We present nanoscale photonic crystal sensor arrays (NPhCSAs) on monolithic substrates. The NPhCSAs can be used as an opto-fluidic architecture for performing highly parallel, label-free detection of biochemical interactions in aqueous environments. The architecture consists of arrays of lattice-shifted resonant cavities side-coupled to a single PhC waveguide. Each resonant cavity has slightly different cavity spacing and is shown to independently shift its resonant peak (a single and narrow drop) in response to the changes in refractive index. The extinction ratio of well-defined single drop exceeds 20 dB. With three-dimensional finite-difference time-domain (3D-FDTD) technique, we demonstrate that the refractive index sensitivity of 115.60 nm/RIU (refractive index unit) is achieved and a refractive index detection limit is approximately of 8.6510−5 for this device. In addition, the sensitivity can be adjusted from 84.39 nm/RIU to 161.25 nm/RIU by changing the number of functionalized holes.
©2011 Optical Society of America
With the development of optical techniques, they represent one of the most popular methods for performing sensitive and label free biomolecular detection. When comparing to analogous mechanical or electrical label free methods , the primary advantages of optical techniques are that the devices can be fabricated relative easy and the broad range of fluids and environments in which they can be used (e.g. gas, water and serum, etc.). Recently, although numerous different microsensor structures have been developed (such as photonic crystal based sensors [2,3], resonant cavity sensors [4,5], whispering gallery mode sensors [6,7], surface plasma resonance (SPR) sensors  and interferometric sensors [9,10], etc.), the detection of all these cases is based on measuring the variation in refractive index. Of all the different architectures that have been developed, the sensors based on photonic crystal are particularly interesting not because they are necessarily more sensitive to intensive or bulk properties (e.g. refractive index) but rather because the small interrogation volume makes them more sensitive to extensive properties (e.g. total bound mass). In addition, the 2D (two-dimensional) photonic-band gap microcavity  sensors with high quality factor (Q) can amplify this effect by reducing the probed volume to the size of the optical cavity, which can be on the order of cubic wavelength. Since the mode volume is so small the total amount of mass required to result in a measurable change in the refractive index (reflected by a change in the wavelength of the resonant peak) can also be very small. Examples of such systems include that of T. W. Lu et al.  who demonstrated an ultra-high sensitivity optical stress sensor based on double-layered photonic crystal microcavity, S. H. Kwon et al.  who demonstrated an optimization of chemical sensor based on photonic crystal cavity and J. Dahdah et al.  who demonstrated a photonic crystal cavity based on a single hole defect filled with a sensitive absorbent layer for sensing applications.
However, the design drawback of these microsensors is that they typically operate as point or single sensor and the number of targets which can be screened for at one time is relatively small. Recently, in order to overcome this drawback and realize multiple sensing sites, sensor arrays using photonic crystal or photonic crystal fiber have been developed. Examples of such systems include that of S. Mandal et al.  who demonstrated a nanoscale opto-fluidic sensor arrays based on a silicon (Si) waveguide with a 1D (one-dimensional) photonic crystal micro-cavity (side resonator) that lies adjacent to the waveguide and Sevilla et al.  who demonstrated a photonic crystal fiber (PCF) sensor array based on modes overlapping. However, in the Ref. , sensor arrays consist of a silicon waveguide with a 1D photonic crystal micro-cavity, which is realized on many separate silicon strips, rather than a monolithic silicon slab. In addition, the extinction ratio of single drop of 1D photonic crystal micro-cavity in the Ref.  is only 4–10 dB. Ideally one would like an architecture that combines high quality factor, low mode volume sensing of the above devices with the ability to multiplex multiple detection sites along a single photonic crystal waveguide (PhCW) on monolithic substrates.
