**4. Simulation results**

We begin our analysis by investigating the potential of the proposed PCF for sensing. The structural parameters used are Λ = 1.5 μm, d1/Λ= 0.2, d2/Λ= 0.35, d01/Λ = 0.15, d3= 1.5 μm and tAu = 40 nm. The slots in the second ring are first filled with an analyte whose refractive index, na = 1.33 (water) after which the confinement loss of the fundamental mode is calculated. The process is repeated with an analyte of refractive index of 1.34 and the calculated loss spectra for both cases are plotted in Fig 2. It can be observed from Fig. 2 that there are two major attenuation peaks which correspond to the excitation of plasmonic modes on the surface of the metalized channels filled with aqueous analyte , na=1.33. It is important to note that the shape of a metallized surface can have a significant effect on the plasmonic excitation spectrum. Hence, a planar metallized surface supports only one plasmonic peak, while a cylindrical metal layer can support several plasmonic peaks.

By changing the analyte refractive index from 1.33 to 1.34, it is observed in Fig. 2 that there is a corresponding shift (dashed curves) in the resonant attenuation peaks. This transduction mechanism is commonly used for detecting the bulk analyte refractive index changes, as

A Novel Compact Photonic Crystal Fibre Surface

(Hassani and Skorobogatiy 2006).

**Confinement**

resulting in higher propagation losses.

values of 0.15 and 0.25 respectively.

plasmonic peak toward longer wavelengths (Fig. 4).

d1/Λ = 0.2, d2/Λ = 0.35.

0

20

40

60

80

100

120

 **Loss (dB/cm)**

Plasmon Resonance Biosensor for an Aqueous Environment 87

Skorobogatiy 2006). Practically, this can be used in the monitoring of concentration of metal nanoparticles attached to the photosensitive drugs in photodynamic cancer therapy

**= 1.5 m**

**tAu =50nm tAu =30nm tAu =40nm**

**Wavelength (nm)**

Fig. 3. Loss spectra of proposed PCF SPR biosensor in the vicinity of the first plasmonic peak for variation in gold layer thickness (tAu). Analyte refractive index (na=1.33), d01/Λ = 0.15,

In this particular design, a central air hole of diameter d1, has been employed to tune the phase matching condition. In what follows, we investigate the effect of size variation of the central air hole, with a view of tuning and optimizing plasmon excitation by the core-guided mode of the proposed PCF SPR biosensor. In order to achieve this, d1/Λ is varied from 0.15 to 0.25 whilst keeping all other structural parameters constant. The micro-fluidics slots are filled with analyte of refractive index, na = 1.33 for each calculation of the loss spectra for every change in the value of d1/Λ. Figure 4 shows that there is an overall increase in the modal losses of the fundamental mode for the larger diameters of the central air hole. An increase in the size of the central air hole promotes expulsion of the modal field from the fiber core. This in turn, leads to the greater modal presence near the metallic interface,

Another consequence of the modal expansion from the fiber core into the air-filled microstructure is reduction of the modal refractive index (Fig. 5), leading to the shift of a

In particular, the resonant wavelength changes from about 615 nm to 620 nm for d1/Λ

The next step of the analysis focuses on the influence of the extra air holes, d01, on the confinement loss and resonant wavelength of the PCF SPR sensor. To achieve this, d01/Λ is varied from 0.10 to 0.20, whilst keeping all other structural parameters constant. The microfluidics slots are filled with analyte of refractive index, na = 1.33 for each computation of the

500 550 600 650 700 750 800

well as monitoring formation of the nanometer-thin biolayers on top of a metallized sensor surface (Hassani and Skorobogatiy 2006). In this particular design, there is considerably more field penetration into the analyte-filled channels for the first plasmonic peak as compared to that of the second. This makes it more sensitive than the second with regards to analyte refractive index changes. All subsequent analysis will be based on the first plasmonic peak as it is the most sensitive to refractive index change.

Fig. 2. Calculated loss spectra of the fundamental modes. Loss spectra (solid curves) feature several attenuation peaks corresponding to the excitation of plasmonic modes on the surface of metallized channels filled with aqueous analyte (na = 1.33). A change in analyte refractive index (dashed curves) leads to a corresponding shift in the points of phase matching between the core-guided and plasmon modes.

