## Abstract

Recently, a new class of laser resonators was introduced that
utilizes diffractive mirrors and an additional intracavity diffractive
phase element. High modal discrimination and low fundamental-mode
loss were achieved simultaneously by use of sinusoidal and pseudorandom
diffractive phase elements. An intracavity phase element consisting
of a simple single-step phase modulation is approximated by a Gaussian
with a small radius. Explicit expressions are obtained for the
modal-discrimination factor as a function of resonator parameters with
a Gaussian output mirror. Numerical simulations are performed for a
phase element with a step singularity in the phase function, the
fundamental mode of this cavity being super-Gaussian. The modal
discrimination of the cavity is studied for different radii of the
single-step phase modulation, the position of the phase plate, and the
cavity Fresnel number. Optimum solutions are found for a plane
output mirror with either a striped or a circular shape.

© 1999 Optical Society of America

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### Equations (10)

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(1)
$$v\left(z,x\right)={v}_{+}\left(z,x\right)exp\left(\mathit{ikz}\right)+{v}_{-}\left(z,x\right)exp\left(-\mathit{ikz}\right),$$
(2)
$${v}_{+}\left(0,x\right)={v}_{0}\left(0,x\right).$$
(3)
$${R}_{\mathrm{DMSM}}\left(x\right)=\overline{{v}_{0}\left(L,x\right)}/{v}_{0}\left(L,x\right),$$
(4)
$$T\left(x\right)=\left\{\begin{array}{ll}exp\left(i\mathrm{\varphi}\right)& |x|<a\\ 1& |x|>a\end{array}\right..$$
(5)
$${v}_{0}\left(x\right)=exp\left(-{x}^{2}/\mathrm{\omega}_{0}{}^{2}\right),$$
(6)
$$T\left(x\right)=\sqrt{2}\left[exp\left(i\mathrm{\varphi}\right)-1\right]exp\left(-{x}^{2}/{a}^{2}\right)+1,$$
(7)
$${\mathrm{\gamma}}_{2}={b}^{3/2}+\overline{\mathrm{\Gamma}}{\left[\frac{2}{\frac{2+g}{g-\mathrm{\alpha}}+2+\left(2-M\right)\left(\frac{1+g}{g-\mathrm{\alpha}}+2+2g-\mathrm{\alpha}\right)}\right]}^{3/2}$$
(8)
$$-\mathrm{\Gamma}{\left[\frac{2}{\frac{2+g}{g-\mathrm{\alpha}}+2+\left(2+M\right)\left(\frac{1+g}{g-\mathrm{\alpha}}+2+2g-\mathrm{\alpha}\right)}\right]}^{3/2},$$
(9)
$$b=\frac{g+2-X\pm {\left[{\left(g+2-X\right)}^{2}-{X}^{2}\right]}^{1/2}}{X},$$
(10)
$${v}_{0}\left(x\right)=exp\left(-{x}^{20}/\mathrm{\omega}_{0}{}^{20}\right),$$