Field solutions for the lateral modes of stripe geometry injection lasers

This paper compares the lateral mode patterns of stripe geometry lasers produced by two theories: 1) an approximate effective dielectric method and 2) an exact method. The exact method for calculating modes uses an expansion of Hermite-Gaussian functions. For small normalized frequencies and a depression of the refractive index under the stripe, the fundamental lateral mode shows structure usually associated with leaky waveguide modes.     

A rigorous boundary value solution for the lateral modes of stripe geometry injection lasers

A new mathematical model useful for analyzing lateral modes of stripe geometry lasers is presented. The oxide stripe laser is modeled as a three-layer waveguide in which the dielectric constant of the active layer varies only along the lateral direction; the dielectric constant of the surrounding passive layers is assumed to be position independent. The solution technique affords a rigorous matching of the fields of the active layer with those of the surrounding passive layers. To illustrate the model, the modes of a waveguide with parabolic dielectric variation along the lateral direction are investigated. The fields are written as a linear combination of Hermite-Gaussian (H-G) functions; heretofore, fields have been described with a single H-G function. Fundamental mode spread (spot size at halfpower) is calculated and related to the gain distribution. (Previous estimates of the lateral field spread of the fundamental mode using a single H-G function not rigorously matched at the boundaries can yield spot sizes as much as 30 percent different from results calculated from linear combinations of H-G functions.) In addition, the peak gain fields are determined at threshold for various waveguide geometries.     

High power single mode operation of AlGaInP visible laser diodewith lateral leaky waveguide structure

AlGaInP visible laser diode with lateral leaky waveguide structure employing 0.025 of negative refractive index step have been fabricated. In comparison to conventional loss guided structure, lateral leaky waveguide structure indicated stable fundamental mode operation. The output power at kink for lateral leaky waveguide laser was around 1.5 times higher than loss guided structure for same stripe widths. The stability was attributed to large mode discrimination against higher order mode. The lateral leaky waveguide laser with 560 μm cavity length employing the antireflection (5%)/high reflection (82%) showed 66 mW of output power with no kinks at 25°C     

Radiation Fields of Optical Stripline Waveguides

Dispersion characteristics and radiation fields of an optical stripline waveguide radiating into free space are calculated. The waveguides are fabricated as multiple layers of differing dielectric materials. A top layer is etched to form a "cap" with an effective waveguide in a layer below the cap. Confinement of the fields to the waveguide is obtained in the vertical direction by dielectric discontinuities, while lateral confinement occurs because of spatial interference of a continuum of plane waves. The radiation field of the fundamental mode in a plane perpendicular to the waveguide layers is characterized by the layer widths and index discontinuities. Beamwidths of the fundamental mode in the plane parallel to the dielectric layers are developed in terms of the waveguide parameters. Values of these parameters which yield the best optical confinement under the stripe can be obtained.     

New stripe-geometry laser with simplified fabrication process

A new type of GaAs-GaAlAs stripe-geometry laser with an appreciably simplified fabrication process is described. Owing to the excellent lateral current confinement of this structure, low threshold current densities are achieved even for very narrow stripe widths. In addition, the built-in passive wave-guiding stabilises the fundamental horizontal transverse mode, thereby avoiding nonlinearities in the light output against current characteristic. For 3?m wide and 175 ?m long lasers, threshold currents of 30?35 mA are achieved and stable transverse and longitudinal monomode emission has been observed up to more than 5 mW light power output.     