#### **4.1 Optimisation of structural parameters**

In order to optimise the several structural parameters of the proposed PCF SPR biosensor for high spectral sensitivity, it is important to understand the effects these parameters have on the sensor properties. Surface plasmon waves, being surface excitations, are very sensitive to the thickness of metallic layers. We therefore investigate the changes in the spectra for the first plasmonic peak when the thickness of gold tAu, is varied from 30 nm to 50 nm. The analyte in this case is fixed at a refractive index of 1.33 and all other structural parameters are kept constant. The confinement loss for the fundamental mode is calculated for each case of tAu and plotted to give the spectra in Fig. 3.

Figure 3 shows a general decrease in modal propagation loss at resonance when the thickness of the gold layer increases. In addition, there is a shift in the resonant wavelength towards longer wavelengths for every increase in tAu. Specifically, the resonant wavelength shifts from about 580 nm to 640 nm for tAu values of 30 nm and 50 nm respectively. This sensitivity of the resonant wavelength to the gold thickness can be used in the study of metal nanoparticle binding events on the metallic surface of the sensor (Hassani and

well as monitoring formation of the nanometer-thin biolayers on top of a metallized sensor surface (Hassani and Skorobogatiy 2006). In this particular design, there is considerably more field penetration into the analyte-filled channels for the first plasmonic peak as compared to that of the second. This makes it more sensitive than the second with regards to analyte refractive index changes. All subsequent analysis will be based on the first

**= 1.5 m**

**Wavelength (nm)**

Fig. 2. Calculated loss spectra of the fundamental modes. Loss spectra (solid curves) feature several attenuation peaks corresponding to the excitation of plasmonic modes on the surface of metallized channels filled with aqueous analyte (na = 1.33). A change in analyte refractive index (dashed curves) leads to a corresponding shift in the points of phase matching

In order to optimise the several structural parameters of the proposed PCF SPR biosensor for high spectral sensitivity, it is important to understand the effects these parameters have on the sensor properties. Surface plasmon waves, being surface excitations, are very sensitive to the thickness of metallic layers. We therefore investigate the changes in the spectra for the first plasmonic peak when the thickness of gold tAu, is varied from 30 nm to 50 nm. The analyte in this case is fixed at a refractive index of 1.33 and all other structural parameters are kept constant. The confinement loss for the fundamental mode is calculated

Figure 3 shows a general decrease in modal propagation loss at resonance when the thickness of the gold layer increases. In addition, there is a shift in the resonant wavelength towards longer wavelengths for every increase in tAu. Specifically, the resonant wavelength shifts from about 580 nm to 640 nm for tAu values of 30 nm and 50 nm respectively. This sensitivity of the resonant wavelength to the gold thickness can be used in the study of metal nanoparticle binding events on the metallic surface of the sensor (Hassani and

500 600 700 800 900 1000 1100

**na=1.33 na=1.34**

plasmonic peak as it is the most sensitive to refractive index change.

**Confinement**

0

between the core-guided and plasmon modes.

**4.1 Optimisation of structural parameters** 

for each case of tAu and plotted to give the spectra in Fig. 3.

20

40

60

80

100

120

140

 **Loss (dB/cm)** Skorobogatiy 2006). Practically, this can be used in the monitoring of concentration of metal nanoparticles attached to the photosensitive drugs in photodynamic cancer therapy (Hassani and Skorobogatiy 2006).

Fig. 3. Loss spectra of proposed PCF SPR biosensor in the vicinity of the first plasmonic peak for variation in gold layer thickness (tAu). Analyte refractive index (na=1.33), d01/Λ = 0.15, d1/Λ = 0.2, d2/Λ = 0.35.

In this particular design, a central air hole of diameter d1, has been employed to tune the phase matching condition. In what follows, we investigate the effect of size variation of the central air hole, with a view of tuning and optimizing plasmon excitation by the core-guided mode of the proposed PCF SPR biosensor. In order to achieve this, d1/Λ is varied from 0.15 to 0.25 whilst keeping all other structural parameters constant. The micro-fluidics slots are filled with analyte of refractive index, na = 1.33 for each calculation of the loss spectra for every change in the value of d1/Λ. Figure 4 shows that there is an overall increase in the modal losses of the fundamental mode for the larger diameters of the central air hole. An increase in the size of the central air hole promotes expulsion of the modal field from the fiber core. This in turn, leads to the greater modal presence near the metallic interface, resulting in higher propagation losses.

