Modelling of diffraction in pillar vertical cavity surface-emitting lasers with embedded Bragg layers

Second-harmonic distortion in vertical-cavity surface-emitting lasers with lateral loss effects

“…The value of can thus be calculated from (7) provided that and are determined. The field reflectivity can be computed from [9] …”

Analysis and design of vertical-cavity surface-emitting lasers for self-sustained pulsation operation

“…The influence of diffraction loss is also included into the model through the carrier dependent cavity loss, . This is because the reflectivity of Bragg reflectors (which is inversely proportional to the cavity loss) varies with the penetration depth (i.e., effective guide width) of the lateral field [11].…”

“…can be eliminated from (8) by adding (9) and (10) and after substituting the expression of back into (8), we get (11), shown at the bottom of the page, where is the cavity loss at steady state. For unstable operation (i.e., SSP), should increase with time and the factor in front of must be positive.…”

“…The guiding structure of lasers determines the sign of . It is shown in [10] that has a negative (11) value for index guiding but a positive value for gain or antiindex guiding devices such that the device with index-guiding structure enhances SSP. In fact, it is shown in [13] that an edge-emitting device with a strong index-guiding structure enhances SSP through the presence of self-focusing effect (i.e., In [13, Fig.…”

“…The optical confinement factors in the core and cladding region, and are defined as and (22) Owing to the cavity-mirror interface structure and the modal nature of the lateral fields, the Bragg reflectivity can be computed by a self-consistent model-matching method [11] with the consideration of Bragg pairs, the cavity dimension, and the profile of the lateral fields. Fig.…”