Modal reflection of quarter-wave mirrors in vertical-cavity lasers

Very high plane-wave reflection coefficients can be obtained with practical semiconductor quarter-wave mirrors, but for beams of finite width, the reflection coefficient of a mirror with no lateral guiding and hence the finesse of cavities that use such structures will be limited by diffraction loss. The authors analytically and numerically study the modal reflection of practical semiconductor quarter-wave mirrors. They introduce a quantity called the diffraction range of a quarter-wave mirror as a means of exact analytical comparison between infinite lossless mirrors (and approximate comparison for finite mirrors) in the Fresnel diffraction limit. The exact modal reflection coefficient for an arbitrary incident mode pattern is determined by vector plane-wave decomposition. The modal reflection coefficients of two representative semiconductor quarter-wave mirrors used in vertical cavity laser technology, AlAs/GaAs and InGaAsP/InP, are studied. >

[1]  A. Schawlow,et al.  Infrared and optical masers , 1958 .

[2]  K. Kojima,et al.  Functional Analysis of Diffraction Integral Transform. II. , 1975 .

[3]  C.L. Xu,et al.  A finite-difference vector beam propagation method for three-dimensional waveguide structures , 1992, IEEE Photonics Technology Letters.

[4]  Martin A. Afromowitz,et al.  Refractive index of Ga1−xAlxAs , 1974 .

[5]  Hemispherical resonator study for surface‐emitting InGaAsP/InP lasers , 1990 .

[6]  L. Coldren,et al.  Refractive indexes of (Al,Ga,In)As epilayers on InP for optoelectronic applications , 1992, IEEE Photonics Technology Letters.

[7]  Y. Yamasaki,et al.  Low-threshold surface-emitting laser diodes with distributed Bragg reflectors and current blocking layers , 1990 .

[8]  U. Koren,et al.  Low-threshold, high-temperature pulsed operation of InGaAsP/InP vertical cavity surface emitting lasers , 1991, IEEE Photonics Technology Letters.

[9]  H. Kogelnik,et al.  Laser beams and resonators. , 1966, Applied optics.

[10]  Masao Nakagawa,et al.  A simple multiplexing method for pulsed analog signal and digital signal in optical communications , 1988 .

[11]  Continuous wave single transverse mode vertical-cavity surface-emitting lasers fabricated by helium implantation and zinc diffusion , 1992, QELS 1992.

[12]  A. Scherer,et al.  Low-vollage-threshold Microlasers , 1992, LEOS '92 Conference Proceedings.

[13]  K. Iga,et al.  GaInAsP/InP Surface Emitting Injection Lasers , 1979 .

[14]  Masayuki Ishikawa,et al.  144 °C operation of 1.3 μm InGaAsP vertical cavity lasers on GaAs substrates , 1992 .

[15]  S. Wang,et al.  Submilliampere continuous‐wave room‐temperature lasing operation of a GaAs mushroom structure surface‐emitting laser , 1990 .

[16]  Kenichi Iga,et al.  Surface emitting semiconductor lasers , 1988 .

[17]  Kenichi Iga,et al.  Single transverse mode condition of surface‐emitting injection lasers , 1988 .

[18]  S. Mccall,et al.  Chemical beam epitaxially grown InP/InGaAsP interference mirror for use near 1.55 μm wavelength , 1987 .

[19]  N. Dagli,et al.  Explicit finite difference vectorial beam propagation method , 1991 .

[20]  W. Kowalsky,et al.  Monolithically integrated InGaAlAs dielectric reflectors for vertical cavity optoelectronic devices , 1991 .

[21]  L. Coldren,et al.  InGaAs vertical-cavity surface-emitting lasers , 1991 .

[22]  T. Ikegami,et al.  Reflectivity of mode at facet and oscillation mode in double-heterostructure injection lasers , 1972 .

[23]  Leo J. Missaggia,et al.  GaInAsP/InP buried‐heterostructure surface‐emitting diode laser with monolithic integrated bifocal microlens , 1990 .

[24]  Scott W. Corzine,et al.  Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors , 1992 .

[25]  A. Scherer,et al.  Low-Voltage-Threshold Microlasers , 1992 .

[26]  A. G. Fox,et al.  Resonant modes in a maser interferometer , 1961 .

[27]  N. Dutta,et al.  Performance of gain-guided surface emitting lasers with semiconductor distributed Bragg reflectors , 1991 .

[28]  J. Bowers,et al.  Effects of nonuniform current injection in GaInAsP/InP vertical‐ cavity lasers , 1992 .

[29]  M. Feit,et al.  Light propagation in graded-index optical fibers. , 1978, Applied optics.

[30]  G. Stewart.  Optical Waveguide Theory , 1983, Handbook of Laser Technology and Applications.

[31]  Gunnar Björk,et al.  Micro-cavity semiconductor lasers with controlled spontaneous emission , 1992 .

[32]  H. Haus.  Waves and fields in optoelectronics , 1983 .

[33]  G. Hasnain,et al.  GaAs vertical-cavity surface emitting lasers fabricated by reactive ion etching , 1991, IEEE Photonics Technology Letters.

[34]  Axel Scherer,et al.  Fabrication of low threshold voltage microlasers , 1992 .

[35]  P. Yeh,et al.  Optical Waves in Layered Media , 1988 .

[36]  Larry A. Coldren,et al.  Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance , 1993 .

[37]  Sadao Adachi,et al.  Refractive indices of III–V compounds: Key properties of InGaAsP relevant to device design , 1982 .

[38]  Youngchul Chung,et al.  Analysis of Z-invariant and Z-variant semiconductor rib waveguides by explicit finite difference beam propagation method with nonuniform mesh configuration , 1991 .

[39]  A. Scherer,et al.  Vertical-cavity surface-emitting lasers: Design, growth, fabrication, characterization , 1991 .

[40]  H. Kogelnik,et al.  Equivalence relations among spherical mirror optical resonators , 1964 .

[41]  H. Okamoto,et al.  Room temperature pulsed operation of 1.5 mu m GaInAsP/InP vertical-cavity surface-emitting laser , 1992, IEEE Photonics Technology Letters.

[42]  R. Harrington.  Time-Harmonic Electromagnetic Fields , 1961 .

[43]  B. Hermansson,et al.  Efficient beam propagation techniques , 1990 .

[44]  J. P. Harbison,et al.  Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers , 1991 .