Optical Correlator for Measuring Ultrashort Pulses

For measurements of optical pulse widths below 1 ps the best choice is a correlation technique that is based on the following principle the optical pulse with the intensity profile I t) =ceo E t) and the halfwidth AT is split into two pulses I t) and hit), which travel different path lengths S and S2 before they are again superimposed (Fig. 11.41). For a path difference As = S —S2 the pulses are separated by the time interval r = As/c and their coherent superposition yields the total intensity 

A linear detector has the output signal 5l(0 =al(t). If the time constant T of the detector is large compared to the pulse length AT, the output signal is 

Optical correlator with translation-retroreflecting prism and second-harmonic generation 

For equal amplitudes of the two pulses E t) 2(0 = o(0 coscu/, the integrand becomes 

For strictly monochromatic cw light (Eo(t) = const) the integral equals 

Mode-locked pulses of duration AT and spectral width 1/AJ are composed of many modes with different frequencies y. The oscillations of these modes have different periods Arico) = njoi AT, and after a time t Tc their phases differ by more than tt and their amplitudes cancel. In other words, the coherence time is Tc AT and interference structure can only be observed for delay times T AT. 

A linear detector with a time constant T t would therefore give an output signal that is independent of x and that yields no information on the time profile I t) This is obvious, because the detector measures only the integral over hit) hit 4- t) that is, the sum of the energies of the two pulses, which is independent of the delay time x as long as T t. Therefore linear detectors with time resolution T cannot be used for the measurement of time profiles of ultrashort pulses with AT T. 

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During recent years the development of fast photodetectors has made impressive progress. For example, PIN photodiodes (Sect. 4.5) are available with a rise time of 20 ps [11.100]. However, until now the only detector that reaches a time resolution slightly below Ips is the streak camera [11.101]. Femtosecond pulses can be measured with optical correlation techniques, even if the detector itself is much slower. Since such correlation methods represent the standard technique for measuring of ultrashort pulses, we will discuss them in more detail. 

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