A novel refractive index sensor based on the two dimensional photonic crystal folded Michelson interferometer employing the self-collimation effect is proposed and its performances are theoretically investigated. Two sensing areas are included in the sensor. Simulation results indicate the branch area is suitable for the small index variety range and fine detection, whereas the reflector area prone to the large index change range and coarse detection. Because of no defect waveguides and no crosstalk of signal, the sensor is desirable to perform monolithic integrated, low-cost, label-free real-time parallel sensing. In addition, a flexible design of self-collimation sensors array is demonstrated.
© 2012 OSA
Optical sensors based on total reflection, such as Mach-Zehnder interferometer sensors of optical fibre type [1, 2] or light waveguide type [3, 4], always cannot meet practical demands: small, high sensitivity, cheap and low power consumption. Photonic crystal (PhC) sensors, as a new type of sensors at present, are approximately three orders of magnitude less than commercial integrated-optic sensors. They have different types, such as the point-defect type [5, 6], the line-defect type [7, 8], guided resonance type  and PhC laser type [10, 11].
In order to realize multiple sensing sites, PhC sensor arrays have been developed. Mandal et al.  demonstrated a nanoscale opto-fluidic sensors array based on a silicon waveguide with an adjacent one-dimensional (1D) photonic crystal micro-cavity. Yang et al.  theoretically investigated the performance of sensors array based on lattice-shifted resonant cavities side-coupled to a single PhC waveguide. However, the former realized sensors array on many separate silicon strips, rather than a monolithic silicon slab. While to the latter, the sensing signal of every cavity may interact each other due to some coupling (i.e. crosstalk) in multi-cavity parallel sensing, and if the variety of one signal caused by the index change is so large that beyond the engenfrequency peak of adjacent cavity, the sensing signal recognition will become difficult. So the crosstalk which is always causing the signal distortion restricts the distribution of the sensors on the monolithic platform.
Self-collimation effect, discovered by Kosaka et al.  and promoted by Prather et al.  and others [16–21], is a research hot spot in PhCs. It is famous for allowing diffractionless light propagation in a perfect PhC without “physical” guiding boundaries (e.g. line-defect waveguide), also enabling light beams to intercross without crosstalk . The no-crosstalk character endows the distribution of single device with a relatively large freedom. How to utilize the effect and maintain its priorities in fast developing micro-nano sensors? As we know, there are two solutions for miniature optical sensors . One is based on the resonant propagation of light when the probe light passes the tested object many times. The other is based on the strong nonresonant attenuation of light caused by scattering and radiation loss. In this paper, we first propose a novel 2D PhC sensor based on the folded Michelson self-collimation interferometer (FMSI) with two sensing areas. The sensor not only uses the branch sensing area (BSA) to cause the change of beam interferential phase, but also uses the reflector sensing area (RSA) to induce the variety of interferential intensity. Thus the sensor combines the features of resonant and attenuation sensors. Its performances are investigated by the finite-difference time-domain (FDTD) method. In the end, we apply it to a flexible sensors array.
2. Simulation model
As shown in Fig. 1(a) , the proposed FMSI is composed of one splitter and four reflector mirrors M1, M2, M3 and M4. The perfect 2D PhC as the design platform consists of square lattice air cylinders etched in silicon with the refractive index 3.5. The radius of the air cylinders r1 = 0.26 a, where a is the lattice constant. TE (the magnetic field is parallel to the axis of air cylinders) equal frequency contours (EFCs) of the second band in the wave-vector space show the PhC has square-shaped EFCs in the frequency range between 0.255 c/a and 0.275 c/a (c is the speed of light in free space), which are shown as the big and small solid line squares in Fig. 1(b), respectively. At these frequencies and in the direction perpendicular to the four flat dispersion surfaces of the EFCs, a narrow light beam can propagate within the PhC without diffraction, which is so-called self-collimation effect. It is interesting that if air cylinders are injected some nanofluid with nsensor = 1.5, the two contours retract without destroying the square shape, which are shown as the big and small dashed line squares in Fig. 1(b). This is because with the increase of nsensor, the effective refractive index increases and the whole band structure moves down. However, the light still keeps the characteristics of self-collimated transmittance as before.
