Short-Pulse Generation by Mode-Locking

We will here describe the use of mode-locking [8.146], where we find, perhaps somewhat surprisingly, that the shortest optical pulses are generated by usmg continuous laser beams Interference effects are employed and a particularly clear and beautiful illustration of the action of the Fourier transform from the frequency to the time domain is obtained. 

Here cjq is the centre angular frequency. The evaluation of this expression involves the same type of mathematics as that used for calculating the spectral intensity distribution from a grating, and we have 

Equation (8.16) represents an optical sinusoidal caiTier wave of frequency cjq, which is amplitude-modulated in time according to (8.17). The hght intensity is propoi tional to A (t), and m Fig. 8.48 the intensity for the case of seven locked modes is given. 

The phase relation (8.14) causes the conthiuous partial waves to interfere constructively to give short pulses separated in time by 

Further reductions in pulse length can be accomplished by pulse compression. A femtosecond pulse is then transmitted through an optical fibre, which has an index of refraction that depends on the intensity. The spectral 

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