Analysis of the optical confinement factor in semiconductor lasers

Abstract

We derive formulas for the optical confinement factor Γ from Maxwell’s equations for TE and TM modes in the slab waveguide. The numerical results show that the formulas yield correct mode gain for the modes propagating in the waveguide. We also compare the formulas with the standard definition of Γ as the ratio of power flow in the active region to the total power flow. The results show that the standard definition will underestimate the difference of optical confinement factors between TE and TM modes, and will underestimate the difference of material gains necessary for polarization insensitive semiconductor laser amplifiers. It is important to use correct optical confinement factors for designing polarization insensitive semiconductor laser amplifiers. For vertical cavity surface-emitting lasers, the numerical results show that Γ can be defined as the proportion of the product of the refractive index and the squared electric field in the active region.

Excitation of plasmon and guided-mode resonances in thin film silicon solar cells

“…Other definitions of confinement factors exist in the waveguide literature, e.g. [21,22]. For illustration of this point, Figure 7 plots the field profiles of the solar cells stack without the ZnO buffer layer for s-and p-modes at 2 eV.…”

Effect of Cavity Lifetime Variation on the Static and Dynamic Properties of 1.3-μm Wafer-Fused VCSELs

“…Using a one-dimensional transfer matrix method [23], we calculate Γ = 2.4% for the VCSELs under study.…”

Modal control in semiconductor optical waveguides with uniaxially patterned layers

“…As an example, we consider an asymmetric InGaAsP waveguide [14] operating at λ=1.55 µm with the core layer index n=3.55, the substrate layer index n s =3.24 and the UAP cladding layer index n c =3.45. Let the energy of the pump excitation be above the cladding bandgap of λ=1.35 µm.…”

“…It depends on the modal gain which in turn depends on both the material gain anisotropy and the mode confinement factor [12]. The traditional 3-layer waveguide design of semiconductor amplifiers with isotropic constituents leads to a better confinement of the TE mode and a larger modal gain for this mode compared to the TM mode [13], [14]. To obtain a polarization-insensitive amplifier one had to use highly anisotropic active layers with the material gain that favors TM polarization.…”