Pulse shaping by a frequency filtering of a sawtooth phase-modulated CW laser

The spectrum of a CW field whose phase experiences a periodic sawtooth modulation is analyzed. Two types of the sawtooth phase modulation are considered. One is created by combining many harmonics of the fundamental frequency. The second is produced by electro-optic modulator fed by the relaxation oscillator, which generates a voltage slowly rising during charging the energy storage capacitor and dropping fast due to discharge by a short circuit. It is proposed to filter out the main spectral component of the sawtooth phase modulated field. This filtering produces short pulses from CW phase modulated field. Several filters are proposed to remove the selected spectral component. It is shown that such a filtering is capable to produce a train of short pulses. Duty cycle of this train is equal to the modulation period and duration of the pulses can vary from $10^{-1}$ to $10^{-2}$ of the period. Depending on the modulation frequency, the proposed method is capable to produce pulses with duration ranging from nanoseconds to a fraction of picosecond.