1. Introduction

Photonic crystals (PCs) have gathered great interest in the realization of compact devices for integrated circuits due to their strong light-matter interaction and having intriguing dispersion relations [1]. PC based devices may offer attractive solutions to biochemical sensing applications due to exhibiting strong optical confinement in a tight volume. Apart from the fluorescent-based detection in which the targeted biochemical molecules are labeled via fluorescence, PCs are suitable for label-free optical detection, in which case refractive index sensing mechanism is used for the detection of biochemical analytes injected in the sensing platform [2].

Beyond the realized photonic devices, PCs-based Mach-Zehnder interferometers (MZIs) are of paramount interest for integrated optics since such modulators could be implemented for wavelength demultiplexing [3], optical switching [4] and filtering [5] applications. Basically, MZIs are capable of converting the phase information of light into intensity modulation. For that purpose, a phase difference is introduced between the arms of MZIs via the change of composing materials’ refractive index [6], modifying their optical paths [7] or using anisotropic materials in any specified arm [8]. As a promising solution to enhance compactness in PC-based MZIs, slow-light effect is offered, which allow required phase modulation with large group indices [9].

MZIs are very convenient for the realization of optical biochemical sensors [10–12]. Depending on the refractive index change $\varDelta n$ in investigated analytes, a relevant phase shift appears between the arms of MZIs, causing constructive or destructive interference at the output channel and hence, a spectral shift on dip/peak transmission frequencies occurs at the output spectrum in the case of any slight changes of analytes’ molarities [13–15].

In this study, a new type of Si-based MZI structure is proposed: One arm of the MZI is composed of cylindrical PCs whereas the other arm is made of low-symmetric PCs, by which the intended phase difference could be obtained. Dip frequencies exist at the output transmission spectrum, which is attributed to the Fano resonance effect in the study, and the optical sensitivity of the designed MZI is investigated for different types of analytes such as gaseous or liquid substances. It is numerically proven that any environmental modifications in terms of refractive index changes could be detected at the output channel of the proposed PC-based MZI platform with high sensitivity and a quality factor higher than $Q = \frac{{\lambda ({peak} )}}{{\delta \lambda }} > 45000,$ where $\delta \lambda $ is the regarding full width at half maximum (FWHM) value at the peak (dip) resonances. Such interferometric sensor systems could be effectively utilized for label-free optical sensing of gaseous/liquid analytes.

2. Dispersion relations of low-symmetric photonic crystals

Symmetry reduction in PC primitive cells brings about intriguing dispersion characteristics such as superprism, super-collimation and so on [16,17]. Optical characteristics of PCs are very sensitive to the orientational symmetry in PC unit cells [18], which is the key element of the proposed MZI system. Figure 1 is prepared to investigate the band structure of square-lattice PCs with different rotational symmetry; the schematic of the regular cylindrical PC unit cell is presented in Fig. 1(a) and C1-symmetric PC cell is shown in Fig. 1(b) with their critical geometrical parameters. The radii of PCs are taken to be $\{{{r_1},{r_2}} \}= \{{0.2a,0.1a} \}$, , where a is the corresponding lattice constant. Permittivities of background medium and dielectric Si rods are set to be $\{{{\varepsilon_a},{\varepsilon_b}} \}= \{{1,12.25} \},$ respectively. It is crucial to note that the proposed system is two-dimensional (2D) and it is uniform in the third ($z$-) direction. 2D Frequency-domain analyses of the regular and low-symmetric PCs with different rotation angles $\theta $ are conducted using plane-wave expansion method [19] and the calculated Bloch modes for transverse-magnetic (TM) polarization are represented in Figs. 1(c) and 1(d), respectively. Corresponding band analyses are performed along $\Gamma {\rm X}$ direction of Brillouin zone, which is given as an inset in Fig. 1(c). Comparing existing Bloch modes shown in both Figs. 1(c) and 1(d), it is certain to note that additional scatterer in regular PC unit cell and its orientation has a strong impact on the band structure. Such optical property could be implemented for efficient dispersion engineering of PCs via adjusting the orientations of smaller PC scatterers in the unit cell. That feature may further be implemented for controllable phase-modulation purposes, which is the aim of the study.

 

Fig. 1. (a) Cylindrical square-lattice PC unit cell with dielectric permittivities of ${\varepsilon _a} = 1$ and ${\varepsilon _b} = 12.25$, and the radius ${r_1} = 0.2a$. (b) The C1 rotational-symmetric PC unit cell formed by two separate PC rods with radii $\{{{r_1},{r_2}} \}= \{{0.2a,0.1a} \}$. Corresponding band structures of (c) regular PC and (d) low symmetric PC with different orientations $\theta = \{{{0^\circ },{{90}^\circ }} \}$. Dispersion analyses are calculated along $\Gamma {\rm X}$ edge of Brillouin zone.