In this paper, we present a novel paradigm for opto-fluidic [16,17] sensing that makes it possible to overcome the above limitations, which we refer to as Nanoscale Photonic Crystal Sensor Arrays (NPhCSAs) on monolithic PhC module. The device consists of a photonic crystal resonant cavity arrays with high quality factor side-coupled to the W1 PhC waveguide. The extensive simulation results demonstrate that the resonant wavelength of the mode localized in the microcavity shifts its spectral drop position following a linear behavior when the refractive index in the region surrounding its cavity changes, and the extinction ratio of well-defined single drop exceeds 20 dB. In addition, the sensitivity of 115.60 nm/RIU is observed when the number of functionalized holes equals 6 (N = 6). The sensitivity can also be varied from 84.39 nm/RIU (when N = 2) to 161.25 nm/RIU (when N = 28) by adjusting the number of functionalized holes. Although the bulk refractive index sensitivity of this device is not higher than that of techniques such as SPR, its chief advantage lies in its potential for low mass limit of detection which is enabled by confining the size of the probed surface area. Each sensing site consists of a side-coupled PhC microcavity (H0-cavity)  that can individually shift its resonant peak in response to changes in refractive index in the region surrounding its cavity. In this paper we describe the device design in details, theoretical simulation methods and analogue device characterizations demonstrating the performance of this architecture. The numerical simulations are used to analyze and confirm the suitability of our NPhCSAs platform as a sensitive biochemical sensor array. To illustrate the working of our device we fill the functionalized area with solutions possessing different refractive indices. We determine the sensitivity of our devices by observing the shift in the resonant wavelength of the resonators as a function of the variations in refractive index in the region surrounding the cavity.
2. PhC slab waveguide (W1) design
Figure 1 shows a 3D illustration of our PhCW structure design which is based on triangular lattice, hole-array based PhC slab. This is because that compared with the pillar-array based PhC , hole-array based PhC is usually selectively removed the material underneath the cavity to form a similar free-standing membrane which can be better to reduce the vertical leakage into the substrate than the pillar-array based PhC cavity. Additionally, a pillar array based 2D PhC is difficult to form a similar free-standing membrane. Moreover, a triangular lattice PhC can be easier to create a large PBG compared with the square lattice PhC. Therefore in order to obtain a PhC slab with large enough PBG and small vertical loss, the structure design in our paper is based on triangular lattice, hole-array based PhC (Fig. 1). It is constructed in a silicon slab (nsi = 3.48) by arranging a triangular lattice of air holes, where the central row of air holes is removed in order to form a line defect waveguide (W1). In our paper, regarding the 2D PhC slab (considering thickness), a preliminary analysis of this structure has been performed by using the open source FDTD software MPB and Meep to calculate their photonic band structure and transmittance spectra, respectively . For example, FDTD analysis of the photonic crystal structure is carried out by using software with sub pixel averaging for increased accuracy (Meep). Meep will discrete the structure in space and time, and that is specified by a single variable, resolution that gives the number of pixels per distance unit. We set this resolution to 20 in our simulations (namely, with a grid spacing of a/20, where a is the lattice constant). All simulations are carried out at the same resolution ( = 20) in order to obtain consistent comparison results. The Gaussian-pulse source is used and run for several iterations. The simulation area is surrounded by one-spatial unit thick perfectly matched layer (PML), which absorbed the fields leaving the simulated region in order to prevent reflections.
As shown in Fig. 1, the W1 PhC slab waveguide is modeled by a PhC single line defect waveguide with a triangular lattice of air holes. The holes in the PhC are 270nm in diameter and the lattice constant of the 2D lattice is a = 423nm. The slab thickness is that T = 0.55a = 232.65nm realized on silicon slab waveguide. With careful design about the structure parameters such as lattice constant, radius of the holes, and thickness of PhC slab as shown in Fig. 1, the leakage into the substrate can be decreased and a high Q hole-array cavity is feasible. In this photonic crystal waveguides (PhCWs), the optical field is confined, horizontally, by a photonic band-gap (PBG) provided by the PhC and, vertically, by total internal reflection due to the refractive index differences between different layers. Figure 2 shows the simulation results of the light propagation through the PhCW, where the TE-like polarized light is confined strongly in both in-plane direction (horizontally) and out-plane direction (vertically), and the leakage of light becomes very small.
Since this type of PhCs favor photonic bandgap (PBG) mainly for TE polarization (electric fields are in-plane), we focus on the TE-like polarization in this work. A typical band diagram for TE-like polarized light in the single line defect waveguide PhC is obtained numerically by using the plane wave expansion method, and shown in Fig. 3(a) . As seen, the line defect PhC supports both even and odd mode in the PBG ranging from 0.206(2πc/a) to 0.285(2πc/a). Figure 3(b) shows the transmission spectra of line defect PhCW and perfect PhC without any defect. From Fig. 3(b) we can get that the effective working frequency of guide mode within the PBG is between 0.22(2πc/a) and 0.283(2πc/a), which is sufficiently wide for the microsensor arrays design.
