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Hybrid Photonic Crystal-Surface Plasmon Polariton Waveguiding System for On-Chip Sensing Applications^{ †}

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## Abstract

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## 1. Introduction

**l**ated refractive-index structure where the characteristic periodicity is the order of optical wavelength to be considered. Photonic crystals can possess a photonic band gap (PBG) under certain conditions, thus enabling it to function as a photonic insulator over a desired range of frequency [3]. In the present work, we use a pillar based photonic crystal waveguide with a schematic representation shown in Figure 1a. The 2-dimensional (2D) calculation of dispersion band diagram for TE polarization (electric field in z direction) is presented in Figure 1b, the shadowed region corresponds to the band gap of the system. For a waveguide functioning within the band gap frequency range, the photonic crystals play the role of a confining region. On the other hand, surface SPPs are commo

**n**ly utilized in visible and near infrared optical sensing applications, thanks to their excellent light confinement and field enhancement properties. In this work, we bring these two well-known concepts together in order to address a common fabrication challenge, i.e., the high aspect ratio of pillars in conventional PhC waveguides needed to confine the mode of interest. We propose a design for the wavelength of 632 nm for which not only this challenge is tackled, but also the other dimensions of the system are reduced. The computations in this work have been performed using the commercial RSoft package based on Finite Difference Time Domain (FDTD) and COMSOL Multi physics based on the finite element method.

## 2. Sensor Based on Photonic Crystal Waveguide

**r**ties of the guided wave, its realization in a fabrication process is either impossible or cumbersome especially for application where mass production is the goal. In this case, a common approach is to incorporate finite 2D structures with certain thickness in the vertical dimension. Finite 2D periodicity can be accomplished either by creating holes inside a slab or by forming pillars of a dense material (Figure 1a). While in the former case the vertical confinement along the z-axis is accomplished by total internal reflection of light, in the latter case, the pillars should be high enough to increase the overall effective refractive index of the guiding mode and therefore being able to confine the wave along the z-axis [6]. For sensing applications, the guiding wave should be in maximum contact with the analyte in order to have a sensitive system [7]. This goal cannot be achieved by a slab photonic crystal. A system of finite pillars can mimic the lateral properties offered by an infinite system, however the electromagnetic field can only be confined if the mode is reasonably confined within the pillar’s height. Figure 2 shows the power confined in the guiding area of a PhC waveguide with a hexagonal periodicity of a/λ = 0.387, where λ = 632 nm is the free-space wavelength and the pillar radius of r = 0.2a on a glass substrate and for different pillar heights, H. It can be seen that in order to have a confinement, in this example, the height of the pillars should be as large as around 3 μm. This implies an aspect ratio of around 30, which is too high to be fabricated, especially when the pillars’ diameter is in the range of 100 nm.

## 3. Hybrid Photonic Crystal Surface Plasmon Polariton System

**l**ine intersects the dispersion diagram of the PhC waveguide with r = 0.22a at its flat region, at the frequency of our interest corresponding to λ = 632 nm (grey dashed line).

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) A 3D Schematic representation of a PhC waveguide formed by removing a row of pillars in a periodic arrays of Si pillars on SiO

_{2}substrate. (

**b**) Transverse electric band structure of a 2D hexagonal PhC made of Si pillars with the radius of r = 0.22a. The shadowed region represents the band gap of this structure. (Inset: schematic view of a 2D hexagonal lattice of Si pillars).

**Figure 2.**Power spectra of PhC waveguides with different pillar heights (H), a latticce constant a = 245 nm and a pillar radius of r = 0.2a.

**Figure 3.**Hybrid waveguide composed of Si pillars (shorter than those in Figure 1a) on SiO

_{2}substrate and embedded in a thin layer of gold.

**Figure 4.**Dispersion diagrams of waveguides obtained by removing one r w of pillars in 2D hexagonal PhC. The radius of Si pillars are varied from r = 0.1a to r = 0.3a. The dashed black graph shows the dispersion diagram of the SPP mode of a 40-nm gold film sandwiched between air and glass substrate. The grey dotted line represents the frequency corresponding to λ = 632 nm.

**Figure 5.**(

**a**) Dispersion diagram of a 22D PhC waveguide with r/a = 0.22 and the SPP modes of the tri-layer (shown in Figure 4) together with the dispersion diagram of the combined syst

**e**m (shown in Figure 3). In the combined system, the height of the pillars is just 400 nm, which is compatible MEME technology. (

**b**) The mode profile of the hybrid system.

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**MDPI and ACS Style**

Jannesari, R.; Abasahl, B.; Grille, T.; Jakoby, B. Hybrid Photonic Crystal-Surface Plasmon Polariton Waveguiding System for On-Chip Sensing Applications. *Proceedings* **2018**, *2*, 864.
https://doi.org/10.3390/proceedings2130864

**AMA Style**

Jannesari R, Abasahl B, Grille T, Jakoby B. Hybrid Photonic Crystal-Surface Plasmon Polariton Waveguiding System for On-Chip Sensing Applications. *Proceedings*. 2018; 2(13):864.
https://doi.org/10.3390/proceedings2130864

**Chicago/Turabian Style**

Jannesari, Reyhaneh, Banafsheh Abasahl, Thomas Grille, and Bernhard Jakoby. 2018. "Hybrid Photonic Crystal-Surface Plasmon Polariton Waveguiding System for On-Chip Sensing Applications" *Proceedings* 2, no. 13: 864.
https://doi.org/10.3390/proceedings2130864