MadSci Network: Physics

Re: Electrooptically changing refractive index- what is Max %?

Date: Thu Sep 23 23:23:38 2004
Posted By: Adrian E. Popa, Laboratory Director Emeritus
Area of science: Physics
ID: 1095714675.Ph

Greetings John:

1. Question in the Mad Science Archives:

How to control optical density and hence the refractive index of a material

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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

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

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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