Beam steering with optical phased arrays is accomplished by introducing a relative phase shift between array elements [1]. This is typically achieved by altering the refractive index difference between elements, which alters the optical path length of incident radiation traveling through the elements. Beam steering with VCSEL arrays has also been shown to rely on such a refractive index variation [2], which is implemented by adjusting the current injection to the elements. However, if we view the VCSEL array as a waveguide from the active region through the distributed Bragg Reflectors, it can be shown that the index-induced phase shift between elements would only account for less than 1/100 th of the observed phase shift [2]. It is thus evident that phased VCSEL arrays rely on a fundamentally different phase-shifting mechanism. To investigate this, we turn to coupled mode theory, which has previously been applied to the dynamics of coupled edge emitting laser arrays and phase tuning in injection-locked VCSELs [3,4].The dynamic coupled mode equations for semiconductor laser arrays can be normalized to yield [3] 1 , 2where is the coupling strength between elements, the photon lifetime, the constant coupling phase (0 for in-phase arrays, for out-of-phase), the linewidth enhancement factor [5], the angular frequency, the normalized field amplitude, the phase, and the normalized excess carrier density in the laser. For a two-element array where = 1(2) for the left (right) element and , the phase shift between elements is found to correspond with the native cavity resonance of each element, per 3 , 4where coupled ω is the angular frequency of the coupled emission.Coherently coupled leaky mode VCSEL arrays with and are examined where the current injection into each element is varied [6]. The 2x1 arrays are coherently coupled together when the difference between their native resonance frequencies, , falls within a certain locking range which corresponds to a range of varying injection current. Outside of this range, the elements are assumed to operate independently at their native resonances, which must be further examined. The far field profiles of these arrays are shown at varying current differences between the elements in Fig. 1. The phase shift between elements at each current difference is extracted from fitting the propagated near field to the far field [7]. The field amplitudes and are determined as the square root of the maximum intensity measured in each element.As can be seen from the inset of Fig. 1(b), for the array. In Fig. 2 we show the phase difference retrieved from experiment and the lasing emission wavelength. The coupling strength is approximated from Eqn. 4 as , where is the maximum detuning between resonant frequencies, outside of which spectral splitting is observed. This value is obtained from as shown in Fig. † Currently at MIT Lincoln Laboratory, Lexington, MA 02420 ( ) ( ) [ ] 1 1 1 1 ( ) sin sin m m m p m m m m m m X X X d t Z X dt κτ φ φ ψ φ φ ψ + + − − = − − + − − + ( ) ( ) ( ) ( ) [ ] ( ) ...