A Ti-doped sapphire laser emits at 800 nm and is mode-locked. It consists of a Ti-sapphire rod with refractive index 1.4 that is 10 cm long within a cavity that is 2 m in length (the laser pulses propagate in air except when passing through the rod). You can neglect the reflectivity of the rod surfaces, assuming they are coated with perfect anti-reflective coatings. The spectral width of the laser is 200 THz. What is the resulting pulse width, pulse repetition rate and spatial separation of the output pulses? How many cavity modes are contributing to the output pulses? Considering the pulse width achieved, comment on what strategy you think might be appropriate to achieve mode locking: would this be a passive or active mechanism? Explain the reasoning behind your answer
Mode-locking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds (10−12 s) or femtoseconds (10−15 s). A laser operated in this way is sometimes referred to as a femtosecond laser, for example in modern refractive surgery. The basis of the technique is to induce a fixed-phase relationship between the longitudinal modes of the laser's resonant cavity. Constructive interference between these modes can cause the laser light to be produced as a train of pulses. The laser is then said to be 'phase-locked' or 'mode-locked'.
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