Another consequence of the modal expansion from the fiber core into the air-filled microstructure is reduction of the modal refractive index (Fig. 5), leading to the shift of a plasmonic peak toward longer wavelengths (Fig. 4).

In particular, the resonant wavelength changes from about 615 nm to 620 nm for d1/Λ values of 0.15 and 0.25 respectively.

The next step of the analysis focuses on the influence of the extra air holes, d01, on the confinement loss and resonant wavelength of the PCF SPR sensor. To achieve this, d01/Λ is varied from 0.10 to 0.20, whilst keeping all other structural parameters constant. The microfluidics slots are filled with analyte of refractive index, na = 1.33 for each computation of the

A Novel Compact Photonic Crystal Fibre Surface

**Confinement**

**Real ( neff )**

1.425

index (na=1.33), tAu = 40 nm, d1/Λ = 0.20, d2/Λ = 0.35.

1.43

1.435

1.44

1.445

1.45

1.455

0

20

40

60

80

100

120

140

160

 **Loss (dB/cm)**

Plasmon Resonance Biosensor for an Aqueous Environment 89

**Wavelength (nm)**

Fig. 6. Loss spectra of proposed PCF SPR biosensor in the vicinity of the first plasmonic peak for variation in d01. Analyte refractive index (na=1.33), tAu = 40 nm, d1/Λ = 0.20, d2/Λ = 0.35.

**= 1.5 m**

**Wavelength (nm)**

Fig. 7. Dispersion relation of the fundamental mode for variation in d01. Analyte refractive

500 550 600 650 700 750 800

500 550 600 650 700 750 800

**d01/=0.20 d01/=0.10 d01/=0.15**

d01/=0.20 d01/=0.10 d01/=0.15

**= 1.5 m**

Fig. 4. Loss spectra of proposed PCF SPR biosensor in the vicinity of the first plasmonic peak for variation in d1. Analyte refractive index (na=1.33), d01/Λ = 0.15, tAu = 40 nm, d2/Λ = 0.35.

Fig. 5. Dispersion relation of the fundamental mode for variation in d1. Analyte refractive index (na=1.33), d01/Λ = 0.15, tAu = 40 nm, d2/Λ = 0.35.

**= 1.5 m**

**Wavelength (nm)**

Fig. 4. Loss spectra of proposed PCF SPR biosensor in the vicinity of the first plasmonic peak for variation in d1. Analyte refractive index (na=1.33), d01/Λ = 0.15, tAu = 40 nm, d2/Λ = 0.35.

**Wavelength (nm)**

Fig. 5. Dispersion relation of the fundamental mode for variation in d1. Analyte refractive

500 550 600 650 700 750 800

500 550 600 650 700 750 800

**d1/=0.15 d1/=0.20 d1/=0.25**

> d1/=0.30 d1/=0.15 d1/=0.20

**Confinement**

**Real ( neff )**

1.425

index (na=1.33), d01/Λ = 0.15, tAu = 40 nm, d2/Λ = 0.35.

1.43

1.435

1.44

1.445

1.45

0

20

40

60

80

100

120

 **Loss (dB/cm)**

Fig. 6. Loss spectra of proposed PCF SPR biosensor in the vicinity of the first plasmonic peak for variation in d01. Analyte refractive index (na=1.33), tAu = 40 nm, d1/Λ = 0.20, d2/Λ = 0.35.

Fig. 7. Dispersion relation of the fundamental mode for variation in d01. Analyte refractive index (na=1.33), tAu = 40 nm, d1/Λ = 0.20, d2/Λ = 0.35.

A Novel Compact Photonic Crystal Fibre Surface

**Confinement**

d2/Λ = 0.35.

0

20

40

60

80

100

120

140

160

 **Loss (dB/cm)**

according to Eqn. (9).

