Vector transmission matrix for the polarization behavior of light propagation in highly scattering media

Abstract

Recently the optical transmission matrix (TM) has been shown to be useful in controlling the propagation of light in highly scattering media. In this paper, we present the vector transmission matrix (VTM) which, unlike the TM, captures both the intensity and polarization transmission property of the scattering medium. We present an experimental technique for measuring the absolute values of the VTM elements which is in contrast to existing techniques whereby the TM elements are measured to within a scaling factor. The usefulness of the VTM is illustrated by showing that it can be used to both predict and control the magnitude of the complex polarization ratio of the light focused through the scattering medium. To the best of our knowledge, this is the first study to show the possibility of controlling the polarization of the light transmitted through highly scattering media.

Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives

“…54 With such MCFs in a lensless endoscope-whose concept relies on the interference between emitted beamlets-one would then require a wave front shaping scheme that controls horizontal and vertical polarization states, in order to make both states interfere constructively on the same (X; Y; Z). Dual-polarization wave front shaping is possible, 33,55,56 yet it is significantly more complex than the single-polarization wave front shaping, which remains the norm. However, a single-polarization wave front shaping scheme together with a nonbirefringent MCF makes the compromise that half of the light-the light in the "wrong" polarization state-is effectively wasted.…”

Focusing light through scattering media by full-polarization digital optical phase conjugation

“…The input light field E (1) ( x, y ) is expressed as a Jones column vector concatenated by two components E H (1) ( x, y ) and E V (1) ( x, y ): $${\mathbf{E}}^{false(1false)}false(x,yfalse)={true(\begin{array}{c}center{E_{\mathrm{H}}}^{(1)}(x,y)\\ center{E_{\mathrm{V}}}^{(1)}(x,y)\end{array}true)}_{2N\times 1},$$ where each component comprises N spatial modes and is represented by an N ×1 column vector. Since light transmission through the scattering medium and the subsequent optics is represented by a vector transmission matrix T [24, 25], the scattered light field on the SLM ${\mathbf{E}}^{false(2false)}false(x\prime ,y\prime false)={true(\begin{array}{c}left{E_{\mathrm{H}}}^{(2)}(x\prime ,y\prime )\\ left{E_{\mathrm{V}}}^{(2)}(x\prime ,y\prime )\end{array}true)}_{2N\times 1}$ can be calculated as $${\mathbf{E}}^{false(2false)}false(x\prime ,y\prime false)=\mathrm{boldT}{\mathbf{E}}^{false(1false)}false(x,yfalse).$$ Specifically, the vector transmission matrix T has the following form: $$\mathrm{boldT}={true(\begin{array}{cc}left{\mathrm{boldT}}_{\mathrm{H}\mathrm{H}}& left{\mathrm{boldT}}_{\mathrm{H}\mathrm{V}}\\ left{\mathrm{boldT}}_{\mathrm{V}\mathrm{H}}& left{\mathrm{boldT}}_{\mathrm{V}\mathrm{V}}\end{array}true)}_{2N\times 2N},$$ in which T AB (A, B = H, V) is an N -by- N matrix that connects the input field with B polarization and the scattered field with A polarization. By using singular value decomposition, each T AB can be further decomposed as T AB = U AB t AB V AB , where U AB and V AB are independent unitary matrices.…”

Focusing through turbid media by polarization modulation

“…Recently, the vector TM was measured which took into account the higher degree of freedom that can be added by relating both complex electric fields and polarization states of incident and outgoing waves [18,19]. The input and output channels of the vector TM describe the optical modes of two orthogonal polarization states; thus, when a wavefront is incident on the medium, the optical responses in terms of polarization states of the single channel in real space can be described by the linear combination of the output signals from two corresponding orthogonal channels.…”

“…The input and output channels of the vector TM describe the optical modes of two orthogonal polarization states; thus, when a wavefront is incident on the medium, the optical responses in terms of polarization states of the single channel in real space can be described by the linear combination of the output signals from two corresponding orthogonal channels. The vector TM can be described as shown below [18] ; (1) where the complex valued entry t ij lm relates the jth axis component of the mth input channel and ith axis component of nth output channel.…”