Analysis of TM-polarized DFB laser structures with metal surface gratings

Grating-coupler assisted infrared spectroscopy on anisotropic multilayer systems: A comparative study

“…Generally, DFB-laser structures are optimized with regard to the guided-guided wave interaction to improve the optical feedback and thus, the single-mode emission characteristics. However, also efficient coupling of the guided modes and radiating modes is desired for secondorder surface-emitting DFB-lasers [11,24,26].…”

“…Recently, we have independently developed and successfully applied: (i) the MEM combined with a transfer-matrix formalism using transfer-or scattering matrices in the calculation of gratingcoupler assisted infrared spectroscopy of lowdimensional electron systems [8,34,40,56], and (ii) a CWM utilizing a direct solution for the fields in the multilayer structure in the rigorous description of metallized-grating coupled semiconductor laser structures [25,26]. Method (i) has been implemented in FORTRAN 77 using slightly modified routines from the EISPACK and Numerical Recipes packages, whereas the practical implementation of method (ii) is done in MATLAB â 5.2.…”

“…Up to now both bandgap laser structures [11][12][13][14][15] emitting in the near infrared wavelength regime and mid-infrared DFB lasers [16][17][18] based on quantum cascade laser (QCL) structures [19,20] have been realized. An accurate description of the optical properties of these devices--which is in fact essential for an efficient device optimization--requires quite sophisticated approaches to the grating-waveguide problem [21][22][23] especially for those structures incorporating metal gratings [24][25][26]. Generally, DFB-laser structures are optimized with regard to the guided-guided wave interaction to improve the optical feedback and thus, the single-mode emission characteristics.…”

“…In general, both methods belong to the class of Floquet-Bloch theories [21][22][23][24][25][26] (this expression is used especially in the field of waveguide optics), since any component of the (due to the periodicity of the grating) quasi-periodic electromagnetic field can be expressed in the form Wðx; y; zjxÞ ¼ expðik x xÞu kx ðx; y; zjxÞ with the periodic part u kx ðx; y; zjxÞ, dictated by Floquet-Bloch's theorem. The MEM and the CWM basically differ in the description of the electromagnetic fields inside the grating region: In the MEM the field is expanded in terms of the eigenfunctions of the periodic grating medium which are obtained from the periodic boundary-value problem.…”

Substrate-emitting ring interband cascade lasers

“…Hereby, we search for Floquet-Bloch solutions of the infinite-length grating-waveguide problem 26 adopted to TE-polarized laser structures. This theory has been developed especially for the case of "strong" metallized gratings, where the original approach of Kogelnik and Shank 27 is not applicable anymore.…”