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Micro/Nano Lithography

Photonic crystals slow light for better sensing

Controlling the speed of light through photonic crystal structures could increase their sensitivity as sensors
26 July 2006, SPIE Newsroom. DOI: 10.1117/2.1200605.0224

Photonic-crystal (PC) structures offer an important platform for optofluidic devices, photonic circuits, and dispersion-engineered metamaterials. These devices promise lab-on-a-chip capabilities with considerable flexibility for managing light. They are also likely to reduce the cost of integrated optical circuits and devices. PC circuits have primarily been defined by their periodicity and the architecture of the holes or columns fabricated in the transparent material. This has encouraged the development of stamping and printing technologies that can produce prototypes quickly and make large quantities of sensors inexpensively.

In addition to being manufacturable, PC platforms have two attractive attributes for sensing applications. First, a gas or liquid analyte can flow directly through the nanoscopic holes within the photonic structure. Second, ‘slow light’ can boost the device's sensitivity. Optical sensors that exploit spectroscopic analysis—such as surface-enhanced Raman phenomena—are already theoretically capable of molecular sensitivity: PC sensors using slow light could increase even this sensitivity.

Because controlling the speed of light has a host of important applications, engineers have learned to manage the dispersion characteristics of a material to control it or, more specifically, to control the group velocity of light. In an isotropic linear medium, the velocity of light is the same in all directions and is defined by the angular frequency (ω) divided by the wavenumber (k). The plot of ω versus k provides the phase velocity of the light. An optical pulse—which one can consider as the envelope or constructive interference arising from a number of frequencies—has a group velocity that is the derivative of ω with respect to k. If this derivative is zero, then at that frequency and for the small band of frequencies in its neighborhood, a pulse has a group velocity that is close to zero.

This interests us because slow-light pulse propagation can enhance the energy density of the electromagnetic field within the structure. Such an effect can lower the threshold for exploiting nonlinear optical effects. These enhanced local fields also have the potential to increase the overall sensitivity of chemical and biological sensors.

There are several approaches to slowing group velocity, including electromagnetically induced transparency. The structure we have been studying is a 1D anisotropic periodic PC or superlattice, which can be engineered to have a very low group velocity over a specific bandwidth. The structure requires two anisotropic layers and one isotropic layer per period.1 Using the theory presented by Alex Figotin and Ilya Vitebskiy in Reference 1, Yang Cao in our group calculated the band-edge resonant effect of a PC structure in which a unit cell has just two misaligned in-plane anisotropic layers with a small air gap between them.2 These calculations use the transfer-matrix method: a single plane wave incident on a parallel layer of an anisotropic medium will, in general, initiate four plane waves in the medium. We can represent the relation between the input and output parameters for anisotropic multiple-layered structures using a 4 × 4 transfer matrix. Using this method, we can calculate most of the characteristics of light traveling through the structure, including the dispersion relation, transmission, reflection, and the field distribution inside the structure. For any given frequency and wavevector components (kx, ky), we can always find the 4 × 4 transmission matrix a and four eigenvalues for kz, i.e., {k1, k2, k3, k4.}. When these eigenvalues are real, based on the order of their degeneracy, three types of special points can be defined at which the group velocity is zero. A special case—known as a degenerate band edge (DBE) —occurs when k1 = k2 = k3 = k4. In this situation, the transverse electric and transverse magnetic modes of light couple to each other. This structure's resonant effect slows light. Theory predicts that in the vicinity of the DBE, the resonant field intensity increases as N4, where N is the total number of periods in the PC. This is in contrast to a regular band edge, at which the field intensity is proportional only toN2. The higher field intensity could be exploited to make more sensitive sensors.

An interesting challenge arises if one wants to make a structure that works at optical frequencies. Materials with the required degree of birefringence at optical wavelengths are rare.3 Therefore, we designed anisotropic structures based on form birefringence, which uses subwavelength features to alter the refractive index in one plane (see Figure 1). A device that works at microwave wavelengths can be made using a rapid-prototyping tool. To make a periodic stack of materials that has a DBE, the misalignment angle between adjacent anisotropic layers must be π/4 (see Figure 2). Also, the ratio of the difference in the refractive indices of the anisotropic layers to the average index range (Δn/n) must be greater than 0.1. Using form birefringence, a large index difference—between the index of the host material and air—can be achieved.

Figure 1. A carefully designed periodic stack with sub-wavelength features can slow certain wavelengths to a crawl and increase the resonant field intensity. The form-birefringent structure in the photo is made of Fullcure 720, a UV-cured material with a refractive index of 1.9 at 8GHz.
Figure 2. In the unit cell of a periodic stack containing two adjacent anisotropic layers, the form-birefringent gratings, A1 and A2, need to differ in orientation by π/4 to produce light-slowing effects.

Based on this approach, the structure shown in Figure 1 was designed to exhibit a near-zero group velocity close to the DBE region. Robert Hudgins at the University of North Carolina (UNC) at Charlotte and Monty Graham at Western Carolina University made the device. Fabricating such structures using rapid-prototyping tools is the focus of a collaborative effort between UNC Charlotte, Clemson University, and Western Carolina University as part of the Carolinas MicroOptics Triangle.4 Ongoing efforts are directed toward reducing the dimensions of the structures to move from millimeter wavelengths and the terahertz frequency regime (in which features measure tens of microns) to infrared and optical wavelengths. Fabricating these stacks using rapid-prototyping tools also offers the possibility of doping the host material with, for example, dyes. This would provide another option for exploiting the inherent nonlinearity associated with the enhanced intensity in the structure.

A device that works at optical wavelengths would require subwavelength gratings with periods of 0.5μm or less, fabricated at the wafer level in a layer thinner than 20μm on a host substrate. In close collaboration with Digital Optics Corporation, we are developing a process in which a silicon layer is patterned on one side, then transferred to another host substrate so that the other side can be patterned. The wafer is then diced, and the patterned unit cells are released from the host substrate and assembled to form the required 1D anisotropic PC structure. We are making these devices. We expect to report on the characteristics of these 1D slow-light structures in July at an Optical Society of America topical meeting on slow and fast light.

We acknowledge the support of DARPA and ARL through grant W911NF-04-1-0319, and the Charlotte Research Institute. We also acknowledge A. Figotin and I. Vitebskiy, whose theoretical work provided the framework for our simulations and fabrication efforts. This inter-institutional research has involved Y. Cao, R. Hudgins, J. Raquet, T.J. Suleski, P.C. Deguzman, and M.A. Fiddy of UNC Charlotte, M. Poutous, J. Morris, A.D. Kathman, and M. Magoon of Digital Optics Corporation, J. Ballato of Clemson University, and K. Burbank, M. Graham, and P. Sanger of Western Carolina University.

Michael A. Fiddy
Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte
Charlotte, NC
Michael Fiddy is the founding director of the Center for Optoelectronics and Optical Communications at UNC Charlotte. He was a faculty member at Kings College, London University, as well as head of the Electrical and Computer Engineering Department at University of Massachusetts at Lowell. He has chaired a number of conferences for SPIE in image and signal recovery and is a fellow of SPIE as well as of the Optical Society of America and the Institute of Physics.