3. Side-coupled resonant nanocavity design
In practice, a 2D photonic crystal slab has emerged as one of the most important plat-forms to fabricate a high quality factor (Q) optical microcavity, such as Ln cavity [21,22], mode-gap cavity [23–25], and H0-nanocavity [26,27]. In this paper, based on the PhC slab waveguide structure mentioned above, we increase the Q-factor of our device by using the high-Q microcavity (H0-cavity) which is further designed by two factors in our paper: one is that shifting the two red holes (in the x direction) outwards slightly in the opposite direction (sx) and the other is that adjusting the radius rx of the red holes and the radius ry of the green holes (in the y direction) at the same time to optimize H0-cavity side-coupled to PhCW as shown in the Fig. 4 . At the same time it provides a better coupling between the W1 waveguide and the defect and improves the Q factor of the microcavity because the envelope function of the in-plane mode profile varies more gently than the single defect case.
The resonant cavities are designed by using 3D FDTD method for a Si device layer. The periodicity of the photonic crystal lattice is a = 423nm, and the air hole radius r = 135.36 nm (r/a = 0.32). The air hole shift sx is scanned from a shift of 0.1a to a maximum shift of 0.35a in order to optimize the Q factor of the cavity. An air hole shift of sx = 0.2a results in an optimal design at (ω = 0.28(2πc/a)) with a Q factor of 1285. The transmission of TE-like polarized lightwave with different lattice shifts ranging from sx = 0.1a to sx = 0.35a is shown in Fig. 5(a) . Figure 5(b) shows the theoretical results for the resonance frequencies and Q factors in terms of the lattice shifts sx. We have observed the desired results, whereas the hole shift increases, the cavity resonance is pushed to lower frequencies, due to the increase in high-dielectric material in the cavity region. In Fig. 5, when the shift sx is between 0.15a and 0.25a, the coupling strength between the resonant cavity and the W1 PhCW is strong enough in W1 PhC slab resonator structure. However, as the transmission spectra of the shift sx is between 0.15a and 0.25a, although the coupling strength between the microcavity and the W1 PhCW is strong enough, namely, the Q factor is sufficiently high, there is a limitation about the microcavity formed by only shifting the two red holes outwards slightly in the opposite direction. The limitation is that resonant frequencies are concentrated and intervals between each other are not large enough.
In order to overcome the limitation mentioned above, the air hole radius rx and ry are also scanned from 0.25a to 0.35a based on the lattice shift sx between 0.15a and 0.25a, which can further optimize the Q factor of the cavity. The theoretical calculations for the resonance frequencies and Q factors as a function of air hole radius rx and ry are shown in Fig. 6(a) and Fig. 6(b), respectively. As seen in Fig. 6(b), an air hole radius of rx = 0.32a, ry = 0.28a results in an optimal design based on sx = 0.2a with a Q factor of 2761. As expected, as the radius of air holes (rx and ry) is increased, the cavity resonance is pushed to higher frequencies.
Based on the sensing element architecture as shown in Fig. 4, by applying the 3D-FDTD method, the simulation of light propagation profile in the x-y plane and the output transmission spectra of TE-like polarized light-wave in PhC are numerically calculated, as plotted in Fig. 7 . As seen in Fig. 7(a), there is a significant amount of light amplification within the resonant cavity. Relative to the evanescent field at the side walls of the nanocavity, we observe that the inner most holes of the side resonant cavity have a stronger optical field. This causes the resonant cavity to be very sensitive to refractive index changes due to the large degree of light-matter interaction inside them. Figure 7(b) is a 3D-FDTD simulation which illustrates the typical output transmission spectra of a sensing element device with a single side-coupled H0-cavity.
4. Functionalized hole number discussion
For applications such as bio-sensing or chemical detection, it is important to note that the device does not measure variations in the bulk refractive index of the surrounding medium, but rather respond to the local variations in refractive index in the area of the individual sensor. As a result, the magnitude of the resonant shift is dependent on the combination of factors such as the effective change in refractive index of the bound targets. To model this, we here perform detailed 3D-FDTD simulations that enable us to study the sensitivity of this sensor design and determine how to achieve the lowest mass limit of detection using this architecture. We assume that the holes around the resonator are initially predeposited with complimentary probes. When a detection event occurs, for instance, a kind of target object is infiltrated into the air holes around the resonant cavity area, the refractive index surrounding its cavity changes which results from the detected targets object bind with complimentary probes that have been predeposited.
