Pierre-André Bélanger

Beam propagation and the ABCD ray matrices

We have generalized the ABCD propagation law, Q(2) = (AQ(1) + B)/(CQ(1) + D), for an optical system by introducing a generalized complex radius of curvature Q for a general optical beam. The real part of 1/Q is related to the mean radius of curvature of the wave front, while the imaginary part is related to the second moment of the amplitude of the beam.

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.

Linear, annular, and radial focusing with axicons and applications to laser machining

New optical combinations of axicons and axicons with spherical mirrors and lenses suitable for laser machining are presented. Linear and annular focusing, coaxially and radially to the laser beam, are possible. Most combinations allow continuous adjustment of exit beam parameters, focal line length, focal ring diameter, and magnification, by varying the relative position of one of the axicons. Potential new laser applications are also discussed in relation to these optical devices.

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.

Ring pattern of a lens-axicon doublet illuminated by a Gaussian beam.

An axicon and a lens are combined to form an optical system producing a ring-shaped pattern. The purpose of this paper is to show that when a lens-axicon combination is illuminated by a Gaussian beam, the transverse distribution of the focal ring is also a Gaussian distribution. The typical width of this distribution was found to be, in the case of the lens-axicon combination, 1.65 times greater than the typical width of the Gaussian beam obtained by focusing the same beam using the lens alone. This focusing system is well suited for the drilling of good quality large diameter holes using a high power laser beam.

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.