Limits...
Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm.

Bossard JA, Lin L, Werner DH - J R Soc Interface (2016)

Bottom Line: Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too 'perfect' to appear natural.Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and 'chaotic' superlattices, such as the ones found in silvery fish.We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, The Pennsylvania State University, 211A Electrical Engineering East, University Park, PA 16802, USA jab678@psu.edu.

No MeSH data available.


Related in: MedlinePlus

Random fractal Cantor bar superlattice with theoretical materials optimized by a GA to have broadband reflectivity in the mid-IR from 3 to 5 µm. (a) Random fractal Cantor bar growth indicating the generator placement and superlattice structure. (b) Simulated normal incidence reflection and transmission magnitudes in the mid-IR. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4759801&req=5

RSIF20150975F5: Random fractal Cantor bar superlattice with theoretical materials optimized by a GA to have broadband reflectivity in the mid-IR from 3 to 5 µm. (a) Random fractal Cantor bar growth indicating the generator placement and superlattice structure. (b) Simulated normal incidence reflection and transmission magnitudes in the mid-IR. (Online version in colour.)

Mentions: In the first example, a superlattice composed of two theoretical materials is synthesized to have a broad mirror band in the mid-IR over the range from 3 to 5 µm. Forty-one stop frequencies were distributed uniformly over this range, so that the GA would optimize for high reflection. The GA optimized two single-gap generators and their assignments within a four-stage multi-generator Cantor bar fractal. The GA also optimized the permittivity of two theoretical materials, with the first material having a permittivity in the range from 1 to 4 and the second in the range from 5 to 11. The total superlattice thickness could range from 20 to 80 µm. The gap sizes for both generators were permitted to vary between 0.05 and 0.5. The GA optimized a population of 32 members over 1000 generations, converging on the random fractal superlattice shown in figure 5. Although the cost typically stopped improving around 500 generations, the GA was allowed to continue for 1000 generations to ensure that it had converged. The total thickness for the optimized superlattice is 38.4 µm, and the generator gap sizes are g0 = 0.148 and g1 = 0.369. The generator assignment is indicated in figure 5a. The optimized permittivities for the theoretical materials are ɛr1 = 1.01 and ɛr2 = 11.0, indicating that better superlattice performance was achieved by a large difference in material permittivities. The simulated reflection and transmission shown in figure 5b reveal that the optimized superlattice has very high reflectivity over the entire 3–5 µm range with no transmission peaks above −10 dB.Figure 5.


Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm.

Bossard JA, Lin L, Werner DH - J R Soc Interface (2016)

Random fractal Cantor bar superlattice with theoretical materials optimized by a GA to have broadband reflectivity in the mid-IR from 3 to 5 µm. (a) Random fractal Cantor bar growth indicating the generator placement and superlattice structure. (b) Simulated normal incidence reflection and transmission magnitudes in the mid-IR. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759801&req=5

RSIF20150975F5: Random fractal Cantor bar superlattice with theoretical materials optimized by a GA to have broadband reflectivity in the mid-IR from 3 to 5 µm. (a) Random fractal Cantor bar growth indicating the generator placement and superlattice structure. (b) Simulated normal incidence reflection and transmission magnitudes in the mid-IR. (Online version in colour.)
Mentions: In the first example, a superlattice composed of two theoretical materials is synthesized to have a broad mirror band in the mid-IR over the range from 3 to 5 µm. Forty-one stop frequencies were distributed uniformly over this range, so that the GA would optimize for high reflection. The GA optimized two single-gap generators and their assignments within a four-stage multi-generator Cantor bar fractal. The GA also optimized the permittivity of two theoretical materials, with the first material having a permittivity in the range from 1 to 4 and the second in the range from 5 to 11. The total superlattice thickness could range from 20 to 80 µm. The gap sizes for both generators were permitted to vary between 0.05 and 0.5. The GA optimized a population of 32 members over 1000 generations, converging on the random fractal superlattice shown in figure 5. Although the cost typically stopped improving around 500 generations, the GA was allowed to continue for 1000 generations to ensure that it had converged. The total thickness for the optimized superlattice is 38.4 µm, and the generator gap sizes are g0 = 0.148 and g1 = 0.369. The generator assignment is indicated in figure 5a. The optimized permittivities for the theoretical materials are ɛr1 = 1.01 and ɛr2 = 11.0, indicating that better superlattice performance was achieved by a large difference in material permittivities. The simulated reflection and transmission shown in figure 5b reveal that the optimized superlattice has very high reflectivity over the entire 3–5 µm range with no transmission peaks above −10 dB.Figure 5.

Bottom Line: Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too 'perfect' to appear natural.Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and 'chaotic' superlattices, such as the ones found in silvery fish.We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, The Pennsylvania State University, 211A Electrical Engineering East, University Park, PA 16802, USA jab678@psu.edu.

No MeSH data available.


Related in: MedlinePlus