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DBR laser using travelling wave laser model (TWLM)

INTERCONNECT Laser and gain

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 in which one of the facet-mirrors, the right one in the figure, is replaced by a grating (the DBR). The Bragg frequency of the grating is set to the desired lasing frequency, providing frequency-selective feedback at the lasing frequency.

For the cavity to have one dominant resonance at the Bragg frequency, its optical length must support a Fabry-Perot mode at the same frequency. This condition is generally not satisfied by the initial cavity design. A phase-tuning section is therefore included to adjust the optical length of the cavity.

Figure 1. Schematic of the DBR laser with active, phase-tuning, and DBR grating sections.

Cold-cavity analysis

  1. Open the INTERCONNECT project file coldCavityLossMod.icp.
  2. Review the three circuits included in the project:
    • DBR reflector
    • DBR laser cold cavity
    • Fabry-Perot cavity with the same length and optical properties as the DBR laser cold cavity, but with a facet mirror instead of the DBR mirror
  3. Run the simulation.
  4. Plot the following ONA results on the same visualizer:
    • For the FP and DBR circuits, plot gain from input 1.
    • For the FP-DBR circuit, plot gain from input 2.
  5. Set the x-axis range to 349–351 THz and the y-axis range to −40–5 dB to reproduce Figure 3.
The circuit schematics are shown in Figure 2. The circuits are excited by the Optical Network Analyzers (ONA) at the locations indicated by the hashed arrows. The corresponding simulation results are measured at the locations indicated by the solid colored arrows in Figure 2 and are plotted in Figure 3.

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 phase tuning section is composed of a straight waveguide element and a modulator element. The modulator changes the effective index of the waveguide mode over the length specified in its properties, which in this example is set equal to the waveguide length. 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. 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).

Figure 2. Circuit schematics used for the cold-cavity analysis
laser_dbr_cold_cavity_results.png
Figure 3. Frequency responses of the Fabry-Perot cavity, DBR reflector, and DBR laser cold cavity

Figure 3 shows the frequency responses of the Fabry-Perot cavity, DBR reflector, and combined DBR laser cold cavity. The DBR reflector provides wavelength-selective feedback near the Bragg frequency, effectively selecting one of the Fabry-Perot cavity resonances. As a result, the DBR laser cold cavity exhibits a single dominant resonance near the Bragg frequency.

Laser operation

  1. Open the INTERCONNECT project file LaserDBRandFPLossModQ20.icp.
  2. Review the DBR laser and Fabry-Perot laser circuits included in the project.
  3. Run the simulation.
  4. Open and run plot_DBR_laser_results.lsf to reproduce Figures 4 and 5.

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 those shown in Figure 2 (DBR, and DBR-FP) except that the current, gain coefficient , and spontaneous emission coupling are set to non-zero values. The ONAs used for the cold-cavity analysis have been removed. Each circuit is instrumented with Optical Spectrum Analyzers (OSA’s), Optical Oscilloscopes (OOSC’s), and an Oscilloscope (OSC) to monitor the diagnostic average carrier density.

laser_dbr_loss_only.png
Figure 4a. Output spectrum of the DBR laser over the full simulation bandwidth. The normalized gain profile is scaled for visualization.
laser_dbr_loss_only_zoomedin.png
Figure 4b. Zoomed view of the DBR laser output spectrum near the lasing frequency.

Figure 4 shows the output spectrum of the DBR laser. A single dominant lasing mode is observed near the Bragg frequency due to the wavelength-selective feedback provided by the DBR reflector.

Figure 5a shows the output spectrum of the Fabry-Perot laser over the full simulation bandwidth, while Figure 5b shows a zoomed view near the DBR laser lasing frequency. Unlike the DBR laser shown in Figure 4, the Fabry-Perot laser supports multiple longitudinal modes within the gain bandwidth because it lacks the wavelength-selective feedback provided by the DBR reflector.

laser_FP_loss_only.png
Figure 5a. Output spectrum of the Fabry-Perot laser over the full simulation bandwidth. The normalized gain profile is scaled for visualization
laser_FP_loss_only_zoomedin.png
Figure 5b. Zoomed view of the Fabry-Perot laser output spectrum near the DBR laser lasing frequency

Wavelength tuning using the phase-tuning section

  1. Open the INTERCONNECT project file coldCavityLossModDetuned.icp.
  2. Review the DBR reflector and DBR laser cold-cavity circuits included in the project.
  3. Run the simulation.
  4. Plot the following ONA results on the same visualizer:
    • For the FP and DBR circuits, plot gain from input 1.
    • For the FP-DBR circuit, plot gain from input 2.
  5. Set the x-axis range to 349–351 THz and the y-axis range to −40–2 dB to reproduce Figure 6.

