1. Introduction

Optical microcavities like microring [1, 2], microtoroids [3, 4] and photonic crystal (PhC) cavities [5] have been widely and intensely researched for label-free biochemical sensing. In typical sensing applications, the shift of resonant wavelength for the microcavities induced by the change of background refractive index is used for analyzing samples. Therefore the detection limit of such sensors is determined by the Q-factor of the cavity mode and its sensitivity (nm/RIU) by the overlap between the light field and the background analytes. PhC cavities have attracted increasing attention owing to the advantage of high Q-factor, wavelength-dimension sensing area and strong light-matter interaction. Two-dimensional (2D) PhC cavities with Q-factor as high as 2 × 10⁶ have been experimentally achieved [6]. Thus, various kinds of micro-sensor based on PhCs have been demonstrated [7–10].

Recently there has been much interest in PhC cavities realized in free standing nanobeams patterned with a one-dimensional lattice of holes [11–17]. Such one-dimensional (1D) nanobeam PhC cavities have been demonstrated with experimental Q-factor over 10⁵ [11, 13], which is comparable to most 2D PhC cavities and much higher than air-slot cavities. In additional, the structural simplicity and small footprint inherent in 1D PhC cavities make them easier to be densely assembled for on-chip integration.

However, there are two intrinsic problems with PhC cavities for refractive index sensing. Firstly, the overlap of the light field with analytes (low-index) is always insufficient because the major part of light field is confined within the high-index area. The sensitivity of a silicon air-hole nanobeam sensor is only 83 nm/RIU [10]. This is usually due to the small percentage of void space in PhC cavities, especially for 1D PhC cavities. Secondly, the high-index membrane material (silicon, etc.) cuts the void space into different pieces, such as isolated air-holes, and blocks the flow of sample fluids [8].

In the present paper, an optical sensor based on 1D PhC stack mode-gap cavity has been designed, fabricated and characterized. Firstly, 1D PhC stack mode-gap cavity has been designed. Then, we analyze the dependence of the quality factor and the sensitivity of the cavity on the geometric parameters of the cavity. Finally, the cavity has been fabricated and the peak wavelength shift with volume concentrations for the water-ethanol mixture was recorded and analyzed.

2. Device design and analysis

Several designs of 1D PhC cavity with ultrahigh Q/V have been reported, such as nanobeam cavity [11] and mode-gap cavity [13]. Instead of modifying the holes periodicity and/or size, B.-H. Ahn et al used an adiabatic parabolic tapering of the width of the nanobeam cavity to demonstrate an on-chip laser in a InGaAsP slab [12]. Figure 1(a) shows the schematic for the 1D PhC stack mode-gap cavity considered in our work. It consists of a simple periodic array of dielectric blocks in analytes. This array has a true 1D PBG on the x axis. The widths (W_y (i)) of the dielectric blocks are quadratically modulated (W_y(i) = W_y(0) + i²(W_y(i_max)-W_y(0))/i_max², from the center to both sides, i increases from 0 to i_max) in order to introduce a defect into the photonic bandgap (PBG) (Fig. 1(d)). Compared to the cavity proposed by M. Notomi et al. in [13, 14], we modulate W_y instead of W_x. By such modulation, the area of the void space in the center of the cavity can be greatly increased. In addition, only a limited variation can be achieved when modulating W_x, because W_x should not be too small regarding the fabrication limitation. All these considerations are intended for the goal of higher sensitivity and make the fabrication easy.

 

Fig. 1 (a) Schematics of width-modulated stack cavity, in which a = 400 nm, W_x = 0.3a and W_y quadratically modulated from W_y(0) = 2.5a in the center to W_y(20) = 5.0a on both sides; (b) Intensity profile (|Ey|²) calculated by 3D FDTD method; (c) Zoomed in picture of the framed part in (a) with annotations; (d) TE band structure of the mode-gap waveguides with W_y = 2.5a (red) and W_y = 5.0a (blue). The black dot indicates the resonant frequency.

