In recent years, chemical and biological sensor arrays using photonic crystals have been vigorously studied because of their potential for nanophotonic label-free environmental monitoring and biomedical detection^[1,2]. The mid-infrared wavelength range (2~20 μm) represents the characteristic absorption fingerprints of most molecules. For instance, aromatic C-H stretch, which is stable in structure, difficult to decompose, and highly toxic, has a strong absorption at λ = 3.3 μm^[3]. The silicon-on-insulator (SOI) structure with a 3~5 μm transmission window is an ideal material to design PhC sensor to detect aromatic compounds^[4].

With photonic band gaps, PhC can afford us complete control over light propagation by preventing light from propagating in certain direction with specific frequencies. Nevertheless, the actual fabrication of a three-dimension periodic structure remains difficult. So PhC slabs using two-dimensional periodicity combined with vertical index-guiding are proposed. By introducing line and point defects in PhC slabs, one can create waveguides^[5], cavities^[6,7], bends^[8,9], splitters ^[10] and filters^[11,12,13] of compact size. Frequency-domain plane-wave expanded method is used for the solution of partial differential equations to find band structure ω(k) and the associated fields for PhC ^[14]. The TE gaps for the triangular lattice of air holes are usually larger than those of the square lattice because the former is more symmetric, and the hexagonal Brullouin zone of the former is more circular. So the triangular lattice of air holes was chosen.

In this paper, we present a four-channel mid-infrared silicon PhC sensor working at λ = 3.3μm, spaced by 10nm. The sensor is designed on SOI platform for standard CMOS technique. The optical characteristics of the nanocavity structure are simulated by 3D-FDTD method. The transmittance of each channel is about 39%, with non-uniformity of transmittance across channels less than 0.25 dB. The capability of the sensor is demonstrated by detecting carbon tetrachloride and benzene solutions, and shows a sensitivity of 209.2 nm/RIU.

The schematic of the designed multiport in-plane sensor is depicted in Fig. 1, which consists of a bus waveguide, drop waveguides, and cavities. Two 60° bend line defects are introduced into multichannel operation.

The band structure for a crystal consisting of air holes in silicon (ε = 11.792) with radius r = 0.4a is plotted in Fig. 2. There is a gap between the first and second TE bands, from ωa/2πc = 0.248 to ωa/2πc = 0.405 with the band width as 47.9%. There are light cones (ω ≥ c|k_|||) for the extended modes propagating in the air or SiO₂ substrate, where k_|| is the horizontal wave vector. As the light cone exists, we select our operating wavelength λ = 2πc/ω = 3.3μm to lie at frequency ωa/2πc = 0.291. So we can calculate the lattice constant as a = 960nm, and the air hole radius r = 0.4a = 384 nm. We set the thickness of slab as 800nm, which is thick enough for the fundamental mode to be well confined and thin enough to forbid higher-order modes to propagate within the slab.

A photonic crystal sensor is composed of a cavity and two waveguides, i.e. the bus waveguide and the drop waveguide. For multi-channel operation, two 60° bend line defects are introduced. We apply a simple optimization method, which makes the bend mode as symmetric as the straight waveguide mode^[15]. The two air holes at the corner are of radius R_b=300 nm, and they are shifted 50 nm away in opposite directions along the symmetric axis of the bend. The mechanism for improvement of transmission is to match both the symmetry of modes and their wave numbers in the straight waveguide and the bend^[4]. Fig. 3(a) and 3(b) show the energy distribution in the bends at λ=3.3 μm. The scattering at the bend corner has been efficiently alleviated. The transmittance in bend waveguide at λ = 3.3μm is 85% compared to normal straight waveguide.

