{"id":2124,"date":"2012-04-25T06:23:27","date_gmt":"2012-04-25T10:23:27","guid":{"rendered":"http:\/\/blogs.vassar.edu\/magnes\/?p=2124"},"modified":"2013-07-11T10:28:57","modified_gmt":"2013-07-11T14:28:57","slug":"jones-gooch-and-tarry-and-transmission","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2012\/04\/25\/jones-gooch-and-tarry-and-transmission\/","title":{"rendered":"Jones, Gooch and Tarry, and Transmission"},"content":{"rendered":"

I am going to start out my calculations by writing out the general form of a Jones matrix for TN-LCD as expressed in “Jones-matrix models for twisted-nematic liquid crystal devices” by Makoto Yamauchi:<\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

where<\/p>\n

(2) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

and represents the constant absolute phase.<\/p>\n

While<\/p>\n

(3) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

representing the total birefrigence.<\/p>\n

The R in equation (1) is the rotation matrix and is represented by<\/p>\n

  <\/span>   <\/span>\"\begin{equation}<\/p>\n

And M is the\u00a0MLC\u00a0<\/sub>Jones matrix.<\/p>\n

We can use this equation in conjunction with the Gooch and Tarry formula in order to help us model the transmission of TN-LCD.<\/p>\n

As stated in my Preliminary Data, the Gooch and Tarry formula is written as\u00a0<\/p>\n

(4) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

Since we will be focusing on TN-LCDs, the twist angle will be\u00a0900\u00a0<\/sup>and the transmission can then be modeled as<\/p>\n

(5) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

Here,<\/p>\n

(6) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

I then used this variation on the Gooch and Tarry formula in order to graph transmission vs. \u00a0d\u2206n\/<\/em>\u03bb<\/p>\n

\"\"<\/a><\/p>\n

This graph shows us the first few transmission peaks (Mathematica Code<\/a>). Transmission operates at 100% when<\/p>\n

(7) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

For N= 1, 2, 3…<\/p>\n

Where N stands for the number of wave plates (an LC-cell being thought of as N wave plates).<\/p>\n

With respect to our graph, then, the transmission peaks are occurring when<\/p>\n

(8) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

This helps us to visualize how the twisted nematic effect operates.<\/p>\n

References:<\/p>\n

Gooch, C.H. and H.A. Tarry. “The optical properties of twisted nematic liquid crystal structures with twist angles less than or equal to 90 degrees.” Applied Physics<\/em>\u00a0Vol. 8(1975): 1575-1584.<\/p>\n

Yamauchi, Makoto.\u00a0“Jones-matrix models for twisted-nematic liquid crystal devices.” Applied Optics <\/em>Vol. 44.21(2005): 4484-4493.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

I am going to start out my calculations by writing out the general form of a Jones matrix for TN-LCD as expressed in “Jones-matrix models for twisted-nematic liquid crystal devices” by Makoto Yamauchi: (1)   where (2)   and represents the constant absolute phase. While (3)   representing the total birefrigence. The R in equation […]<\/p>\n","protected":false},"author":432,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4101,29897,29905],"tags":[],"class_list":["post-2124","post","type-post","status-publish","format-standard","hentry","category-advanced-em","category-libby","category-spring-2012"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2124","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/432"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=2124"}],"version-history":[{"count":16,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2124\/revisions"}],"predecessor-version":[{"id":2393,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2124\/revisions\/2393"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=2124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=2124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=2124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}