Modeling and Optimization of LCD Optical Performance (eBook)

Dmitry A. Yakovlev, Vladimir G. Chigrinov, Hoi-Sing Kwok (Autoren)

eBook Download: EPUB

2015
John Wiley & Sons (Verlag)
9781118706718 (ISBN)

Infos

The aim of this book is to present the theoretical foundations of modeling the optical characteristics of liquid crystal displays, critically reviewing modern modeling methods and examining areas of applicability. The modern matrix formalisms of optics of anisotropic stratified media, most convenient for solving problems of numerical modeling and optimization of LCD, will be considered in detail. The benefits of combined use of the matrix methods will be shown, which generally provides the best compromise between physical adequacy and accuracy with computational efficiency and optimization facilities in the theoretical model. The book will include algorithms for solving common problems of LCD optics, and will give recommendations of how to build the basic theoretical model and choose mathematical tools to solve particular problems. Special attention will be paid to solving optimization and inverse problems of liquid crystal optics. Earlier books have covered the classic Jones Matrix method, but the authors will cover the newer, more universal and successful electrodynamic Jones matrix method; this has extremely high accuracy and is especially useful in oblique light incidence and because it acknowledges multiple reflection. This book will prove a useful tool for developers of new generations of liquid crystal displays, and for scientists dealing with optical investigation of liquid crystals. An appendix will be provided which includes a robust technique for calculating the equilibrium LC director field in 1D case.

Autor

Dmitry A. Yakovlev, Saratov State University, Russia Dr Yakovlev is a senior researcher in the Department of Physics at Saratov State University, Russia. He is the head developer of commercial software MOUSE-LCD (MOdeling Universal System of Electrooptics of LCDs), developed in cooperation with HKUST, and the author of a number of efficient methods for computer modeling and optimization of LCDs used within many research projects performed in cooperation with Center Display Research of Hong Kong University of Science and Technology, ROLIC Research Ltd (Switzerland), TechnoDisplay AS (Norway. He has authored 30 refereed journal papers. Vladimir G. Chigrinov, Hong Kong University of Science and Technology, Hong Kong Professor Chigrinov is a member of the department of electrical and electronic engineering at Hong Kong University of Science and Technology. He is the author of 3 books, including Photoalignment of Liquid Crystalline Materials (with Professor Kwok), published by Wiley (2008). He has authored more than 150 refereed journal papers and holds 56 patents in the field of liquid crystals. He is a member of the editorial board of Liquid Crystal Today and Associate Editor of the Journal of SID. Prof. Chigrinov is Vice-President of the Russian SID chapter and a SID Fellow. Hoi Sing Kwok, Hong Kong University of Science and Technology, Hong Kong Professor Kwok is a member of the department of electrical and electronic engineering at Hong Kong University of Science and Technology. He is a fellow of the IEEE, Optical Society of America and the Hong Kong Institution of Engineers. Prof. Kwok is the co-author of Photoalignment of Crystalline Materials (Wiley, 2008) with Prof. Chigrinov and Vladimir M. Kozenkov, and has authored over 300 refereed journal papers.

Textauszug

1
Polarization of Monochromatic Waves. Background of the Jones Matrix Methods. The Jones Calculus

1.1 Homogeneous Waves in Isotropic Media

1.1.1 Plane Waves

Light is an electromagnetic radiation with frequencies ν lying in the range from ∼4 × 1014 to ∼8 × 1014 Hz. An elementary model of light is a plane monochromatic wave. The electric field of a plane monochromatic wave can be represented, in complex form, as

(1.1)

where ω = 2πν is the circular frequency and k is the wave vector of the wave, r is a position vector, and t is time. If the wave propagates in an isotropic nonabsorbing medium with refractive index n and is homogeneous (see Section 8.1.2), the vector k can be expressed as

(1.2)

where l is the wave normal, a unit vector perpendicular to the wavefronts of the wave and indicating its propagation direction; c is the velocity of light in vacuum (free space). In this case, the wave is strictly transverse, satisfying the condition

(1.3)

The phase velocity of the wave is

(1.4)

The true wavelength (λtrue) of the wave in the medium is defined as

where

is the temporal period of the wave. Along with the true wavelength, one can associate with this wave the so-called wavelength in free space, defined as follows:

(1.5)

Throughout this book, speaking on monochromatic fields or monochromatic components of polychromatic fields, we will use the term “wavelength” only in the latter sense (often omitting “in free space”). Also, we will use the parameter

(1.6)

called the wave number in free space. In terms of λ and k0, equation (1.1) can be rewritten as follows:

(1.7)

The field (1.1) must satisfy the following wave equation [1]:

(1.8)

where ϵ is the electric permittivity of the medium, ∇ is the nabla operator, and is the null vector. Throughout this book, we use the Gaussian system of units and consider only media that are nonmagnetic (i.e., having their magnetic permeability μ equal to 1) at optical frequencies. Substituting (1.1) into (1.8) gives the equation

(1.9a)

which can be rewritten as

(1.9b)

where k2 ≡ k · k. Scalarly multiplying any of these equations by k, we see that these equations include the condition

(1.10)

this condition may also be derived from the Maxwell equation ∇(ϵE) = 0. We should note that condition (1.10) is valid for inhomogeneous waves of the form (1.1) as well (see Sections 8.1.2 and 9.2). In the case of a homogeneous wave, condition (1.10) is tantamount to (1.3). In view of (1.10), equation (1.9b) can be reduced to the following one:

(1.11)

This equation requires that

(1.12)

In the case of a homogeneous wave, equation (1.12) leads to (1.2) with

(1.13)

With complex n and ϵ, equations (1.1)–(1.3) and (1.13) can be used to describe homogeneous waves propagating in absorbing media (see Section 8.1.2).

