Photonic Inverse Design of Simple Particles with Realistic Losses in the Visible Frequency Range †
<p>(<b>a</b>) Schematic diagram of the forward and inverse design of an electromagnetic system (reproduced with permission from [<a href="#B7-photonics-06-00023" class="html-bibr">7</a>]); (<b>b</b>) illustrative description of the optimization process sweeping the model parameters.</p> "> Figure 2
<p>(<b>a</b>) Approximate loci of the complex permittivities of basic metals and chemical compounds for various frequencies of visible light (reproduced with permission from [<a href="#B7-photonics-06-00023" class="html-bibr">7</a>]); (<b>b</b>) exact dispersion of the real part of permittivities across the visible spectrum of the used materials; (<b>c</b>) physical configuration of the considered radiation-enhancing particles.</p> "> Figure 3
<p>(<b>a</b>,<b>b</b>) Maximum relative radiation as function of operational wavelength <math display="inline"><semantics> <mi>λ</mi> </semantics></math> with use of covers made of several materials for: (<b>a</b>) TM excitation and (<b>b</b>) TE excitation; (<b>c</b>,<b>d</b>) trajectories of optimal designs on the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>,</mo> <mi>b</mi> <mo>/</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics></math> plane as the wavelength <math display="inline"><semantics> <mi>λ</mi> </semantics></math> changes for: (<b>c</b>) TM excitation of the systems of (<b>a</b>) and (<b>c</b>) TE excitation of the systems of (<b>b</b>).</p> "> Figure 4
<p>Spatial distribution of the normalized electric field <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for: free space (left), optimal Ag cladding (center), and arbitrary, but close to optimal Ag cladding (right). The optimal design corresponds to the point of <a href="#photonics-06-00023-f003" class="html-fig">Figure 3</a>a’s curve at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>693</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math>. Design parameters: <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.82</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>/</mo> <mi>λ</mi> <mo>=</mo> <mn>0.42</mn> </mrow> </semantics></math>.</p> "> Figure 5
<p>Spatial distribution of the normalized magnetic field <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for: free space (<b>left</b>), optimal GaP cladding (<b>center</b>), and arbitrary, but close to optimal GaP cladding (<b>right</b>). The optimal design corresponds to the point of <a href="#photonics-06-00023-f003" class="html-fig">Figure 3</a>b’s curve at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>460</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math>. Design parameters: <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>/</mo> <mi>λ</mi> <mo>=</mo> <mn>0.10</mn> </mrow> </semantics></math>.</p> "> Figure 6
<p>Linear plots of the normalized signal (field squared in arbitrary units) as a function of electrical radial distance <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>/</mo> <mi>λ</mi> </mrow> </semantics></math> for: (<b>a</b>) the optimal dimensions of the TM Ag-based design (of <a href="#photonics-06-00023-f004" class="html-fig">Figure 4</a>) when the shell is empty (vacuum), silver (optimal), and a material with <math display="inline"><semantics> <mi>ε</mi> </semantics></math> of the opposite real part than that of silver; (<b>b</b>) the optimal dimensions of the TE GaP-based design (of <a href="#photonics-06-00023-f005" class="html-fig">Figure 5</a>) when the shell is empty (vacuum), GaP (optimal), and material with <math display="inline"><semantics> <mi>ε</mi> </semantics></math> of the opposite real part than that of gallium phosphide. Vertical dashed lines denote the boundaries of the radiation-enhancing shell.</p> "> Figure 7
<p>Relative radiative power <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>d</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> variation with respect to changes in aspect ratio <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> </mrow> </semantics></math> and electrical size <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>/</mo> <mi>λ</mi> </mrow> </semantics></math> around the optimal designs (marked by ×) of: (<b>a</b>) TM waves of the Ag cladding of <a href="#photonics-06-00023-f004" class="html-fig">Figure 4</a> at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>693</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math> and (<b>b</b>) TE waves of the GaP cladding of <a href="#photonics-06-00023-f005" class="html-fig">Figure 5</a> at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>460</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math>.</p> "> Figure 8
<p>(<b>a</b>,<b>c</b>) Radiation efficiency <math display="inline"><semantics> <msub> <mi>e</mi> <mi>R</mi> </msub> </semantics></math> in dB and (<b>b</b>,<b>d</b>) relative radiation power <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>d</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> in dB as a function of the aspect ratio <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> </mrow> </semantics></math> and electrical size <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>/</mo> <mi>λ</mi> </mrow> </semantics></math> for: (<b>a</b>,<b>b</b>) TM waves of Ag cladding and (<b>c</b>,<b>d</b>) TE waves of GaP cladding.</p> "> Figure 9
<p>Frequency response for both excitations (TE and TM waves) of: (<b>a</b>) the Ag cladding of <a href="#photonics-06-00023-f004" class="html-fig">Figure 4</a>, TM-optimized at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>693</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math>, and (<b>b</b>) the GaP cladding of <a href="#photonics-06-00023-f005" class="html-fig">Figure 5</a>, TE-optimized at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>460</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math>.</p> ">
Abstract
:1. Introduction
2. General Description of the Proposed Inverse Design Concept
3. Concept Demonstration through a Simplistic Particular Example
4. Concluding Remarks
Funding
Conflicts of Interest
References
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Ag | Al | Au | AlSb | a-Si | GaP | InAs | |
---|---|---|---|---|---|---|---|
TM | 95 @ 693 nm | 8 @ 400 nm | 40 @ 699 nm | 13 @ 620 nm | 4.7 @ 568 nm | 14 @ 460 nm | 3.8 @ 590 nm |
a/b = 0.82 | a/b = 0.87 | a/b = 0.83 | a/b = 0.86 | a/b = 0.87 | a/b = 0.85 | a/b = 0.87 | |
b/λ = 0.42 | b/λ = 0.39 | b/λ = 0.42 | b/λ = 0.44 | b/λ = 0.44 | b/λ = 0.45 | b/λ = 0.45 | |
TE | 96 @ 671 nm | 7.9 @ 414 nm | 39 @ 693 nm | 64 @ 620 nm | 11 @ 568 nm | 76 @ 460 nm | 8.7 @ 590 nm |
a/b = 0.89 | a/b = 0.93 | a/b = 0.89 | a/b = 0.01 | a/b = 0.01 | a/b = 0.01 | a/b = 0.01 | |
b/λ = 0.65 | b/λ = 0.62 | b/λ = 0.64 | b/λ = 0.09 | b/λ = 0.08 | b/λ = 0.10 | b/λ = 0.84 |
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Valagiannopoulos, C. Photonic Inverse Design of Simple Particles with Realistic Losses in the Visible Frequency Range. Photonics 2019, 6, 23. https://doi.org/10.3390/photonics6010023
Valagiannopoulos C. Photonic Inverse Design of Simple Particles with Realistic Losses in the Visible Frequency Range. Photonics. 2019; 6(1):23. https://doi.org/10.3390/photonics6010023
Chicago/Turabian StyleValagiannopoulos, Constantinos. 2019. "Photonic Inverse Design of Simple Particles with Realistic Losses in the Visible Frequency Range" Photonics 6, no. 1: 23. https://doi.org/10.3390/photonics6010023