We discuss the use of photorefractive four-wave mixing for coupling and locking of lasers. A demonstration of the double phase-conjugate mirror and the semilinear passive phase-conjugate mirror, pumped simultaneously by different lasers, is described. Cleanup of a distorted laser beam using another local laser and configurations for the phase locking of lasers are discussed.

http://webee.technion.ac.il/people/fischer/Papers/1986%20OL%2011,%20528%20Beam%20Coupling%20and%20Locking%20of%20Lasers%20using%20PR%204WM.pdf

Beam coupling and locking of lasers using photorefractive four-wave mixing

The rate equations used to find carrier and photon densities in semiconductor lasers are extended to include a spatial variation of the carrier density in the junction plane and combined with a field equation for calculation of the intensity distribution. The equations are solved for both static and dynamic cases, and the model is able to account for nonlinear light current characteristics, near field displacements, and self-sustained pulsations in lasers without a built-in guiding mechanism. The results are compared to both experimental results and predictions from other models.

Models of the static and dynamic behavior of stripe geometry lasers

A multi-mode diode laser with an external cavity is studied experimentally and theoretically for its application to intra-cavity spectroscopy. One facet of a typical Ga0.89Al0.11As laser diode was antireflection-coated by deposition of HfO2 such that 10−3 residual reflectivity was left over. This diode was placed in an external optical cavity. The emission spectrum of this diode laser is highly sensitive to any frequency-dependent loss in the cavity, and the detectivity of such a loss grows with the pump rate. Even close to threshold, the absorption at 780 nm of Rb atoms with a density of 5×1010 cm−3 has been detected. An adequate model for diode lasers based on rate equations and including frequency-dependent gain saturation is developed and applied to the calculations of output spectra. The sensitivity of these spectra to intra-cavity absorption is determined by the overall cavity loss — which is rather high — and the fraction of spontaneous emission in the total emission, in contrast with dye lasers where it is limited by nonlinear mode coupling. Various criteria for the sensitivity are suggested. The smallest detectable absorption with a perfectly antireflection-coated laser is 10−6 cm−1. Improvement of the characteristics of the laser diode would increase the sensitivity.

Intra-cavity spectroscopy with diode lasers

For InGaAsP/InP devices emitting in the wavelength range of 1.1-1.65 \mu m, we present novel and accurate analytical approximations of the crucial parameters in laser design: the radiation confinement factor \Gamma ; the effective refractive index N eff ; and the transverse beamwidth \theta_{\perp} . It is found that \Gamma is independent of wavelength or step-index difference and \theta_{\perp} becomes independent of wavelength as the active layer thicknesses d decreases below 0.15 μm. An explicit analytical expression is derived for the threshold current density J th . The new linear gain-current relationship g (cm-1) = 28.5 (J/d) - 50 is deduced from a critical assessment of recent experimental data. A theoretical framework is provided to explain experimental observations such as: the J th versus d curve is independent of wavelength, the threshold has a negligible variation over the 0.1-0.3 \mu m active-layer thickness range, and the normalized threshold current density ( J_{th}/d , for d \geq 0.5 \mu m) varies strongly (3-5 kA/cm2/μm) with cavity length.

InGaAsP/InP double-heterostructure lasers: Simple expressions for wave confinement, beamwidth, and threshold current over wide ranges in wavelength (1.1-1.65 &#181;m)

The mechanism of current leakage at high temperatures in InGaAsP/InP buried heterostructure (BH) lasers with p-n-p-n current-blocking structures is analyzed using two-dimensional computer simulation. It is found that no junction in the blocking layers is reverse-biased and that current confinement is due to electrically floating regions in the blocking structures. To minimize the leakage current in these BH lasers, it is necessary to decrease the device width and the connection length between the blocking and cladding layers and to increase the doping level and thickness of the blocking layers. >

Analysis of current leakage in InGaAsP/InP buried heterostructure lasers

Various models for calculation of refractive indices in semiconductor laser materials are discussed and the results for GalnAsP compounds are compared. It is shown that the modified single-oscillator model appears to be the most reliable. The group index is also considered since it can be found easily from measurements of laser spectra. The value of the group index is more model sensitive than the refractive index, but it is also a function of the active-layer thickness in double heterostructures as a consequence of waveguide dispersion. A simple formula connecting group and phase indices for a symmetrical dielectric slab waveguide is derived and used to calculate the effective group index for double-heterostructure lasers

Phase and group indices for double heterostructure lasers

A simple three-mirror composite laser cavity is analyzed and optimum structures proposed in terms of the position of the central reflector and the value of its reflectivity in order to give single longitudinal mode operation. Two optimum structures are discussed, the first corresponding to relatively long cavities where a large period in the gain modulation is required in order to avoid a jump to the next mode with a high effective reflectivity, usually in a second mode group (as defined by a neighboring period of the gain modulation). The second corresponds to shorter lasers where jumps to neighboring modes should be avoided, since the spectral gain variation prevents jumps to other mode groups. The effects of mode discrimination due to external feedback have been analyzed and minimum values of reflectivity for the third mirror derived in order to preserve the internal mode selectivity.

Two-segment cavity theory for mode selection in semiconductor lasers

Recent publications on the C3 laser appear to have presented contradictory results for the optimum gap width to give maximum mode discrimination and thus enhance single-mode behaviour. We give here a simple analysis which shows that the optimum width is equal to an odd multiple of a quarter wavelength in cases where loss in the gap can be neglected, but to an even multiple for cases with significant gap loss.

Influence of gap width on mode discrimination in cleaved coupled cavity lasers

A detailed experimental investigation of a SiO2insulated GaAlAs laser is performed. The results are compared with theoretical calculations, including strain from the SiO2layer, and good agreement is found. The theory can account for a kink seen in the light/cunent characteristic.

J. Buus

Papers

Phase and group indices for double heterostructure lasers

Two-segment cavity theory for mode selection in semiconductor lasers

Influence of gap width on mode discrimination in cleaved coupled cavity lasers

Characteristic and near field for a broad SiO2insulated d.h. laser: experiment and theory