High-power operation of highly reliable narrow stripe pseudomorphicsingle quantum well lasers emitting at 980 nm

Ridge waveguide pseudomorphic InGaAs/GaAs/AlGaAs single-quantum-well lasers exhibiting record high quantum efficiencies and high output power densities (105 mW per facet from a 6 μm wide stripe) at a lasing wavelength of 980 nm are discussed that were fabricated from a graded index separate confinement heterostructure grown by molecular beam epitaxy. Life testing at an output power of 30 mW per uncoated facet reveals a slow gradual degradation during the initial 500 h of operation after which the operating characteristics of the lasers become stable. The emission wavelength, the high output power, and the fundamental lateral mode operation render these lasers suitable for pumping Er³⁺-doped fiber amplifiers     

New design rules and experimental study of slightly flared 1480-nm pump lasers

Slightly flared lasers are investigated in order to minimize the longitudinal spatial hole burning impact on the output power saturation of 1480-nm pump lasers. In such a device, the stripe width is narrow at the rear facet for strong single lateral mode operation whereas at the front facet the stripe widens in order to reduce the photon density and as a consequence decrease gain saturation through hole burning effect. We proposed a slightly flared lasers design in order to maintain a uniform photon density along the active stripe. Experimentally, this novel structure exhibits single transverse-mode operation and a 30% output power improvement is obtained compared to the straight active waveguide.     

Semiconductor laser with regrown-lens-train unstable resonator:theory and design

The authors derive the geometrical optical properties of the fundamental mode of the unstable resonator consisting of a train of weak cylindrical lenses and obtain expressions for the effective distributed loss and the increase in threshold current due to the beam expansion. These properties are the same as for the continuous unstable resonator with a quadratic lateral variation of the index of refraction, to a very good approximation. The wave aberration introduced by passage through the lenses and through the output facet is not severe for stripe widths up to 170 μm. The authors discuss the rationale for selecting a specific transverse structure for the regrown-lens-train laser and present the results of calculations of the waveguide modes and values of the effective index of refraction     

High-performance 640-nm-range GaInP-AlGaInP lasers based on the longitudinal photonic bandgap crystal with narrow vertical beam divergence

We address the design and performance issues of 640-nm range GaInP-AlGaInP laser diodes based on a longitudinal photonic bandgap crystal (PBC). The all-epitaxial design is based on selective filtering of high-order modes and allows extending of the fundamental mode over a PBC waveguide achieving very large vertical modal spot size. At the same time the robustness of the narrow far-field vertical beam divergence is remarkably high with respect to layer thickness variations. Optimal design ensures that all high-order optical modes show high absolute values of leakage loss (> 30 cm/sup -1/), which are order (orders) of magnitude higher than the leakage loss for the fundamental mode. This PBC-induced "resonant tunneling effect" for high-order modes leads to preferential excitation of the fundamental mode and the high-order modes are not excited even at the highest injection current densities. Broad-area (100 /spl mu/m) devices show vertical beam divergence of 8' (full-width at half-maximum) and lateral beam divergence of 7'-8'. The far-field pattern is circular shaped and stable upon an increase in injection current. Differential quantum efficiency is as high as 85 %. Maximum pulsed total optical output power is 20 W for 100-tim-wide stripe lasers with uncoated fac.     

The effect of device geometry on lateral mode content of stripe geometry lasers

The dielectric profile of stripe geometry injection lasers is modeled with an objective of structure design requirements for fundamental lateral mode operation. Heterostructure lasers are modeled with a dielectric step profile using an effective dielectric discontinuity based on the gain/loss profile of the active layer as well as the overall geometrical structure. The analysis provides a quantitative comparison of the performance of two important double-heterostructure lasers: 1) the oxide-stripe geometry laser and 2) the channeled-substrate planar (CSP) laser. Modes of oxide-stripe lasers have lateral gain confinement, whereas, modes of CSP devices have strong lateral index confinement. To isolate the influence of geometry on the effective dielectric profile we assume that the real refractive index of the active layer is position independent. Resulting calculations show that a stripe geometry laser inherently has a depressed effective index in the active region below the metallic contact. This phenomenon alone produces index anti-guiding. In actual devices, both geometry and free carrier injection into the active region produce lateral index antiguiding. Lateral mode cut-off conditions are calculated as functions of the effective complex dielectric step and the stripe width. The results show that cutoff is related in a unique fashion to the ratio of the real and imaginary parts of the complex dielectric step; the ratio is positive for index guided modes and negative for gain guided ones.     

