Download Basic Optics I-II by Avijit Lahiri PDF
By Avijit Lahiri
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2). In 61 particular, solutions to diffraction problems in optics are fundamentally based on finding solutions to the Helmholtz equations. While building up of solutions to the Maxwell equations by the superposition of simpler solutions constitutes a basic approach in electromagnetic theory and optics, such superpositions are often not adequate in reproducing optical fields in real life situations. A superposition of the form Σciψi, obtained from known wave functions ψi (i = 1, 2, . , ones that require a statistical description.
One can say that some amount of energy is contained within any and every finite volume within the region occupied by the field, and arrive at the concept of the electromagnetic 50 energy density, the latter being the field energy per unit volume around any given point in space. Evidently, the concept of energy in any finite volume within the field is not as uniquely defined as that for the entire field, but the integrand on the right hand side of eq. 33) can be interpreted to be a consistent expression for the energy density w.
What is of greater relevance is the time averaged energy density, where the averaging is done over a time large compared to the typical time interval over which the fields fluctuate. Indeed, compared to the latter, the averaging time may be assumed to be infinitely large without causing any appreciable modification in the interpretation of the averaged energy density. 35a) where the symbols E, D, etc. 35c) At times, the angular brackets are omitted in expressions representing the energy density for the sake of brevity, it being usually clear from the context that a appropriate time averaging is implied.