Abstract
The electro-magnetic (EM) waves transmitted through a thin object with fine structures are observed by a microsphere located above the thin object. The EM radiation transmitted through the object produces both evanescent waves, which include information on the fine structures of the object (smaller than a wavelength), and propagating waves, which include the large image of the object (with dimensions larger than a wavelength). The super-resolutions are calculated by using the Helmholtz equation. According to this equation, evanescent waves have an imaginary component of the wavevector in the z direction, leading the components of the wavevector in the transversal directions to become very large so that the fine structures of the object can be observed. Due to the decay of the evanescent waves, only a small region near the contact point between the thin object and the microsphere is effective for producing the super resolution effects. The image with super-resolution can be increased by a movement of the microsphere over the object or by using arrays of microspheres. Both propagating and evanescent waves arrive at the inner surface of the microsphere. A coupling between the transmitted EM waves and resonances produced in the dielectric sphere, possibly obtained by the Mie method, leads to a product of the EM distribution function with the transfer function. While this transfer function might be calculated by the Mie method, it is also possible to use it as an experimental function. By Fourier transform of the above product, we get convolution between the EM spatial modes and those of the transfer function arriving at the nano-jet, which leads the evanescent waves to become propagating waves with effective very small wavelengths and thus increase the resolution.
Keywords
microsphere; super-resolution; evanescent waves; nano-jet; transfer function; Mie method
References
Lipson A, Lipson SG, Lipson H. Optical Physics. Cambridge University Press; 2010. doi: 10.1017/cbo9780511763120
Zhang T, Yu H, Li P, et al. Microsphere-Based Super-Resolution Imaging for Visualized Nanomanipulation. ACS Applied Materials & Interfaces. 2020; 12(42): 48093-48100. doi: 10.1021/acsami.0c12126
Xie Y, Cai D, Pan J, et al. Chalcogenide Microsphere‐Assisted Optical Super‐Resolution Imaging. Advanced Optical Materials. 2022; 10(6). doi: 10.1002/adom.202102269
Li Y, Qiu C, Ji H, et al. Microsphere‐Aided Super‐Resolution Scanning Spectral and Photocurrent Microscopy for Optoelectronic Devices. Advanced Optical Materials. 2023; 11(16). doi: 10.1002/adom.202300172
Wu G, Hong M. Optical Microsphere Nano-Imaging: Progress and Challenges. Engineering. 2024; 36: 102-123. doi: 10.1016/j.eng.2023.10.019
Zhou J, Lian Z, Zhou C, et al. Scanning microsphere array optical microscope for efficient and large area super-resolution imaging. Journal of Optics. 2020; 22(10): 105602. doi: 10.1088/2040-8986/abb17b
Upreti N, Jin G, Rich J, et al. Advances in Microsphere-based Super-resolution Imaging. IEEE Reviews in Biomedical Engineering. 2024; 1-16. doi: 10.1109/rbme.2024.3355875
Liu C, Ye A. Microsphere assisted optical super-resolution imaging with narrowband illumination. Optics Communications. 2021; 485: 126658. doi: 10.1016/j.optcom.2020.126658
Shang Q, Tang F, Yu L, et al. Super-Resolution Imaging with Patchy Microspheres. Photonics. 2021; 8(11): 513. doi: 10.3390/photonics8110513
Jiang W, Wang J, Yang Y, et al. A Review of Microsphere Super-Resolution Imaging Techniques. Sensors. 2024; 24(8): 2511. doi: 10.3390/s24082511
Geints YE, E.K. Panina. Surface roughness influence on photonic nanojet parameters of dielectric microspheres. Computer Optics. 2023; 47(4): 559-566. doi: 10.18287/2412-6179-co-1280
Gasparic V, Mayerhofer TG, Zopf D, et al. To generate a photonic nanojet outside a high refractive index microsphere illuminated by a Gaussian beam. Optics Letters. 2022; 47(10): 2534. doi: 10.1364/ol.459001
Gasparic V, Ristic D, Mayerhofer TG, et al. Photonic nanojet of a Gaussian beam illuminated low refractive index microsphere in air: A comprehensive variation of parameters. Journal of Quantitative Spectroscopy and Radiative Transfer. 2022; 282: 108121. doi: 10.1016/j.jqsrt.2022.108121
Darafsheh A. Photonic nanojets and their applications. Journal of Physics: Photonics. 2021; 3(2): 022001. doi: 10.1088/2515-7647/abdb05
Mandal A, Tiwari P, Upputuri PK, et al. Characteristic parameters of photonic nanojets of single dielectric microspheres illuminated by focused broadband radiation. Scientific Reports. 2022; 12(1). doi: 10.1038/s41598-021-03610-3
Kwon S, Park J, Kim K, et al. Microsphere-assisted, nanospot, non-destructive metrology for semiconductor devices. Light: Science & Applications. 2022; 11(1). doi: 10.1038/s41377-022-00720-z
Goodman JW. Introduction to Fourier Optics. Roberts and Company Publishers; 2017.
