Relation of laser pulse length and the Output Coupler trasmissivity

[BPHH85]

Dear all,

I'm within my Ph.D. studies in laser engineering and most of the details are rather new to me. Working on short pulse systems, my advisor told me some times about the relation of the output coupler transmissivity and the outcoupled pulse length, but more as a rule of thumb. According to this, the higher the transmissivity of the OC the shorter is the pulse (until a lower boundary). Some similar relation I'm searching a formal expression for is about pulse length vs. cavity length. This should be vaild for pulsed laser systems utilizing the principles of q-switching as well as gain-switching. Unfortunately this is more based on experiances then on formal relations. I did some literature researches on this but had no luck yet. Does anyone know a formal discription about this two relations? The most important for me is the first one between pulse length and OC.

Best regards

PS: I'm not sure if this is the right sub forum for my thread. Please feel free to move it if nessecary.
PPS: Merry Christmas to all

 

[sophiecentaur]

Hi. Welcome tp PF.
I would imagine that it could be to do with the bandwidth of the laser. The Power taken by the OC would affect the Q of the laser and this will affect the pulse length.
A bandwidth of Δf would imply a possible pulse width in the order of 1/Δf with oscillators in general - if you are modulating the oscillator itself. That wouldn't apply to 'downstream' modulation of a high accuracy sinusoid as the modulation system itself would add sidebands.

 

[BPHH85]

Thank you for your reply

Hi. Welcome tp PF.
I would imagine that it could be to do with the bandwidth of the laser. The Power taken by the OC would affect the Q of the laser and this will affect the pulse length.
A bandwidth of Δf would imply a possible pulse width in the order of 1/Δf with oscillators in general - if you are modulating the oscillator itself. That wouldn't apply to 'downstream' modulation of a high accuracy sinusoid as the modulation system itself would add sidebands.

What bandwidth of the laser do you mean especially? Because the gain bandwidth is relatively fixed and may be indipendent from the OC mirror as well as the longitudinal mode bandwidth, that should in first order just depend on the cavity length.

Nevertheless, bandwidth may be still a good point. A laser resonator is based on the model of the Fabry-Perot interferometer. For high reflectivity mirrors, the finesse and thus the transmission bandwidth is small. As pulsewidth t ~ $1/\Delta f$, for short pulses the bandwidth needs to be high. But if the transmission bandwidth of the resonator is small, the spectrum of the laser pulse may be truncated and so the pulse has now a smaller spectral bandwidth and thus has to be broader in time. But this is just a guess and I'm not sure if this is the way these models are working.

 

[sophiecentaur]

What bandwidth of the laser do you mean especially?

I was referring to how fast you could turn it on and off. My comment was a general one about all oscillators and I guess it would have to apply to a laser cavity as much as anything else. The details escape me but we usually find that these sort of fundamentals apply all over the place. It would depend on how the pulses are formed . There are a number of laser aficionados on PF. I expect one of them will pick up on the thread title before too long.
Perhaps I should rattle the cage of @Andy Resnick and see if he takes the bait.

 

[BPHH85]

The topic is still important to me. So any help is welcome.

 

[tech99]

The topic is still important to me. So any help is welcome.

There are several ways of looking at this problem. For a resonator which is many wavelengths long, you will notice that a small change in frequency causes a large change in phase. The phase change is multiplied as a result of the resonator length, compared to a half wave long resonator. If, for instance, we use the resonator in the feedback path of an oscillator, the frequency of oscillation will be when the phase shift around the loop is n x 360 degrees. So if we try to move frequency a little, it is the phase shift generated by the resonator which pulls the oscillator back on frequency. If phase changes rapidly, frequency is held closer. A resonator with a higher Q-factor gives a more rapid phase shift when frequency is altered, so a long resonator exhibits a higher Q.
High Q is usually very desirable, but if we want to modulate the system with a pulse, it will prolong the build-up and decay of the pulse. As BPHH85 has mentioned, pulse duration is dictated by bandwidth, so a brief pulse requires wider bandwidth and a lower Q. Hence, a long resonator is a disadvantage in this case.
Alternatively, we can say that if the pulse is shorter than the resonator, it is going to be difficult to turn it off and on fast enough whilst still maintaining laser oscillation.