Plasmon Resonance Biosensor for an Aqueous Environment 91

the thickness of the gold layer becomes significantly larger than that of its skin depth, (~20– 30 nm), the fibre core mode becomes effectively screened from a plasmon, resulting in a low coupling efficiency, culminating in low sensitivity. Hence, the maximum shift of 20 nm occurs for tAu of 30 nm (Fig. 8). This results in a maximum sensitivity of 2000 nm/RIU

The next step involves investigating the influence of d1 on the spectral sensitivity of the PCF SPR sensor under consideration. It can be observed from Fig. 9 that the effect of d1 on the spectral sensitivity follows the same trend as that of tAu. Specifically, the sensitivity increases with d1/Λ to a maximum of approximately 2100 nm / RIU for d1/Λ value of 0.25. An increase in d1/Λ ensures more leakage of the fundamental mode into the metal / analyte layer in the

The analysis done so far gives some insight into the effects the structural parameters have

**= 1.5 m**

t

t

t

t

t

t

Au =50nm, na=1.34

Au =30nm, na=1.33

Au =30nm, na=1.34

Au =40nm, na=1.33

Au =40nm, na=1.34

Au =50nm, na=1.33

**Wavelength (nm)**

According to Table 1, d01, tAu and d1 can be considered as loss control parameters. With regards to spectral sensitivity, the main candidates to consider are tAu and d1. Of these two parameters, d1 appears relatively easier to control as compared to tAu. It will therefore be more convenient to fix tAu to an appropriate value and optimise d1 to achieve the desired sensitivity. It must also be noted that there is a limit to which d1 can be increased due to the associated high confinement losses. To minimise the confinement losses, d01 can optimised

Fig. 8. Shift in resonant wavelength of the loss spectrum for a variation in tAu of the proposed SPR sensor. Analyte refractive index (na =1.33), d01/Λ = 0.15, d1/Λ = 0.2,

500 550 600 650 700 750 800

microfluidic slots, resulting in greater sensitivity of analyte refractive index change.

**5. An optimised structure for higher spectral sensitivity** 

on sensor performance. These results are summarised in Table 1.

loss spectra for a change in the value of d01/Λ. Figure 6 shows that the extra air holes could be used to play a significant role in confinement loss reduction. Unlike d1, increasing d01 reduces the confinement loss whilst shifting the resonant wavelength towards longer wavelength. However, d01 has less influence on the resonant wavelength as compared to d1 and can be considered as a loss control parameter. An increase in d01 prevents expulsion of the modal field from the fibre core, thus ensuring better confinement to the core. This ultimately reduces the confinement loss at the resonant wavelength. The decrease in the modal effective index (Fig. 7) for an increase d01/Λ is due to the fact that the "escaping" mode field from the core interacts with relatively larger air filled spaces.

#### **4.1.1 Characterization of sensitivity of the proposed PCF SPR biosensor**

The detection of changes in the bulk refractive index of an analyte is the simplest mode of operation of fibre - based SPR biosensors (Hassani and Skorobogatiy 2006; Piliarik, Párová, and Homola 2009; Homola 2003). There is a strong dependence of the real part of a plasmon refractive index on the analyte refractive index, which makes the wavelength of phase matching between the core-guided and plasmon modes sensitive to the changes in the analyte refractive index (Homola 2003; Piliarik, Párová, and Homola 2009). Amplitude (phase) and wavelength interrogation are two main detection methods (Homola 2003; Piliarik, Párová, and Homola 2009).

In the amplitude or phase based method, all measurements are done at a single wavelength (Homola 2003). This approach has the merit of its simplicity and low cost as there is no spectral manipulation needed (Homola 2003). The disadvantage however, is that a smaller operational range and lower sensitivity when compared with the wavelength interrogation methods, where the transmission spectra are taken and compared before and after a change in in analyte refractive index has occurred(Homola 2003).

The amplitude sensitivity is given by(Hassani and Skorobogatiy 2006):

$$S\_A(\lambda) = -\left(\hat{c}\mathbf{a}(\lambda, n\_a) / \hat{c}n\_a\right) / \left(\mathbf{a}(\lambda, n\_a) \text{ [RIU^{-1}]}\right) \tag{9}$$

where α(λ, na) represents the propagation loss of the core mode as a function of wavelength.

