Light waves can be expressed as: y=acos[2π (vt-x/λ)]-----(1)
Can also be expressed as: Y=aexp[2πi (vt-x/λ)]-------(2)
In linear optics, the imaginary part has no meaning. In nonlinear optics, the sum of two conjugated e exponential complex numbers is to be written. ”
In fact, the imaginary part in linear optics is not meaningless, it mainly depends on the condition of the research object.
1. As for the theory of interferometric diffraction, which is a phase-by-face extinction theorem for a long enough time, the imaginary part is so important that it is very difficult to describe it simply by the real part.
In the theory of diffraction angle spectra in Fourier optics, diffraction is regarded as an inherent low-pass filtering process, that is, the details of the size smaller than the transmitted light wave length will not be carried to the output plane by the light wave, and the conclusion is that the attenuation term is obtained by using the operation of the imaginary part.
Also, the generation of evanescent waves is closely related to the imaginary part, when the surface of the metal is transmitted by light waves or when the general medium is reflected in the total reflection state.
2. In nonlinear optics, the main research object is that the intensity of light is enough to cause the nonlinearity of the medium, so that the intensity of light is necessary, so the nonlinear polarization vector is expressed by (1), but for the convenience of calculation, the sum of two conjugate indices is expressed.
In fact, the two kinds of situations can be expressed in different light waves, mainly because they are Maxwell's equations of the intrinsic function, all satisfy the Maxwell equation, this is the fundamental. Although the form is different, and different forms to deal with different problems will have a very good difference, but for a specific light wave, its physical characteristics only one, as long as the two descriptions, determine the nature of the light waves of the same parameters.
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