Page 220 - Introduction to Information Optics

4.2. All-Optical Switches 205

medium is given by

2n 2n 2n
A0 = — nl = ~ n 0L + —r n 2IL, (4.6)
x / /

where A is the wavelength and L is the length of the medium over which the
phase shift is accumulated. The phase shift due to nonlinear effect can be
significant when L is large, even though n 2 is small. Therefore, it is a logical
choice that all-optical switches are based on nonlinear phase shift.
For high-speed switching applications, nonlinear media are required to have
a high nonlinear coefficient, high transparency at the operation wavelength,
and fast response time. A general rule for selecting nonlinear media is that a
change of n in phase can be achieved at a practical optical power level [5].
Since materials with a high nonlinear coefficient normally have high loss, it
appears that most passive nonlinear materials are not suitable for high-speed
switching applications. The best nonlinear medium is active semiconductor
amplifiers, to be discussed in Sec. 4.2.4.3.
Refractive index can also be controlled by electro-optical effects, where the
refractive index of the medium depends on an externally applied electric field.
Electro-optical switches based on this effect will be discussed in Sec. 4.3.

4.2.2. ETALON SWITCHING DEVICES

A nonlinear optical medium in a Fabry-Perot etalon perhaps is the first
optical switching device [6], The scheme creates a system that can reduce the
length required to produce a nonlinear phase shift, since the intracavity
intensity can be much higher than the input intensity. When used for self-
switching, the system has feedback, and exhibits optical bistability which has
two possible stable output states for given input power. Optical bistability has
many applications in optical signal routing, image processing, and set reset
operations.
This switching scheme is shown in Fig. 4.3. It consists of two mirrors with
reflectivities R 1 and R 2, respectively, separated by a distance D. The medium
in the etalon is assumed to be lossless, and have a refractive index n.
Let us consider the case of linear medium (n 2 — 0) and normal light
incidence from the left-hand side. The transmittance of the etalon is given by [7]

2
T = / out // in = A/(l + F sin <5), (4.7)
2
1 2
2
where A = (I - R^l - R 2)/(l - R) , F = 4R/(1 - R) , R = (K 1 ^ 2 ) , $ =
(2n/A)(n 0 + n 2I)D is the phase delay between the mirrors.