We can design a cavity by removing or adjusting some holes around a single point. Resonant phenomena in cavities are dependent on the precise geometric properties, such as size and shape. To excite the whispering gallery mode (WGM) ^[16], we remove the central air hole and reduce the radius of the border holes in the cavity which is denoted as R_c. Such bound modes are guided by means of repeated reflections. After infinite repetitions, absorption, scattering, and material dispersion could be neglected. The structure schemes diagram and energy distribution of the hexapole mode are shown in Fig. 4(a). Due to the hexagonally symmetric WGM field distribution, the phases of adjacent lobes are opposite to each other, so destructive interference occurs and decreases the horizontal radiation. Near the resonant frequency, light from the input waveguide can couple into the cavity, and the cavity in turn can couple into the output waveguide efficiently when Q_v = Q_h is obtained ^[17], where Q_v is vertical quality factor representing the emission phenomena occurring between the cavities and free space, and Q_h is horizontal quality factor representing the trapping phenomena occurring between the waveguides and the cavities. The total quality factor Q for a coupled cavity can be written as Q^-1 = Q_h^-1+ Q_v^-1. The expected high quality factor is deduced by the decaying signal in the simulation, because the electromagnetic fields cannot completely decay in the simulation in a reasonably time. The largest Q ~1.2×10³ is obtained when R_c is 200nm. The cavity works as a WGM cavity, and the resonant peak is dependent on the cavity diameter D = mλ/2n_eff, where m is the order of peaks. The desirable resonant frequency could be reached by shifting the border holes to change the diameter of the cavity.

The six nearest-neighbor holes in each cavity are pushed 49, 55, 61 and 67nm (denoted as S_i, i = 1, 2, 3 and 4) away from the cavity center to reach the resonant wavelength λ = 3.29, 3.30, 3.31 and 3.32μm, respectively. When the direct reflected light and the light decaying backwards from the cavity cancel exactly by destructive interference, the energy in the cavity decays into the two waveguides at equal rates and the transmission reaches maximum value. The transmission spectrum of the device is depicted in Fig.5. The transmittance in the channel with center wavelength at λ = 3.30μm is 0.386 and the nonuniformity of transmittance across the four channels is less than 0.022(i.e.0.25dB). Quality factors Q is calculated using 3D-FDTD method and listed in Table 1.

The device works as a sensor for solutions with different chemical compositions and concentrations, since the resonant wavelength is sensitive to the refractive index of surrounding environment. We choose the mixture of carbon tetrachloride and benzene as the testing solutions, with the refractive index changing from1.4607(corresponding to pure carbon tetrachloride) to 1.5012(corresponding to pure benzene). As shown in Fig. 6(a), the resonant wavelength of the sensor (center wavelength λ = 3.3μm in air) in different solutions shifts from 3.3772 μm (in carbon tetrachloride solution) to 3.3856 μm (in benzene solution). The linear fits of four channels of the sensor (with center wavelength λ = 3.29, 3.30, 3.31 and 3.32μm in air) between changes of resonant wavelength and changes of concentration are shown in Fig. 6(b). The sensitivity of a sensor is defined as the rate of resonant wavelength shifts with respect to the change in the refractive index, with the corresponding unit of nm/RIU. The sensitivity is calculated as 209.2nm /RIU. This linear red-shift could be explained as the perturbation theory for linear Hermitian eigenproblem. The kernel of the Maxwell equations for a harmonic mode in a mixed dielectric medium is a differential equation for electric field E(r), given by:

∇×∇×E(r)=ω/c2ε(r)E(r)

By applying the perturbation procedure to equation (1), we obtain a formula for the frequency shift △ω that results from a small perturbation △ε of the dielectric function^[18]:

Δω=-ω/2⋅∫d3rΔεrEr2/∫d3rεrEr2+oΔε2

In this equation, ω and E(r) are the frequency and the mode profile for the perfectly linear and unperturbed dielectric function ε. Consider the case of the holes with a refractive index n = ε^1/2, in which the index is perturbed in some regions by an amount △n. The volume integral in the numerator of equation (2) has nonzero contributions only from the perturbed regions. The fractional change in frequency is equal to the fractional change in index multiplied by fraction of the electric-field energy inside the perturbed regions:

Δω/ω=-F⋅Δn/n

F is a sensitivity function related tothe mode profile for the dielectric function ε, and it is a constant since the change of the mode profile is negligible in this case shown in Fig. 4(b). The change is proportional to the analyte concentration and represents quantitative information about the concentration of the chemical.

