Light scattering from anisotropic block copolymer grains in a planar waveguide

Measurement and Analysis of the Angular Guided-Wave Depolarized Light Scattering Patterns from Block Copolymer Thin Films

“…The substrate, film, and air layers are labeled with subscripts 1, 2, and 3, respectively. In the previous theoretical work, it was shown that the scattered electric field at point r within the waveguide from a source point r ′ can be obtained from the Green’s function approach as E ( m κ ) ( r ) = − k 0 2 ε 0 G⃡ ( m κ ) ( r , r′ ) · δ ε ↔ ( r′ ) · E ( m κ′ ) ( r′ ) where the indicators κ and κ′ = {0, 1} represent the {TE, TM} polarization and integers m 0 and m 1 label the waveguide modes; k 0 = 2π/λ 0 and ε 0 are the wavenumber and permittivity in vacuum, respectively; G⃡ ( m κ ) ( r , r ′) is the Green’s function corresponding to the m κ th waveguide mode, derived in the previous work, with detailed expressions given in the Appendix; δε⃡ ( r ′) is the dielectric perturbation at the source point; E ( m κ ′ ) ( r ′) is the incident guided-wave propagating in the m κ′ th waveguide mode.…”

“…In conventional DPLS, two methods were applied to analyze the scattered patterns, termed the correlation method and the amplitude method . The correlation method was used to calculate the integrated scattered optical power from prism-coupled GWDLS, and the derivation relied on the assumption of the simplest ideal grain models . In the present analysis, a Monte Carlo simulation based on the amplitude method is used to analyze the angular GWDLS patterns.…”

“…As the light propagated along the film it generated depolarized scattered light, which was then coupled out of the film and analyzed. To date, this method, called guided-wave depolarized light scattering (GWDLS), remains the only reciprocal space technique that quantifies the grain structures within ordered block copolymer thin films. − …”

“…GWDLS experiments have been conducted using two different coupling methods. Prism-coupled GWDLS was the first attempt at this technique, in which the absolute grain size was measured from the ratio of the integrated depolarized power to the integrated polarized power. , However, this coupling method is applicable only to hard films and cannot be used to study soft samples near the order−disorder transition temperature ( T ODT ). Grating-coupled GWDLS was developed to overcome these shortcomings.…”

“…The main purpose of this paper is to report the first measurement and analysis of the angular GWDLS pattern from a block copolymer thin film. In the previous work on prism-coupled GWDLS, the quantitative relationship between the scattered field and the grain structure was derived based on a Green’s function approach, and the integrated depolarized power ratio was calculated using a correlation method . However, the calculation was based on a simple ideal grain model, and only one length scale could be determined.…”