Here, we vary the number of holes (N) nearby the resonant cavity being functionalized holes to study the mass sensitivity (here defined as: ∆λ/N) of the device as a function of the number of functionalized holes. Simulations are performed for the cases with two holes (the two green holes of the cavity shown in Fig. 4), four holes (the inner four holes including the two green and the two red holes of the cavity), six holes, 15 holes and up to 28 holes (as shown in Fig. 8(b) ) being functionalized holes with predeposited capture probe. We have calculated the term ∆λ/N in all these cases where ∆λ is the shift in the resonant wavelength of the device caused due to positive binding events and N is the number of functionalized holes. ∆λ/N is indicative of the mass sensitivity of the device.
The purple circles in Fig. 8(a) show the calculated mass sensitivity (∆λ/N) for these different cases. As can be seen, the innermost holes in the y direction (the two green holes shown in Fig. 4) are the most sensitive to any refractive index changes in the local environment as opposed to the holes that are further away from the center of cavity. These results can be explained by noting that in Fig. 7(a) the evanescent field is largest inside the innermost holes and decreases inside holes that are situated further away from the cavity. This is important to note because targeting only the inner most holes in the y direction for functionalization (N = 2) allows the lowest possible limit of mass detection for this device.
Figure 9 illustrates the dependence of the wavelength shift ∆λ on the number of functionalized holes N. We observe that an exponential function of the form shown in red line in Fig. 8(a) and Fig. 9, where a, b, c and d are arbitrary constants approximates this dependency quite well. Thus taking all of the above into consideration we can express the mass sensitivity (∆λ/N) as follows:
where a, b, c and d are constant parameters. From Eq. (1), we observe that the mass sensitivity increases if we lower the number of functionalized holes N. Equation (1) is used to fit the red curve in Fig. 8(a) where the values a, b, c and d are 19.09, −0.365, 5.089, and −0.0347, respectively and the regression coefficient is 0.9997. Therefore, this analytical expression indicates a good agreement with the FDTD simulation results and helps us to understand that the mass sensitivity of the device increases with a decrease in the number of holes which are functionalized. However, as seen in Fig. 9, the resonant shift is larger for the greater number of functionalized holes, and the point of N = 6 can be seen as a demarcation point. In the left area of N = 6 (Fig. 9, N = 2, 4), the sensing element can realize higher mass sensitivity (∆λ/N), but the refractive index sensitivity (∆λ/∆n, ∆n is the change of refractive index in functionalized area) is lower; while in the right area of N = 6 (Fig. 9, N = 15,28), the sensing element can realize higher refractive index sensitivity, but the mass sensitivity is lower. Thus in our sensor design we make a tradeoff between the refractive index sensitivity and the mass sensitivity and determine that the functionalized hole number is N = 6 in the sensing element.
5. NPhCSAs design and simulation results
Through the design and discussion about the high Q factor H0-cavity side-coupled to PhCW and the number of functionalized holes N in above sections, the nanoscale photonic crystal sensor arrays is made up of five H0-cavities side-coupled to a PhC line defect waveguide (W1) with a triangular lattice of air holes realized on silicon slab waveguide. When n sensors are set in cascade side-coupled to the W1 waveguide, the transmission of the series exhibits n dips. The dips are independent of each other, thus a shift in one of them does not perturb the others. This allows the implementation of simple but functional PhC-based sensor arrays, and eventually of more complex optical integrated circuit (OIC) and integrated optical devices. The structure of the simulated PhC sensor arrays used here is shown in Fig. 10 . Each resonator of the PhC sensor arrays is designed slightly differently. The specific structural parameters of each resonant cavity are as follows: H0-cavity-1: sx = 0.175a = 74.025nm, rx = 0.32a = 135.36nm, ry = 0.30a = 126.9nm; H0-cavity-2: sx = 0.20a = 84.6nm, rx = 0.32a = 135.36nm, ry = 0.30a = 126.9nm; H0-cavity-3: sx = 0.20a = 84.6nm, rx = ry = 0.32a = 135.36nm; H0-cavity-4:sx = 0.20a = 84.6nm, rx = 0.29a = 118.44nm, ry = 0.30a = 126.9nm; H0-cavity-5: sx = 0.225a = 95.175nm, rx = 0.32a = 135.36nm, ry = 0.28a = 118.44nm.
As shown in Fig. 7, the device exhibits a single and narrow dip in the transmission spectra. The multiplexing is quite straightforward-by setting n resonant cavity sensors side-coupled to a same W1 waveguide, therefore, n dips can be expected. On a monolithic of W1 PhC module n resonant cavity sensors can be set in series and all of them can be interrogated simultaneously. In addition, to increase the number of sensors in the arrays parallel connections of W1 PhC waveguide can be used. To verify the performance of the sensors when they are in series, each sensor is independently subjected to the changes in refractive index (RI-1, RI-2, RI-3 and RI-4, respectively). Figure 11(a) shows the composed transmission spectra of the series when one sensor is under the variations in refractive index and other sensors are not. The shift in only one dip is evident with other dips remain completely unchanged. Figure 11(b) shows electric field distribution for a PhC sensor arrays in the five resonant cavity sensors of the series.
