Photonic crystals reduce the size of optical sensors

Today, sensors play fundamental roles in many applications, including automotive safety, consumer gadgets, defense and homeland security, environmental monitoring, household appliances, and medical equipment. Among the various kinds of sensors, opto-chemical devices make up an important class.¹ In particular, Mach-Zehnder interferometers (MZI)—invented in 1891 by physicists Ernst Mach and Ludwig Zehnder—create effective chemical sensors with high sensitivities. In these devices, a material in the sensor path induces a phase shift that changes the output power at two detectors due to the interference of the beams (see Figure 1).

A typical MZI sensor requires precise alignment of four optical elements: two beam splitters and two mirrors. For this reason integrated optical components have been used to fabricate MZIs with lateral dimensions on the order of centimeters. A typical integrated-optical MZI biochemical sensor can measure the change in the sensor path length caused by the interaction of the evanescent optical field with a film that captures, or reacts with, a particular analyte. To create increased specificity or to detect multiple chemistries, an array of sensors with varying films is used. We have engineered the unique dispersive properties of photonic-crystal (PhC) structures to create a robust yet compact array of micro-scale Mach-Zehnder optical sensors.²

PhCs are periodic-dielectric structures that manipulate the propagation of electromagnetic waves, much like semiconductors direct the flow of electrons. Moreover, PhCs possess a photonic bandgap, which means that light of certain wavelengths cannot propagate through them. Additionally, the structures can possess unique dispersion characteristics that enable the structures to behave like a lens or superprism.³

We use software and hardware acceleration tools to optimize a PhC's dispersion characteristics for use in optical sensors. An example of a PhC structure with such desirable characteristics is a square lattice of air columns in silicon with pitch a, a radius of 0.26a, and a refractive index of 3.5 (see Figure 2). By examining the unit cell of the structure with software based on the plane-wave method, we can calculate the dispersion surfaces that indicate the allowed wavevectors (k_x,k_y), as a function of normalized frequency or wavelength.⁴ By slicing the dispersion contours at fixed frequencies, we can show that this structure has the equal frequency contours (EFCs) for a transverse-electrical (TE) optical beam (Figure 3).

The group velocity vector—which, by definition, is normal to the dispersion surface or EFCs—governs the direction of light propagation within PhC structures.⁵ The square pattern of the EFCs at a normalized frequency of 0.26a/λ results in most incident wave vectors traveling north-south or east-west in the structure. This is known as the self-collimation effect, and it allows a narrow beam to propagate within a PhC lattice without any significant broadening. This effect was first experimentally demonstrated in 1999, ⁵ and it can be used for wave guiding and the dense routing of optical signals.⁶ Using the self-collimating silicon-PhC structure shown in Figure 2, and adding PhC mirrors and a one-row beam splitter, we designed a compact MZI sensor (see Figure 4).² The beam splitter is designed to equally split the optical signal and cuts diagonally through the device. Two PhC mirrors—one in the upper right corner and another in the lower left—direct the beams to the output ports. If half of the MZI is exposed to a gas or liquid and the other half is protected from the material under test, the MZI becomes a relative-refractive index sensor. In this particular device, the MZI is 12 × 2μm with a path length of 24μm for each branch. These dimensions are approximately three orders of magnitude less than commercial integrated-optic MZIs.

Figure 5 shows the steady-state amplitude of the electromagnetic field in the sensor, as the refractive index in the air columns in the lower part of the sensor varied: 1.0 (baseline), 1.1, and 1.2. The simulation area is 30μm wide and 22μm tall, with a 10nm (∼λ₀/150) cell size—resulting in a mesh with 6.6 million nodes (3000 × 2200). Each side includes 100 perfectly matching layers, each being 1μm thick. We performed the simulations with our EMPLab™ software, accelerated with an integrated, graphics card-based, finite-difference time domain (FDTD) engine. This engine and sample files are available for free download from the EM Photonics website (see author information). The accelerator computed the simulation in less than 14min—roughly 270 times faster than MATLAB® code, which took roughly 60 hours. The increased computing power enables the modeling of numerous configurations to optimize a device. Figure.6 is a plot of the relative power at the two output ports of our MZI sensor as the refractive index in the lower part of the interferometer is varied from 1.0 (air) to 1.5.

In conclusion, our MZI sensor relies on self-collimation and a PhC beam splitter to guide light in a two-dimensional structure. The roughly 12μm by 12μm MZI sensor can detect a refractive-index shift of less than 0.01 (see Figure 6). The sensitivity of the sensor could be improved by enlarging the device and/or incorporating PhC structures that can slow down the propagation of the light.⁷ On the other hand, the micron-scale dimensions of our device allow the fabrication of low-weight, compact, dense, and highly parallel sensors. By adding further beam splitters, but using the same optical source, multiple MZI sensors could be fabricated in parallel to sense multiple biological or chemical agents.

The authors acknowledge John Humphrey and Dan Price of EM Photonics for their efforts in the development of the graphical-processing-unit accelerated FDTD solver.