External Bow Tie or Ring doubling cavities have one mirror on a piezo to phase match the diode laser.
Even stabilized diode lasers wander like crazy in frequency. So active electronics are used to peak the power, often using Pound Drever Hall or Peak Power locking.
A hobbyist would use a tiny ramp with DC offset to sweep the piezo to get a flash, and worry about locking later.
Cavity length Requirement:
((C* Lambda/2L(delta cavity)) length must equal a integer half multiple of ((C* Lambda/2L (Source)) At near IR and Visible wavelengths, The integer can and will be huge, and there are many, many integer multiples that will work for a given setup. So there is a "band" of motion it will lock over. If the Cavity has a enough of a FSR (Free Spectral Range) you will see it lock and fade out in a sinusoidal pattern as you move the piezo.
In fact if using analog Pound Drever Hall locking, you'll always put a slight modulation on the cavity so the lock-in amplifier will guide the piezo.
The other technique is to use a brute force Q-switched pump laser and not worry about most of the locking crap. Frequency conversion for the most part is best done using high peak powers.
Interesting quantum mechanical conundrum, as the external cavity approaches lock to the source laser, the mirror in which the pump beam enters effectively partially disappears. (there are a host of conditions required for this to happen).
Never built one, but have been in the room with them. Have adjusted/peaked one long,long,long long, ago.
Attached is TWO PDFs used under educational provisions of copyright law. I will remove these PDF in one week.
Note the second PDF using a polarization locking scheme without a P-D-H reference or a Lock-In Amplifier to drive the Piezo. While used Lock-Ins are cheap...... This might be easier if you have less/zero/no electronics skills.
I have these PDFs from a past need for a UV laser for Raman Spectroscopy.
The project was abandoned because the professor had no idea of what he was doing, so I never built one.
Note, no laboratory CW Laser experimenter in their right mind lives without a Lock-In Amplifier. Older beat up simple ones are the best. One should at least learn what one does. The math used to explain it is high school algebra I. They are all over Ebay.
Quick explanation: A Lock-In finds signals below the system noise, provided you can import a modulation on the signal to be found and give it time to average the signal from the noise. It returns the magnitude and phase of the signal.
One should start with 1064->532 as that is tricky enough for a beginner, but has the most chance of success. A 532 ring cavity could come from very inexpensive Casix parts. However I'd build a two or three mirror 532 nm conventional laser before I tried rings or exotics. One should crawl before one walks, there are many things to be learned before jumping to the high end.
Attached is TWO PDFs used under fair educational provisions of copyright law. I will remove these PDF in three days.
Steve
