Fourier-method beam analysis for coherent vertical cavity surface emitting laser arrays

Abstract

Effective engineering and exploitation of coherently coupled vertical cavity surface emitting laser arrays will benefit from simple and fast characterization of the optical coupling and coherence. We propose a Fourier method of analyzing beam profiles as an alternative to the prior beam visibility analysis and show that the mode suppression ratio and phase between a pair of supermodes can be extracted. Our analysis enables fast quantitative determination of the array coherence and supermode characteristics.

Investigating supermodes in coupled dual-element photonic crystal VCSEL arrays: a comparative analysis under strong and weak anti-guiding conditions

“…This adjustment proves advantageous for directly modulating the arrays, offering an improved signal-to-noise ratio and a more pronounced photon-photon resonance. This enhanced resonance is believed to contribute to superior modulation rates, as discussed in previous studies 18 .…”

Analysis and Characterization of Photon-Photon Resonance in Coupled Dual-Element Photonic Crystal Vertical Cavity Surface Emitting Laser Arrays

“…6, we plot representative far-field beam profiles measured at different injection currents along the coherently coupled ridge with an inset showing the calculated visibility and mode suppression ratio. We calculate the visibility from Fourier transform and the mode suppression ratio from 𝑀𝑀𝑀𝑀𝑀𝑀 = 1+𝑉𝑉 1−𝑉𝑉 where 𝑉𝑉 is visibility [29]. Fig.…”

“…Interestingly, when the imaginary index separation is zero, which occurs at an index suppression of 0.0065, the equal gain implies equal contributions from both supermodes resulting in a Gaussian-like far-field beam profile. Moreover, we can do the reverse and find the mode suppression ratio from the far-field beam profile by calculating the Fourier transform of the farfield beam profile [29].…”

Fourier beam analysis of photonic crystal coupled triangular VCSEL array

“…For the far-field intensities of the three supermodes with distinctive interference patterns we perform Fourier transform in Figure 3(g-i) and also determine the central (DC-peak) and side lobes labeled using white dots. Peak ratio is then defined as the ratio of the magnitudes of the side peaks, 𝐼 the DC peak, 𝐼 16 :…”

“…First, we compute the three supermodes from the complex waveguide modal simulation. Following a previous approach 16 , we then define what we call the "peak ratio" as the ratio between any side peak to the central peak of the Fourier transform of the far-field beam. Next, we apply the Fourier technique to our experimentally extracted coupled far-field beam profiles with nearly equal injection and a single spectral peak.…”