Spectral domain analysis of dispersion management without averaging.

It is shown how a straightforward regular perturbative analysis can be used to derive an integral equation for the spectral shape of a dispersion-managed soliton that takes fiber loss and amplification into account without resorting to averaging. Using functional analysis, one can then find an accurate approximate Gaussian solution that should prove useful for the design of a dispersion-managed transmission link.

Coupled-field description of zero-average dispersion management.

Using a coupled-field formalism and a standard perturbation analysis, we analyze a dispersion-managed system under zero-average dispersion conditions. A nonlinear integral equation in the spectral domain allows the determination of the critical strength parameter of a two-step dispersion map. Higher-order correction terms confirm the difference observed in the pulse shapes in each fiber and comparisons with fully numerical results reveal a good agreement. The existence of an antisymmetric dispersion-managed soliton is also confirmed.

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.

Method for direct measurement of the variance of laser beams.

A method permitting direct measurement of the spatial variance along a given transverse direction of any laser beam is described. The procedure relies on the use of a transmission filter whose local transmissivity varies spatially as an inverted parabola. The variance and the first moment of a transverse beam intensity distribution are readily obtained simply by measurement of the maximum power transmitted through the filter as this filter is moved across the beam's section.

CO2 laser annular thermokeratoplasty: a preliminary study.

Since most techniques of refractive surgery currently in use or being developed have the potential for significant side effects, there is a need for investigating alternative procedures. We herein report on the use of a pulsed CO2 laser beam delivered through a pair of complementary axicons to produce a ring of stromal collagen contraction resulting in the flattening of the corneal apex of cadaver eyes. Irradiances of 29 W/cm2 and 23 W/cm2 were used for rings of 5.5 mm and 7.0 mm, respectively. The creation of a ring of 7.0 mm in diameter did not affect the corneal curvature significantly but when the diameter was reduced to 5.5 mm, substantial flattening proportional to the dose of radiation took place. In our system, it was possible to achieve up to 11.3 diopters of mean keratometry flattening (90 joules, 5.5 mm of diameter). In addition, a 1 mm posterior displacement of the corneal dome without histological evidence of closure of the iridocorneal angle was observed. Annular thermokeratoplasty (ATK) may minimize side effects encountered with other refractive procedures since it does not require ablation, incisions, or interaction with the central optical zone.

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.

Diffractive analysis of annular resonators.

The modal properties of annular resonators are investigated by using an approximate version of the Kirchhoff-Fresnel integral. It is shown that the radial diffraction of a thin annular beam with a large inside radius is similar to that of a cylindrical field distribution. This permits the formal demonstration of the equivalence that exists between large Fresnel number annular resonators and infinite strip resonators. The model explains the properties of annular resonators that have been observed either experimentally or numerically by others, such as the lack of azimuthal discrimination.

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.

Soliton self-frequency shift versus Galilean-like symmetry.

We show that the soliton self-frequency shift (SSFS) law as well as an approximate analytical description of the pulse deformation can be obtained on the basis of a Galilean-like symmetry of the simplest SSFS model.

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.

Dark soliton in a Kerr defocusing medium.

The soliton solution in a Kerr defocusing medium is obtained. This solution is essentially a dip in a uniform plane wave and is thus called a dark soliton. This solution is then used to supply a qualitative explanation of the optical branching effect, which has been observed recently in a photorefractive slab waveguide.

Complex index of refraction of dental enamel at CO(2) laser wavelengths.

The reflectance vs angle of incidence method was used to determine the refractive index and absorption coefficient of dental enamel at CO(2) laser wavelengths. A strong wavelength dependence of the optical constants was observed in this spectral region which corresponds to a well-known absorption band of hydroxyapatite, the main constitutent of dental enamel. A directional dependence of the optical constants of dental enamel was also observed. The absorption coefficient reaches a maximum between 9.75 and 10 microm. This particularity may be important for the main CO(2) laser treatments proposed in dentistry up to now: surface treatment of teeth and fusion of dental materials.

Mode locking of a homogeneous gain laser through temporally modulated phase-conjugate reflectivity.

Mode locking of a homogeneous gain laser by a temporally modulated phase-conjugate mirror is investigated through a dispersive model. Phase conjugation is assumed to be due to degenerate four-wave mixing with external pumps consisting of two trains of temporally Gaussian pulses. Approximate solutions are found in terms of Gaussian pulses whose width depends on the duration of the pump pulses, the coherence time of the homogeneous gain medium, and the relaxation time of the nonlinear medium. Numerical solutions are in excellent agreement with the Gaussian-pulse solutions.

Orthogonality properties of phase conjugate optical resonators.

The orthogonality properties of the eigenmodes of general optical resonators which have a phase conjugate mirror at one end are derived. It is shown that essentially these are biorthogonal relations as in conventional resonators, which are satisfied between the set of modes propagating in one direction around the resonator and the adjoint set of modes propagating in the reversed direction.

Transverse modes of a stimulated scattering phase-conjugate resonator.

Gaussian transverse eigenmodes of a stimulated scattering phase-conjugate resonator are calculated. The experimental setup which provides the stimulated scattering phase-conjugate resonator is described.

Transverse mode-locking by short pulse injection in large aperture TEA CO(2) oscillators.

Single short pulses were injected in TEA-CO(2) laser cavities made of two copper mirrors. Simultaneous longitudinal and transverse mode-locking was evidenced by periodic focusing of the internal short pulse. The focusing action could be eliminated by short train injection.