveguide bend is described. Numerical simulations show that a transmittance of more than 95% can be obtained over a wide range of frequencies. The results suggest that various types of optical circuits, such as a T-branch waveguide, can be created by removing or adding stripes in the stacked-stripe structure.

Highly confined waveguides and waveguide bends in three-dimensional photonic crystal

We demonstrate a method to create a highly confined waveguide with sharp bend in three-dimensional photonic crystal. By theoretical calculation, we show that a single-mode waveguide can be created in the stacked-bar structure by removing one stripe. Crossing waveguides of the adjacent layers can create the waveguide bend and by this way, the guided modes after and before the bend remain the same so that the transmission through the bend is optimized. These results provide very important guidelines for designing a three-dimensional photonic crystal waveguide.