A numerical investigation of wave interactions in dielectric waveguides with periodic surface corrugations

High-temperature continuous-wave operation of 1310-nm single-mode grating-outcoupled surface-emitting semiconductor lasers

“…15,16 The theoretical radiation from a 15 µm long GSE outcoupler as a function of detuning from the Bragg condition is shown in Fig.16 as the input phase at one end of the grating is varied, assuming that the field amplitudes are equal at both inputs to the grating. This plot, calculated using Floquet Bloch theory, 12 indicates that if the outcoupler is detuned ∼ ±20 nm, the outcoupled intensity in insensitive to phase variations. …”

1550-nm single-mode grating-outcoupled surface emitting lasers

“…8,9 The theoretical radiation from a 15 µm long GSE outcoupler as a function of detuning from the Bragg condition is shown in Fig.7 as the input phase at one end of the grating is varied, assuming that the field amplitudes are equal at both inputs to the grating. This plot, calculated using Floquet Bloch theory, 10 indicates that if the outcoupler is detuned ∼ ±20 nm, the outcoupled intensity in insensitive to phase variations. …”

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

“…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.…”

“…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.…”