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We present a mathematical approach to appreciate that short pulse characterization requires recognizing inseparability of the measurements of the amplitude envelope-correlation and spectral measurements and then use a suitable iterative approach to derive the real characteristics. We will use a standard Michelson interferometer, as usual, to introduce the autocorrelation function of a pulse containing single and multiple frequencies. In the process, we also underscore that detectors play the key role in generating measurable Superposition Effects (SE), recognized as fringes after the detectors carry out the square modulus operation. Simple mathematical summation of amplitude factors, the Superposition Principle (SP), is not directly observable. We underscore this by mentioning that we present EM waves as classical and detectors as quantum mechanical. This semi-classical approach has been established by Lamb and Jaynes, which is indirectly supported by Glauber’s comment, “A photon is what a detector detects”. The semi-classical approach helps us separate the phenomenological difference between the absorbed detected energy by a detector (SE) from the energy supplied by the simultaneously present multiple wave amplitudes (SP). As in atomic and molecular physics, we use the detector’s dipolar stimulation as the product of its linear dipolar polarizability multiplied by all the EM fields stimulating it simultaneously. The analysis also demonstrates that for a pulse containing multiple frequencies, the two-beam autocorrelation function becomes a product of the traditional amplitude correlation factor and a frequency-comb correlation factor. Hence, the spectral interpretation of a short pulse and two-beam autocorrelation are inseparable. Therefore, the detailed characterization would require iterative computational approach by guessing the most plausible functional forms. This deeper understanding can be applied to rapid re-calibration of pulsed lasers that need to be maintained at single mode but has the tendency to move to multimode behavior. If the newly measured autocorrelation function differs from the original amplitude correlation factor, then one should check for the spectral characteristics first, before assuming that only the pulse shape has changed.
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