ABSTRACT
The close form of the Eq. (3.3) indicates that a ring resonator in this particular case is very similar to a Fabry-Pérot cavity, which has an input and output mirror with a field reflectivity, (1 – k) and a fully reflecting mirror. k is the coupling coefficient, x = exp(–aL/2) represents a roundtrip loss coefficient, f0 = kLn0 and z kLn ENL 2 in= 2 are the linear and nonlinear phase shifts, p l= 2k is the wave propagation number in a vacuum, where L and a are a waveguide length and linear absorption coefficient, respectively. In this chapter, the iterative method is introduced to obtain the results as shown in the Eq. (3.3) and similarly, when the output field is connected and input into the other ring resonators. After the signals are multiplexed with the generated chaotic noise, the chaotic cancellation is required by the individual user. To retrieve the signals from the chaotic noise, we propose to use the add/drop device with the appropriate parameters. This is given in the details that follow. The optical circuits of ring-resonator add/drop filters for the throughput and drop port can be given by Eqs (3.4) and (3.5), respectively [20]
( ) ( ) ( )
( ) ( ) ( )
1 2 1 1 cos 1
1 1 1 2 1 1 cos
e k L eE E
e e k L
k k k k
k k k k
- - - - + - =
+ - - - - - (3.4)
and
( ) ( ) ( )
1 2 1 21 1 1 2 1 1 cos
E e E
e e k L
k k
k k k k
+ - - - - - (3.5)
here Et and Ed represent the optical fields of the throughput and drop ports respectively. b = kneff is the propagation constant, neff is the effective
refractive index of the waveguide and the circumference of the ring is L = 2pR, here R is the radius of the ring. In the following, new parameters will be used for simplification: f = bL is the phase constant. The chaotic noise cancellation can be managed by using the specific parameters of the add/drop device so that the required signals can be retrieved by the specific users. k1 and k2 are coupling coefficient of add/drop filters, kn = 2p/l is the wave propagation number for a vacuum and the waveguide (ring resonator) loss is a = 0:5 dBmm-1. The fractional coupler intensity loss is g = 0:1. In the case of the add/drop device, the nonlinear refractive index is neglected.
