**1. Introduction**

Surface plasmon resonance (SPR) sensors provide high sensitivity without the use of molecular labels (Homola, Yee, and Gauglitz 1999). They been widely used in the analysis of biomolecular interactions (BIA) and detection of chemical and biological analytes (Homola, Yee, and Gauglitz 1999), where they provide benefits of real-time, sensitive and label-free technology. They have also been used for the detection of various chemical and biological compounds in areas such as environmental protection, food safety and medical diagnostics (Mouvet et al. 1997; Nooke et al. 2010).

Most commercial SPR biosensors are based on the simple, robust and highly sensitive traditional prism-coupled configuration. However, they are not amenable to miniaturization and integration (Jha and Sharma 2009). There is therefore a growing interest in the development of robust, portable and highly sensitive SPR sensing devices capable of out of laboratory measurements (Akowuah et al. 2010; Piliarik et al. 2009; Wang et al. 2010).

Several compact configurations, enabling coupling between optical waveguide modes and surface plasmon waves have been investigated over the last decade. Among these inlcude metalized single-mode, polarization maintaining, and multimode waveguides, metalized tapered fibers, metalized fiber Bragg gratings and lapped D-shaped fiber sensors have been studied(Jorgenson and Yee 1993; Monzon-Hernandez and Villatoro 2006). Fibre optic SPR biosensors offer miniaturization, a high degree of integration, and remote sensing capabilities (Patskovsky et al. 2010; Hoa, Kirk, and Tabrizian 2007).

There is currently interest in the design of photonic crystal fibre (PCF) SPR sensors, which are based on the coupling of a leaky core mode to the SPP mode along a metalized fiber micro-structure (Dhawan, Gerhold, and Muth 2008). This has resulted in the proposal of many types of PCF and micro structured optical fiber (MOF) SPR biosensors, some of which include a three-hole MOF SPR biosensor with a gold layer deposited on the holes, PCF SPR biosensor with enhanced micro fluids and photonic bandgap SPR biosensors (Gauvreau et al. 2007; Hassani et al. 2008; Hassani and Skorobogatiy 2006; Hautakorpi, Mattinen, and Ludvigsen 2008). PCFs are thin silica glass fibers possessing a regular array of microscopic

A Novel Compact Photonic Crystal Fibre Surface

**2.1 Implementation of FEM on PCFs** 

where 1 *xyz ppp* , <sup>2</sup> *x x q n* , <sup>2</sup>

*x*

*p*

1

*x*

, 2

*p*

*y*

1

*y*

*n*

*n*

**2.2 Analysis of FEM with anisotropic PML** 

<sup>1</sup> *xyz qqq* , 2

respectively.

**2. Full Vectorial FEM** 

Saitoh 2001).

Plasmon Resonance Biosensor for an Aqueous Environment 83

confinement losses with structural parameters such as air hole diameter and gold thickness

The finite element method (FEM) can be applied to waveguides in general and PCFs in particular to investigate propagation characteristics of modes. In the case of PCFs, the fibre cross section is divided into homogeneous subspaces where Maxwell's equations are solved by accounting for the adjacent subspaces. These subspaces are triangles which give good

In order to allow the study of fibers with arbitrary air filling fraction and refractive index contrast, a full vector formulation is required. A full vector FEM formulation based on anisotropic perfectly matched layers (PMLs) is able to calculate as many modes as desired in a single run without setting any iterative procedure (Saitoh and Koshiba 2001; Koshiba and

The full – vectorial wave equation can be derived from Maxwell's equations for an optical

<sup>2</sup>

where represents the electric **E** or magnetic **H** field. The relative permittivity and

*x*

*x*

1

*z*

expressions, *nx* , *ny* and *nx* represent the refractive indices in the x, y and z directions

Technically, a PML is not a boundary condition but an additional domain that absorbs the incident radiation without producing reflections. It can have arbitrary thickness and is specified to be made of an artificial absorbing material. The material has anisotropic

*n*

*q q q*

*p p p*

0 0 0 0 0 0

0 0 0 0 0 0

*y*

*z*

*z*

*q*

*p*

*y*

<sup>0</sup> *p kq* 0 (1)

*<sup>y</sup> <sup>y</sup> <sup>q</sup> <sup>n</sup>* , <sup>2</sup> *z z q n* for electric field ( = E ) and

for magnetic field ( H ). In the above

(2)

(3)

in the next section of the chapter, followed by conclusion in the final section.

approximation of circular structures (Saitoh and Koshiba 2001).

waveguide with an arbitrary cross section as (Koshiba 1992):

permeability tensors [p] and [q] can be written as (Koshiba 1992);

, 2

*p*

*z*

holes that extend along the whole fiber length (Ferrando et al. 2000). The discovery of PCFs has led to several possibilities, ranging from guidance of light in vacuum, to achieving unusual dispersion properties, from enhancing non-linear effects to high confinement of light and minimizing the same non-linear effects through very large mode area single mode fibers (Ademgil et al. 2009). These unusual properties of PCFs have led to an increasing interest in their application in areas such as sensing, signal processing and optical communication systems (Ferrando et al. 2000; Ademgil et al. 2009).

This chapter presents the numerical analysis of a novel sensitive PCF SPR biosensor optimised for operation in aqueous environments. The proposed sensor, shown in Fig. 1, consists of two metalized micro fluidic slots, air holes for light guidance and a small central air hole to facilitate phase matching between guided and plasmon modes. The proposed PCF SPR sensor incorporates extra air holes between the main air holes as a means of reducing the propagation losses whilst ensuring efficient coupling between the core guided and plasma modes.

It will be shown that the proposed PCF SPR sensor can be optimised to achieve a sensitivity of 4000 nm/RIU with regards to spectral interrogation, which is much higher than the 1000 nm/RIU and 3000 nm/RIU reported by (Hautakorpi, Mattinen, and Ludvigsen 2008) and (Hassani and Skorobogatiy 2006) respectively.

With regards to fabrication, the proposed structure should be relatively easy to fabricate due to the notably large micro fluidic slots. Deposition of metal layers inside of the micro fluidic slots can be performed either with the high-pressure chemical vapour deposition technique (Sazio 2006) or electroless plating techniques used in fabrication of metalized hollow waveguides and microstructures (Harrington 2000; Takeyasu, Tanaka, and Kawata 2005).

Fig. 1. Cross section of the proposed PCF SPR biosensor showing various sections.

A full – vectorial Finite Element Method (FEM) with perfectly matched layers (PML) is employed to investigate the variation of key performance parameters such as sensitivity and confinement losses with structural parameters such as air hole diameter and gold thickness in the next section of the chapter, followed by conclusion in the final section.
