AI-based Metasurface Lens Design - Revision history

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Metasurface Optic

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	For conventional laws of reflection and refraction, the term on the right hand side of the equation is 0. The generalized Snell's law implies that we can control the refraction angle by designing the phase profile of the metalens.		For conventional laws of reflection and refraction, the term on the right hand side of the equation is 0. The generalized Snell's law implies that we can control the refraction angle by designing the phase profile of the metalens.

			[[File:Gsl.png\|thumb\|center\|350 px\|Figure 2: Generalized Snell's law. (Source: Yu 2011)]]

	=== Hyperbolic Phase Profile ===		=== Hyperbolic Phase Profile ===

JCheng: /* Metasurface Optic */

2025-03-20T04:43:53Z

Metasurface Optic

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	=== Metasurface Optic ===		=== Metasurface Optic ===

	e		The transfer function of conventional thin refractive lenses has both amplitude and phase modulation. When a plane wave propagates through a lens, the phase change induced by the lens material alters the wave vector, resulting in a change in the wave's propagation direction. In metalenses, phase modulation occurs through the optical response of nanostructures arranged on the metasurface. By inducing local, gradient phase shifts to incoming waves, metalenses enable precise control over light propagation, extending the traditional laws of reflection and refraction into what is known as the generalized Snell's law.

			The generalized Snell's law describes the altered paths of reflected and refracted waves due to the imposed phase gradient. In the equation below, <math> \theta_t </math>, <math> \theta_i </math> are the reflection/refraction and incident angle, respectively; <math> n_t </math>, <math> n_i </math> are the refractive index of the corresponding material; <math> \lambda </math> is the wavelength of the light; and <math> \Phi </math> is the phase profile of the metalens.

			<math display="block"> n_t \sin \theta_t - n_i \sin \theta_i = \frac{\lambda}{2\pi} \frac{\text{d}\Phi}{\text{d}x} </math>

			For conventional laws of reflection and refraction, the term on the right hand side of the equation is 0. The generalized Snell's law implies that we can control the refraction angle by designing the phase profile of the metalens.

	=== Hyperbolic Phase Profile ===		=== Hyperbolic Phase Profile ===

JCheng at 04:38, 20 March 2025

2025-03-20T04:38:25Z

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JCheng: /* Conclusions */

2024-12-13T19:12:27Z

Conclusions

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	== Conclusions ==		== Conclusions ==

			In this report, we introduce an AI-driven computational framework for the design of metalenses, aiming to address the limitations of traditional metasurface lenses, particularly their susceptibility to monochromatic aberrations. By parameterizing the metalens profile and employing customized loss functions within our optimization algorithm, we have achieved significant improvements in imaging performance across various incident angles.

			Our simulation results demonstrate that metalenses designed with this AI-based approach exhibit reduced coma aberration and enhanced Strehl ratios at oblique incident angles, thereby expanding the effective FOV. However, this optimization introduces a trade-off, slightly increasing in spherical aberration at normal incidence. This balance between different aberrations (coma and spherical) underscores the complexity inherent in metalens design.

			Furthermore, the modulation transfer function (MTF) analysis indicates that the optimized metalens maintains more consistent image contrast across a range of incident angles compared to lenses with a hyperbolic phase profile. This consistency is crucial for applications requiring uniform imaging quality over wide fields of view. Additionally, our space-varying 2D convolution simulations visually confirm the superior performance of the optimized metalens in reducing blurring effects at the periphery of the field.

			In conclusion, this framework offers a promising way for developing high-performance metalenses capable of wide-angle imaging with corrected aberrations. By effectively balancing various optical aberrations, this approach enhances the applicability of metalenses in compact, portable imaging systems. Future work will focus on exploring the extension of this methodology to address chromatic aberrations, thereby broadening the bandwidth of metalenses.

	== References ==		== References ==

JCheng: /* Image Simulations */

2024-12-13T19:02:28Z

Image Simulations

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	=== Image Simulations ===		=== Image Simulations ===

			To better illustrate the impact of PSF variations at different incident angles, we convolve the PSFs generated by the metalens with a target image of the letter ‘S.’ This approach visualizes how optical aberrations distort the image, providing an intuitive visual representation of the metalens’s imaging performance.

			When using the hyperbolic phase profile metalens, the resulting image appears severely blurred at larger incident angles. This degradation is attributed to pronounced coma aberrations, which cause the PSF to spread unevenly, reducing image sharpness and contrast. The letter ‘S’ becomes distorted and loses its defined edges. By contrast, the optimized phase profile significantly improves the clarity of the convolved image. The letter ‘S’ appears much sharper and more defined across a wider range of incident angles, reflecting the metalens’s improved aberration correction.

