Liquid Crystal Optics and Electro-Optics

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Liquid Crystal Optics and Electro-Optics

• Chang-Kui Duan

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Introduction

• Most studied applied properties
  light-scattering ability
• externally applied field control or realign the
  anisotropic liquid crystal axis, thereby
  controlling the effective refractive index and
  phase shift
• form the basis for various optical transmission,
  reflection, switching, and modulation
  applications.
• LCs are noted for their large birefringence and
  easy susceptibility to external field
  perturbation.
• basic principles and seek only some general
  understanding by dealing with analytically or
  conceptually solvable cases.

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LCD pixel

• Schematic of a typical liquid crystal display
  pixel consisting of electronic driving circuit,
  polarizers, liquid crystal cell, color filter,
  and phase plate

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Content

• 0. Introduction
• Electro-Optics of Anisotropic and Birefringent
  Crystals
• Electro-Optics of Nematic Liquid Crystals
• Nematic Liquid Crystal Switches and Displays
• Electro-Optical Effects in Other Phases of Liquid
  Crystals
• Nondisplay Applications of Liquid Crystals

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1. Electro-Optics of Anisotropic and Birefringent
Crystals

1. Anisotropic, Uniaxial, and Biaxial Optical
   Crystals
2. Index Ellipsoid in the Presence of an Electric
   Field Linear Electro-Optics Effect
3. Polarizers and Retardation Plate
4. Basic Electro-Optics Modulation

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Permittivity tensor (????)
The polarization and dielectric displacement are
now given by
The elements of the permittivity tensor depend on
the choice of coordinate system
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Principal axes

• A coordinate system can be found such that the
  tensor is diagonal i.e.

This coordinate system define the principal
axes and principal planes associated to the
crystal. The corresponding refractive indexes
are known as principal indexes.
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Biaxial, Uniaxial isotropic crystal

• Crystals with three different principal
  refractive indexes are referred to as biaxial
  crystals
• Crystal with two different principal refractive
  indexes are referred to as uniaxial crystals
• For uniaxial crystals, the refractive indexes
  are nxnyno, and nzne where o stands for
  ordinary axis and e for extraordinary axis.
• If nogtne the crystal is said to be a positive
  uniaxial crystal

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Uniaxial crystal

• such as nematic liquid crystal
• n1 n2 no, ordinary ray n3 ne
  extraordinary ray
• index ellipsoid

The ellipsoid in (x, y, z) intersect the axis
at x nx y ny z nz
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For light propagate along direction k The
direction of D is in the plan perpendicular to k.
Ordinary wave Do perpendicular to the z-k
plane no(?) ? n0
Extraordinary wave De in the z-k plane but
perpendicular to k
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Uniaxial crystals (cont)
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Presence of an Electric FieldLinear
Electro-Optics Effect
In the presence of an applied field, the index
ellipsoid becomes
(1/n2)i are dependent on the applied field E.
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Linear optical effect
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Examples

• For a widely used electro-optics crystal such as
  lithium niobate (LiNbO3), r33 30.8 (in units of
  10-12 m/V), r13 8.6,r22 3.4, and r42 28,
  with ne 2.29 and no 2.20 (at 550 nm).
• For these values of electro-optics coefficients
  (10-11 m/V), an applied dc voltage of 10,000 V is
  needed to create a phase shift of in a crystal
  of centimeter length.
• liquid crystal electro-optics devices, the
  typical ac voltage needed is around 1 V and the
  liquid crystal thickness is on the order of a few
  microns

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Polarizers and Retardation Plate
Typical electro-optic modulation scheme with
polarizeranalyzer sandwiching an electro-optics
crystals and a retardation plate.
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Linear and circular polarizers

• Linear polarizers are usually made of anisotropic
  absorbing materials in which the absorption along
  a crystalline axis is much stronger than the
  orthogonal axis
• Circular polarizers are usually made by putting
  in tandem(??) a linear polarizer and a
  birefringent retardation (????) plate, with the
  polarization vector bisecting the so-called fast
  and slow axes of the retardation plate

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Polarization of output light
Various states of polarization resulting from the
addition of two orthogonal components of a
polarized light with a relative phase shift.
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Basic Electro-Optics Modulation
For A is oriented at 45 with respect to the
crystalline axes
?
?
At the exit plane of the crystal of length l
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Basic Electro-Optics Modulation
? ? crystal phase shift by retardation plate.
By summing the components of Ex? and Ey? on the
transmission axis of the output polarizer (along
y)
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2. Electro-optics of Nematic Liquid Crystals

• In general, the distortions on the electronic
  wave function of liquid crystal molecules caused
  by an applied field do not cause appreciable
  change to its contribution to the refractive
  indices
• However, the orientation of the molecules can be
  dramatically altered by the applied field
• principal mechanism used in liquid-crystal-based
  electro-optical devices.

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Dual-Frequency Liquid Crystals
transparent conductor ITO to allow the
application of an electric field across the cell
AC instead of DC Avoid current flow, degration
along E away E
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Mixing and doping
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Dual-frequency liquid crystal

• Since the dielectric anisotropy is frequency
  dependent (cf. Fig. 3.5), one could create a
  mixture of liquid crystals with different
  dielectric dispersions such that the resulting
  so-called dual-frequency liquid crystal (DFLC)
  possesses an effective positive anisotropy at one
  frequency of the applied ac electric field, but
  possesses a negative anisotropy at another ac
  frequency.

