TWLM Laser Frequency Shift and Mode Hopping

INTERCONNECT

During laser operation, as input power changes, various physical effects cause shifts in the lasing frequency, leading to mode hopping. This is typically a result of changes in gain peak shift and refractive index due to changes in temperature \(T\) and carrier density \(N\).

The TWLM captures changes \(T\) and \(N\) during operation with various models. These changes affect the peak gain and refractive index through their dependence on \(T\) and \(N\). Together, they capture the full mode hopping behaviour.

Changes in T and N During Operation

Temperature Change

During laser operation, self-heating effects directly causes the temperature in the laser to increase. The self-heating model for TWLM is described in the INTERCONNECT as a Laser Design Platform article.

Carrier Density Changes

During laser operation above threshold, the carrier density is approximately held constant at the threshold value due to gain clamping, with excess injected carriers converted into photons. This carrier density remains constant, as long as the optical loss is unchanged.

As the loss changes, the gain also changes to sustain lasing. Since the gain is a function of carrier density, changes in loss directly results in changes in the carrier density.

Specifically, the carriers above threshold may vary due to the following effects that affect loss, or a combination of them:

Gain compression: At higher optical powers (photon densities), the peak gain in the cavity reduces due a direct non-linear effect. The TWLM incorporates this effect via a gain compression factor, explained in the TWLM Built-in Lorentzian Gain Options article. This gain compression effect is applied to both the built-in and user-defined gain profiles. When gain compression occurs, the carrier density increases to compensate for this loss of gain, which causes other changes as explained in the following sections.
Self-heating: For continuous wave operations, the laser heats up, which causes an increase in non-radiative recombination, thermionic leakage, and a direct reduction in gain. These changes in loss also affects carrier density and causes other changes explained in the following sections. TWLM incorporates the first two mechanisms through its recombination model, and thermionic leakage model. The direct reduction in gain can be simulated with the MQW solver in Ansys Lumerical Multiphysics™ or via measurements, and then captured in TWLM by either importing a gain profile or via the Waveguide/Gain/Temperature Properties.

Gain Peak and Refractive Dependence on N and T

Gain Peak Dependence

The gain peak depends on temperature and carrier density through the following physical effects:

Band-filling effect: An increase in carrier density in the quantum wells fills lower energy states, forcing optical transitions to occur at higher energies. This causes a blue shift in the gain peak.
Band gap reduction: Self-heating reduces the band gap of the active material, lowering the transition energies. This causes a red shift in the gain peak.
Thermal broadening of the carrier energy distribution: Self-heating broadens the carrier energy distribution, increasing the occupancy of higher energy states. This modifies and broadens the gain spectrum and can contribute to slight blue shift of the gain peak, although this effect is typically weaker than the band-gap reduction.

To capture these effects in the TWLM, you can either use an imported gain profile, or by tuning the built-in Lorentzian gain profile:

Imported gain profile: An imported gain profile, which may be simulated using the MQW solver in Ansys Lumerical Multiphysics™, can capture the combined effects of carrier density and temperature on the gain spectrum, including band filling, band‑gap reduction, and thermal broadening, provided these effects are included in the underlying simulation.
Built-in Lorentzian gain profile: The built-in Lorentzian gain profile model supports carrier density dependent shift of the gain peak, which you can use to model carrier-induced effects such as band filling. Temperature-dependent effects are handled through the Waveguide/Gain/Temperature Properties.

Refractive Index Dependence

The refractive index, which is the real part of the complex refractive index, depends on the carrier density and temperature through both direct and indirect ways.

The refractive index depends directly on carrier density and temperature through effects such as free carrier absorption. The resulting refractive index perturbations can be obtained using analytical relationships from the literature or extracted from measurements and fitting.

Indirect refractive index changes occur through modifications of the optical gain, which are related to changes in refractive index via the Kramers-Kronig relations. If the detailed composition and structure of the active layer are known, you can extract these index perturbations by simulating the structure in the MQW solver, which outputs the complex refractive index. If such details are not available, you can model this effect using the linewidth enhancement factor.

In the TWLM, carrier‑induced refractive index changes can be modeled using one of two approaches, depending on the desired level of physical detail.

A detailed approach is to import refractive index perturbation tables that relate refractive index to carrier density and temperature. You can obtain these data either from MQW simulations, or experimental data, explicitly modeling the the carrier- and temperature-dependent refractive index effects of the refractive index independently of gain. In the TWLM Element, assign carrier‑density‑dependent index tables using the Waveguide/Spontaneous Emission properties, and assign temperature‑dependent index tables using the Waveguide/Mode 1/Temperature Dependence properties.

A simpler approach is to use a linewidth enhancement factor to relate changes in refractive index to changes in gain caused by variations in carrier density. This method captures carrier‑induced refractive index changes without requiring detailed material information but does not explicitly model temperature‑dependent or gain‑independent index effects. In the TWLM, assign the linewidth enhancement factor using the Waveguide/Spontaneous Emission properties. Further information on this model is in the Spontaneous Emission Spectrum Model in the TWLM Knowledge Base article.