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As discussed earlier, phase index profile of low-symmetric PCs could be manipulated with respect to the orientations of PC unit cells. To better observe such optical effect, a line-defect PC waveguide (PCW) with a width of $w = 1a$ is constructed as shown in Fig. 2(a); the neighboring rods to air line-defect is composed of low-symmetric PCs given in Fig. 1(b) and all the remaining part of the PCW is composed of regular PCs as given in Fig. 1(a). Dispersion characteristics of PCW is calculated for varying PC orientations from $\theta = {0^\circ }$ to $\theta = {90^\circ }$ and the fundamental waveguide modes (TM₀) are superimposed in Fig. 2(b). Based on the guided mode analyses, the phase-index profiles are also investigated for different PC orientations, see Fig. 2(c). It is clear from the phase-index profile in Fig. 2(c) that increasing the rotational angle $\theta $ results in a red-shift (down-shift) in the band structure and consequently, corresponding phase-index is decreased at a fixed frequency while increasing the rotational angle $\theta $. That condition enables the introduction of adjustable phase delays in the propagating modes at the PCWs, which forms arms of the MZI design in the study.

 

Fig. 2. (a) PCW waveguide having a line-defect with $w = 1a$ is formed by C1 symmetric and regular PCs. The arrow indicates the direction of beam propagation. (b) Corresponding band structure and (c) phase index profile of the PCW are calculated for varying angular orientation $\theta $.

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By definition, interferometers are multi-functional optical devices that are able to detect any phase changes at each arm via beam interference effect. With this regard, low symmetric PCW structures could be a good candidate for interferometric device applications. In this study, a dual-channel MZI formed by PCWs is proposed, see the schematic of the MZI design in Fig. 3(a). The designed MZI structure includes four sections; The input and output channels with the widths of $({{w_{in}},{w_{out}}} )= 2a$ and the two PCW arms. The upper channel is formed by low-symmetric PCW and the PC unit cell orientations indicated by dashed area in Fig. 3(a) are manipulated to generate intended phase delays at the output transmission spectra. As mentioned earlier, orientations in primitive PC cells influence the corresponding phase indices ${n_{phase}}$ and then, a phase difference $({\varDelta \varphi } )$ exists between the upper and bottom MZI channels: if the phase difference between the two arms equals $\varDelta \varphi = 2\pi n$, “constructive” type of interference occurs, whereas for $\varDelta \varphi = \pi n$, “destructive type” of interference is obtained, in which relations the constant parameter n varies as $({n = 0,1,2, \ldots } ).$ Figs. 3(b) and 3(c) are devoted to exploring the phase manipulation as well as the spectral response of the MZI design with respect to different PC orientations at the wavelength ranges ${\lambda _1} = \{{1417\; \textrm{nm} - 1427\; \textrm{nm}} \}$ and ${\lambda _2} = \{{1453\; \textrm{nm} - 1465\; \textrm{nm}} \}$, respectively. The time-domain calculations are conducted by 2D finite-difference time-domain method (FDTD) using commercial LUMERICAL software [20]. The designed MZI structure is excited by a broadband source having Gaussian amplitude profile and lattice constant of the periodic structure is taken as $a = 512\; \textrm{nm}$. In that case, the entire dimension of the sensor platform turns out to be $12.8\; \mathrm{\mu m} \times 10.2\; \mathrm{\mu m}$. The grid size of the computational domain is fixed as $\varDelta x = \varDelta y = a/28$ and boundaries of the FDTD region are surrounded by perfectly matched layers to eliminate the undesired back-reflections. In the calculated transmission spectra in Figs. 3(b) and 3(c), transmission dips appear at certain wavelengths due to existing destructive interferences. The wavelength dips expose to a spectral shift towards higher wavelength ranges (lower frequencies) and the quality factor of obtained transmission dips gets enhanced while increasing the rotation angle $\theta $. On the other hand, such transmission dips as well as spectral shift is not possible to observe in conventional PC-based MZI structures [21]. The performed FDTD analyses also reveal that the spectral response of the proposed MZI is highly sensitive to the PC unit cell orientations as well as the environmental changes, which feature could be exploited for all-optical sensing as the aim of this study.