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Silicon-on-Insulator platform is considered in our work. The refractive index of the silicon stack and the silica insulator layer are 3.46, 1.44 respectively. The thickness of the silicon layer and the insulating layer are 220 nm and 2 μm, respectively. The lateral size of the silicon block (W_x) is chosen to be 0.3a so that the sample fluid can easily infiltrate into the void space between silicon blocks and effectively interact with the light field. The simulation is performed with commercial finite difference time domain (FDTD) software (Lumerical FDTD Solutions). The cavity was optimized using the deterministic high-Q design method introduced by Q. Quan [17]. Figure 1(b) shows the intensity profile (|Ey|²) calculated by 3D FDTD method. The calculated Q-factor is 1.74 × 10⁷ (evaluated according to the decay of electromagnetic energy as a function of time) and the effective mode volume is 1.48(λ/n_Si)³ (defined as $V={{\displaystyle \int dV\epsilon \left|E\right|}}^2/{[\epsilon |E{|}^2]}_{\max }$). Although the peak energy density is still confined in silicon, a large part of electric field (about 35%) locates in the void space which enables more interaction with analytes. The percentage of electric field in the void space can be further increased by varying W_x and W_y(0). Figure 1(d) shows the TE band diagram, also calculated by 3D FDTD method. The defect mode locates close to the center of the bandgap.

For the application in an optical sensor, cavities with high Q-factors and high sensitivity are preferred. Thus, the dependence of sensitivity and Q-factor on the key geometric parameters is systematically studied. Here sensitivity is defined as the shift of resonation wavelength when the background refractive index changes by one refractive index unit (RIU). The value of sensitivity and Q-factor vary with W_x and W_y(0) are given in Figs. 2(a) and 2(b). From Fig. 2, we can find that the cavities with smaller W_x and W_y(0) give higher sensitivity. This can be easily understood since more percent of electric field energy locates in the void space for the cavities with smaller W_x / W_y(0). However, a moderate Q-factor must be maintained in this optimization. Figure 2(a) shows that Q-factor remains high enough when W_x is larger than 0.3a but will drop sharply if W_x is further reduced.When W_x is large enough (>0.3a in this case), the electric field can be well confined by the robust silicon stacks. However, it will too narrow to confine the electric field if W_x is further reduced (from 0.3a to 0 in this case), thus Q-factor will drop then. From Fig. 2(b), we can find that the highest theoretical Q-factor can be achieved when W_y(0) = 2.5a. This is reasonable since the resonant mode locates around the center of photonic bandgap at this value. Thus, W_x ad W_y(0) are set to be 0.3a and 2.5a respectively, considering the trade-off between sensitivity and Q-factor.

 

Fig. 2 Influence of (a) W_x, (b) W_y(0) and (c) number of Gaussian mirror segments (NG) on the Q-factor and sensitivity of width-modulated stack cavity sensor;(d) Wavelength shift and variance of Q-factor over different background refractive indices.

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The number of Gaussian mirrors segments (NG) on either side of the stack cavity will also influence the sensitivity and Q-factor. From Fig. 2(c), we can find that Q-factor increases exponentially by adding more Gaussian mirrors when NG<20. Meanwhile mode volume and footprint of the stack cavity sensor will also be inevitably increased. However, sensitivity remains almost unchanged for different NG. This is significant that the Q-factor, mode volume and footprint of the stack cavity sensor can be flexibly tailored to different requirements without sacrificing sensitivity. To achieve a high Q-factor while keep a reasonable footprint, we choose NG = 20 in our work.

From the above analysis, the final parameters for the cavity are: W_x = 0.3a, W_y(0) = 2.5a, NG = 20. The resonant wavelength and Q-factor for the cavity vary with the refractive indices of the covering analytes is given in Fig. 2(d). From Fig. 2(d), we can find that the Q-factor maintains a high value over a wide range of background refractive index, indicating a very large sensing range of the device. This is especially advantageous compared to the microring based sensors whose sensing range is inevitably limited by the free spectrum range (FSR).

3. Fabrication and optical measurement

We fabricated and characterized the stack cavity sensor. The device was fabricated on a SOI wafer (SOITEC Inc.) with a silicon layer of 220 nm and insulating layer of 2 μm. The geometric parameters for the cavity are: a = 400 nm, W_x = 126 nm, W_y(0) = 1017 nm, W_y(20) = 2012 nm, the width for input/output waveguide is 2 μm. The pattern was defined on a positive electron beam resist film (PMMA 950K) of 310 nm thickness with an e-beam lithography tool (Raith 150 II) using 20kV acceleration voltage. Then the pattern was transferred to the 220 nm SOI device layer by inductively coupled plasma (ICP) etcher using a gas mixture of SF₆ and C₄F₈. The resist was then removed with acetone in ultrasonic cleaner followed by an ashing process. In order to measure the transmission spectrum, we used the grating coupler approach for coupling from input/output waveguides to fibers. The grating couplers are fabricated on both the input and output waveguide by another overlay exposure followed by a shallow etching (70 nm). Scanning electron microscope (SEM) of the fabricated device is shown in Fig. 3 .