Figure 6 illustrates the case where the desired lasing frequency does not coincide with a Fabry-Perot cavity resonance. In this example, the Bragg frequency of the DBR reflector is changed from 350 THz to 349.95 THz. The figure was generated using the project file coldCavityLossModDetuned.icp, which is similar to the project shown in Figure 2 except for the modified DBR Bragg frequency.

laser_dbr_cold_cavity_detuned_results.png
Figure 6. Frequency responses of the Fabry-Perot cavity, DBR reflector, and DBR laser cold cavity with the DBR Bragg frequency detuned to 349.95 THz.
Figure 6 shows the frequency responses when the DBR Bragg frequency is shifted to 349.95 THz while the cavity remains unchanged. In this case, no Fabry-Perot cavity resonance coincides with the Bragg frequency. As a result, the cold cavity no longer exhibits a single dominant resonance. Instead, two resonances of similar amplitude appear near the edges of the DBR stop band. Under these conditions, the cavity is not expected to support stable single-mode lasing.
  1. Open the INTERCONNECT project file coldCavityLossModDetuned.icp.
  2. Run the simulation.
  3. Run the sweep coldModSweep.
  4. Open and run plotSweep.lsf to reproduce Figure 7.

If it is desired to have a lasing frequency that is different from the original cavity resonance, there will not necessarily be a Fabry-Perot mode aligned with that frequency. In this example, the desired lasing frequency is changed to 349.95 THz (instead of 350 THz) and the Bragg frequency of the DBR reflector is adjusted accordingly.

To achieve single-mode operation, the cavity must be tuned using the phase-tuning section. This is accomplished by sweeping the amplitudes applied to DC_2 and DC_4, which drive the modulators in the phase-tuning section. The sweep is implemented as coldModSweep in coldCavityLossModDetuned.icp. The modulation tables used in this example have been populated with arbitrary values for demonstration purposes.

laser_sweep_plot.png
Figure 7. Cold-cavity sweep results showing the movement of the Fabry-Perot resonances relative to the DBR reflector response as the phase-tuning section is adjusted. One tuning condition aligns a cavity resonance with the DBR Bragg frequency at 349.95 THz.
Figure 7 shows the effect of varying the phase-tuning section on the cold-cavity response. With the cavity initially detuned, no Fabry-Perot resonance is aligned with the DBR Bragg frequency of 349.95 THz. As the phase tuning is varied, the cavity resonances shift relative to the DBR response. In this example, the tuning condition corresponding to I = -2.5 aligns a Fabry-Perot resonance with the center of the DBR reflection band. This restores the desired cold-cavity condition for single-mode laser operation.
  1. Open the INTERCONNECT project file LaserDBRonlyLossModQ20shifted.icp.
  2. Review the DBR laser circuit with the phase-tuning section set to the tuned value obtained from Figure 7.
  3. Run the simulation.
  4. Open and run plot_TunedDBR_spectrum.lsf to reproduce Figures 9a and 9b.

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. Figures 9a and 9b show the resulting output spectrum of the tuned DBR laser. Figure 9a compares the laser spectrum with the scaled gain profile, while Figure 9b provides a zoomed view around the lasing frequency.

laser_tuneddbr_loss_only.png
Figure 9a. Output spectrum of the tuned DBR laser over the full simulation bandwidth. The normalized gain profile is scaled for visualization.
laser_tuneddbr_loss_only_zoomedin.png
Figure 9b. Zoomed view of the tuned DBR laser output spectrum near the lasing frequency.