When the sensor operates in the wavelength interrogation mode, changes in the analyte refractive index are detected by measuring the displacement of a plasmonic peak. The sensitivity in this case is given by (Hassani et al. 2008; Homola 2003):

$$S\_{\lambda} \text{( $\lambda$ )}=\frac{\partial \lambda\_{peak}}{\partial n\_a} \text{ [nm / RIU]}\tag{10}$$

where λpeak is the wavelength corresponding to the resonance (peak loss) condition. The proposed SPR sensor operates in wavelength interrogation mode. Thus all sensitivity analysis will be limited to spectral interrogation.

It can be observed from Fig. 8 that the thickness of the gold layer (tAu) in the microfluidic slots has an influence on the shift in resonant wavelength. Specifically, the change in resonant wavelength (λpeak) is inversely proportional to tAu. This is due to the fact that when

loss spectra for a change in the value of d01/Λ. Figure 6 shows that the extra air holes could be used to play a significant role in confinement loss reduction. Unlike d1, increasing d01 reduces the confinement loss whilst shifting the resonant wavelength towards longer wavelength. However, d01 has less influence on the resonant wavelength as compared to d1 and can be considered as a loss control parameter. An increase in d01 prevents expulsion of the modal field from the fibre core, thus ensuring better confinement to the core. This ultimately reduces the confinement loss at the resonant wavelength. The decrease in the modal effective index (Fig. 7) for an increase d01/Λ is due to the fact that the "escaping" mode field from the core interacts with relatively larger air

The detection of changes in the bulk refractive index of an analyte is the simplest mode of operation of fibre - based SPR biosensors (Hassani and Skorobogatiy 2006; Piliarik, Párová, and Homola 2009; Homola 2003). There is a strong dependence of the real part of a plasmon refractive index on the analyte refractive index, which makes the wavelength of phase matching between the core-guided and plasmon modes sensitive to the changes in the analyte refractive index (Homola 2003; Piliarik, Párová, and Homola 2009). Amplitude (phase) and wavelength interrogation are two main detection methods (Homola 2003;

In the amplitude or phase based method, all measurements are done at a single wavelength (Homola 2003). This approach has the merit of its simplicity and low cost as there is no spectral manipulation needed (Homola 2003). The disadvantage however, is that a smaller operational range and lower sensitivity when compared with the wavelength interrogation methods, where the transmission spectra are taken and compared before and after a change

where α(λ, na) represents the propagation loss of the core mode as a function of wavelength. When the sensor operates in the wavelength interrogation mode, changes in the analyte refractive index are detected by measuring the displacement of a plasmonic peak. The

*<sup>A</sup>*( ) ( ( , )/ )/ ( , ) *S nn n aa a* [RIU-1] (9)

[nm / RIU] (10)

**4.1.1 Characterization of sensitivity of the proposed PCF SPR biosensor** 

filled spaces.

Piliarik, Párová, and Homola 2009).

in in analyte refractive index has occurred(Homola 2003).

The amplitude sensitivity is given by(Hassani and Skorobogatiy 2006):

sensitivity in this case is given by (Hassani et al. 2008; Homola 2003):

*S*

analysis will be limited to spectral interrogation.

( ) *peak*

 

*a*

where λpeak is the wavelength corresponding to the resonance (peak loss) condition. The proposed SPR sensor operates in wavelength interrogation mode. Thus all sensitivity

It can be observed from Fig. 8 that the thickness of the gold layer (tAu) in the microfluidic slots has an influence on the shift in resonant wavelength. Specifically, the change in resonant wavelength (λpeak) is inversely proportional to tAu. This is due to the fact that when

*n*

the thickness of the gold layer becomes significantly larger than that of its skin depth, (~20– 30 nm), the fibre core mode becomes effectively screened from a plasmon, resulting in a low coupling efficiency, culminating in low sensitivity. Hence, the maximum shift of 20 nm occurs for tAu of 30 nm (Fig. 8). This results in a maximum sensitivity of 2000 nm/RIU according to Eqn. (9).

The next step involves investigating the influence of d1 on the spectral sensitivity of the PCF SPR sensor under consideration. It can be observed from Fig. 9 that the effect of d1 on the spectral sensitivity follows the same trend as that of tAu. Specifically, the sensitivity increases with d1/Λ to a maximum of approximately 2100 nm / RIU for d1/Λ value of 0.25. An increase in d1/Λ ensures more leakage of the fundamental mode into the metal / analyte layer in the microfluidic slots, resulting in greater sensitivity of analyte refractive index change.