 

Fig. 3. (a) Proposed MZI design including input and output ports; low-symmetric PCW at the upper arm (dashed section); regular PCW at the bottom arm. Output transmission spectrum of the studied MZI are calculated at the wavelength ranges of (b) $\lambda = \{{1417\; nm - 1427\; nm} \}$ and (c) $\lambda = \{{1453\; nm - 1465\; nm} \}$ with respect to different orientation angles $\theta $. (d) Transmissions of regular PC and low-symmetric PC with $\theta = {50^\circ }$ are superimposed to better visualize existing Fano resonances in the MZI design. Steady-state field profiles of the designed MZI at the wavelengths (e) $\lambda = 1422.2\; nm$ and (f) $\lambda = 1459.7\; nm$, respectively. Selected frequencies are marked with arrows in (b)-(c).

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The existing transmission dips can be explained by Fano-resonance effect [22]. In particular, Fano-resonances can be considered as a particular state of the side-coupled defect. Fano effect could be considered as a transition state between continuum state (in our case, guided modes at the MZI arms) and discrete state (smaller PC rods at the upper arms could be interpreted as Fabry-Perot cavities and hence, defect-states). In the case of symmetric Fano-defects, resonant suppression of transmission occurs and thus, no sharp transmission curves are obtained, see Fig. 3(d). On the other hand, the additional smaller PCs introduced at the upper channel form an asymmetric Fano-defect so that a sharp transition and large phase change occur between the peak and dip resonances, leading to high-quality spectral response of higher than $Q > 45000$ in our study, which is clear to see in Fig. 3(d). To better understand the Fano-effect for the designed MZI, two selected resonant dips are selected from Figs. 3(b)–3(c), marked with arrows. The electric field distributions are calculated and represented in Figs. 3(e)–3(f) for the orientation case of $\theta = {50^\circ }$ under light excitation at ${\lambda _1} = 1422.2\; \textrm{nm}$ and ${\lambda _1} = 1459.7\; \textrm{nm}$, respectively. It should be noted that the sensing capability of the MZI platform is investigated in the orientation case of $\theta = {50^\circ }$ later in the study. As can be observed in Figs. 3(e)–3(f), due to existing asymmetric Fano effect, destructive interferences occur at the detected output channel and a recirculation of resonance modes exists in the MZI structure. That situation extends the optical path of the propagating mode and thus, enhances the strong light-matter interactions inside the MZI structure, which is applicable for optical refractive-index sensing purposes. Thanks to the sharp variation of scattering phase, mode-order conversion could also be achieved by means of proper adjustment of the input/output ports’ widths, which could be another potential implementation of the proposed Mach-Zehnder Fano interferometric design.

3. Spectral response of the proposed interferometric PC-based sensor device

As discussed earlier, due to existing Fano-resonance effect, the proposed MZI design is very sensitive to biochemical alterations at surrounding area. Such phenomenon can be implemented for detection of even slight refractive index variations in background medium including different gases/liquids as analytes, which is the fundamental feature of all-optical refractive-index sensing in MZI platforms. Figure 4 is prepared to conceptually demonstrate the operating basics of proposed PC interferometer as a gas/liquid sensor system as well as to present its spectral response depending on the refractive index variations. For that purpose, the proposed MZI sensor is placed into a chamber that allows inflow/outflow of either gas particles or liquids. The MZI sensor is illuminated with a fiber-coupled laser source passing through polarization-controller in order to excite TM-mode. The output beam is collimated onto a photodetector and corresponding spectral response of the proposed MZI sensor is measured by a power meter, see the schematic in Fig. 4(a). Depending on the refractive index change of the system’s environment, the system response varies accordingly; dip frequencies in transmission spectrum, where destructive interference occurs, red-shifts towards higher wavelengths related with the increase in the refractive index of the background.

 

Fig. 4. (a) Schematic view of the MZI setup for all optical refractive-index sensing. Either gas or liquid analytes could be identified via the proposed sensing platform. The zoomed version of MZI structure is also given in the figure. Spectral response of the studied MZI sensor for the cases of (b) gaseous, (c) liquid analytes. Corresponding refractive indices of analytes under investigation range in ${n_{gas}} = 1.000 - 1.010$ and ${n_{liquid}} = 1.010 - 1.200$, respectively.

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Overall optical sensing performance of the proposed PC system could be associated with two critical sensor parameters: (1) Sensitivity parameter is defined by $S = \frac{{\varDelta \lambda ({dip} )}}{{\varDelta {n_{analyte}}}}\textrm{ }[{\textrm{nm}/\textrm{RIU}} ]$, indicating how the MZI device is sensitive to the refractive index variation of analytes. (2) Figure-of-Merit (FoM) is another parameter indicating the label-free sensing performance of device and defined by $FoM = \frac{S}{{\delta \lambda }}[{\textrm{RI}{\textrm{U}^{ - 1}}} ]$, where $\delta \lambda $ is the FWHM bandwidth at peak resonance wavelengths.

