This application example shows how INTERCONNECT can be used to design and model a simple Distributed Bragg Reflector (DBR) laser using the travelling wave laser model (TWLM).
Set up model
A simple Distributed Bragg Reflector (DBR) laser, shown schematically in Figure 1 can be thought of as a Fabry-Perot laser where one of the facet-mirrors (the right one in the figure shown below), is replaced by a grating (the DBR) with Bragg frequency equal to the desired lasing frequency. This is done in order to provide frequency selective feedback at the lasing frequency. The complication of this design is that in order for this cavity to have only one dominant resonance and have it occur at the Bragg frequency, the optical length of the cavity must be such that one of the Fabry-Perot modes would be supported with just a facet reflectance instead of DBR, and it would be precisely at the Bragg frequency. This is generally not the case, so a phase tuning section should be added to allow for tuning of the optical length.
The INTERCONNECT project file coldCavityLossMod.icp contains three circuits, the DBR reflector, the DBR laser cold cavity, and a Fabry-Perot cavity of the same length and optical characteristics except for the DBR mirror. Figure 2 shows the schematics for the circuits. Figure 3 shows the corresponding simulation results for the three circuits, probed at points indicated by the solid colored arrows in Figure 2. The circuits are excited by the Optical Network Analyzer (ONA) at the points indicated by hashed arrows.
The input currents, gain, and spontaneous emission coupling have all been set to zero in the gain elements so that they behave essentially as straight waveguide elements.
The aforementioned phase tuning section is made of the combination of a straight waveguide element and a modulator element. The modulator modulates the effective index of the waveguide mode over the length specified in its properties. It has been set to the length of the waveguide in this example. It is important to note that while the modulator and DC source give the appearance of an electro-optic modulator, the modulator input can represent any scalar value that affects the material index of the waveguide and therefore the effective index of its guiding mode. For instance, the modulating signal could just as well represent temperature as in a silicon waveguide with heater, and this will be shown in the next page. In this project file, the modulating elements for phase tuning have been included but are not yet made use of (the modulating signal is set to 0).
As can be seen from Figure 3, the effect of the DBR reflector is to pick out one of the Fabry-Perot modes such that it yields a cold cavity with a single dominant resonance.
The project file LaserDBRandFPLossModQ20.icp contains circuits for the DBR Laser and Fabry-Perot Laser of the same length. They are essentially the same circuits as in Figure 2 (DBR, and DBR-FP) except with the current, gain coefficient , and spontaneous emission coupling set to non-zero values, i.e., gain on, and they are no longer excited by the ONAs. They are each instrumented with Optical Spectrum Analyzers (OSA’s), Optical Oscilloscopes (OOSC’s), and an Oscilloscope (OSC) to monitor the diagnostic average carrier density.
Figure 4 shows the output spectrum from the DBR laser, from OSA_1, in the vicinity of the lasing frequency and the inset shows the spectrum over the entire simulation bandwidth as well as the scaled gain curve.
Figure 5 shows the output spectrum from a Fabry-Perot Laser of the same length and material properties as the DBR laser, which is also simulated in the same project file, in a narrow band centered on the lasing frequency of the DBR laser. The inset shows the spectrum over a broad band, again superimposed with the scaled material gain curve.
If it is desired to have a lasing frequency that is different, then there will not necessarily be a Fabry-Perot like mode that is aligned with this new lasing frequency. Figure 6 depicts this situation. The new desired lasing frequency is now 349.95 THz (instead of 350THz previously) and the Bragg frequency of the DBR has been adjusted to this value. As can be seen, with the cavity not tuned, there is no Fabry-Perot like resonance at the Bragg frequency, and two cold cavity resonances of similar amplitude at the edges of the DBR stop band can be found. This situation will not result in single mode lasing. These figures were produced with circuits that are similar to those in Figure 2 (with the only difference being the value of the Bragg frequency in the DBR’s). The project file for this simulation is coldCavityLossModDetuned.icp.
In order to get single mode operation, the cavity must be tuned using the phase tuning section. This can be done by running the sweep called coldModSweep, which sweeps the amplitudes on DC_1 and DC_2 (which drive the modulators), inside the file coldCavityLossModDetuned.icp. It should be noted that, the table that determine the modulation characteristics have been populated with some arbitrary values. Running the script file plotSweep.lsf will plot the sweep results of ColdModSweep as shown in Figure 7 and Figure 8.
If the modulator input is now set to the value (-2.5 in the example) which tunes the cavity such that one of the Fabry-Perot like modes is at the Bragg frequency of the DBR then a single mode spectrum will result. This is done in project LaserDBRonlyLossModQ20shifted.icp. Figure 9 shows the resulting spectrum along with the gain shape, which has been scaled to show that the single mode lasing is not at the gain peak but is determined by the Bragg frequency of the grating and by the tuning. The right figure shows the spectrum over almost the entire simulation bandwidth.
To study the effect of the stray optical feedback on the DBR laser performance, the following circuit is created in the project file LaserDBRandRingModulator.icp. Here, the laser is placed in an optical circuit with a ring resonator that is tuned to an adjacent frequency. The ring resonator has a reflection of 4% at port 1. In figure 10, the resonance frequencies of the ring modulator are shown.
In the project file, the ring resonator has been placed around 75 um from the main cavity of the laser. Run the project file and plot OSA_1 to see the spectrum. Figure 11 shows that the lasing frequency is shifted to around 349.8 THz, which is one of the resonance frequencies of the ring resonator that falls in the gain region of the laser.
This result shows how the laser mode locks to the external cavity resonance in case of a coherent back-scattering. Since in this example waveguide WGD_2 has no loss, there will be no decoherence and the results will not be dependent on the length of WGD_2, which corresponds to the path length to the external cavity.
It is important to note that to find accurate steady state results the length of WGD_2, the simulation time and the OSA start time are related to each other. The simulation time should be long enough to allow reaching steady state due to back-scattering. This depends on the distance of the back-scatterer to the laser and the group velocity. In the figure below you can see the OOSC_1 result showing the laser power vs time and how the OSA time window is set to only capture steady state results.