新型正方晶格基横模光子晶体面发射激光器

高功率基横模垂直腔面发射激光器（VCSEL）在光通信、传感、原子频标和光电混合集成等领域有着重要的应用,将光子晶体结构引入到VCSEL中,通过设计结构尺寸和分布,可以有效控制VCSEL的横向模式。课题组将正方形排列的光子晶体结构引入到VCSEL中,实现对VCSEL的横向模式和基横模出光功率控制,获得高基横模出光功率器件。通过采用平面波展开法（PWE）和全矢量三维时域有限差分方法（FDTD）对正方晶格结构光子晶体的合理设计,获得正方形排布光子晶体周期、占空比和刻蚀深度等重要参数。成功地制备出基横模出光功率大于3 mW,边模抑制比大于40 dB的正方晶格光子晶体VCSEL。     

Gain suppression in GaAs/AlGaAs TJS lasers

Experimental results on gain suppression in transverse junetion stripe (TJS) lasers with a heavily doped active region is reported for the first time. These lasers oscillate in the fundamental transverse and lateral modes with gain suppression, and reproducibly operate in a single-longitudinal mode up to 1.8 times the threshold current.     

Effects of lateral mode and carrier density profile on dynamic behaviors of semiconductor lasers

Dynamic behaviors of the semiconductor lasers have been investigated both theoretically and experimentally. A single-mode rate equation, which takes account of the lateral mode profile and the carrier density profile, has been solved numerically. Effects of the carrier and lateral mode confinement have been clarified. The lateral mode deformation in lasers without a built-in mode confinement structure greatly enhances the relaxation oscillations. In lasers whose stripe width is narrower thansim10 mum, the carrier diffusion is found to play an important role in suppressing the relaxation oscillations, especially for lasers without a lateral carrier confinement structure. On the other hand, the fraction of the spontaneous emission going into the lasing mode is significant for lasers with a lateral carrier confinement structure. The slow increase of the laser output at the transient is confirmed to be due to the carrier diffusion.     

Optical guiding properties of high-brightness parabolic bow-tie laser arrays

This paper presents the characteristics of parabolic bow-tie laser arrays (PBTLAs) which are a novel category of laser diodes specially designed to achieve high power with high brightness at 980 nm. Output powers in excess of 2.8 W/facet have been measured from five-element PBTLAs with output beam less than twice the diffraction limit, achieving high brightness of 275 MWcm/sup -2/srad/sup -1/ at 3 A (pulsed) injection current (=22 times the threshold). Changes in the achievable brightness due to changes in the optical cavity geometry and in the lateral optical guiding strength are discussed in detail, using the coupled-mode theory to interpret the experimental results. At threshold all devices operate in the highest (double lobed) array mode. At higher currents the arrays of tapered lasers change to quasi-in-phase operation when the modal gain of the fundamental array mode dominates because of the combined effect of carrier hole burning and spatial filtering from the narrow stripe central section of the device. Similar trends have been observed under continuous-wave operation. The reduction of lateral optical guiding strength is deleterious for the operational characteristics of PBTLAs and linear bow-tie arrays, and it leads to filamentation in gain-guided devices even at low currents. Theoretical results presented in this paper show that scalability is in principle possible; however, changes in the lateral gain profile due to hole-burning can significantly increase the modal gain of higher order modes and, therefore, strongly influence the optical output profile.     

Planar stripe with waist and/or notch (SWAN) injection laser

This paper describes a novel planar stripe-geometry injection laser (referred as SWAN laser) showing a single transverse and longitudinal mode operation made by a simple fabrication method. This stripe-geometry is composed of a main stripe section with the width of around 10 μm and mode control section with the nominal width near to carrier diffusion length, less than 5 μm, a shape of which looks like waist(s) and/or notch(es) along the stripe. A "kink", which often appears in the relation between a light output and a current in conventional planar injection lasers, is not observed at the power level of more than 20 mw/ facet. The laser has advantage of controlling modulation dynamics by the shape of waist(s) and/or notch(es) along the stripe that enables control of the lateral carrier diffusion profile in the vicinity of an active layer and the amount of spontaneous emission into laser mode.     

