  Light scattering within scattering media presents a substantial obstacle to
optical transmission. A speckle pattern with random amplitude and phase
distribution is observed when coherent light travels through strong scattering
media. Fortunately, wavefront shaping has been successfully employed with a
spatial light modulator to recover intensity targets after scattering media,
such as a sharp focus point or specified two-dimensional patterns. There have,
however, been few studies that attempted to separately manipulate the amplitude
and phase of the focusing field. In this paper, we propose a feedback-based
wavefront shaping method to generate complex optical fields through scattering
medium. A reliable phase retrieval approach is introduced to provide the
complex feedback information, i.e., the amplitude and phase of the focusing
field. Accordingly, in order to modulate the speckle field into a desired
complex structured optical field, a multi-objective genetic algorithm is used
to find the best phase map. To demonstrate the proposed method's high
performance, experimental tests have been carried out. High fidelity is
demonstrated in the generation of diverse complex light fields, both in
amplitude and phase. Our findings may facilitate the manipulation of light
field through scattering medium, and are anticipated to further promote future
applications such as optogenetics, vortex optical communication, and optical
trapping through scattering media.