The mirrors are formed by another type of PhCs with the radius 0.392 a, which results in the bandgap between 0.2526 c/a and 0.2762 c/a (see Fig. 1(c)), hence the reflectivity 100% is obtained for the self-collimation beams. By enlarging the radius of a row of PhC air cylinders in the ΓΜ direction to 0.434 a, the splitter has the transmittivity between 26.44% and 54.61%, and the reflectivity between 72.74% and 41.46%, which are shown in Fig. 1(d). A 5 a wide light is incident from the input port. After the splitter, it is divided into two beams which transmit along two different branchs, i.e. Banch 1 and Branch 2 (see Fig. 1(a)). When they reach M4, they are reflected respectively, then splitted again and finally interfere in the output port. In Fig. 1(a), the thick red arrow lines indicate the propagation paths of the self-collimated beams in the FMSI. The air cylinders in M4 and parts of branch 2, which are shown as RSA and BSA in Fig. 1(a) respectively, are open to be filled with the nanofluid whose refractive index nsensor is increased from 1.0 to 1.5.
3. Simulation results and analysis
The simulation area is 50 × 50 a2. Perfectly matched layer (PML) absorbing boundary conditions are applied surrounding the computation domain. Firstly, only RSA is used. The calculation results validated by the 2D FDTD demonstrate five transmission peaks in the self-collimation frequency range with transmittivities over 80% are obtained when nsensor in the air cylinders of RSA is 1.0, which is shown in Fig. 2(a) . With the increase of nsensor, the intensity of each transmission peak is decreased. Such decrease is small in case of nsensor between 1.0 and 1.15, which is shown in the inset of Fig. 2(a). But when nsensor is kept increasing to 1.5, the transmission is below 5% for the peaks in the central frequency range due to the gradual disappearance of M4 band gap, which results in the decreased reflectivity for the self-collimation beam. Figure 2(b) clearly reveals the increase of nsensor leads to the band gap of M4 narrowing and moving towards lower frequencies. When nsensor is increased over 1.33, the band gap moves out of the self-collimation frequency range. In that case, M4 has a low reflectivity only originating from the heterostructure formed by M4 and the perfect PhC. The splitter causes the nearly equal intensity destructive interference of the self-collimation beams. Consequently, the transmission corresponding to the nsensor region decreases drastically. While at those frequencies far from the center, the transmission increases a little because there is a large difference of intensity between the two beams thus the incompletely destructive interference happens. From the transmission spectrum corresponding to nsensor = 1.5, we can see some peaks occur. The transmission spectrum is analogy to the spectrum got from the FMSI without M4 (i.e. Sagnec self-collimation interferometer), which is shown in Fig. 2(c). The number of peaks is about 2 times of that when nsensor is below 1.4 (see Fig. 2(a)), since the light path length is increased to two times in the interferometer. For nsensor below 1.33, although the light depth of penetration in M4 is changed with nsensor, the light path length difference between beams in two branches is not influenced. Therefore, the peak frequencies are almost unchanged. Figures 2(d) and 2(e) show the steady-state magnetic field distributions of the light with frequency 0.2643 c/a when nsensor = 1.0 and 1.5, respectively. It is clear that when nsensor = 1.5, the self-collimation beams transmit through M4 completely, forming the intensive standing wave oscillation in the FMSI without the output intensity. The detected transmission is only 2.97%, agreeing well with the theoretical presumption. While for nsensor = 1.0, the constructive interference makes the input light totally output, and the detected transmission is as high as 98.68%. Other transmissions are 94.82%, 83.10%, 50.84% and 11.16% for nsensor = 1.1, 1.2, 1.3 and 1.4, respectively. Figure 2(f) displays the figure of merit (FOM*) according to24]. The maximum 14.7 corresponds to the frequency 0.2718 c/a, which means that a self-collimation beam with such frequency is most sensitive to the change of refractive index in RSA sensing.
Secondly, only BSA is utilized. When nsensor in the air cylinders of BSA is increased from 1.00 to 1.15, the effective refractive index is increased, leading to the decrease of peak frequency. All the obtained spectra corresponding to various nsensor have the sinusoidal shapes, and the transmission peaks shift to lower frequencies with nearly the same peak spacing, which are shown in Fig. 3(a) . One shifting peak corresponding to j is marked with the red arrow head. Here, j is an integer, representing the jth peak. It can be seen that the total shift of the peak is almost a peak spacing. We deduce the relation of the light path length difference with the same order jth interference peak as following:Eq. (2) with Eq. (3) and getEq. (4) we obtain j = 52.93, i.e. j ≈53. Bringing j and other parameters into Eq. (2), we confirm the numerical values by the two sides are equal. The above theoretical analysis is necessary for the confirmation of sensitivity of the sensor.
