User:RPFB Thin Films/sandbox

Two Curl Equations

 * $$\begin{align}

\mathbf{k} \times \mathbf{X_o} - \Delta^- \mathbf{Y_o} = 0 \quad \quad \mathbf{k} \times \mathbf{Y_o} + \Delta^+ \mathbf{X_o} = 0 \end{align}$$

Special Case

 * $$\begin{align}

\mathbf{k} = k \mathbf{\hat{z}} \quad \mathbf{X_o} = X_o \mathbf{\hat{x}} \quad \mathbf{Y_o} = Y_o \mathbf{\hat{y}} \end{align}$$

Matrix Equation


\begin{align} \begin{pmatrix} \ 0 & \mu\\ \epsilon & 0 \end{pmatrix}

\begin{pmatrix} X_o\\ Y_o \end{pmatrix} = n \begin{pmatrix} X_o\\ Y_o \end{pmatrix} \end{align} $$

Optical Thin Film Structures

 * $$\begin{align}

\Delta^- \equiv \mu     \frac{\omega}{c} \quad \quad \Delta^+ \equiv \epsilon \frac{\omega}{c} \end{align}$$

Multiple Quantum Well Structures

 * $$\begin{align}

\Delta^- \equiv \frac{\hbar \omega - m_o c^2 - e\phi}{\hbar c} \quad \quad \Delta^+ \equiv \frac{\hbar \omega + m_o c^2 - e\phi}{\hbar c} \end{align}$$