Coherently coupled VCSEL arrays have shown enhanced modulation that is attributed to photon-photon resonance (PPR) effects. PPR is a multimode effect that stems from the field interference between quasi-phase-locked optical modes. Consider an array of two dielectric waveguides. If the two waveguides are not identical, such as having different waveguide widths or waveguide core index values, then it is likely that the waveguides will not couple. As a result, the power of the optical modes will be largely confined to a single waveguide:
If all of the waveguides are identical, then they will tend to couple. The modes of coupled waveguides will have optical power that is spread across multiple waveguides. We often refer to these modes as array supermodes:
However, symmetry and identical waveguides is not a strict requirement for optical coupling. It is possible to engineer an array of non-identical waveguides that couple by tuning the core index to compensate for differences in waveguide width:
As mentioned previously, PPR stems from the interference of two (or more) modes. The two array supermodes shown in the previous figure have different propagation constants and frequencies, and as a result the relative phase between them will vary in a periodic fashion (with a frequency equal to the difference in the modal frequencies). This interference with varying relative phase leads to periodic beating of the optical power, which appears as a shifting of optical power from one waveguide to the other, and then back again:
We can calculate the fraction of the total optical power contained in each of the two waveguides (confinement factor) as a function of the relative phase. The confinement factor with each of the individual waveguides varies periodically and antisynchronously relative to each other (a decrease in confinement in the left cavity leads to an increase in confinement with the right cavity, and vice versa):
This time-varying confinement factor is the source of the PPR modulation enhancement effect. We can use the laser rate equations to model the effect of time-varying confinement factor on the small-signal modulation response. Consider the modulation response for an individual VCSEL. The modulation bandwidth is largely limited by the relaxation frequency related to the carrier-photon resonance:
If we add another identical VCSEL to create a symmetric 2-element VCSEL array and assume PPR mode beating between the two array supermodes, we can calculate a new modulation response for this array. While there is some enhancement in the modulation bandwidth, it is due to the extra optical power from having two lasers rather than PPR effects:
Prior rate equation modeling using the coupling coefficient analysis has also predicted that perfectly symmetric arrays would not show a modulation enhancement from PPR. PPR enhancement stems from variation in the coupling coefficient, and while a perfectly symmetric array can have significant variation in coupling coefficient on the level of a single VCSEL, the overall variation on the array scale is zero as any change in confinement in one cavity is perfectly counter-balanced by the change in the other cavity. However, introducing slight asymmetry into the array (as may be expected due to fabrication tolerances) enables confinement to vary on the array level, and leads to a resonance peak in the modulation response at the PPR frequency:
We can use our rate equation model to evaluate the effect of different system parameters, such as the array asymmetry, mode suppression ratio, and PPR frequency, on the modulation response:
We find that the PPR modulation enhancement is greatest when:
Most effective exploitation of PPR for modulation enhancement is also dependent on engineering the PPR frequency to be high enough to increase the bandwidth but not too high as to avoid the modulation response fall too low between the carrier-photon and photon-photon resonance frequencies.