Yves Champagne

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.

Numerical procedure for the lateral-mode analysis of broad-area semiconductor lasers with an external cavity

A numerical procedure for the investigation of the lateral modes of semiconductor lasers with an external cavity is described. The propagation of the optical field inside the semiconductor laser is carried out via a standard beam-propagation scheme, while the method of coordinate scaling with the generalized Huygens-Fresnel integral allows for a computationally efficient propagation of the field in the external cavity. Using an eigenfunction solver based on the Prony method, it is shown that a simple external-cavity configuration comprising a broad area laser, a collimation lens, and a uniform end reflector can exhibit a complex modal behavior. Compared to a solitary broad area laser, optimized external cavities can yield enhanced modal discriminations, resulting in a single-lateral-mode operation with output power in excess of 100 mW along with a clean, single-lobed far-field pattern. The spatial-filtering action of the broad-area laser is highlighted, and we also discuss of the role played by the wavefront curvature of the beam incident upon the broad-area laser for achieving an efficient suppression of the higher order modes along with minimum increase of the threshold current. >

Influence of the axially varying quasi‐Fermi‐level separation of the active region on spatial hole burning in distributed‐feedback semiconductor lasers

The longitudinal‐mode characteristics of distributed‐feedback semiconductor lasers subjected to longitudinal spatial hole burning have been investigated using an improved numerical modeling scheme. The main new feature of the model is that it allows for the natural axial variations of the separation between the quasi‐Fermi levels (Fermi voltage) in the laser’s active region. This gives rise to a current density injected into the active region that varies along the laser axis, even for uniformly biased lasers. It is found that compared to the results obtained by assuming an uniform current density, the detrimental influence of the longitudinal spatial hole burning on important static characteristics of quarter‐wave‐shifted distributed‐feedback lasers, such as the gain margin and the lasing wavelength stability, is weakened. Therefore, the usual assumption of an uniform injected current density gives rise to an overestimated influence of the spatial hole burning, this overestimation being more important for...

Global excess spontaneous emission factor of semiconductor lasers with axially varying characteristics

An expression of the excess spontaneous emission factor of semiconductor lasers having axially varying characteristics has been derived, using a classical treatment for the contribution of spontaneous emission to the lasers noise figure. Although the analysis is focused on semiconductor laser structures, including DFB lasers, the expression obtained can be applied with minor changes to other standing-wave laser geometries. This global excess spontaneous emission factor, accounting for transverse as well as longitudinal effects, is relevant even for laser structures wherein the longitudinal and lateral field distributions are mutually coupled. In this situation, this factor is not equivalent to the product of Petermanns excess noise factor and a longitudinal correction factor accounting for outcoupling losses. >

Laser pointing stability measurements

Experiments have been conducted to evaluate the feasibility of conducting pointing stability measurements with a relatively low cost stand alone apparatus. These experiments also aimed at collecting beam wandering data for pointing stability measurement system engineering purposes. The system consists of two dual-axes position sensing detectors (PSDs) that simultaneously measure variations of the beam position in two different planes. Sample-and-hold circuits are used to synchronize measurements taken by both PSDs. Detector signals are amplified and processed analogically in order to obtain voltage outputs directly related to beam position. The output signals are then A/D converted for computations. Software allows pointing stability calculations as well as frequency spectrum analysis of position fluctuations.

Second-moment approach to the time-averaged spatial characterization of multiple-transverse-mode laser beams

Analytical expressions are derived for the time-averaged propagation characteristics of multimode light beams made up of a superposition of paraxial transverse modes. The transverse-mode distributions are not restricted to the usual Hermite–Gaussian or Laguerre–Gaussian functions and may thus have arbitrary characteristics. It is shown that the propagation characteristics of multimode beams can be expressed in simple form in terms of those of the constituent transverse modes, which can be obtained directly from the modal complex-amplitude profiles in any given transverse plane. These expressions may simplify considerably the calculation of the second-moment characteristics of multimode beams because the numerical propagation of each modal field in free space is no longer required. The expressions are used to investigate numerically the degradation of the spatial quality of the output beam radiated by a broad-area semiconductor laser as its fundamental-lateral-mode operation ceases.

Optical phase-conjugate feedback effects on gain-guided diode laser characteristics

The effects of optical phase-conjugate feedback on the characteristics of stripe-geometry gain-guided GaAlAs lasers are theoretically investigated using a model based on the beam-propagation method. Compared to standard diode lasers, the use of a phase-conjugate mirror yields lower threshold currents and improves the optical quality of the output beam over a wide range of stripe widths and cavity lengths. The results obtained for 3 mu m stripe lasers are particularly noteworthy since the twin-peaked far field of standard lasers can become single lobed. Moreover, when one cleaved facet is replaced by a phase-conjugate mirror having the same overall reflectivity, the threshold current can be reduced by more than 50% for short cavity lengths. >

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 beams section.

Lateral‐mode discrimination in broad‐area semiconductor lasers with a smooth spatially filtering output facet

We present numerical simulations of broad‐area semiconductor lasers with smooth spatial filtering at the output facet. The beam‐propagation and Prony methods are used to calculate the beam characteristics and discrimination against higher‐order lateral modes of the laser devices. With an output facet having a Gaussian reflectivity profile, the fundamental lateral mode is favored. Discrimination between the two lowest‐order modes increases significantly with narrow reflectivity profiles.

Laser beam variance measurements using a parabolic transmission filter

We report preliminary experimental results on the use of a filter with a parabolic transmission profile for a direct measurement of the spatial variance of the intensity distribution of a laser beam. It is shown that by recording, at various planes, the maximum transmitted power through such a filter, one can characterize the beam without having to determine the corresponding intensity profiles. A simple parabolic fit of the data allows the determination of the required parameters for a second-moment-based beam characterization.