Far field asymmetry in narrow stripe gain-guided lasers

A number of 5 μm stripe width shallow proton-bombarded double heterostructure (DH) AlGaAs LPE grown lasers show asymmetric light versus current characteristics and far fields. The optical power output above threshold is not the same for both faces at a given current. The far field patterns in the junction plane from the two mirrors are also different: the angular distribution of the optical power emitted in the junction plane is not the same for both mirrors. The asymmetry in the far fields is the subject of this paper. It is suggested that a large optical loss near the face with lower optical power output may explain the different far fields observed from the two mirrors. Possible explanations for the origin of this optical loss are discussed.     

Stress-induced effects by the anodic oxide in ridge waveguide laserdiodes

This paper studies, both theoretically and experimentally, stress-induced effects on the lateral far-field behavior for ridge-type semiconductor laser diodes where anodic oxide is used for the definition of the stripe width. These effects consist of antiguiding under the stripe region, and of two positive waveguiding features near the stripe edges. For low-threshold devices, these effects may be more important than thermal effects, depending on the stress in the oxide. They put a lower limit on the built-in index guiding to be introduced by lateral etch outside the ridge region in order to maintain fundamental mode operation for wider stripes. The magnitude of these effects may be as large as Δn_ef=1×10^-3. An analytical mathematical model is deduced for computing stresses and strains for a certain ridge-shaped interface which bounds the elastic medium     

InGaAsP/InP separated multiclad layer stripe geometry laser emitting at 1.5 µm wavelength

We have developed an InGaAsP/InP separated multiclad layer (SML) stripe geometry laser emitting at 1.5 μm wavelength. In this laser, the optical confinement is done by the effective refractive index step owing to the formation of the coupled waveguide outside the stripe region. The current confinement is done by the p-n-p-n structure outside the stripe region. The CW threshold current at 25 °C is only 82 mA for the stripe width and the cavity length of 6 μm and 250 μm, respectively. The maximum temperature where the CW lasing is obtained is 65°C. The characteristic temperature of the threshold current is 60 K. The transverse mode is fundamental up to 1.8 times the threshold. Ten samples are operated at 50°C with constant optical output of 5 mW/facet. These samples are still operating at over 10 000 h with a slight increase in the driving current. The appreciable change in the characteristics due to aging is not observed.     

Lateral transverse mode instability and its stabilization in stripe geometry injection lasers

A numerical analysis has been carried out on the behavior of semiconductor injection lasers with a stripe geometry double-heterostructure, taking into account spatial hole-burning and its effect on the waveguiding. It is shown that spatial hole-burning, the negative dependence of refractive indexetaon the excited carrier densityn (d_{eta}/ dn < 0), and the lack of complete symmetry in any real laser structure are the three critical factors responsible for the lateral mode instability leading to such anomalous behaviors these lasers exhibit as a "kink" in the light output versus current relation and the lateral shift in the emission spot. Effects of rigid refractive index and gain-loss profiles built into the laser crystal on the mode stability have been examined, and conditions for kink-free, single lateral mode oscillations have been investigated.     

Optimum design conditions for AlGaAs window stripe lasers

The maximum available CW optical power from the AlGaAs window stripe laser was investigated both theoretically and experimentally. It is found that a thin third AlGaAs layer thickness and high-quality pulsed lasing characteristics, such as low threshold current density and high external differential quantum efficiency, which are obtained from refractive index guiding and short window-region length, are necessary to increase CW optical power. Stable fundamental lateral transverse mode CW operation was achieved at 55 mW (∼4.7 MW/cm²) in a window stripe (WS) laser with 3 μm stripewidth, which is about five times higher than the typical catastrophic optical damage (COD) threshold in conventional structure lasers. It was also found that a high-quality window stripe laser with 3 μm stripewidth operated at 30 mW (∼2.6 MW/cm²) for more than 3500 h.