From Fig. 3(b), we can see the shift in the range of nsensor between 1.00 and 1.15 is nearly a linear increase, so the linear fit is utilized to obtain the sensitivity 157.5 nm/RIU, where RIU is the refractive index unit. If we assume a spectral resolution of the spectral detector is 10 picometers, the numerical simulations show that the detectable minimum changes in refractive index is about 6.35 × 10−5. Moreover, the sensitivity can be further improved by increasing the path length difference of the branches. We also calculate FOM, which is introduced by Sherry  and calculated in our previous work . It is expressed as13, 24–28]. Additionally, the PhC devices of the same type, e.g. symmetric or asymmetric Mach-Zehnder self-collimation interferometers (MZSIs) [29, 30], can also be used as sensors. However, according to our calculations, their sensitivities at the same size are lower than that of the proposed FMSI sensor. This is the sensing advantage of FMSI, for detecting light can pass BSA two times. While for the asymmetric or symmetric MZSI, light passes BSA only one time. In FMSI, the same nsensor change results in larger light path length difference and thus bigger shift of transmission peak is created.
Figures 3(c) and 3(d) display the steady-state magnetic field distributions of the light with frequency 0.2643 c/a when nsensor = 1.15 and 1.09, respectively. It is clear that as nsensor = 1.15, the light almost comes out from the output port entirely, and the detected transmission is 94.60%. While for nsensor = 1.03, the light mainly oscillates in the FMSI. All the peak transmissions cannot reach the unit due to the inserting loss introduced by the splitter and mirrors.
When RSA is used, the transmission of the light with frequency 0.2643 c/a in the range of nsensor between 1.00 and 1.15 is decreased slowly, from 98.68% to 86.94% (see Fig. 4 ). But if we use BSA, the transmission is varied largely, from 98.68% to 5.78%, and back to 94.60%. In this range, the RSA-based sensor has much lower sensitivity than that of the BSA-based sensor. However, if the range of nsensor is expanded, i.e. from 1.0 to 1.5, the transmission peaks of the BSA-based sensor will red shift over a peak spacing. Thus the sensing range is limited. While for the RSA-based sensor, the transmission will keep monotone decreasing with the increase of nsensor. Considering if something wrong with the intensity reading, the RSA-based sensor is not easy to recognize, we only apply it in the detection of large index change range. The BSA-based sensor is prone to the small range and fine index detection. Accordingly, both large and small index range detection of nanofluid can be realized in such a single FMSI sensor. Maybe we can firstly do the RSA-based sensing and know the approximate index variety region, then confirm the index of nanofuid precisely by the BSA-based sensing.
4. Design of sensors array
Here, we give our design of the monolithic integrated parallel self-collimation sensors array, which sufficiently utilizes no crosstalk of self-collimation beam in perfect PhC. As shown in Fig. 5 , the light is input by the external optical fiber at the input port, then splitted into three beams which fulfil the sensing tasks in three separate FMSI sensors, respectively. Some mirrors are shared by flexibly arranging the sensors to reduce the fabrication process. Finally, three sensing signals output from port 1, 2 and 3, respectively, and are coupled into the fibers and received by the external power meters or spectrometers. Though the sensing signals intercross with the input light in the PhC, there is no crosstalk to cause distortion. The more practical self-collimation sensors array will be based on PhC slabs, or Silicon-On-Insulator. The simulation and experimental results will be shown in our future work. For the operating wavelength around 1550 nm, the size of single sensor is approximately 20 × 20 μm2. Although here only 3 sensors are integrated on the monolithic platform, but according to the supercollimation beams with the transmittance distance as far as centimeter scale , the ideal integrated number in parallel sensing can reach 250 without considering the inserting loss of single element.
We have proposed a novel refractive index sensor based on the 2D PhC FMSI and investigated its performance by the FDTD simulation. Two sensing areas, i.e. RSA and BSA, play different roles for the sensor. It can realize not only the large index change range and coarse detection, but also the small index variety range and fine detection. Fully utilizing the advantage of no crosstalk, we applied the sensor to a parallel sensors array. Although some parameters have not been optimized, it does not affect our analysis of device sensing characteristics. Because of no defect waveguides, no crosstalk and small size, the sensor and sensors array are desirable to perform monolithic integrated, low-cost, label-free real-time sensing.
The authors thank Prof. Xiyao Chen and Prof. Zexuan Qiang for valuable discussions. This work is supported by the Chinese National Key Basic Research Special Fund/CNKBRSF (Grant Nos. 2012CB933501 and 2011CB922002), the National Natural Science Foundation of China (Grant Nos. 61025025, 61137003 and 60838003) and the Technology of Fujian Education Office of China (Grant No. JA09226).
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