Tunable optical diffractive structures from liquid crystalline materials

Bošnjaković, Dejan (author), Drevenšek Olenik, Irena (mentor)

This thesis is linked to parallel experimental research conducted by researchers in the Physics of complex matter group. It is focused on the theoretical modelling of electric and magnetic tuning of optical diffractive properties of grating structures fabricated as periodic configurations of a liquid crystal (LC) and a polymer. Due to the surface relief present on the sidewalls of the polymer ribbons, which is generated during their fabrication by the direct laser writing (DLW) process, the LC-director is oriented along the grooves in the relief. With the help of an external electric or magnetic field, the orientation of the LC medium between the ribbons can be changed, and, as a result, the optical properties of the structure are modified. For a theoretical description of optical properties, it is necessary to solve Maxwell's equations in a medium with periodic spatial modulation of optical dielectric permittivity tensor. We performed a numerical procedure based on the rigorous coupled-wave analysis (RCWA). The calculations began by modelling "empty" gratings, in which the channels between the polymer ribbons are filled with air. With this, we determined the parameters of the polymer scaffolds that best reproduced the experimental data. Then, we modelled structures in which the magnetic field caused a reorientation of a ferromagnetic LC in the plane of the grating. And also structures in which the electric field caused a reorientation of the LC in the direction perpendicular to it. Initially, numerical calculations were performed with the assumption that the reorientation of the LC medium between two polymer ribbons takes place homogeneously, thus neglecting the details related to surface anchoring. We then upgraded the simulations by calculating the spatially dependent orientational structure of the LC as a function of the applied electric or magnetic field by minimizing the Landau-de Gennes free energy, including the surface anchoring energy. These calculations were performed numerically and also analytically. Analytical results were obtained using the one-constant approximation and the approximations of the high and the low applied fields. The obtained theoretical results for electrically and magnetically tunable gratings agree very well with the experimental results. Therefore, the developed methodology provides an efficient tool for designing diffractive optical elements (DOEs) based on LC and polymers. It also enables simulations of their operation controlled by external fields. At the end of the thesis, we also show that the developed methodology can be utilized to analyse the operation of gratings with a hybrid control, in which active regulation takes place with an electric and a magnetic field. This type of configuration is very interesting for usage in practical devices, as it provides much shorter switching times than standard LC-based optical gratings that typically rely on applying only one active switching process.

• Language: English
• Keywords: nematic liquid crystals, ferromagnetic materials, photoresist polymeric materials, laser-based micro structuring, optical diffractive structures, transmission gratings, surface anchoring energy
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-145304
• COBISS.SI-ID: 149366275
• Publication date in RUL: 15.04.2023

Secondary language

• Language: Slovenian
• Title: Nastavljive optične uklonske strukture iz tekočekristalnih materialov

Abstract

Pričujoče doktorsko delo je povezano z vzporednimi eksperimentalnimi raziskavami, ki jih izvajajo raziskovalci v skupini za fiziko kompleksnih snovi. Osredotočeno je na teoretično modeliranje električnega in magnetnega uravnavanja uklonskih lastnosti optičnih uklonskih mrežic pripravljenih v obliki periodičnih skladov iz tekočega kristala (TK) in polimera. Zaradi površinskega reliefa na stranskih stenah polimernih trakov, ki nastane pri njihovi izdelavi s postopkom direktnega laserskega vzorčenja (DLV), je TK v prostoru med trakovi orientacijsko urejen vzdolž utorov v reliefu. S tem dosežemo minimalno deformacijsko elastično energijo na stiku med TK in trakovi. S pomočjo zunanjega električnega ali magnetnega polja lahko orientacijo TK materiala med trakovi spremenimo in posledično vplivamo na optične lastnosti opisane strukture. Za teoretični opis njenih optičnih lastnosti je treba rešiti Maxwellove enačbe v mediju s periodično prostorsko modulacijo tenzorja optične dielektrične permitivnosti, kar smo izvedli z numeričnim postopkom slonečim na rigorozni analizi sklopljenih valov (RASV). Najprej smo modelirali »prazne« eno dimenzionalne uklonske mrežice, v katerih so bili kanali med polimernimi trakovi napolnjeni z zrakom. S tem smo določili parametre polimernega ogrodja, ki najbolje reproducirajo eksperimentalne podatke. Nato smo modelirali še strukture, v katerih je magnetno polje povzročilo reorientacijo feromagnetnega TK v ravnini mrežice ter strukture, v katerih je električno polje povzročilo reorientacijo TK v smeri pravokotno na ravnino mrežice. Začetni numerični izračuni so bili narejeni ob predpostavki, da reorientacija TK materiala med dvema polimernima trakovoma poteka homogeno, s čimer smo zanemarili podrobnosti povezane s površinskim sidranjem. Nato smo simulacije nadgradili tako, da smo prostorsko odvisno orientacijsko strukturo TK kot funkcijo uporabljenega električnega ali magnetnega polja izračunali z minimizacijo Landau-de Gennesove proste energije vključno z energijo površinskega sidranja. Omenjene izračune smo izvedli numerično in pa tudi analitično z uporabo enokonstantnega približka in približkov močnega oz. šibkega polja. Dobljeni teoretični rezultati, tako za električno kot tudi magnetno nastavljive mrežice, se zelo dobro ujemajo z eksperimentalnimi rezultati. To dokazuje, da razvita metodologija predstavlja učinkovito orodje za načrtovanje uklonskih optičnih elementov (UOE) na osnovi TK in polimerov ter omogoča simulacije njihovega krmiljenja z zunanjimi polji. Na koncu dela pokažemo še, da je razvito metodologijo mogoče uporabiti za analizo delovanja hibridno nadzorovanih mrežic, pri katerih aktivno krmiljenje poteka tako z električnim kot tudi z magnetnim poljem. Tovrstna konfiguracije je zelo zanimiva za uporabo v praktičnih napravah, saj zagotavlja veliko krajše preklopne čase od standardnih optičnih mrežic na osnovi TK, ki tipično slonijo na vključitvi enega samega aktivnega preklopnega procesa.

• Keywords: nematski tekoči kristali, feromagnetni materiali, fotorezistentni polimerni materiali, lasersko mikrostrukturiranje, optične uklonske strukture, transmisijske mrežice, energija površinskega sidranja