This design of a Ring Vernier Laser was proposed and experimentally demonstrated in the reference shown below. This application example does not purport to reproduce all of the quantitative results from the paper because the gain media parameters are not available, but it will illustrate how you would go about doing so if the gain media parameters were available. Some arbitrary values similar to those in the Fabry-Perot application example were used for the gain parameters.
The laser design, shown schematically in Figure 1, consists of an Silicon on isolator (SOI) structure including of a pair of bus waveguides coupled to a double bus ring at each end. The optical modes circulate in the long racetrack structure, highlighted in red, with the rings providing frequency selective feedback in picking out frequencies that get fed back into the racetrack. The bus waveguides are flared out in the central region and an InGaAs/InP QW gain medium is bonded onto them in that region. By making the ring sizes slightly different, a Vernier effect can then be created in the frequency selective feedback.
Using the Vernier Effect, the idea is to have two feedback resonances having free spectral ranges (FSRs) that are slightly different, as shown in Figure 2 (in this case due to the difference in ring circumference) such that they overlap perfectly only at multiples of their individual FSRs.
This overlap repeats periodically in the spectrum, however the spectral period of repetition is made to be larger than the bandwidth of the gain curve such that single mode lasing occurs.
Additionally, one of the rings can be tuned by the difference of the ring FSR’s to get the perfect of the overlap to occur one fringe over, thus providing for discrete tuning on a discrete frequency grid with spacing equal to the FSR of one of the rings.
Set up model
The ring feedback spectra, i.e., the spectra that get fed back into the racetrack at either end, are shown in the vicinity of their perfect overlap in Figure 3. Figure 3 also shows the two circuits used to generate the spectra figure, and their excitation and probe points by means of the hashed and solid arrows, respectively.
The overall feedback spectrum, i.e., the combined feedback from the two rings, is shown in Figure 4 and can be produced by placing the rings in series. The circuits for all of the above simulations can be found in the INTERCONNECT project file RingsBowersFig2ab.icp.
These time domain ring elements, labelled TW_DBLE_RING are actually compound elements consisting of a pair of couplers, a pair of straight waveguides and modulators as shown in Figure 5.
To get a clean single mode laser with maximal SMSR, one of the racetrack modes also need to overlap with the frequency selective feedback. To achieve this, in general, a separate phase tuning section is needed.
The INTERCONNECT circuit used to model the racetrack modes is shown in Figure 6. It includes a pair of phase tuning sections (two were included for symmetry, one would suffice), each of which is made up of the combination of a straight waveguide and a modulator. The modulator modulates the effective index of the waveguide mode over the length specified in its properties. 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 guided mode. In this case, the modulating signal could just as well represent temperature as in a silicon waveguide with heater.
A couple of gain elements for the gain sections are also included in the example file, and a waveguide modulator combination at each end to model the half rings comprising the turns in the racetrack, as the rings can also be modulated for tuning the feedback resonances. Finally, a couple of attenuators have been included to account for the taper losses to and from the flared out waveguide sections below the gain media. The effect of these attenuators would be to affect the round trip gain of the laser cavity.
However, in the absence of detailed information about the characteristics of the gain sections, the attenuation parameters were set to zero for simplicity in the simulation. They are also set to zero here for purposes of modeling the cold cavity racetrack modes, which is carried out with the gain coefficient, spontaneous emission coupling, and drive current set to zero in the gain elements such that they behave essentially as straight waveguide elements.
Figure 7 shows a spectrum of the racetrack modes with the inputs to all of the modulators set to zero superimposed with the ring spectra from Figure 3. The racetrack mode spectrum has been shifted vertically to make the position of its peaks relative to those of the ring spectra more clear. As can be seen, there is a perfect overlap of the combined feedback resonance (i.e., peaks of spectra from both rings) with one of the racetrack modes at 1.565 µm. The project file for this simulation can be found in bowersRacetrackNoMod.icp and the Lumerical script file to plot the results shown in Figure 7 is plotRaceTrackNoMod.lsf.
