TIR BIOSENSOR$/$EXAMPLE

$$ Sensitivity Based on Varying the Reflectance Phase

Mohame

Given Parameters:

Refractive index of silicon prism $(n_{\text{p}\text{r}\text{i}\text{s}\text{m}})$: $3\mathrm{.}4$

Refractive index of water $(n_{\text{w}\text{a}\text{t}\text{e}\text{r}})$:$1.$$$3$

Wavelength of light $()$ : $850$ nm $($chosen in the near$-$infrared region$)$

Rate of change of refractive index with glucose concentration:

Critical angle for total internal reflection $($TIR$)$: We assume the light is incident at an angle ${}_i$ close to the critical angle, which results in TIR.

${}_c=arcsin(\frac{1\mathrm{.}331}{3\mathrm{.}4})$

${}_c=arcsin(0\mathrm{.}391)$

${}_c$~~$23\mathrm{.}0$

Nihal Fayez Fahmy Areed

TIR BIOSENSOR$/$EXAMPLE

Sensitivity Based on Varying the Reflectance Phase

$tan(\frac{{}_T}{2})=-\frac{\sqrt[\phantom{2}]{si{n}^2-n^2}}{cos}$

$tan(\frac{{}_{TM}-}{2})=-\frac{\sqrt[\phantom{2}]{si{n}^2-n^2}}{n^{2}cos}$

$n=\frac{n_2}{n_1}$

$\backslash$table$[[$Refractive Index $($n$),$Phase $($TE Mode$),$Phase $($TM Mode$),$Sensitivity $($TE$),$Sensitivity $($TM$)],[1\mathrm{.}33,{}_{TE1},{}_{TM1},$S $1($TE$),$S $1($TM$)],[1\mathrm{.}34,{}_{TE2},{}_{TM2},$S $2($TE$),S2(TM)$