	[[File:S_sim.png\|thumb\|center\|600 px\|Figure 8: ]]		[[File:S_sim.png\|thumb\|center\|600 px\|Figure 8: Convolution of PSFs of the two metalenses at different incident angles with target image 'S'.]]

	The simulated images shown were generated using a space-varying 2D convolution algorithm, designed to model the imaging performance of the metalens across its entire field of view (FOV). In this approach, the FOV is partitioned into an <math> n </math>-by-<math> n </math> grid of isoplanatic patches, where the PSF is assumed to remain invariant within each patch. This approximation simplifies the computation while still capturing the varying optical response across the FOV. For each isoplanatic patch, we apply space-invariant 2D convolution using the corresponding PSF. To ensure smooth transitions between adjacent patches and reduce boundary artifacts, we merge the patches using a Gaussian window function, which applies a weighted blending of overlapping regions. This technique effectively simulates the metalens’s imaging performance, accounting for spatially varying aberrations.		The simulated images shown were generated using a space-varying 2D convolution algorithm, designed to model the imaging performance of the metalens across its entire field of view (FOV). In this approach, the FOV is partitioned into an <math> n </math>-by-<math> n </math> grid of isoplanatic patches, where the PSF is assumed to remain invariant within each patch. This approximation simplifies the computation while still capturing the varying optical response across the FOV. For each isoplanatic patch, we apply space-invariant 2D convolution using the corresponding PSF. To ensure smooth transitions between adjacent patches and reduce boundary artifacts, we merge the patches using a Gaussian window function, which applies a weighted blending of overlapping regions. This technique effectively simulates the metalens’s imaging performance, accounting for spatially varying aberrations.

JCheng: /* References */

2024-12-13T18:41:59Z

References

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	[1] Meinzer, N., Barnes, W. & Hooper, I. Plasmonic meta-atoms and metasurfaces. Nature Photon 8, 889–898 (2014). https://doi.org/10.1038/nphoton.2014.247		[1] Meinzer, N., Barnes, W. & Hooper, I. Plasmonic meta-atoms and metasurfaces. Nature Photon 8, 889–898 (2014). https://doi.org/10.1038/nphoton.2014.247

	[2] Mohammadreza Khorasaninejad et al. ,Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging.Science352,1190-1194(2016).DOI:10.1126/science.aaf6644		[2] Mohammadreza Khorasaninejad et al. ,Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging.Science352,1190-1194(2016).DOI:10.1126/science.aaf6644

	[3] Arbabi, A., Arbabi, E., Kamali, S. et al. Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations. Nat Commun 7, 13682 (2016). https://doi.org/10.1038/ncomms13682		[3] Arbabi, A., Arbabi, E., Kamali, S. et al. Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations. Nat Commun 7, 13682 (2016). https://doi.org/10.1038/ncomms13682

	[4] Guenther, R. D., Steel, D. G. & Bayvel, L. Encyclopedia of modern optics. Choice Reviews Online 43, 43–0036 (2005).		[4] Guenther, R. D., Steel, D. G. & Bayvel, L. Encyclopedia of modern optics. Choice Reviews Online 43, 43–0036 (2005).

JCheng at 18:41, 13 December 2024

2024-12-13T18:41:47Z

← Older revision		Revision as of 18:41, 13 December 2024
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	=== References ===		== References ==


			[1] Meinzer, N., Barnes, W. & Hooper, I. Plasmonic meta-atoms and metasurfaces. Nature Photon 8, 889–898 (2014). https://doi.org/10.1038/nphoton.2014.247
			[2] Mohammadreza Khorasaninejad et al. ,Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging.Science352,1190-1194(2016).DOI:10.1126/science.aaf6644
			[3] Arbabi, A., Arbabi, E., Kamali, S. et al. Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations. Nat Commun 7, 13682 (2016). https://doi.org/10.1038/ncomms13682
			[4] Guenther, R. D., Steel, D. G. & Bayvel, L. Encyclopedia of modern optics. Choice Reviews Online 43, 43–0036 (2005).

	== Appendix ==		== Appendix ==

	GitHub repository: https://github.com/jiazhou-cheng/ai-based_metalens		GitHub repository: https://github.com/jiazhou-cheng/ai-based_metalens

JCheng at 18:40, 13 December 2024

2024-12-13T18:40:53Z

← Older revision		Revision as of 18:40, 13 December 2024
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	== Conclusions ==		== Conclusions ==



			=== References ===



	== Appendix ==		== Appendix ==

	GitHub repository: https://github.com/jiazhou-cheng/ai-based_metalens		GitHub repository: https://github.com/jiazhou-cheng/ai-based_metalens