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# HW6 - ECE 455 Optical Electronics Homework 6 Due Oct 20...

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ECE 455: Optical Electronics Homework 6 Due: Oct. 20, 2010 1 Derivations Derive the following equations. Writing down the final expressions without derivation or explanation will not receive credit. (a) Derive the relationship between intensity and energy density for a plane wave. Hint: Consider a box with sides dx , dy and dz = cdt . Consider the flux of energy through the dxdy surface. (b) Derive an expression for dI dz including the effect of saturation in terms of γ 0 and I . Hint: Consider the effect of an optical field on the steady state populations. Write two rate equations, one including stimulated emission and one without. (c) Integrate the expression in part (b) to find the gain of a plane was as it passes through a gaim medium length L . Obtain an equation containing I out /I in . (d) (Optional) What does this equation become in the limit that I out I sat ? (e) (Optional) What does this equation become in the limit that I out I sat ?

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HW6 - ECE 455 Optical Electronics Homework 6 Due Oct 20...

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