Array mode analysis of two-dimension phased arrays of vertical cavity surface emitting lasers

Abstract

We have investigated the modal properties of two-dimensional phase-locked arrays of vertical cavity surface emitting lasers where the spatial coherency across the aperture comes from the evanescent coupling of the optical fields of the lasers. Typical two-dimensional arrays can be separated into three categories: the periodic array, the circular array, and the centered polygonal array (or concentric circular array). The circular array and centered polygonal array support a more circular symmetric output beam than the periodic array which is a simple two-dimensional extension of a linear array. The farfield pattern of the two-dimensional array has an azimuthal angle dependence such that near zenith, the fundamental array mode shows a single-lobe beam but with increasing angle many sidelohes appear. The highest array mode has a double-lobed far-field pattern near zenith, as in the case of the linear array. The centered polygonal array shows the most circularly symmetric beam pattern of the three which can be controlled by varying the excitation amplitude of the center laser. We have shown that symmetry plays an important role in determining the array mode and that the use of VCSE lasers give a good longitudinal mode selection leading to dynamic single-mode operation. These results can be extended to a quantum box laser array to give better optical beam control.

Coupled Lasers Rotation Sensor (CLARS)

“…Therefore, the nondegenerate solutions are unusable (see e.g., [10] and [11] for a general discussion on the role of mode-degeneracy under rotation). However, it is well known that (nondegenerate) anti-phase mode tends to be the dominant lasing solution in coupled laser arrays, having the lowest lasing threshold [13]. On the other hand, the in-phase mode generally has the highest threshold level and is seldom exhibited unless specific arrangements are made [13].…”

“…However, it is well known that (nondegenerate) anti-phase mode tends to be the dominant lasing solution in coupled laser arrays, having the lowest lasing threshold [13]. On the other hand, the in-phase mode generally has the highest threshold level and is seldom exhibited unless specific arrangements are made [13]. Therefore, in order to suppress the anti-phase lasing mode, it is advantageous to use an array of odd number of lasers.…”

“…The RHS describes two effects; that of rotation and that of structural disorder. Following a similar analysis to [10] with the exception that an additional term (structural disorder) appears in the RHS, the total field is a summation over serving merely as building blocks: (13) We substitute this expansion into (12), use (10), perform inner product of the resulting equation with and use their mutual orthogonality. The result is the following 2 2 matrix-eigenvalue equation for the expansion coefficients and frequency splitting (14) where (15a) and where is the inner-product.…”

Photonic crystal vertical cavity surface emitting laser arrays

“…Evanescent optical coupling between 2-dimensional (2D) array elements of vertical cavity surface emitting lasers (VCSELs) has been studied extensively [1][2][3][4][5][6][7]. One of the major disadvantages with this coupling approach is that the large inherent loss between cavities typically causes the laser phases to lock together out-of-phase [1].…”

Incoherence in phase-locked VCSEL arrays: tolerance to cavity parameter variations

“…While considerable attention has so far been devoted in analyzing collective array modes, including evanescently coupled semiconductor lasers [1], [2], actively coupled VCSELs [3], [4], wave coupled "anti-guided" arrays [5], [6] and external feedback coupled cavities [7], the effect of random (or systematic) parameter deviations from their assumed nominal values has attracted less attention.…”