To investigate the RI sensitivity of the device, we have performed a typical simulation of a PhC sensor arrays under two different conditions. Figure 12(a) shows the output transmission spectra, namely, the composed transmission spectra of the series when one sensor (H0-cavity-3) is filled with water and other sensors are not. The shift in only one dip is evident and other dips remain completely unchanged. As seen in the transmission spectra, (1) the red line represents the case where the functionalized holes (under the red shaded area, Fig. 10) of all five resonant cavity sensors are filled with air (RI = 1.0), (2) while the blue line represents the case that only the functionalized holes of the H0-cavity-3 are filled with water (RI = 1.33) and other sensors are still filled with air. When a higher refractive index solution of water is filled in the functionalized holes of the resonant cavity sensor, it changes the resonance condition of the resonant cavity and pushes its unique resonant dip towards the red end of the spectra as shown in Fig. 12(a). It is important to note that only the resonating frequency of the resonator filled with the water shifts and the other peaks are unaffected. In this way one can confirm positive binding events occurring at any one of the resonators since only their corresponding resonances would show a shift in the output spectra. Resonators with no binding occurring will show no shift in their output resonance. Figure 12(b) shows the shifts in the resonant peak as a function of the variations in refractive index of the functionalized holes.
Here in order to quantitatively analyze the RI sensitivity of the silicon slab PhC sensor arrays, we choose the sensitivity of our device by observing the shifts in the resonant wavelength of the sensor as a function of the variations in refractive index. The shift of the peak resonant wavelength Δλ is a function of the change in refractive index (Δn), the sensor’s RI sensitivity is expressed as follow:
From the simulation results shown in Fig. 12, it is possible to calculate the sensor’s refractive index sensitivity that is equal to 115.60 nm/RIU. Therefore, 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 8.65 × 10−5 which is agreement with the Ref. 14. Besides, compared with the techniques like SPR, the ability to drastically confine the detection volume by targeting the holes (especially the innermost holes in vertical direction as shown in the simulations) in our design allows us to lower the mass limit of detection.
In addition, as can be seen from Fig. 12(a), each resonator contributes a sharp drop to the output spectra of the device. We observe that each H0-cavity resonator possesses a large Q-factor from 1000 to 3000. This is very useful and important for two reasons. The first one is that it could make it effortless to detect very small shifts in the resonances when the resonator possessed higher Q-factors. The other reason is that as the peaks get narrower it enables us to pack the output spectra with a larger number of closely spaced dips without crosstalk. As a result, it allows us to multiplex a larger number of microcavity resonators onto the PhCW on monolithic substrates, which is an inherent advantage of our sensor design for optical integrated circuit (OIC) and integrated optical devices and is more suitable to monolithic integration.
In this paper we have proposed a novel silicon slab PhC biosensor platform, referred to as nanoscale photonic crystal sensor arrays, which are demonstrated and characterized through the structure design and simulations. The PhC sensor arrays consist of a PhC waveguide and a series of side-coupled resonant cavities with high Q factor. A change in the refractive index of the near field region surrounding the resonant cavity results in a shift in the resonant wavelength. From the simulation results, we have demonstrated that the sensitivity of this device of 115.60 nm/RIU is achieved and a limitation of the refractive index detection is on the order of 10−5 range. In addition, the sensitivity of this device can also be varied from 84.39 nm/RIU (when N = 2) to 161.25 nm/RIU (when N = 28) by adjusting the number of functionalized holes. While other techniques such as surface plasma resonance possess an equivalent refractive index (RI) detection limit, the advantage of this architecture lies in the ability to confine the size of the probed volume thus allowing for a low mass limit of detection. Besides, the Q factors of these resonant microcavities can be significantly enhanced by further optimizing the device geometry or the structure of the microcavity to allow an even larger degree of multiplexing on monolithic substrates, which is an inherent advantage of our design for optical integrated circuit (OIC) and integrated optical devices and is more suited to monolithic integration.
This research was supported in part by National 973 Program (No. 2011CB302702), NSFC (No. 60932004), National 863 Program (No. 2009AA01A345), P. R. China.
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