IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 24, NO. 6, JUNE 1988

Solid-state Laser Unstable Resonators with Tapered

Reflectivity Mirrors: The Super-Gaussian Approach

SANDRO DE SILVESTRI, PAOLO LAPORTA, VITTORIO MAGNI, AND 0. SVELTO

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 26, NO. 9, SEPTEMBER 1990

Lasers with Super-Gaussian Mirrors

SANDRO DE SILVESTRI, VITTORIO MAGNI, ORAZIO SVELTO, AND G. VALENTINI

Such systems have amplifier rods that are usually pumped radially by flashlamps. Two things: 1) These rods are usually quite expensive, so often it is most cost effective to buy rods that are not oversized enough to avoid circular diffraction, and 2) There is a lot of gain around the edges of the rod, so one often fills the rods much as possible to extract the full amount of available energy. Generally speaking, many of these lasers have circular diffraction; more important (for many applications) is that the overall distribution of the energy is uniform.

Dear Eric, this laser has telescopic unstable cavity with VRM to eliminate the hole in the center of laser spot. Near field pattern here, in general, is determined by diffraction on VRM aperture. As a rule, laser rod diameter for unstable laser cavity will be selected larger than spot diameter, determined by cavity configuration (radius of convex and concave mirrors curvative). If rod diameter is less, then it can produce additional diffraction pattern, but the main factor is diffraction on convex mirror aperture. This factor is common for all unstable telescopic cavities, with VRM , or with total convex mirror of small diameter.

More details and better understanding of the properties of unstable cavities with VRM you can get from references above.

Dear A.A.Tarasov

Thank you for your and Eric's response

1) I already have the two papers you had cited, i do not find anywhere in it specifically addressing about the rings, IF it is there could you please tell me where it is in the paper?

2) as far as Eric answer is concerned i feel it is not addressing my issue

3) i read your reply to eric's comment. The purpose of citing ekspla product in my question is to make my question clear, I noticed it is a telescopic resonator.Such rings are not only seen in eksma product but also other commercial products employing positive branch unstable resonators with super Gaussian VRM's (PBUR with SGVRM)also shows such rings.

4) Further, the active medium aperture is selected in such a way that it cuts the beam intensity to a maximum of 13%(the papers you have referred) to avoid diffraction rings. If that condition is satisfied whether there would be such rings? i have active medium cutting at

Dear Sundar,

You can see beam profile at Fig. 5 a, c in the first paper and Fig. 7 a-d in the second paper. If you want to understand better the fundamentals of mode formation, you can use the book: N. Hodgson and H. Weber "Laser resonators and beam propagation" or very good review: Y. A. Anane`ev "Unstable resonators and their applications", Sov. J. Quant. Electron, v.1, p. 565 (1972). I have this paper, but in Russian. Try to find english version of this paper. Also Y. A. Anane`ev is an author of a book "Laser resonanors and the beam divergence problem", Ed. A. Hilger, 1992.

In simple words, again, near field o-ring structure of lasers with unstable telescopic cavities is caused by diffraction at small mirror. Laser generation starts near cavity axis and spreads (after each reflection from small convex mirror) in radial direction. This small mirror size determines mode size at the output: D(out) = d(small mirror) x M, where M is magnification. You cam increase diameter of laser rod and concave mirror, but diffraction at small mirror edge still remains. It is common problem for all types of such resonators. At first time unstable cavities used hard aperture small convex mirrors, attached to flat glass large diameter substrate. Output laser radiation (near field) here has the hole in the center. Development of VRM has a goal to eliminate central hole and reduce intensity of o-rings by smoothening of mirror`s edge. That`s why different VRM profiles have been investigated. On practice it is difficult to realise exact Gaussian or supergaussian profile, so the quality of output laser beam, on practice, is restricted, in main, by real quality of VRM.

Impossible to eliminate o-rings in total.

Hope it will help.

Sundar, the answer to your questions is in the last reply of Tarasov.

In other words, VRM and other smooth apodizing aperture are never perfect and it is sufficient a small imperfection of the reflectivity shape near the edges to generate (weak) diffraction rings in the near field. Even residual substrate reflectivity outside the VRM aperture can give problems.

Viceversa, in the far-field such rings are obvious and can be calculated according to, e.g., S. Bollanti, P. Di Lazzaro, D. Murra, A. Torre, C.E. Zheng: “Propagation of doughnut-shaped super-Gaussian beams, convolution theorem and Hankel transform” Journal of Modern Optics (2005) vol. 52, 551-561 (You may find this paper here in RG).

Unfortunately, experimental physics seldom matches theory!

Best wishes

Paolo