Alisha Vira deleted Suppose_then_that_the_original__.tex  over 8 years ago

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Suppose then that the original angle of polarization of the light emitted from the laser is $\theta_0$, the change in polarization angle due the application of the magnetic field (as the light passes through a rod-shaped material) is $\Delta \theta(B) = C_v L B$, the angle of the polarization of the light after passing through the rod is $\theta_1 = \theta_0 + \Delta \theta$, and the angle of the second polarizer though which the polarized light passes before being detected by the photodiode (but after exiting the rod) is $\theta_2$.   Then, as noted by \cite{Melissinos_2003} if the voltage output from the photodiode $V_{\textrm{ pd}}$ is proportional to the light intensity, the photodiode response is given by   \begin{equation}  \label{eq:Diode_Response}  V_{\mathrm{pd}}(B) = V_0 \cos^2[\phi(B)]  \end{equation}  and the photodiode sensitivity $\eta$ = $dV_{pd}/dB$ is given by   \begin{eqnarray}  \eta & = & - 2 V_0 \cos[\phi]\sin[\phi] \frac{d\phi}{dB} \\  & = & -V_0 \sin[2\phi] \frac{d\phi}{dB} \\  & = & + c_V LV_0 \sin[2\phi] \\  \end{eqnarray}  since $\phi = \theta_{2} - \theta_{1} = \theta_{2} - \left(\theta_0 + \Delta \theta(B)\right)$.   An example of a fit to Eq.~\ref{eq:Diode_Response} is shown in Fig.~\ref{fig:PolarizationDataAtZeroField}         

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