Inversion of Complex Refractive Index of Gold Nanospheres based on Contour Intersection Method

Long Cheng; Paerhatijiang Tuersun; Dengpan Ma; Yuxia Zheng; Remilai Abulaiti

doi:10.3788/LOP222615

Laser & Optoelectronics Progress, Volume. 60, Issue 21, 2116003(2023)

Inversion of Complex Refractive Index of Gold Nanospheres based on Contour Intersection Method

Long Cheng^1,2, Paerhatijiang Tuersun^1,2、*, Dengpan Ma^1,2, Yuxia Zheng^1,2, and Remilai Abulaiti^1,2

Author Affiliations

¹School of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830054, Xinjiang , China

²Key Laboratory of Mineral Luminescent Material and Microstructure of Xinjiang, Urumqi 830054, Xinjiang , China

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Figures & Tables(12)

Fig. 1. Flowchart of the inversion phases of the contour intersection method

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$Complex refractive index of Au nanoparticles with a diameter of 50 nm at a wavelength of 632.8 nm. (a) Scattering efficiency; (b) absorption efficiency; (c) scattering efficiency and absorption efficiency isometric projection on the n-k plane are inverted by the contour intersection method$

Fig. 2. Complex refractive index of Au nanoparticles with a diameter of 50 nm at a wavelength of 632.8 nm. (a) Scattering efficiency; (b) absorption efficiency; (c) scattering efficiency and absorption efficiency isometric projection on the n-k plane are inverted by the contour intersection method

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Fig. 3. Complex refractive index of Au nanoparticles with a diameter of 50 nm at a wavelength of 632.8 nm. (a) Scattering efficiency; (b) absorption efficiency; (c) scattering efficiency and absorption efficiency isometric projection on the n-k plane are inverted by the contour intersection method

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$Complex refractive index of Au nanoparticles with a diameter of 50 nm at 632.8 nm. (a) Backscattering efficiency; (b) projection of contour lines in the n-k plane$

Fig. 4. Complex refractive index of Au nanoparticles with a diameter of 50 nm at 632.8 nm. (a) Backscattering efficiency; (b) projection of contour lines in the n-k plane

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$Effect of the step length on the real (n) and imaginary (k) of the refractive index of inversion. (a) Inversion result of the real part of the refractive index; (b) relative error of the real part of the refractive index inversion result; (c) inversion result of the imaginary part of the refractive index; (d) relative error of the inversion result of the imaginary part of the refractive index$

Fig. 5. Effect of the step length on the real (n) and imaginary (k) of the refractive index of inversion. (a) Inversion result of the real part of the refractive index; (b) relative error of the real part of the refractive index inversion result; (c) inversion result of the imaginary part of the refractive index; (d) relative error of the inversion result of the imaginary part of the refractive index

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$Average relative error of the results of the contour intersection method and the iterative method changes with the refractive index range value step. (a) Average relative error of the real inversion result of the refractive index; (b) average relative error of the imaginary inversion result of the refractive index$

Fig. 6. Average relative error of the results of the contour intersection method and the iterative method changes with the refractive index range value step. (a) Average relative error of the real inversion result of the refractive index; (b) average relative error of the imaginary inversion result of the refractive index

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$Effect of size on the real (n) and imaginary (k) of the refractive index when inverted by the contour intersection method. (a) Inversion result of the real part of the refractive index; (b) the relative error of the real part of the refractive index inversion result; (c) inversion result of the imaginary part of the refractive index; (d) relative error of the inversion result of the imaginary part of the refractive index$

Fig. 7. Effect of size on the real (n) and imaginary (k) of the refractive index when inverted by the contour intersection method. (a) Inversion result of the real part of the refractive index; (b) the relative error of the real part of the refractive index inversion result; (c) inversion result of the imaginary part of the refractive index; (d) relative error of the inversion result of the imaginary part of the refractive index

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$Average relative error of the results of the contour intersection method and the iterative method as a function of particle size. (a) Average relative error of the real inversion result of the refractive index; (b) average relative error of the imaginary inversion result of the refractive index$

Fig. 8. Average relative error of the results of the contour intersection method and the iterative method as a function of particle size. (a) Average relative error of the real inversion result of the refractive index; (b) average relative error of the imaginary inversion result of the refractive index

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$Effect of measurement error on the refractive index of inversion during conformal intersection method inversion. (a) Inversion result of the real part of the refractive index; (b) relative error of the inversion result of the real part of the refractive index; (c) inversion result of the imaginary part of the refractive index; (d) relative error of the inversion result of the imaginary part of the refractive index$

Fig. 9. Effect of measurement error on the refractive index of inversion during conformal intersection method inversion. (a) Inversion result of the real part of the refractive index; (b) relative error of the inversion result of the real part of the refractive index; (c) inversion result of the imaginary part of the refractive index; (d) relative error of the inversion result of the imaginary part of the refractive index

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$Average relative error of the results of the contour intersection method and the iterative method as a result of the measurement error. (a) Average relative error of real inversion result of the refractive index; (b) average relative error of the imaginary inversion result of the refractive index$

Fig. 10. Average relative error of the results of the contour intersection method and the iterative method as a result of the measurement error. (a) Average relative error of real inversion result of the refractive index; (b) average relative error of the imaginary inversion result of the refractive index

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Table 1. Inversion of the contour intersection method and the iterative method
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Table 1. Inversion of the contour intersection method and the iterative method
Method n_o k_o n_i k_i E_n /% E_k /%
Contour intersection method 0.21667 3.52451 0.22 3.53 0.15 0.16

Table 2. Contour intersection method the time taken, memory occupation and CPU ratio
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Table 2. Contour intersection method the time taken, memory occupation and CPU ratio
Step size Calculate quantity Time /s Used internal memory /GB CPU usage /%
0.001 1750 16395.53 0.5069 11.60
0.01 350 123.60 0.3343 11.54

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Long Cheng, Paerhatijiang Tuersun, Dengpan Ma, Yuxia Zheng, Remilai Abulaiti. Inversion of Complex Refractive Index of Gold Nanospheres based on Contour Intersection Method[J]. Laser & Optoelectronics Progress, 2023, 60(21): 2116003

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