1.1.2 Polarization. Jones Vectors

Polarization Parameters

Let us consider a plane wave satisfying (1.3). We introduce a rectangular right-handed Cartesian system (x, y, z) with the z-axis codirectional with the wave normal l. Denote the unit vectors indicating the positive directions of the axes x, y, and z by x, y, and z. Using this coordinate system, we can represent the electric field of the wave as follows:

(1.14a)

or

(1.14b)

where and are the scalar complex amplitudes, and δx and δy are the phases of the x-component and the y-component of the field. The quantity

(1.15)

where δ = δy−δx, fully describes the state of polarization (SOP) of the wave. For completely polarized waves, which we consider here, the SOP is essentially the shape, orientation, and sense of the trajectory that is described with time by the end of the true electric vector [Re(E)] associated with a given point in space (r). It is well known that in general such a trajectory is an ellipse. With the help of Figure 1.1, we present basic parameters used for description of the SOP of completely polarized waves [1–3]:

1. The azimuth (orientation angle) γe of a polarization ellipse is defined as the angle between the positive direction of the x-axis and the major axis of the ellipse (Figure 1.1).
2. The ellipticity ee is defined as
   (1.16)
   where a and b are the lengths of the semimajor axis and semiminor axis of the ellipse, respectively. The ellipticity is taken positive if the polarization is right-handed and negative if the polarization is left-handed. The handedness of the polarization ellipse determines the sense in which the ellipse is described. In the literature, different conventions on the handedness of polarization are used. In this book, we use the convention adopted in the books [1,2, 4]: the polarization is called right-handed if the polarization ellipse is described in the clockwise sense when looking against the direction of propagation of the light [this is the case in Figure 1.1 where the z-axis and the wave normal l are directed out of the page, toward the viewer] and left-handed otherwise. For a linearly polarized wave, ee = 0. For right- and left-circularly polarized waves, ee equals 1 and –1, respectively.
3. The ellipticity angle is defined by
   (1.17)
   The values of lie between −π/4 (left circular polarization) and π/4 (right circular polarization).

Figure 1.1 A polarization ellipse

The azimuth γe and ellipticity angle are related to the complex polarization parameter χ as follows:

(1.18)

(1.19)

Thus, given χ, the parameters γe, , and ee can be calculated by formulas (1.18), (1.19), and (1.17). Note that for linearly polarized waves χ is purely real, while for circular polarizations it is purely imaginary (χ = −i for the right circular polarization and χ = i for the left circular polarization). We stress that relations (1.18) and (1.19) and all other relations for polarization parameters presented in this book correspond to the above choice of the convention on handedness and of the time factor in complex representation (e− iωt).

The spatial evolution of the amplitudes and in (1.14) can be described by the following equations:

(1.20)

where z′ is any given value of z. Even if the wave propagates in an absorbing medium (with complex n) and, consequently, is damped, its parameter χ is independent of z. This means that χ and the other polarization parameters listed above are spatially invariant and characterize the wave as a whole, that is, they are global characteristics of the wave.

Jones Vectors

The column

(1.21)

represents a Jones vector of the wave (1.14). Different kinds of Jones vectors are used in practice. Some of them are considered in Section 5.4 and Chapter 8. Definition (1.21) corresponds to one of those kinds. The Jones vector defined by (1.21) is a local characteristic of the wave, being dependent on z. According to (1.20), its values for two arbitrary values of z, z′ and z′′ (z′′ > z′), are related by

(1.22)

This relation can be rewritten as

(1.23)

where

(1.24)

The 2 × 2 matrix appearing here is a simple example of the Jones matrix.

If the medium where the wave propagates is nonabsorbing, the Jones vector can be represented as

(1.25)

where

(1.26)

is a spatially invariant Jones vector of the wave (see Section 5.4.3), aδ is a scalar complex phase coefficient of unit magnitude (aδa*δ = 1), and aI is a real coefficient that makes the following relation valid:

(1.27)

where I represents a quantity (usually...

Produkt-Details

• Erscheint lt. Verlag: 5.2.2015
• Reihe/Serie: Wiley Series in Display Technology
• Reihe/Serie: Wiley Series in Display Technology
• Reihe/Serie: Wiley Series in Display Technology
• Sprache: englisch
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Dmitry A. Yakovlev • Electrical & Electronics Engineering • Electrical Engineering - Displays • Elektronische Displays • Elektrotechnik u. Elektronik • Flüssigkristallanzeige • Flüssigkristallanzeige • Hoi-Sing Kwok • LCD • Materials Science • Materialwissenschaften • Modeling and Optimization of Liquid Crystal Displays • Optical and Non-Linear Optical Materials • Optical Communications • Optics & Photonics • optics of anisotropic media • optics of stratified media • Optik u. Photonik • Optische Nachrichtentechnik • Optische u. Nichtlineare Optische Materialien • Physics • Physik • Polarization Optics • Vladimir G. Chigrinov
• ISBN-13: 9781118706718 / 9781118706718