05 Maxwells Equations II

05 Maxwells Equations II - Maxwells Equations The optical...

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Unformatted text preview: Maxwells Equations The optical spectrum extends from wavelengths of 300 nm to 15000 nm. As humans, we can see light in the range from 400 nm to ~800 nm the visible range. Nonetheless the phenomena that describe light apply at all wavelengths. We often treat light in the geometrical optics limit, i.e. ray optics, when the variations of the optical properties vary on a scale long compared to the wavelength of light. Variations occurring on a shorter scale we must use the wave optics formalism for which Maxwells equations are the bases. This is the limit we must work in to describe the light propagation in optoelectronic devices. We will deal with the quantum limit of optics, i.e. photon optics when we deal with light emission and detection. xE (1) E xH (2) H 0 (3) loop area loop area area surface B dl B dS t t D J dl J dS D dS t t B B = - = - = + = + = ur ur ur ur ur ur ur ur ur ur ur ur ur ur ur (4) enclosed surface dS D D dS Q = = = ur ur ur ur Eye Sensitivity Function Visible Light Definitions C Charge C/ Density Charge A/ Density Current W/ Density Flux Magnetic C/ Density Flux Electric A/ Amplitude Field Magnetic V/ Amplitude Field Electric 3 2 2 2 Q m m J m B m D m H m E These quantities are continuous functions of space and time and have continuous derivatives. All solutions are bounded and single valued. At surfaces where the distribution of charge or current is modified, boundary conditions are used to connect the solutions in adjacent regions. The integral forms of Maxwells equations arise from applying Stokes Theorem and Gauss' Divergence Theorem. Gauss dv F F Stokes A ) A x ( enclosed Volume surface closed loop area = = S d l d S d Constitutive Relations The flux densities are related to the field amplitudes by the constitutive relations for an isotropic medium: Where is the magnetic permeability (Henrys/m) and is the electric permitivity (Farads / m). The vacuum values for and are E H B = = D Henrys/m 10 x 4 Farads/m 10 x 8.85 7- o-12 = = o In a medium other than vacuum, and are not necessarily scalar quantities but tensors. That is, = = j j ij i E D E D Wave Equation We will now derive the wave equation for the electric and magnetic field amplitudes by using Maxwells Equations 1-4. In doing so we will assume that and are independent of time ( 29 ( 29 ( 29 2 2 2 2 2 2 2 2 2 2 2 2 2 but where x y z B H H E E H t t t t t E E E E E x E y...
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This note was uploaded on 02/23/2011 for the course EE 474 taught by Professor Lingo during the Spring '11 term at USC.

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05 Maxwells Equations II - Maxwells Equations The optical...

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