Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers

Abstract

The spatial coherence and the optical phase distribution across a two-dimensional ͑2D͒ photonic crystal implemented with coupled arrays of vertical cavity surface emitting lasers ͑VCSELs͒ are experimentally characterized. This is achieved by performing Young's interference experiments between pairs of array elements using a spatial light modulator arrangement. In contrast to far-field measurements that provide information only on the global spatial coherence, this approach can yield full mapping of the complex degree of spatial coherence. Examples of such analysis are presented for nominally uniform one-dimensional and 2D arrays of coupled VCSELs and possible mechanisms of the observed coherence degradation are discussed. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2431474͔The output power of single-mode vertical cavity surface emitting lasers ͑VCSELs͒ is typically limited to a few milliwatts because of their small aperture area required for higher-order spatial mode suppression.1 Increasing the aperture size leads to poor selection between spatial modes and, above a certain size, results in uncontrolled filamentation, which limits the output power and degrades the spatial coherence and beam quality of the device. The problem of filamentation can be overcome by coupling a large number of single-mode VCSEL, forming two-dimensional ͑2D͒ arrays of phase-locked emitters. [2][3][4][5] In addition, these arrays exhibit a high degree of spatial coherence, as inferred from their nearly diffraction limited, four-lobed far-field patterns, which indicate that they oscillate predominantly at the lowest loss out-of-phase supermode. 2-5Evaluating the features of spatial coherence of coupled-VCSEL arrays is important not only for optimizing their coupling but also for developing functionalities that rely on such coherence. An example of such application is beam steering, where control over the mutual phase of the emitters is necessary.The spatial coherence in phase-locked VCSEL arrays has traditionally been evaluated using measurements of their far-field patterns 2,3 complemented by model calculations of their supermodes. 4,5 However, this approach yields information only on the global coherence properties of the array, in particular, the deviation of the beam pattern from the expected diffraction limited distribution. Moreover, such analysis generally cannot give direct indications on the mechanisms of coherence degradation. Spectral analysis of such arrays, e.g., using spectrally resolved far-field patterns or spatially resolved emission spectra, could give more indications on spatial coherence, but is difficult due to the small spectral splitting of the supermodes in large arrays.A more complete evaluation of the spatial coherence across a VCSEL array would be to measure the complex degree of spatial coherence ␥͑x , y ; xЈ , yЈ͒ between pairs of points in the array plane ͑x , y͒. This can be accomplished by performing Young's interference experiments, in which the interference pattern corresponding to two selected...

Spatial-Mode Discrimination in Guided and Antiguided Arrays of Long-Wavelength VCSELs

“…Since 1985, when the groundbreaking work on VCSEL arrays by Uchiyama and Iga [11] was published, there has been a significant number of works investigating these devices both experimentally [12]- [14] and theoretically [15]- [17]. Only few representative reports are cited here.…”

Quantum Langevin model for nonequilibrium condensation

“…Only recently, the advances in optical technology are providing examples of spatially extended laser devices for which the large system limit is a legitimate approximation, the so-called VCSELs (Vertical Cavity Surface Emitting Lasers) [12]. While these devices have received a great attention from point of view of nonlinear optics and of all-optical information processing [13], their potential to study the non-equilibrium statistical mechanics of the laser phase transition has been so far only marginally exploited [14].…”

On the application of a monolithic array for detecting intensity-correlated photons emitted by different source types

“…The other end of the fiber was used to illuminate the SPAD array in the far field zone of the fiber end, at a variable distance L (1 -3 cm) from the fiber such that the whole 4×4 SPAD array is over illuminated. Such extended thermal light source is of the small angular width w/L=10 −2 rad and exhibits first-order correlations g (1) , when the SPAD array is replaced by Young double-pinhole interferometer as in Fig. 4 (a), which was taken in the same setup configuration but with the Hg-Ar lamp driven from the AC power supply.…”

“…The first-order correlation function, g (1) , is widely used in optical applications because a simple experimental arrangement makes it easily accessible, e.g. Young's double-slit interferometer [1].…”

“…In Young's experiment, two points on the wavefront separated by a distance x 12 produce a fringe pattern with resultant intensity I 1 + I 2 + 2 √ I 1 I 2 |g (1) (x 12 , τ)| cos(∆ϕ 12 ) at a screen location where the phase difference is ∆ϕ 12 and the propagation time-difference is τ. The fringe visibility V measures the magnitude of the first-order correlation function |g (1) …”