Final Report


"Improvement of Laser Efficiency using Multi-Gaussian Beams"

A Full 2002 Summer Stipend


Eastern Oregon University


Anthony A. Tovar, Ph. D.,

Associate Professor, Physics and Engineering Programs

Work Completed:

The basic proposal for the full summer stipend consisted of a laser resonator design that could be used to increase its efficiency. The increase in efficiency was to be achieved by designing a laser resonator to produce an intracavity beam mode which yielded a higher mode volume than the conventional Gaussian beam.   Before commencing on the project a lot of foundational work had to be done on determining the propagation characteristics of multi-Gaussian beams.  That foundational work was done during a previous stipend, and led to a journal publication [1].  The expected product of this work is also a manuscript to be submitted to a major optics/lasers journal.  The manuscript is currently about 80% finished [2], and is to be completed this school year.  (This web page will be updated when the manuscipt is submitted, and again when it is accepted.)
[1] A. A. Tovar, Propagation of flat-topped multi-Gaussian beams, Journal of the Optical Society of America A, vol. 18, pp. 1897 - 1904 (2001).
The abstract is web published at
[2] A. A. Tovar, Intracavity beam shaping for increased amplifier gain extraction in high gain lasers, Journal of the Optical Society of America A (to be submitted).


Technical Summary:

In laser resonator design, intracavity beam shaping is sometimes used to alter the output beam characteristics.  For example, intracavity telescopes are used to make the output beam size smaller.  This allows the laser designer to design a laser with a wide amplifier that nonetheless produces narrow beams.

Another example of intracavity beam shaping involves not only the size of the beam mode entering the amplifier, but the shape of the mode as well.  The ability of a laser resonator to extract energy from its intracavity amplifier is limited by the shape of the mode profile.  In the typical uniformly pumped Gaussian mode resonator, the center of the Gaussian beam saturates the amplifier and the gain at the sides of the beam is wasted. If the beam mode had a circ shape, it would increase the energy extraction efficiency for a short length, but would quickly degenerate into a beam much worse than the Gaussian at extracting energy from the amplifier.  The disadvantage of the Gaussian shape is that the slow intensity drop off at the sides of the beam often does not make it a good approximation to the desired top-hat shape. The laser designer is left with the decision of how rounded to make the intracavity profile, and how to design a resonator to produce the desire beam profile.

One of the approaches to obtaining the desired profile involves the using of variable phase mirrors.  These mirrors can be made using computer generated holograms or engineering the curved mirror shape.  The disadvantage of these passive cavity resonators is their lack of mode stability.  The use of wide amplifiers in these resonators, such as those desired for high power lasers, result in the laser operating in undesirable higher-order transverse modes.  Another method involves the use of variable reflectivity mirrors.  While the resulting mode is very stable, it is difficult to develop design criteria for these resonators.  The approach taken here involves the use of a variable phase/variable reflectivity mirror.  Simple design criteria are developed which allow for the production of lasers with perturbation-stable modes.

A compromise between the circ shape and the Gaussian shape is the multi-Gaussian.  A zero order multi-Gaussian beam has the Gaussian shape, while the infinite order multi-Gaussian beam has the circ shape.  Below is shown several different order multi-Gaussian beams:


It can be seen that higher order multi-Gaussian beams approach a circ (flat-topped).  Since the multi-Gaussian beam is to be used as an intracavity laser beam mode, it is useful to compute the energy extraction efficiency improvement (over a Gaussian beam) for a beam of a given order.  These calculations have been done as part of the research, and the plot is shown below:


It has been shown for the first time that a resonator of the form

will have a multi-Gaussian as its intracavity mode if the reflectivity profile of the output coupler (OC in the figure) has the form

The propagation characteristics of multi-Gaussian beams through optical systems represented by real or complex ABCD systems have been obtained from previous research during a summer stipend.  These results were used to show quantitatively that a laser with such an intracavity mode would have increased energy extraction efficiency.  This efficiency is especially important in high power lasers, as extra energy is converted to heat which destabilizes and under a variety of circumstances destroys the laser.  For the first time, it has been shown how to design a laser that has a multi-Gaussian intracavity mode.