The previously reported PhC sensors have achieved sensitivities of 363.8 nm/RIU^[19],396 nm/RIU^[20],460 nm/RIU^[21,22], 500 nm/RIU^[1], higher than the sensitivity of our sensors. However, these sensors have only one channel. A reported multichannel PhC sensor^[23] is able to detect four different analytes (with refractive index n=2.25, 2, 1.75 and 1.5) in four channels, respectively. But this sensor is unable to detect the change of the concentration of analytes (with minor change of refractive index) thus no sensitivity data is shown in this work, which limits the practical application. Besides, the nonuniformity of transmission across the four-channel device in this work is rather large, with the transmittance of four channels ranging from 35% to 95%. In our work, we have achieved a four-channel sensor, which is able to detect the concentration change of mixture of carbon tetrachloride and benzene solutions with a sensitivity of 209.2nm/RIU. And the nonuniformity of transmittance across the four channels in our work is very small, less than 0.022(i.e.0.25dB).

The fabrication of the proposed silicon PhC sensor can be realized on an SOI platform using elelctron beam lithography (EBL) and inductively-coupled plasma(ICP) dry eching which includes the following steps. First, SOI wafer with appropriate top-silicon-thickness should be chosed. Then, electron-beam resist (eg, ZEP520) is spin coated on top of an SOI wafer. Then after exposure to electron beam, the developing and fixing steps are carried out. After that, ICP etching in a gas environment of SF6 and C4F8 is used to form the air holes in PhC sensor. Finally, by removing the resist, the fabrication of PhC sensors is completed. As for the mass production in the future, EBL is replaced by ultra-violet (UV) lithography. First, a mask is fabricated according to the design parameters. Then, using UV lithography technique and the folloing ICP etching technique, thousands of PhC sensors are fabricated on an SOI wafer. Finally, slicing, encapsulation and testing of PhC sensors are carried out.

Standard CMOS process can introduce variations to hole size because of optical proximity effects. The variations in hole size can be considered as deviations from the designed lattice, affecting out-of-plane loss and the photon lifetime of the cavity. Different hole radius, ranging from 374 nm to 394 nm, are simulated to evaluate the tolerance of the sensor, and the results are listed in Table 2. These simulations verify that the sensitivity function is stable with a level about 200nm/RIU though resonant wavelength has shifted as expected. The stability of the sensitivity function can be explained by the unchanged energy distribution of the hexapole whispering gallery mode and quality factor of the sensor. The tolerance of the sensor is large enough to be fabricated by deep UV lithograph for the batch production nowadays.

Before the successful application to label-free environmental monitoring and biomedical detection, further work should be done. In this work, we use mixture of carbon tetrachloride and benzene solutions as an example. We need to broaden the working waveband in order to detect more kinds of chemical compounds and molecules. Furthermore, sensitivity should be raised to detect minor change of concentration. In addition, integration of sensors with sources and analyzers are necessary, which includes broadband mid-IR source, polarizer, input fiber, PhC sensor, output fiber, optical spectrum analyzer. Finally, reliability and portability should be considered in future applications.

We have proposed a four-channel SOI based 2-D photonic crystal optical sensor suitable for label-free sensing. First, our simulation shows a transmission of 60% for the linear defect waveguide (i.e. the bus waveguide) at λ = 3.3 μm. Second, we have designed cavities with hexagonally symmetric WGM field distribution reaching a quality factor of about 1.2×10³. And then, the output bend waveguide is optimized to obtain 85% transmission compared to normal straight waveguide. Finally, the nonuniformity of transmittance across the four-channel device is less than 0.25 dB, and a sensitivity of 209.2 nm /RIU is presented. The sensitivity function remains stable when the hole diameter varies ±10 nm. This sensor has potential applications in nanophotonic label-free environmental monitoring and biomedical detection.