Chapter 4 Optical Properties of PCFs
4.5 Additional Simulation
For the first time, we also study the dispersion property of square-lattice PCF with elliptical air holes, which is shown in Fig. 34. The elliptical air
holes of this struc ar air holes with
different stress factor s, which is defined as
ture are formed by stressing the circul
d
Another parameter, the air filling ratio a, which stands for the size of the air holes is given as
Fig. 35 shows the dispersion curve for different s with fixed pitch 2.32 mµ . In this case, the dispersion slope is positive. Fig.36 shows the dispersion curves with the itch fixp ed to 1 mµ , and the dispersion slope turns to be negative, thu n utilize the ne ispersion slop ion
com o 6 hat
the of o fa wo
properties are consistent with the case in the square-lattice HF with circular makes difference for this elliptical s assisted structure is the vertical dispersion offset. If the air filling with smaller s moves to higher region.
ith the stress factor s, designers can have more degrees of freedom to l the dispersion curves in a specific region.
s we ca gative d e in the dispers
pensation design. Besides, fr m Fig. 35 and Fig. 3 one can find t value dispersion is larger f r a large air filling ctor a. These t air holes [A. H. Bouk et al., 2004]. What
air hole
ratio a is fixed, the dispersion curve W
d
d′x
Fig. 34 The square-lattice HF with elliptical air holes.
d′y
Λ
1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 65
70 75 80 85 90 95
Dispersion
Ps nm- 1 km- 1
um
a=0.7,s=0.8 a=0.7,s=0.9 a=0.6,s=0.8 a=0.6,s=0.9 pitch 2.32 um
Fig. 35 Positive GVD (anomalous dispersion) with pitch = 2.32 um.
1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 -260
-240 -220 -200 -180 -160 -140 -120 -100 -80 -60
um Ps nm-1 km-1
Dispersion
a=0.7,s=0.8 a=0.7,s=0.9 a=0.6,s=0.8 a=0.6,s=0.9
pitch 1 um
Fig. 36 Negative GVD (normal dispersion) with pitch = 1um.
Conclusion and Future Work
In this work, a simulation tool for studying the modal properties of optical wave-guides with arbitrary cross-sections has been developed based on the finite element method using CT/LN edge element. In the previous sections, we discuss the optical properties of HFs and demonstrate some simulation results. Finally, for the first time, we discuss the dispersion characteristics of square-lattice HFs with elliptical air holes. It is shown that besides the air filling ratio a, the designer can have one more degree of freedom to control the dispersion curve in a specific region by tuning the stress factor s.
For the following days to come, we will continue to work on modifying the code with the use of higher order elements to get fast-converged solutions with fewer unknowns. Moreover, if the optical properties of the wave-guides with longitudinal-variant cross-sections are desired, then the method in this study is not applicable anymore. For this reason, we still need method (BPM) to obtain a complete analysis.
Recently, the combination of the finite element and the genetic algorithm (GA) has been demonstrated for obtaining the optimization design of the PCF dispersion property [Emmanuel Kerrinckx, 2004]. We believe that a lot of research efforts still needed in this field. Actually an evolutionary programming algorithm has been developed for the design of fiber gratings in our group. So how to combine the FEM with the optimization algorithm efficiently will be an interesting issue for us to investigate in the future.
to combine the use of the finite element method with the beam propagation
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