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Basic Optics I-II by Avijit Lahiri

By Avijit Lahiri

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39) Assuming that the temporal variation of the field vectors is a harmonic one, and making use of the complex representation of vectors as explained in sec. 40) where Ẽ and stand for the complex amplitudes corresponding to the respective real time dependent vectors (appearing in eq. 39)) at the point under consideration. 41) where the angular brackets indicating the time average has been omitted for the sake of brevity and ŝ denotes the unit vector along S . One way of looking at Maxwell’s equations is to say that these equations describe how the 54 temporal variations of the field vectors in one region of space get transmitted to adjacent regions.

4 Electromagnetic potentials An alternative, and often more convenient, way of writing Maxwell’s equations is the one making use of electromagnetic potentials instead of the field vectors. To see how this is done, let us consider a linear homogeneous isotropic dielectric with material constants ε and μ. 16b) The remaining two of the Maxwell equations, eq. 1a) and eq. 1d) can then be expressed in terms of these two potentials which involve four scalar variables, in the place of the six scalar components of E and B, in addition to the material constants.

Ray optics (or geometrical optics) and diffraction theory constitute two such approximation schemes of wide usefulness in optics. , their range of applicability extends to frequencies beyond the range one associates with visible light. This is not to convey the impression that one cannot acquire working knowledge in ray optics or diffraction theory without a thorough grounding in electromagnetic theory. In this book, however, my approach will be to trace the origins of the working rules of these approximation schemes to the principles of electromagnetic theory.

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