Page 228 - Introduction to Information Optics

42. All-Optical Switches 21 3

a fraction of a wavelength, it is difficult to use two physically separate fibers to
implement a long interferometer. The best choice, therefore, is a nonlinear
Sagnac interferometer or a nonlinear optical loop mirror (NOLM) where the
two counterpropagating directions serve as the arm of the interferometer (Fig.
4.10). The configuration is very stable since both arms have exactly the same
optical path length. The phase difference in the two counterpropagating beams
comes from the nonlinear effect of the medium. For clockwise field 1, the phase
2 2
shift after the loop is \E l\ n 2L, and for the counterclockwise field it is \E 2\ n 2L.
Therefore, if E l is different from £ 2; i.e., the coupling ratio of the 2 x 2
input/output coupler is not •£, there will be phase difference in these two
counterpropagating beams.
The operation of NOLM can be described as follows. Assume that the 2x 2
coupler has a power coupling ratio q:(l — q). Then the fields E l, £ 2, £ 3, and
E 4 in Fig. 4.10 are coupled through the equations [10]:

1
E 3 = vtfE, + ../V -qE 2

Consider the case of a single input at port 1, Ej = £ in and E 2 = 0. We have

(4.2,

Loop L

Data output Data output
(portl) (port 2)
Fig. 4.10. A nonlinear optical loop mirror.