Imagine we have an ideal cavity consist of two curved mirrors, if we added an aperture less than beam waist, what will happen? I also know that this resonator is operating at TEM00 mode. An image related to this question is also attached.
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Hello!
Inte this café the loss in the cavity will increese and you need a much
highter amplification to compensate for that.
Best regards
Sven-Göran Pettersson
Dear Petterson,
Thanks for your answer.
I know that, but I am looking for some paper journals or books in which this important issue has been studied. For example, in the attached paper researchers investigated the effect of a circular aperture on the Guassian beam profile, but what about a aperture size less than beam-waist?
Best regards,
Davood Danaei
Dear Davood!
According to your attached paper it is clear that an aperture that is smaller than the beam waist will create diffraciton effects. This will lead to a spreading of the beam over the mirrors and a ring pattern in stead of a gaussian spot will be observed. When the light is reflected some light will be lost at the aperture and the laser will die. To still have a gaussian beam the mirrors have to move father away from the beam waist so that the curvature will be correct and the beam waist be so small that the aperture will have a neglishable effect.. I have a simple program with a gaussian beam that shows what happens with the curvature and beam size for different cases, I can send it to you if you want it. However, if you expect a more rigorious mathematical description of what happens I don't know of such a paper but a good textbook is Photonics by Saleh.
Best regards
Sven-Göran Pettersson
Dear Petterson.
Thanks you.
I would be happy if I cold receive your program or any other interesting information about this issue.
Imagine you have a special Gaussian profile in the resonator and you added a pin-hole in the resonator in order to get beam quality factor (M2 ) near to diffraction limited order.So, it is very important to know the effect of this circular aperture because in some cases it is not possible to pump all the Nd:YAG rod diameter.
Best regards,
Davood Danaei
Dear Davood
The use of apertures in laser cavities to achieve TEM00 is not unusual (it is used in several types of CW lasers, including large frame Ar+ lasers) however in this case the aperture is not there to cut off the beam (which as noted will cause diffraction effects due to the 'top hat' function being convoluted with the Gaussian distribution function), but rather stops other modes in the cavity from lasing. A carefully positioned and correctly sized aperture will then force the laser to oscillate in TEM00 mode, so that your beam quality is improved. With careful placement of the aperture wrt the beam waist in the cavity (as set by the curvature of the mirrors) you should be able to still use most of the gain in the rod if this is positioned so that the intra-cavity beam at the rod position closely matches that of the diameter of the rod.
Regards
Andrew Murray.
Dear David,
I fully agree with Andrew. It is probably possible to obtain
a good TEM00-mode from your laser. One problem maybe the high amplification you
have in a solid state laser. Is it a pulsed laser?
I have attached the simple program for gaussian beams.
Best regards
Sven-GöranPettersson
There is a very short discussion about this case in Hodgson, Weber - Laser resonators and beam propagation (p. 259):
" For instance, if we decrease the aperture radius so that is becomes smaller than the fundamental mode beam radius, the angle of divergence will increase resulting in an increased power fraction hitting the aperture after each round trip. The intensity distribution at the mirrors is no longer Gaussian and the beam propagation inside the resonator does not follow the Gaussian beam propagation rules."
Later they provide a field integral equation for a general circular case (5.73).
On a finger level it is quite obvious - you'll have a diffraction on an aperture what will ruin your Gaussian beam to a certain degree. How bad? It is a relative matter, like your pump ability to compensate increased losses.
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