# Design of a High Q-Factor Label-Free Optical Biosensor Based on a Photonic Crystal Coupled Cavity Waveguide

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## Abstract

**:**

## 1. Introduction

## 2. Photonic Crystal and Coupled Cavity Waveguide Structure

## 3. Results and Discussion

_{2}layer will be eliminated in a wet etching process, in which a chemical solution will selectively remove the oxide.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic of the structure. The grey area shows the silicon and the red circles indicate the air holes. The white dashed lines indicate the coupled cavity waveguide (CCW) area. Slab waveguides at the input and output mentioned in the text are extended from the tapered regions to the left and right, respectively. The structure has symmetrical input and output ports. (

**b**) The first Brillouin zone of a triangular lattice is represented by a hexagonal shape. The vertices of this hexagon, which are referred to as high-symmetry points, have the following Cartesian coordinates: $\mathsf{\Gamma}\left(\mathrm{0,0}\right)$, K$(\frac{4\pi}{3a},0)$, M$(\frac{\pi}{a},\frac{\pi}{a\sqrt{3}})$.

**Figure 2.**(

**a**) The TE band structure of the considered CCW cavity modes with $r=0.34a$ and ${R}_{\mathrm{c}}=0.38a$ (green dotted lines) and dispersion curve of the line defect waveguide (red dotted line). The entire shadow area illustrates the photonic band gap of the unaltered crystal. (

**b**) A schematic representation of the CCW; the red circles define the cavity holes with radius ${R}_{\mathrm{c}}$, and the black circles define the PhC holes with radius $r$. Blue dotted/dashed lines define the boards of unit cells with periodic boundary conditions (PBCs).

**Figure 3.**The simulated Hz profile in the x–y plane for a CCW with ${R}_{\mathrm{c}}=0.38a$ and $r=0.34a$; (

**a**) lower frequency even mode, (

**b**) lower frequency odd mode, (

**c**) higher frequency even mode, (

**d**) higher frequency odd mode. Dashed circles define the positions of air holes. The modes are displayed at the Γ(0,0) in the dispersion diagram; each band is illustrated in Figure 2a.

**Figure 4.**(

**a**) The transmission spectra of coupling light from the slab waveguide to a W1 waveguide followed by the CCW, with ${R}_{\mathrm{c}}=0.38a$ composed of seven coupled cavities, and then to the output W1 and slab waveguide. The higher frequency mode presents Fabry–Perot oscillations. (

**b**) Linear relationship between the number of coupled cavities in the CCW and the number of Fabry–Perot modes. (

**c**) Hz profile of propagating mode with normalized frequency $a/\lambda =0.285$ along the sensor. This PhC waveguide and CCW mode have even symmetry. Low lateral radiation loss in the coupling from input taper to PhC waveguide and from PhC waveguide to CCW can be seen.

**Figure 5.**(

**a**) The Q-factors and (

**b**) resonance frequencies as a function of ${R}_{c}$ in the CCW structure for even modes.

**Figure 6.**(

**a**) Resonant wavelength of the high-frequency even mode for different refractive indices. (

**b**) Transmission spectrum of the low-frequency even mode for different refractive indices. (

**c**) The blue circles and red diamonds indicate the shift values of resonant wavelengths for different refractive index variations, and the dashed lines are linearly fit when ${R}_{\mathrm{c}}=0.455a$. The expressions for the two linear fitting curves are $y=203x$ and $y=150.1x+0.2524$ for the dashed red and blue lines, respectively.

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**MDPI and ACS Style**

Jannesari, R.; Pühringer, G.; Stocker, G.; Grille, T.; Jakoby, B.
Design of a High *Q*-Factor Label-Free Optical Biosensor Based on a Photonic Crystal Coupled Cavity Waveguide. *Sensors* **2024**, *24*, 193.
https://doi.org/10.3390/s24010193

**AMA Style**

Jannesari R, Pühringer G, Stocker G, Grille T, Jakoby B.
Design of a High *Q*-Factor Label-Free Optical Biosensor Based on a Photonic Crystal Coupled Cavity Waveguide. *Sensors*. 2024; 24(1):193.
https://doi.org/10.3390/s24010193

**Chicago/Turabian Style**

Jannesari, Reyhaneh, Gerald Pühringer, Gerald Stocker, Thomas Grille, and Bernhard Jakoby.
2024. "Design of a High *Q*-Factor Label-Free Optical Biosensor Based on a Photonic Crystal Coupled Cavity Waveguide" *Sensors* 24, no. 1: 193.
https://doi.org/10.3390/s24010193