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Freedericksz Transition Revisited
Geometry for observing (a) the S (splay)
deformation, (b) the B (bend) deformation, and
(c) the T (twist) deformation.
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Case 1 One-elastic-constant approximation.
Standard variation method
??
Reminder ? ?(2/d)?m d?/dz z2/d 0!
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Solution
For relatively small reorientation angles
only if E gt EF
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Case 2 Freedericksz transition voltage including
elastic anisotropies.
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Case 3 Freedericksz transition voltage including
elastic conductivity.

• The maximum reorientation angle ?m is described
  by

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Field-Induced Refractive Index Change and Phase
Shift
Director axis reorientation profile in the cell
at various applied voltage above the Freedericksz
transition.
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Phase shift for light passing through
Approximation
Twisted configuration with maximum angle 900
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current liquid crystal display devices twisted
configuration.

• Tilting and unwinding of the director axis of a
  90 twisted nematic liquid crystal cell under the
  action of an applied field.

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3. NEMATIC LIQUID CRYSTAL SWITCHES AND DISPLAYS

• To obtain higher resolution, faster response,
  wider field of view, larger display area, and
  more functions in each display pixel.
• Two types transmissive and reflective
• make use of the polarizing and birefringent
  properties
• conjunction with polarizers and phase
  (retardation) plates
• broadband (from near UV to far infrared)
  birefringence, and transparency

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A twisted nematic liquid-crystal switch.

1. When the electric field is absent, the LC
   cell acts as a polarization rotator the
   light is trans-mitted.
2. When the electric field is present, the
   cells rotatory power is suspended and the
   light is blocked.

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Liquid Crystal Switch On-Axis Consideration for
Twist,Planar, and Homeotropic Aligned Cells

• normally black (NB) mode two parallel polarizers
• normally white (NW) mode two orthogonal
  polarizers

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Off-Axis Transmission, Viewing Angle, and
Birefringence Compensation

• Has to be considered for display application
• transmission function T is now a function of many
  variables
• Example NB mode
• For on-axis light, the initial transmission is 0.
  When the voltage is on, the transmission is at a
  maximum for the on-axis light
• for the off-axis light, the e and o waves will
  pick up an extra phase shift because of the extra
  optical path length

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Birefringent compensation film

• to place a birefringent film (of opposite
  anisotropy to that of the liquid crystal)
  adjacent to the LC film

limiting case of ? 0
compensation film should have birefringence of
opposite sign to that of the liquid crystal
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Sophisticated treatment

• For arbitrary angle ? or director axis
  angular and spatial distributions, and more
  complicated cell structure, the phase shift, and
  therefore the transmission of light through the
  cell and other accompanying polarization
  selective elements, is not amenable to simple
  analytical treatment. More sophisticated Jones
  matrix methods or numerical technique such as the
  finite difference time domain (FDTD) numerical
  methods discussed in the next chapter are needed
  to solve such a complex propaga- tion problem.

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Liquid Crystal Display Electronics
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Optical modulation of LCD
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4. Electro-optical Effects in Other Phases of
Liquid Crystals

• nematics are the most extensively used
• other phases (smectic, cholesteric, etc.) and
  mixed systems capable of field-induced
  reorientation have also been employed for
  electro-optical studies and applications
• ferroelectric liquid crystals, generally switch
  faster than nematic cells

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Surface Stabilized FLC

• Ferroelectric liquid crystal under an applied
  field,

Typical values
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Approximation

• Under the assumption that e is appreciable, the
  first term can be neglected

solution
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An practical case
? tilt angle phase retardation ? 2?d?n/?
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Soft-Mode FLCs

• SMFLCs use changes in the tilt ? while ? remains
  constant. capable of continuous intensity change
• SMFLCs employ smectic-A phase
• experimental setup

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5. NONDISPLAY APPLICATIONS OF LIQUID CRYSTALS

• extremely broad spectral range (from near UV to
  far infrared and into the microwave regime).
• fluid nature and compatibility with most
  optoelectronic materials
• a whole host of tunable lens, filters, switches,
  and beam/image processing devices have emerged.
• good candidates for biochemical sensing
  applications due to organic nature
• light emitting diodes and electroluminescence
  devices

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LC Spatial Light Modulator

• A typical optically addressed liquid crystal
  spatial light modulator (OALCSLM) operating in
  the reflective mode

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Tunable Photonic Crystals with LC Infiltrated
Nanostructures

• Photonic crystals in 1-, 2- and 3D forms made of
  various optoelectronic materials
• photonic crystals can function as tunable
  filters, switches, and lasing devices
• optical holography offers a quick one-step
  process for the fabrication of photonic crystals
  (limited)

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Tunable Frequency Selective Planar Structures
Transmission
Unit cell of an all-dielectric polarization
independent FSS for operation in the visible
region as a stop-band filter.
reflection
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Covered with LC
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Liquid Crystals for Molecular Sensing and
Detection
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Beam Steering, Routing, and Optical Switching and
Laser Hardened Optics

• Although most optical elements involve low level
  light, liquid crystals are actually excellent
  laser-hardened materials capable of handling very
  intense pulsed lasers or high power continuous
  wave cw lasers.
• Intensity 1010 W/cm2
• liquid crystals also do not suffer any
  structural/chemical damages.