Electro-optic modulator

Electro-optic modulator (EOM) is an optical device in which a signal-controlled element displaying electro-optic effect is used to modulate a beam of light. In Telecommunication, signalling (UK spelling or signaling (US spelling has the following meanings The use of signals for controlling communications An electro-optic effect is a change in the optical properties of a material in response to an Electric field that varies slowly compared with the frequency of light Beam may refer to Beam (structure, a construction element Beam (nautical, the most extreme width (or breadth of a nautical vessel or a Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 The modulation may be imposed on the phase, frequency, amplitude, or direction of the modulated beam. In Telecommunications, modulation is the process of varying a periodic Waveform, i The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 Frequency is a measure of the number of occurrences of a repeating event per unit Time. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Modulation bandwidths extending into the gigahertz range are possible with the use of laser-controlled modulators. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission.

Generally a nonlinear optical material (organic polymers have the fastest response rates, and thus are best for this application) with an incident static or low frequency optical field will see a modulation of its refractive index. Nonlinear optics (NLO is the branch of Optics that describes the behaviour of Light in nonlinear media, that is media in which the dielectric polarization A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds The optical field is a term used in physics and vector calculus to designate the electric field shown as E in the Electromagnetic wave equation which can be derived The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium

Source: Federal Standard 1037C and MIL-STD-188

1 Types of EOMs
- 1.1 Phase modulation
- 1.2 Amplitude modulation
2 Applications
3 See also
4 References
5 External links

Types of EOMs

Phase modulation

The simplest kind of EOM consists of a crystal, such as Lithium niobate, whose refractive index is a function of the strength of the local electric field. Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration MIL-STD-188 is a series of US military standards relating to Telecommunications Purpose Faced with “past technical deficiencies in telecommunications Lithium niobate ( is a compound of Niobium, Lithium, and Oxygen. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can That means that if lithium niobate is exposed to an electric field, light will travel more slowly through it. But the phase of the light leaving the crystal is directly proportional to the length of time it took that light to pass through it. Therefore, the phase of the laser light exiting an EOM can be controlled by changing the electric field in the crystal.

Note that the electric field can be created placing a parallel plate capacitor across the crystal. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors Since the field inside a parallel plate capacitor depends linearly on the potential, the index of refraction depends linearly on the field (for crystals where Pockel's effect dominates), and the phase depends linearly on the index of refraction, the phase modulation must depend linearly on the potential applied to the EOM. The word linear comes from the Latin word linearis, which means created by lines. The Pockels effect, or Pockels electro-optic effect produces Birefringence in an optical medium induced by a constant or varying Electric field.

Amplitude modulation

Once one can make a phase modulating EOM, it's a fairly simple matter to turn that into an amplitude modulating EOM by using a Mach-Zehnder interferometer. The Mach-Zehnder interferometer (named after physicists Ludwig Mach (son of Ernst Mach) and Ludwig Zehnder) is a device used to determine the phase shift Simply use a beam splitter to divide the laser light into two paths, one of which has a phase modulator as described above, and then recombine the two beams. By changing the electric field on the phase modulating path, one can control whether the two beams constructively or destructively interfere and thereby control the amplitude or intensity of the exiting light.

Applications

A very common application of EOMs is for creating sidebands in a monochromatic laser beam. In Radio communications a sideband is a band of Frequencies higher than or lower than the Carrier frequency, containing power as a result of Monochrome comes from the Greek μονόχρωμος ( monochromos) meaning “of one color” which is a combination To see how this works, first imagine that the strength of a laser beam with frequency $ω$ leaving the EOM is given by

A e i ω t . Frequency is a measure of the number of occurrences of a repeating event per unit Time.

Now suppose we apply a sinusoidally varying potential to the EOM with frequency $Ω$ and small amplitude $β$ . This adds a time dependent phase to the above expression,

A e i ω t + i βsin(Ω t) .

Since $β$ is small, we can use the Taylor expansion for the exponential

$Ae^{i\omega t}\left( 1+i\beta\sin(\Omega t)\right) ,$

to which we apply a simple identity for sine,

$Ae^{i\omega t}\left( 1+\frac{\beta}{2}(e^{i\Omega t} - e^{-i\Omega t})\right) = A\left( e^{i\omega t}+\frac{\beta}{2}e^{i(\omega+\Omega) t}-\frac{\beta}{2}e^{i(\omega-\Omega) t}\right) .$

This expression we interpret to mean that we have the original carrier frequency plus two small sidebands, one at $ω + Ω$ and another at $ω - Ω$ . In Mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its Derivatives Notice however that we only used the first term in the Taylor expansion - in truth there are an infinite number of sidebands. There is a useful identity involving Bessel functions

$Ae^{i\omega t + i\beta\sin(\Omega t)} = Ae^{i\omega t}\left( J_0(\beta) + \sum_{k=1}^{\infty}J_k(\beta)e^{ik\Omega t} + \sum_{k=1}^{\infty}(-1)^k J_k(\beta)e^{-ik\Omega t}\right) ,$

which gives the amplitudes of all the sidebands. In Mathematics, Bessel functions, first defined by the Mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are Canonical Notice that if one modulates the amplitude instead of the phase, one gets only the first set of sidebands,

$\left( 1 + \beta\sin(\Omega t)\right) Ae^{i\omega t} = Ae^{i\omega t} + \frac{A\beta}{2i}\left( e^{i(\omega+\Omega) t} - e^{i(\omega-\Omega)t} \right) .$

References

Karna, Shashi and Yeates, Alan (ed. The Pockels effect, or Pockels electro-optic effect produces Birefringence in an optical medium induced by a constant or varying Electric field. An acousto-optic modulator (AOM also called a Bragg cell, uses the Acousto-optic effect to diffract and shift the frequency of light using Sound Phase modulation (PM is a form of Modulation that represents information as variations in the instantaneous phase of a Carrier wave. ) (1996). Nonlinear Optical Materials: Theory and Modeling. Washington, DC: American Chemical Society, 2-3. ISBN 0-8412-3401-9.

External links

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents