Semiconductor lasers with microring resonator are becoming more important for a wide range of applications for their wide tunability and narrow linewidth in the range of kHz. In this example we demonstrate the simulation of a gain element with micro-rings used as an external cavity reflector in INTERCONNECT using TWLM laser model following parameters from [1]; we reproduce most reported results and demonstrate good match.
Overview
Understand the simulation workflow and key results
In this application example we model the external feedback circuit with a low-loss Si 3 N 4 waveguide chip with two microring resonators (MRR). Light is first divided by a symmetric 50/50 splitter (Y-junction), and then guided sequentially through the two cascaded MRRs before being combined and fed back to the gain section. A second symmetric 50/50 splitter (Y-junction) combines the light that passes by the throughputs of the MRRs, which can be used as laser output. The two MRRs provide a so-called Vernier mirror, and act as wavelength-selective reflective filters. The InP laser diode gain section is modeled with TWLM gain element with one high-reflectivity facet with power-reflectivity of 0.85 on the left, while the right facet has an effective reflectively of almost 0. The coupling parameter, β , is used to control the power coupling strength between the gain medium and the passive waveguide chip and is modeled in this example using an attenuator.
Vernier Effect is used to have two feedback resonances with free spectral ranges (FSRs) that are slightly different (in this case due to the difference in ring circumference) such that they overlap perfectly only at multiples of their individual FSRs.
The feedback circuit is built from the two MRRs with different radius (49.5um and 54 um). We see the two circuits used to generate the spectra figure. The FSR of the MRRs is 48.2 nm which agrees with ref [1].
The combined feedback circuit from the two rings along with the waveguides and y-branches, is shown below:
The attenuator (ATT_1) in the circuit represents the coupling efficiency between the feedback circuit and the gain chip. The absolute value of the frequency dependent reflection coefficient is plotted below and compared with Fig3(a) in ref [1] for β =1. The circuits for all of the above simulations can be found in the INTERCONNECT project file FeedbackCircuit.icp with script plotFeedbackCircuit_MRRs.lsf to plot results.
These time domain ring elements, labelled TW_DBLE_RING are actually compound elements consisting of a pair of couplers, and a pair of straight waveguides:
The next step is to add a gain element, TWLM element, and connect it to the above feedback circuit:
Most parameters used in TWLM is from reference [1] except for few key parameters such as the effective index, index perturbation, and spontaneous emission factor that were not provided in the reference and so typical value were used to match the results.
Run and results
Instructions for running the model and discussion of key results
- Open and run FeedbackCircuit_TWLM.icp which includes the complete circuit. Once the simulation is run (this will take a few minutes) you can check the output power by visualizing the results in OPWM_1 . This is the results for one DC source data point. The next step will repeat this for different input currents so LI curve can be obtained.
- Load and run the script runCurrentSweeps.lsf . The script runs the sweep "CurrentSweep" for three coupling efficiencies (1, 0.7, 0.3). Since this is a sweep the completion will take considerable time.
The script plots the power-current (LI) and detuning curves. Optical power emitted from the TWLM left facet (in steady-state) is calculated as a function of different drive currents up to 100 mA and for different coupling efficiencies. We observe the expected linear relation between drive current and output optical power:
The discontinuities in the curves represent mode hopping, and we see that the power level drops at lower efficiency ( β ) values. Also, a good match of the LI curve magnitudes and number of mode hops are observed. The obtained response can better match measurements by having more information about the design parameters. This is detailed in the Update the model with your parameters section.
In this step we also obtain the laser frequency detuning from the center frequency as a function of drive current. Good agreement of the detuning magnitudes and number of mode hops with reference data is observed:
It is worth mentioning that if we increase the data points for current we might get more noisy curve with more mode hopping.
- Open script plot_PSD.lsf and run it. The script will load project file FeedbackCircuit_TWLM.icp then set all parameters for OFNSA then run simulation twice for drive current 20 mA and 60 mA. Frequency noise spectra for two different drive current (20 mA and 60 mA) with coupling coefficient of 0.7 will be demonstrated.
Here we see the calculated PSD for both drive currents:
The spectral linewidth is determined from the PSD in the flat, low-frequency part of the noise spectrum. The narrow peak at around 14 GHz corresponds to the beating between adjacent longitudinal modes. The estimated linewidth decreases from 26 kHz at 20mA to 10 kHz at 60 mA. The low-frequency flat part in the PSD curve is short here; a longer time window will increase the accuracy of the results.
Another way to improve the accuracy (without increasing the time window) is by setting the number of segments to 2 and then performing a sweep and an average of the results. For this, run the sweeps "sweep_linewidth_20mA_betaPointSeven" and "sweep_linewidth_60mA_betaPointSeven" in the project file FeedbackCircuit_TWLM.icp . Use the script plot_PSD_sweep.lsf to plot the results:
In addition to the narrow peak at 14 GHz, we can see a shallower and broader peak occurs at around 2-3 GHz and corresponds to damped relaxation oscillations. The estimated linewidth here decreases from 15.6 kHz at 20mA to 8.7 kHz at 60 mA.
Important model settings
Description of important objects and settings used in this model
Gain profile: By default, the Lorentzian gain has a linear dependence on carrier density. In order to match ref. [1] and set the Lorentzian gain to have a logarithmic dependence on carrier density, a user defined gain profile can be created and then imported in TWLM. You can use the script LogarithmicGainProfile.lsf to create a logarithmic gain profile. In addition, the script creates a .mcfdb file which contains the fitting coefficients information that can be uploaded to the TWLM element . For the implementation details of the script command mczfit and this gain fitting feature, please visit the pages mczfit and Gain Fitting . Finally, the Material or modal gain can be set by specifying the mode confinement factor. The following plot shows the difference between linear and logarithmic gain profile for carrier density of 1.7x10 18 1/cm 3 .
Recombination rates: Set appropriate linear, quadratic, and cubic recombination rates. Spontaneous emission coupled into the lasing mode is a product of the normalized spectrum, radiative recombination rate, and the spontaneous emission factor. Make sure the radiative recombination rate is nonzero, otherwise the lasing action cannot start due to the lack of spontaneous emission.
Effective index and index perturbation: To better illustrate mode hopping and linewidth enhancement, the index perturbation parameter is set to user defined instead of linewidth enhancement factor . Use the script IndexPerturbation.lsf to set the index perturbation table as a function of the carrier density in the active layer.
Spontaneous emission factor: Set this to define the ratio of the total spontaneous recombination that is coupled into the lasing mode. This influences the linewidth (phase noise) and RIN (intensity noise). A typical value of 4 x 10 -4 is used in this simulation.
Capture and escape rates: Enable the SCH layer and set these rates to model the transient behavior. Capture/escape rates determine how fast the injected carriers from the contacts reach the active layer by diffusion over the total barrier thickness.
Resource configuration: If you have the required license it is recommended to set up capacity in resources to be more than 1 for sweep parallelization.
Additional resources
Related publications
[1] Y. Fan, R. E. M. Lammerink, J. Mak, R. M. Oldenbeuving, P. J. M. van der Slot, and K.-J. Boller, “Spectral linewidth analysis of semiconductor hybrid lasers with feedback from an external waveguide resonator circuit,” Opt. Express 25 , 32767–32782 (2017).