ABSTRACT
In operation, dark-bright soliton conversion that uses a ring resonator optical channel dropping filter (OCDF) is composed of two sets of coupled waveguides as shown in Fig. 11.1a, b, where for convenience, Fig. 11.1b is the equivalence diagram of Fig.11.1a. The relative phase of the two output light signals after coupling into the optical coupler and before coupling into the ring and the input bus is /2.This means that the signals that couple into the drop and through ports acquired a phase of p with respect to the input port signal. If coupling coefficients are engineered appropriately, then the fields coupled into the through port would completely extinguish the wavelength on resonance and all power would be coupled into the drop port. We will show how this is possible later in this section.ra 1 i 1 rdE j E E k (11.1) rb raexp 2 exp 4E j T L E w a (11.2)rc 2 rb 2 aE E j E k (11.3) rd rcexp 2 exp 4E j T L E w a (11.4)t 1 i 1 rdE E j E k (11.5)d 2 a 2 rbE E j E k (11.6) Here Eiis the input field, Ea the add (control) field, Et the through field, Edthe drop field, Era...Erd the fields in the ring at points a...d, k1 the field coupling coefficient between the input bus and ring, k2 the field coupling coefficient between the ring and output bus, L s the circumference of the ring, T the time taken for one roundtrip (roundtrip time), and a the power loss in the ring per unit length. We assume that this is lossless coupling, i.e., 21,2 1,21 k , and T = Ln
The output power/intensities at the drop and through ports are given by
22 1 2 1/2 1/2 2 1d i a1 2 1 21 1A AE E EA Ak k F F F F (11.7)
22 1 2 1/2 1/22 1t i a1 2 1 21 1 AAE E EA Ak k F F F F (11.8) Here A 1/2
2 , F
In
Add
Th
Drop
Add/Drop Filter
(a)
Rad Era Erb
Erd Erc
Ea Ed
EtEik1,t1
k2,t2 (b)
a
bc
d
(a) (b)
(c) Figure 11.1 A schematic diagram of a simultaneous optical logic XOR and XNOR gate. The input and control fields at the input and add ports are formed by the dark-bright optical soliton, expressed by Eqs. 11.9 and 11.10.