Figure 8 depicts the INTERCONNECT circuit used to model the laser, which is in file bowers_ring_gainTW.icp. The modulator waveguide combination at the ends in Figure 6, which is used to model the turns in the racetrack, have been replaced by the ring elements. The gain, spontaneous emission coupling, and drive current to gain elements have been set to non-zero values.
In this model shown above, the output spectrum from port 3 of the TW_RING_2 are the clockwise propagating modes, which is shown in Figure 9 and Figure 10, over a narrow and wide band, respectively; and single mode lasing can be clearly seen.
The next part shows how to tune the laser to operate at the adjacent long-wavelength peak of Ring 1. This provides discrete tuning on discrete grid with a spacing corresponding to the free-spectral range of Ring 1. The first step is to tune Ring 2, by sweeping the input value to the source driving its modulator input, DC_2, until the overlap of the ring feedback spectra occurs at the longer-wavelength peak of Ring 1 adjacent to 1.565µm as shown in Figure 11. This is done using the pair of circuits depicted in Figure 3, in the project file RingsBowersFig2aSweepRing2TD.icp. It should be noted that the tables that determine the modulation characteristics have been populated with arbitrary values.
The sweep results can be plotted by using the script file plotSweepRing2.lsf. Alternatively, or in addition, an optimization can be performed using the script file optimizeRing2.lsf. The optimization optimizes the value of the result variable called “peakfreq2”, in the root element, which is generated using an analysis script, to the target value which is that of the long-wavelength peak of Ring1 adjacent to the peak at 1.565 µm.
Next, the racetrack must be tuned using its phase tuning sections such that one of its resonant modes is aligned with the new combined feedback resonance of the two rings, as shown in Figure 12. This is accomplished using the project file bowersRacetrack.icp. There are three circuits in the project file: two rings with Ring 2 tuned to have the feedback spectrum shown in Figure 11, and the racetrack circuit of Figure 11. The racetrack circuit has the amplitude of the source providing the modulating signal to the phase tuning sections. The script file plotSweepRaceTrack.lsf will plot the results from the sweep as well as the feedback spectra from the rings. For the latter, it should be ensured that the simulation (rather than just the sweep) has also been run. The results for the racetrack modes will be shifted vertically to make the amount of tuning with the feedback more apparent. Alternatively, or in addition, the racetrack can be tuned using the script file optimizeRacetrack.lsf which works in a manner similar to that for tuning Ring 2. The tuned results can be plotted using the script file plotOptimizeRacetrack.lsf.
When the ring laser circuit depicted in Figure 8 is simulated with the modulation on Ring 2 (DC_2) set to the value that tunes the combined feedback to the longer-wavelength peak of Ring 1 adjacent to 1.565µm, and with the modulation on the racetrack phase tuning sections (DC_4) set to the value that tunes one of the racetrack modes to that same frequency, the single mode lasing spectrum has the results depicted in Figure 13 (narrowband) and Figure 14 (wideband). The INTERCONNECT project file for this simulation is bowers_ring_gainTWshifted.icp.
As shown in Figure 13, the single mode lasing spectrum is shifted over to the new desired lasing frequency determined by the ring feedback spectrum and cavity tuning.
It should be emphasized that, the referenced paper does not use a phase tuning section. They instead use small drive current adjustments to tune the racetrack. In other words, they use the gain section as the phase tuning section, through the variation in the material index with drive current. Since the INTERCONNECT gain element includes this effect through the linewidth enhancement factor, it is also possible to model this type of tuning in INTERCONNECT in a similar fashion. Finally, as mentioned in the referenced paper it is also possible to have continuous tuning of the lasing wavelength by tuning both rings and the racetrack modes simultaneously.
 J. C. Hulme, J. K. Doylend, J. E. Bowers, “Widely tunable Vernier ring laser on hybrid Silicon”, Optics Express, Vol. 21, No. 17, 19722, 2013