Effect of optical feedback

To study the effect of the stray optical feedback on the DBR laser performance, the laser is embedded in the optical circuit shown in Figure 10. The circuit includes a ring resonator that is tuned to a frequency adjacent to the nominal laser operating frequency. The ring resonator provides approximately 4% reflection at port 1. The ring resonator is located approximately 75 μm from the main laser cavity and exhibits a series of resonances separated by its free spectral range (FSR) of approximately 0.7 THz. One of these resonances (349.8 THz) is intentionally positioned near the nominal laser operating frequency of 350 THz

circuit.PNG
Figure 10. INTERCONNECT circuit used to study optical feedback from a ring resonator.
  1. Open the INTERCONNECT project file LaserDBRandRingModulator.icp.
  2. Review the optical feedback circuit shown in Figure 10.
  3. Run the simulation.
  4. Plot the laser spectrum from OSA_1 in the circuit.
  5. Set the x-axis range to 348.5–351.5 THz and the y-axis range to −80–20 dB to reproduce Figure 11.
Figure 11 shows the optical spectrum measured at the output of the circuit (OSA_1). Although the laser is designed to operate near 350 THz, the dominant lasing mode shifts to approximately 349.8 THz, corresponding to one of the resonances of the ring resonator that lies within the laser gain bandwidth. The neighboring ring resonances are separated by approximately 0.7 THz, consistent with the ring resonator FSR. The secondary peak near 350.5 THz corresponds to the adjacent ring resonance.
This result demonstrates how coherent optical feedback can cause the laser mode to lock to an external cavity resonance. In this example, waveguide WGD_2 is lossless, so no decoherence occurs in the feedback path. As a result, the response is independent of the length of WGD_2, which corresponds to the optical path between the laser cavity and the ring resonator
laser_tuneddbr_zoomedin.png
Figure 11. Output spectrum of the DBR laser in the presence of optical feedback from the ring resonator.
Accurate steady-state results require the simulation time, the distance to the back-scattering element, and the OSA acquisition window to be chosen consistently. The simulation must run long enough for the effect of optical feedback to reach a steady state. In this example, the OSA start time is set to 0.55 ns and the stop time is set to 5 ns, ensuring that only steady-state data is used for spectral analysis.
Figure 12 shows the transient laser response before steady state is reached. By delaying the OSA acquisition window until after the transient has decayed, the measured spectrum reflects the steady-state behavior of the laser.
dbr_steadystate.png
Figure 12. Output power measured by OOSC_1. The laser reaches steady state after an initial transient response caused by optical feedback from the external cavity.

DBR laser using multisection TWLM

In previous file, the DBR laser is built with three individual sections including an active section, phase tunning section and a DBR grating section. From 2024R2, TWLM supports multisection definition. Therefore, it is possible to define all sections in one single TWLM.

The script file multisectionDBR.lsf shows how to set the active, phase tunning and the DBR grating sections in a single TWLM through a struct. The script would open the interconnect project, set the TWLM and then compare the result between a single multisection TWLM and the DBR laser with discrete sections.

struct.png
Figure 13. Example of a multisection TWLM definition implemented using a structure.

In order to obtain integer multiple of segments in the TWLM model, the lengths of the three sections are recalculated based on the equation below(see number of segments in TWLM object):

$$ L = N * \frac{c}{n_g}*{\Delta T}  $$

N is the number of segments.

  1. Open and run multisectionDBR.lsf.
  2. The script configures the multisection TWLM, runs the simulation, and plots the results shown in Figure 14.

Figure 14 compares the output spectrum of the multisection TWLM implementation with the spectrum obtained from the equivalent DBR laser constructed using discrete INTERCONNECT elements. The excellent agreement between the two results demonstrates that a multisection TWLM can accurately reproduce the behavior of a DBR laser while significantly simplifying the circuit implementation.

DBR_multisection.png
Figure 14. Comparison of the output spectra obtained using the multisection TWLM and the equivalent DBR laser implemented with discrete INTERCONNECT elements.

It should be noted that TWLM does not support “sinusoidal gratings”, which is defined by “effective index change” in WBG element. Therefore, the WBG is set with another option “coupling coefficient”, i.e. the step-index grating. The relation between coupling coefficient and index change is (ref):

$$ \kappa=\frac{2 \Delta n}{\lambda_B}  $$

Additionally, the grating period is set to meet the Bragg frequency (350THz) using the following equation:

$$ f_B=\frac{c}{2\Lambda n_{eff}}  $$

See Also

Laser TW (TWLM), Fabry-Perot Laser, DFB Laser, Multi-section DFB laser, Ring Vernier Laser, Gain Fitting, INTERCONNECT as a Laser Design Platform

Associated files

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