MadSci Network: Physics |
Greetings John:
References:
1. Question in the Mad Science Archives:
How to control optical density and hence the refractive index of a
material
htt
p://www.madsci.org/posts/archives/apr2001/988635671.Ph.r.html
As I wrote in the answer to Reference 1.:
"In electrooptic (EO) materials, the index of refraction can be
controlled by
changing an electric field across the material. Many materials exhibit
a small
EO effect including quartz; however, the EO materials with the largest
EO
effect that are commonly used in laser based systems are GaAs, KH2PO4,
NH4H2PO4, CdTe, LiNbO3, LiTaO3, and BaTiO3. Lithium Niobate (LiNbO3)
has
become the most common EO material used for amplitude modulating fiber
optic
communications systems operating at data rates exceeding 10 gigabits
per
second."
The Half-Wave Voltage of an EO material provides a measure of
the
optical
phase shift through a unit cube of the material in a specified
electrical field.
The half-wave voltage is the distance required for light at a given
wavelength
to travel an extra one-half wavelength when passing through a unit
cube of crystal.
The half-wave voltage is usually labeled V (pi), where the pi is the
Greek
letter pi. V(pi) is also a function of the wavelength of light. For
example,
Gallium Arsenide (GaAs) has a value of 92, 000 volts (92 kV) for V{pi)
at a
wavelength of 10 micrometers in the infrared and a value of 9.2 kV for
V(pi) at
a wavelength of 1 micrometer in the infrared. Gallium Arsenide is
opaque to visible
light wavelengths cutting off at a wavelength of about 900 nanometers
(nm) in the
infrared.
Lithium Niobate has a value for V(pi) of 7 kV at 1 micrometer
wavelength in
the infrared and a value of 3.5 kV at 500 nm wavelength in the green
portion of
the
visible spectrum. Lithium Niobate is opaque at 10 micrometers
wavelength in
the infrared. This means that a unit cube of EO material will delay
the light
passing through it by an extra one-half wavelength when voltage V(pi)
is placed
across the cube. For example, 3.5 kV placed across a (10 mm) cube of
Lithium Niobate will delay 500 nm green light an extra one half
wavelength
(250 nm)
passing through the 10 mm length of the cube. If 3.5 kV is applied
across a
1 mm cube of Lithium Niobate it will delay light one -half wave length
when
passing through 1 mm of the material. Thus to answer your
question
about the percent change, a 250 nm delay in 1 mm of Lithium Niobate
material
is equal to:
250 x 10^-9/ 1 x 10^-3 = 2.50 x 10^-4 or 0.00025 which = 0.025%,
This a very small number indicating that the EO effect is much to
small to
be used to make lenses and other large optical components except for
some very
exotic applications, such as laser theronuclear fusion experiments,
where Lithium
Niobate cyrstals several feet in diameter have been grown and cost is
not
an issue.
How do we make practical EO devices? We make them by reducing the
thickness
of the EO material between the electrodes where the voltage is applied
as
thin (T) as possible so that we have a strong electrical field and we
make
the length (L ) of the device material through which the light passes
as
long as possible to increase the phase shift. These parameters
modify the
voltage required for a one - half wavelength phase shift to:
V(1/2) = V(pi) x [T / L ]
Thus if we have a 1 mm thick crystal 10 mm long [T/L] = 0.1 and
V(1/2) would = 350 volts which is a practical value for voltages.
Another example, in an integrated optical(IO) Lithium Niobate
modulator,
T = 10 micrometers and L = 10 mm thus:
T/L = 1 x 10^-5 meters/ 1 x 10^-2 meters = 1 x10^-3 or 0.001.
then V(1/2) = 3500 x [0.001] = 3.5 volts!
This is a suitable voltage for multi-gigabit GaAs transistor drivers
to excite integrated EO modulators to produce optical amplitude, phase
or pulse
modulation. These are the type of modulators being used today in long
distance
fiber optic telecommunications cables.
Best regards, Your Mad Scientist
Adrian Popa
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