 

Fig. 3 Scanning electron microscope (SEM) image of the fabricated stack cavity sensor.

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Optical transmission measurement for the stack cavity sensor was taken by scanning a tunable laser with a power meter. A polarizer is used to filter out the TM-like modes. Figure 4(a) shows the measured transmission spectrum when the device is immersed in 5% water-ethanol mixture (5% ethanol and 95% water in volume). The estimated input power is intentionally reduced to 6 μw here to exclude any nonlinear effect. The full width at half maximum (FWHM) of the extracted transmission peak is about 58 pm, corresponding to a high Q-factor of 27,000. The degradation of measured Q-factor compared to the simulation value may come from fabrication errors, absorption loss [14] and scatterings due to impurities in the analytes. In order to measure the sensitivity we immersed the device with water-ethanol mixture of different volume concentrations (0%, 5%, 10%, 20%, 30%, 50%) and measured the transmission spectrum (Fig. 4(b)). The estimated input power for sensing measurement is increased to 180 μw for getting higher signal-to-noise ratio. Meanwhile, we also checked the possibility whether the high-order modes will be excited in the sensing range (1581nm-1591nm) by using higher input power, since the absolute output power of the high order modes is too low to be detected if the input power is 6 μw. We did find that the cavity supports high order modes, but these high order modes are well separated from the fundamental mode and the intensity of the high order modes are much smaller. Before another optical fluid was applied, the device was cleaned carefully to remove the previous one. The chip was rinsed with acetone and deionized water and dried after we changed a mixture of different concentration. In our experiment, the Q-factor remains about 27, 000 across the whole wavelength window (~50 nm) defined by the grating coupler and scanning tunable laser. According to the refractive index of ethanol-water mixtures [1, 18], the sensitivity for the proposed sensor is determined to be about 269nm/RIU after a linear fitting (Fig. 4(c)). The experimental data fit to a linear calibration curve and show quite good agreement with the FDTD simulation (273nm/RIU). Because there is no limitation of FSR, the sensing range of our stack cavity sensor is only limited by the decreasing Q-factor with increasing background index. From the measurements, we can found that Q-factor keeps at similar values for our cavity covered water-ethanol mixture of different volume concentrations. Thus, a wide sensing range can be achieved.

 

Fig. 4 (a) Measured transmission spectrum with estimated input power of about 6 μw. The dots are the experimental data and the line is the fit to Lorentzian lineshape. The full width at half maximum (FWHM) is about 58 pm; (b) The transmission spectrum taken as the cavity was immersed into water-ethanol mixture of different volume concentrations with estimated input power of about 180 μw (c) Wavelengths of the cavity mode in different background refractive indices; (d) Wavelengths of cavity mode in different background temperatures when the estimated input power is about 6 μw. The slope is about −0.025nm/°C.

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Besides, the sensing performance of stack cavity sensor may be slightly influenced by ambient temperature. This is because the resonating wavelength is mostly determined by the refractive indices of the device layer (silicon) and analytes (water-ethanol mixture in this experiment), and in turn these refractive indices varies slightly with temperature. To evaluate such effect, a temperature dependent measurement is carried out with minimized input power to eliminate the thermo-optic effect due to optical power heating [14]. The chip is heated by a thermo resistor and the temperature is controlled by tuning the applied voltage. The wavelength drift induced by temperature is shown in Fig. 4(d). There will be a blue shift of approximately 0.025 nm when the ambient temperature is increased by 1 °C. Owing to the good linearity of the wavelength drift with temperature, the thermal drift can be conveniently compensated by a reference cavity sensor if necessary.

4. Conclusion

In this paper, we have demonstrated an ultra-sensitive optical sensor based on 1D-PhC stack mode-gap cavity. A Q-factor as high as 27,000 was measured. The confined mode has a large percent of electric field energy locating in the void space and has large interaction with the analytes. The parameters for the cavity are optimized to achieve a high sensitivity while keeping a high Q-factor. We fabricated the stack cavity sensor and characterized in solutions of different concentration to confirm the numerical results. The measurement shows a sensitivity of 269nm/RIU. In additional, the sensing range of the proposed sensor is quite large since there is no limitation of FSR. Considering the benefits of high Q-factor, high sensitivity, large sensing range and small sensing area, we believe that this device will be a promising candidate in on-chip biochemical sensing.