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Optical resonators using graded-phase mirrors

Optical resonators using graded-phase mirrors are analyzed with the help of the generalized ABCD propagation law for a real optical beam. This analysis gives the second-order moment gross characteristics of the eigenmode and indicates a design procedure. An example of a super-Gaussian output beam shows that this type of optical resonator might have large transverse-mode discrimination that could provide operation in a large fundamental-mode beamwidth.

Solitary pulses in an amplified nonlinear dispersive medium

An analytical solution is obtained for solitary pulse propagation in an amplified nonlinear dispersive system. For a homogeneously broadened gain medium, this solitary pulse has a hyperbolic secant amplitude and a hyperbolic tangent instantaneous frequency variation. The pulse is a gain-guided pulse in either the positive or the negative dispersion regime as well as in the self-focusing or self-defocusing regime. A dark solitary pulse that has a hyperbolic tangent amplitude and a similar instantaneous frequency variation is also obtained.

Compensating for dispersion and the nonlinear Kerr effect without phase conjugation.

We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates.

Super-Gaussian output from a CO(2) laser by using a graded-phase mirror resonator.

Two super-Gaussian output resonators of orders 4 and 6 have been designed by using the inverse-propagation method for the calculation of the graded-phase feedback mirrors. The graded-phase mirrors were made by using the diamond cutting technique on a copper substrate. An increase of 40% and 50% of monomode energy extraction has been measured compared with that of a semiconfocal resonator of the same dimension in a TEA CO(2) laser.

Custom laser resonators using graded-phase mirrors

The authors derive a simple algorithm for designing a stable graded-phase-mirror resonator. First, the desired output beam profile of the fundamental mode is propagated into the laser medium. The wavefront is then extracted and serves to determine the appropriate phase profile of the mirror. The diffractional analysis of the resonator using this graded-phase mirror indicates a very low loss for the fundamental mode with a very large discrimination of higher modes. Practical design parameters such as the geometric factor, the Fresnel numbers, and phase profile perturbations are discussed. The authors conclude that this type of resonator can increase significantly the mode volume and favor the single-mode operation of laser systems relying on a stable resonator geometry. >

Beam propagation factor of diffracted laser beams

Abstract The recent emergence of the characterization of general optical beams by means of the variance of their transverse intensity distribution has given rise to the concept of the beam propagation factor (usually referred to as the beam quality factor), which appears as a meaningful way for comparing the divergences of optical beams having the same minimum spot size. Unfortunately, a direct calculation of this factor for a beam having sharp discontinuities in its transverse intensity profile leads to an infinite result. This difficulty is addressed by deriving a general expression for the axial dependence of the variance of the beams transverse intensity profile in free space. A new definition for the beam propagation factor can be introduced, provided that the evanescent waves of the plane-wave spectrum of the beam are ignored. This modified beam propagation factor is then calculated for some specific diffracted intensity profiles. Finally, it is shown how the proposed definition for the variance of the plane-wave spectrum of an optical beam is connected to its far-field angular spread.

Propagation law and quasi-invariance properties of the truncated second-order moment of a diffracted laser beam

The propagation of the truncated second-order moment (i.e. integrated over a finite interval enclosing a constant fraction of the total power) of a diffracted beam is analyzed. An asymptotic analysis, supported by numerical simulations, shows that the propagation law becomes nearly perfectly parabolic as the power fraction increases. It is also demonstrated, on a general basis, that a parabolic propagation law implies the invariance of the infered beam-propagation factor.

Antisymmetric soliton in a dispersion-managed system

We show that, in addition to the soliton of even parity, a dispersion-managed system can also support an antisymmetric stationary pulse. Its existence is predicted on the basis of an approximate differential equation that describes the temporal profile of dispersion-managed solitons. Numerical simulations are used to confirm this prediction and check the robustness of this pulse.

Graded-phase mirror resonator with a super-Gaussian output in a CW-CO/sub 2/ laser

Two graded-phase mirror (GPM) resonators have been designed to produce super-Gaussian output beam profiles of order 4 and 6. An inverse propagation method was used to calculate the appropriate shape of the GPMs. Previous experimental work with a pulsed TEA-CO/sub 2/ laser has already confirmed the high transverse mode discrimination offered by such custom resonators, as anticipated by a theoretical analysis of their diffractional properties. Here, we extend these results by presenting new experimental measurements with a CW-CO/sub 2/ laser. The main objective of this paper is to demonstrate the super-Gaussian beam shape produced by these custom resonators. This is assessed with numerical simulations involving the incoherent superposition of transverses modes. The experimental results obtained with the GPM resonators, including measurements of the propagation of the output beam profile, are compared to those of a conventional semiconfocal cavity, and show higher monomode power extraction. >

Custom laser resonators using graded-phase mirrors: circular geometry

The properties of a new class of resonators using graded-phase mirrors designed for delivering a prescribed intensity output profile are analyzed in the circular geometry. It is shown that the diffraction losses of super-Gaussian custom resonators strongly favor the single-transverse-mode operation, and optimum design parameters are suggested. Simulations indicate that these resonators behave reasonably well in the presence of perturbations such as thermal lensing fluctuations or gain saturation. >