Alisha Vira edited Math symbols.tex  over 8 years ago

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\section{Method}  Eqs.~\ref{eq:Diode_Response} and \ref{eq:MaxSensitivity} suggest 3 methods of measuring the Verdet constant $c_V$.   \begin{enumerate}  \item Use Eq.~\ref{eq:Diode_Response} to Calculate $d\phi / dB$ and then $c_V$ from measurements of $V_{\mathrm{pd}}(B,\theta_2)$ as a function of polarizer angle $\theta_2$ for two or more magnetic field strengths $B$ (one of which could be zero).  \item Use Eq.~\ref{eq:MaxSensitivity} to calculate $dV_{\mathrm{pd}}(B)/dB$, $d\phi / dB$ and $c_V$ from measurements of $V_{\mathrm{pd}}(B)$ as a function of magnetic field $B$ (at the relative polarizer angle $\phi(0) = \pi/4$).   \item Use Eq.~\ref{eq:MaxSensitivity} to calculate $d\phi / dB$ and $c_V$ from direct measurements of $dV_{\mathrm{pd}}(B)/dB$ (using a lock-in amplifier) for a modulated magnetic field $B = B_0 + B_1 \cos[2 \pi f t]$ (at the relative polarizer angle $\phi(0) = \pi/4$).   \end{enumerate}  To find $c_V$ using Eq.~\ref{eq:Diode_Response} , we need to fit a plot of our data to Eq.~\ref{eq:Diode_Response} to determine $\theta_1(B)$ for each value of $B$.   To find $c_V$ using Eq.~\ref{eq:MaxSensitivity}, note that at that maximum sensitivity setting, $\phi(B) = \pi/4 - c_V L B$ and $V_{\mathrm{pd}}(0) =V_0 / 2 $. methods