INDEPENDENT PHASE AND AMPLITUDE CONTROL OF A LASER BEAM USING A SINGLE-PHASE-ONLY SPATIAL LIGHT MODULATOR
Independent Phase and Amplitude Control of a Laser Beam Using a Single-Phase-Only Spatial Light Modulator Laser-beam shaping is a rapidly developing field of research driven by both technological improvements of beam-shaping devices and the ever-increasing demands of applications. In high-energy laser chains, efficient beam shaping is successfully achieved in the front ends by passive methods such as beam apodization1 or intracavity mode shaping;2 however, these static techniques are unable to correct dynamic laserbeam profiles caused by alignment drifts or thermal problems. Spatial light modulators (SLM’s) are versatile devices that can modulate the polarization or the phase of laser beams at high refresh rates. It has been demonstrated that a SLM can be used to compensate for the thermal phase distortion occurring in high-energy glass amplifiers.3 Similarly, SLM’s have been used in high-energy laser applications, such as intracavity beam shaping4 or focal-spot control.5 In all these applications, only the phase-modulation capability of the SLM was used; however, there are numerous applications where phase-only modulation can be achieved differently. For instance, deformable mirrors are more attractive when it comes to wavefront correction of a large, high-energy, laser beam. Their scale and damage threshold allow them to be used within the power amplifier, while SLM’s are confined to the front end because of their modest size and low damage threshold. Nevertheless, a corrective device that would address both phase and amplitude simultaneously may be successfully used in high-energy lasers to significantly reduce the alignment procedure time, to improve the amplifier fill factor by injecting a more-adapted beam shape, to reduce the risk of damage in the laser chain by removing hot spots, and to improve the on-target characteristics of the beam by better control of the phase. Several techniques have been proposed to produce complex modulation of an electromagnetic field with an SLM for encoding computer-generated holograms.6,7 In both cases, two neighboring pixels with a single-dimension modulation capability are coupled to provide the two degrees of freedom required for independent phase and amplitude modulation. In our work, we use a similar approach, but our requirements differ from that of the hologram generation. First, the number of modulation points across the beam does not need to be high because spatial filtering imposes a low-pass limit on the spatial frequencies allowed in the system. Second, a high-efficiency modulation process is required to minimize passive losses. Lastly, the required amplitude-modulation accuracy should be better than measured shot-to-shot beam fluctuations for the correction to be fully beneficial. In this article, we propose a new method to modulate both the phase and amplitude of a laser beam, with a single-phaseonly SLM using a carrier spatial frequency and a spatial filter. As a result, the local intensity in the beam spatial profile is related to the amplitude of the carrier modulation, while its phase is related to the mean phase of the carrier. In the first part of this article, we show the simple relation between the transmitted intensity and the phase-modulation amplitude, and in the second part, we experimentally verify this scheme and use it to demonstrate beam shaping in a closed-loop configuration. The principle of the modulation is depicted in Fig. 96.19 for the case of a plane wave. The SLM is used as a phase-only device that applies a one-dimensional phase grating to the electric field. As a consequence, the two-dimensional propagation integral reduces to a one-dimensional one. In such a case, the electric field transmitted—or reflected—through the modulator accumulates a phase f given by E ¢ = E0 exp [ jf ( x )], (1)
where E0 can be complex and f is a periodic...
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