Synthesis of Im-Bessel correlated beams via coherent modes

Abstract

We present the first high-quality experimental realization of a random optical beam as a linear superposition of its coherent modes. The individual modes are generated by passing a laser beam through a phase-only spatial light modulator. A random stationary beam is obtained by using a temporally randomized sequence of its coherent modes, each contributing, on average, with a weight proportional to the corresponding mode eigenvalue. As an example, the new method is applied to a I-Bessel correlated beam which was originally introduced in theory via the coherent mode decomposition, but could not have been experimentally generated so far by any other method.

Review on vortex beams with low spatial coherence

“…By using this method, one can precisely control the initial coherence width of the generated partially coherent beam by manipulating the beam spot size on the surface of the rotating-ground glass disk [26], however, the energy loss of this method is also inevitable. The third method is to superpose a sequence of coherent modes because partially coherent beam can be decomposed as a superposition of multiple coherent modes [152,153], and one can increase the power of the generated partially coherent beam with this method. On the other hand, various optical elements and methods have been proposed to generate vortex phase, e.g.…”

Generating electromagnetic dark and antidark partially coherent sources

“…In the latter, the deterministic field consists of a single weighted mode. The scalar PCS is formed by summing the weighted modes incoherently typically at the detector [4,15,16]. Here, a stochastic field realization is formed from the randomly weighted, coherent addition of many modes.…”

“…We note that because of the Kronecker delta functions in equations (18) and (20), there is no coupling between different index modes in equation (16). Taking this into account and expanding b n and c n in real and imaginary parts produces Summarizing this method, an electromagnetic DAD PCS with a CSD matrix given in equation (1) can be generated by incoherently summing many realizations of the E x and E y given in equation (16).…”

“…Prior scalar DAD source work showed that 50-60 modes were sufficient to accurately represent the PCS [3,4]. To create high-fidelity stochastic fields, we used 121 modes (n=−60, −59, L, 60) in the expansions in equation (16). Figure 1 shows stochastic electromagnetic DAD field realizations (magnitudes and phases of E x and E y ) for both methods 1 and 2.…”

“…The branch points (phase vortices) evident in the lower images of figures 1(b) and (d) occur at points of perfect destructive interference (amplitude or intensity nulls). These branch point locations and more generally, the interference patterns themselves, will change with the random weights [b n and c n in equation (16)] from field realization to field realization. Figures 2 and 3 shows the spectral density S and CSD matrix ( ) x…”