The One-dimensional photonic crystal finds
applications in high-accomplishment fiber optics communication systems, chemical and biological imaging, eye protection glasses, as
well as anti-reflecting coating for solar cells and security screening 1. During the last decade the researchers in the field of fiber optics have been
attracted by the design of photonic filter. The literature about one-dimensional
photonic crystal selective filters exposes a wide range of synthesis methods.
The (1-D PhC) synthesis problem can be defined as
that of finding the layer thicknesses to produce the required spectral response
Several methods have been exposed for the design of PhC, including,
among others, the simulated annealing 3, the minimax optimization
approach 4, direct tabu search algorithm 5, hybrid of Tabu Search (TS) and Nelder-Mead (NM) Simplex algorithm
6, layer peeling technique 7, quadratic response surface methodology 8, and a
statistical design centering approach 9.
In this work, we show the application of
three computational methods, genetic algorithm, improved particle swarm
optimization and the hybrid genetical swarm optimizer to the synthesis of one-dimensional
photonic crystal selective filters by acting on the Bragg grating layer thicknesses.
This paper is organized, besides the
introduction, in four
sections. Section 2 describes the governing equations
of the propagated electromagnetic wave, the general structure of 1-D PhC
filters as well as the formulation of the design problem. Brief
Overviews of the applied well-known algorithms are described in section 3. Section 4 is devoted to
review the obtained results and the comparative study. Finally,
conclusions are drawn in section 5.
To evaluate the efficiency and
effectiveness of the proposed algorithms in this paper, the 1-D PhCs selective
filters are used to demonstrate the application of the suggested formulation.
The problem formulation has been implemented in Matlab 7 programming software. Our
designed photonic filters are required to present a maximum of transmission
related to wavelength values located at pass band regions of 1.1 mm, 1.2 mm, 1.3 mm, 1.4 mm, 1.55 mm, 1.65 mm, 1.75 mm and 1.85 mm, and to reject the signals within the stop band
The presented approaches show their abilities to get
the optimal design of one-dimensional photonic crystal filter and optimal layer
thicknesses of the given filter with a maximum of transmission in the range
1.05mm -1.15mm. The obtained values of the optimization method’s
errors are as follows: 0.0239, 0.0275 and 0.0333 for the GSO, IPSO and GA
respectively. According to the results of the simulations carried out depicted
in figures 1, 2, 3 respectively, GSO has lowerest error value than IPSO and
also GA. Comparing GSO with IPSO and GA, the filters designed by the GSO
approach were found to be more effective, the GSO exposes higher convergence
rate than the IPSO and GA methods. IPSO was found to produce better convergence
speed than the GA.
Now, we want to design a photonic crystal which
presents a pick of power transmission spectra at 1.2mm using GA approach, IPSO procedure and GSO
methodology, the desired and synthesized responses are depicted in figure 4, 5
All the applied methods were performed well in terms
of effectiveness. However, GSO appears to achieve the minimum error value as
compared to IPSO and GA. This is due to the maintain of diversity of solutions.
The filters optimized by GSO performed better than the
IPSO and GA, however noting that for IPSO and GA, the results of both
optimization algorithms were quite similar.
The obtained results leading to the conclusion that
GSO converged faster than IPSO and GA, IPSO is more quickly than GA.
In This studied case we compare the effectiveness of the three
methodologies for the optimal design of
1-D PhCs selective filters with maximum transmission value obtained at
the wavelength 1.3 mm.
Figures 7, 8 and 9 show how effectively
each algorithm achieved the objective function. The results in reveal that the
GSO provides an excellent design in terms of lowering undesired picks of
transmission levels while maintaining strong transmission in desired
wavelengths compared to GA and IPSO.
Table 2 shows that, GSO converged once again faster
than the other two approaches. However, IPSO led to lower iteration value than
Comparing GSO with IPSO and GA, the synthesis 1-D PhCs
selective filters with the maximum transmission at the wavelength value equal
to1.4 mm by the GSO method were found to be more
efficient, with the GSO exhibiting much better performance and a higher convergence rate than
IPSO and GA. This can be attributed to GSO’s ability to avoid premature
convergence and thus produces higher quality solutions, and IPSO is found to
provide better results than the GA in terms of error reduction and in terms of
how fast the algorithm obtained the optimum solution.
For the chosen wavelength ? equal to 1.55 mm, it can be deduced from Figures 8, 9 and
10 that the GSO algorithm was the one to provide the lowest error ( ), with
IPSO coming a close second. GA produced error an
order of magnitude greater than IPSO, so GA produced the worst results.
According to table 2 GSO is proven to be the fastest among all these
algorithms followed by the IPSO and GA.
For the case ? equal to 1.65 mm, GSO produced the lowest error value
(0.0316). GA was once again the worst approach with an error equal to (0.0505),
IPSO that actually produced the second lowest error value (0.0448). The synthesized function by each algorithm can be seen
in Figures 11, 12 and 13.
In terms of efficiency, GSO and IPSO performance are higher compared to
GA. GSO indicates to be the fastest method that converges to the minimum error
value, followed by IPSO and then GA.
The best performing algorithm for the
synthesis another filter which must resonate at wavelengths of 1.75 mm, GSO, produced the lowest error value (0.0544).
The IPSO algorithm performed quite similar
than GA (0.0639) with an error value equal (0.0606)
GSO appears to achieve the minimum error value rapidly
as compared to IPSO and GA, It was found that IPSO converged faster than GA.