Three-Dimensional Model of Holographic Formation of Inhomogeneous PPLC Diffraction Structures

Holographic Formation of Non-uniform Diffraction Structures by Arbitrary Polarized Recording Beams in Liquid Crystal-photopolymer Compositions

“…Since the changes in the dielectric permittivity tensor of the PSLC (PDLC) sample, caused by the recording processes, are small relative to the unperturbed state [31,32,33,34], it is possible to present the resulting distribution of perturbed dielectric permittivity tensor in the form:for PSLC – trueε^(boldnormalr,t)=false(1−sans-serifρfalse)[εp⋅trueI^+true∑m=o,eΔsans-serifε^pm(boldnormalr,t)]+sans-serifρ[sans-serifε^lc+true∑m=o,eΔsans-serifε^lcm(boldnormalr,t)+Δsans-serifε^lcpolfalse(boldnormalr,tfalse)], for PDLC – trueε^(boldnormalr,t)=false(1−sans-serifρfalse)[ε…”

“…If in Expression (5), the vectors Ejm are not orthogonal, then in the media a periodic interference pattern will be observed, the intensity distribution of which can be represented as [31]:I(boldnormalr,t)=true∑m=o,eIm(boldnormalr,t)⋅[1+mm(r)cos(Km⋅boldnormalr)], where mm(boldnormalr,t)=2I0m(boldnormalr,t)⋅I1m(boldnormalr,t)⋅(e0m⋅e1m)/(I0m(boldnormalr,t)+I1m(boldnormalr,t))…”

“…According to [31], similar to [22,28,30], the general case of the photo-polymerization-diffusion process of a HDS formation is completely described by a system of kinetic equations:∂Mmfalse(boldnormalr,tfalse)∂t=div(DMfalse(boldnormalr,tfalse)⋅gradMmfalse(boldnormalr,tfalse))−h⋅(Imfalse(boldnormalr,tfalse))k⋅Mmfalse(boldr,tfalse), ∂npmfalse(boldnormalr,tfalse)∂t=sans-serifδnp⋅h⋅(Imfalse(boldnormalr,tfalse))k⋅Mmfalse(boldr,tfalse), ∂nlcmfalse(boldnormalr,tfalse)∂t=sans-serifδnlc⋅div(D…”

“…Parameter bm(boldnormalr,sans-serifτ) (30) is a key generic parameter of photo-polymerization-diffusion recording process. Due to its definition, it takes into account all of the possible non-uniformities of amplitude and phase distributions of recording field [31].…”

“…Some theoretical models of HDS formation in photopolymerizable compositions [22,23,24,25,26,27,28], including photopolymer-liquid crystals ones [29,30,31], are developed by the present time.…”