2D FDTD analyses are performed to explore spectral response of the proposed MZI sensor that may operate under different environments: Refractive indices of gaseous analytes range from ${n_{gas}} = 1.000\; ({air} )$ to ${n_{gas}} = 1.010$, which corresponds to variation on the order of ${10^{ - 2}}\; \textrm{RIU}$ compared to free-space. Furthermore, the sensitivity performance of the designed MZI is investigated for liquid analytes, whose refractive index range is set to be ${n_{liquid}} = 1.010 - 1.200$. Under these conditions, the transmission spectra of the proposed MZI sensor are calculated for varying refractive indices of background medium and represented in Figs. 4(b)–4(c) for gaseous and liquid analytes, respectively. Increasing the refractive index of analytes results in spectral shift in the transmission dips: A sensitivity of about $300\; \textrm{nm}/\textrm{RIU}$ is calculated for gaseous analytes with calculated $FoM\sim 8950\textrm{RI}{\textrm{U}^{ - 1}}$ whereas that sensitivity value is around $263.2\; \textrm{nm}/\textrm{RIU}$ for the case of liquid analytes with $FoM\sim 7690$ $\textrm{RI}{\textrm{U}^{ - 1}}$.

The most well-exploited techniques for optical sensing are listed in Table 1 for quantitative performance comparison with our proposed MZI sensor in terms of their optical sensing parameters $\{{S,\textrm{ }FoM,\delta \lambda } \}$. Examining the optical sensors one-by-one, although PC cavity sensors have quality factors as high as $Q\sim {10^6}$, existing narrow bandgap may cause weak light confinement inside the PC cavity, which diminishes its sensing capability [23]. Compared to our MZI sensor, the ring resonator performs better figure-of-merit $FoM > 1.3 \times {10^4}$; however, the ring sensors are in micron-scale, requiring larger footprints than our case, which is the major drawback in dense integrated circuit implementations [24]. Slotted PC waveguides possess relatively high sensitivities compared to their counterparts. Nevertheless, regarding quality factor is around $Q\sim 3 \times {10^3}$, corresponding to a lower value of $FoM$, which reduces the optical limit-of-detection [25,26]. Another type of sensors is plasmonic sensor showing a quite good sensitivity performance at infrared spectrum. However, the recorded $FoM$ level is still below the present study [27]. Small footprint, high quality factor and enhanced light-matter interaction are superiorities of PC based interferometers for optical sensing applications. Furthermore, PC based MZI device could be integrated with PICs, providing our sensor design for lab-on-chip implementations [28].

Table 1. Performance comparison with our proposed MZI sensor in terms of their optical sensing parameters $\{{{\boldsymbol S},\; {\boldsymbol FoM},{\boldsymbol \delta \lambda }} \}$

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4. Conclusion

In this study, the symmetry reduction in PCs with their dispersion relations are investigated and an interferometric design is proposed for label-free all-optical sensing application. The proposed sensing platform is relatively compact, feasible with conventional SOI technologies and highly sensitive to slight changes in refractive indices of analytes, which allow its widespread use for optical label-free sensing applications. Optical response of the designed Si-based MZI structure can be manipulated via the structural modifications of PC primitive cells as well as the environmental refractive index changes. Output transmission behavior of the MZI sensing platform exposes to narrow spectral shift with respect to the slight changes of refractive index in background medium, which is the indication of relatively high sensitivity and high quality factor $Q > 45000$. Existing transmission dips are attributed to the Fano-resonance effect and it is explored numerically. It is also numerically proven that the designed optical sensor has a sensitivity of about ${\sim} 300\; \textrm{nm}/\textrm{RIU}$ with $FoM\sim 8950\textrm{RI}{\textrm{U}^{ - 1}}$ for gaseous analytes’ refractive indices ranging in ${n_{gas}} = 1.000 - 1.010$, which corresponds to variation on the order of ${10^{ - 2}}\; \textrm{RIU}$, whereas that sensitivity value is around $263.2\; \textrm{nm}/\textrm{RIU}$ with $FoM\sim 7690$ $\textrm{RI}{\textrm{U}^{ - 1}}$ for the case of liquid analytes for ${n_{liquid}} = 1.010 - 1.200$ refractive index range. Considering all the above-mentioned advantages, the proposed low-symmetric PC-based MZIs could be a good candidate for photonic applications that require output power modulation or label-free optical sensing of gaseous and liquid analytes.