Lee S, Li L, Wang Z. Optical resonances in microsphere photonic nanojets. Journal of Optics. 2013; 16(1): 015704. doi: 10.1088/2040-8978/16/1/015704
Lecler S, Perrin S, Leong-Hoi A, et al. Photonic jet lens. Scientific Reports. 2019; 9(1). doi: 10.1038/s41598-019-41193-2
Lee S, Li L, Ben-Aryeh Y, et al. Overcoming the diffraction limit induced by microsphere optical nanoscopy. Journal of Optics. 2013; 15(12): 125710. doi: 10.1088/2040-8978/15/12/125710
Wang Z, Guo W, Li L, et al. Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope. Nature Communications. 2011; 2(1). doi: 10.1038/ncomms1211
Darafsheh A, Walsh GF, Dal Negro L, et al. Optical super-resolution by high-index liquid-immersed microspheres. Applied Physics Letters. 2012; 101(14). doi: 10.1063/1.4757600
Lai HSS, Wang F, Li Y, et al. Super-Resolution Real Imaging in Microsphere-Assisted Microscopy. PLOS ONE. 2016; 11(10): e0165194. doi: 10.1371/journal.pone.0165194
Lecler S, Takakura Y, Meyrueis P. Properties of a three-dimensional photonic jet. Optics Letters. 2005; 30(19): 2641. doi: 10.1364/ol.30.002641
Horiuchi N. Photonic nanojets. Nature Photonics. 2012; 6(3): 138-139. doi: 10.1038/nphoton.2012.43
Durnin J. Exact solutions for nondiffracting beams I The scalar theory. Journal of the Optical Society of America A. 1987; 4(4): 651. doi: 10.1364/josaa.4.000651
Ben-Aryeh Y. Nano-jet related to Bessel beams and to super-resolutions in microsphere optical experiments. EPJ Techniques and Instrumentation. 2017; 4(1). doi: 10.1140/epjti/s40485-017-0038-5
Ben-Aryeh Y. Superresolution observed from evanescent waves transmitted through nano-corrugated metallic films. Applied Physics B. 2012; 109(1): 165-170. doi: 10.1007/s00340-012-5193-4
Ben-Aryeh Y. Increase of resolution by use of microspheres related to complex Snell’s law. Journal of the Optical Society of America A. 2016; 33(12): 2284. doi: 10.1364/josaa.33.002284
Yan Y, Li L, Feng C, et al. Microsphere-Coupled Scanning Laser Confocal Nanoscope for Sub-Diffraction-Limited Imaging at 25 nm Lateral Resolution in the Visible Spectrum. ACS Nano. 2014; 8(2): 1809-1816. doi: 10.1021/nn406201q
Wu G, Hong M. Optical nano-imaging via microsphere compound lenses working in non-contact mode. Optics Express. 2021; 29(15): 23073. doi: 10.1364/oe.426231
Maslov AV, Astratov VN. Origin of the super-resolution of microsphere-assisted imaging. Applied Physics Letters. 2024; 124(6). doi: 10.1063/5.0188450
Maslov AV, Astratov VN. Resolution and Reciprocity in Microspherical Nanoscopy: Point-Spread Function Versus Photonic Nanojets. Physical Review Applied. 2019; 11(6). doi: 10.1103/physrevapplied.11.064004
Huszka G, Yang H, Gijs MAM. Microsphere-based super-resolution scanning optical microscope. Optics Express. 2017; 25(13): 15079. doi: 10.1364/oe.25.015079
Ebbesen TW, Lezec HJ, Ghaemi HF, et al. Extraordinary optical transmission through sub-wavelength hole arrays. Nature. 1998; 391(6668): 667-669. doi: 10.1038/35570
Ghaemi HF, Thio T, Grupp DE, et al. Surface plasmons enhance optical transmission through subwavelength holes. Physical Review B. 1998; 58(11): 6779-6782. doi: 10.1103/physrevb.58.6779
Ben-Aryeh Y. Transmission enhancement by conversion of evanescent waves into propagating waves. Applied Physics B. 2008; 91(1): 157-165. doi: 10.1007/s00340-008-2945-2
Ben-Aryeh Y. Tunneling of evanescent waves into propagating waves. Applied Physics B. 2006; 84(1-2): 121-124. doi: 10.1007/s00340-006-2220-3
Ben-Aryeh Y. Nonclassical high resolution optical effects produced by evanescent waves. Journal of Optics B: Quantum and Semiclassical Optics. 2003; 5(6): S553-S556. doi: 10.1088/1464-4266/5/6/002
Ben-Aryeh Y. Super resolution of nanomaterials and quantum effects obtained by microspheres. Progress in Materials Science. 2019; 1(3): 1-21. doi:10.21926/rpm.1903003
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