• Opto-Electronic Advances
  • Vol. 4, Issue 10, 210013-1 (2021)
Yechuan Zhu, Xiaolin Chen, Weizheng Yuan, Zhiqin Chu, Kwok-yin Wong, Dangyuan Lei*, and Yiting Yu*
DOI: 10.29026/oea.2021.210013 Cite this Article
Yechuan Zhu, Xiaolin Chen, Weizheng Yuan, Zhiqin Chu, Kwok-yin Wong, Dangyuan Lei, Yiting Yu. A waveguide metasurface based quasi-far-field transverse-electric superlens[J]. Opto-Electronic Advances, 2021, 4(10): 210013-1 Copy Citation Text show less

Abstract

The imaging capability of conventional lenses is mainly limited by the diffraction of light, and the so-called superlens has been developed allowing the recovery of evanescent waves in the focal plane. However, the remarkable focusing behavior of the superlens is greatly confined in the near-field regime due to the exponential decay of evanescent waves. To tackle this issue, we design a waveguide metasurface-based superlens with an extraordinary quasi-far-field focusing capability beyond the diffraction limit in the present work. Specifically, we analyze the underlying physical mechanism and provide experimental verification of the proposed superlens. The metasurface superlens is formed by an array of gradient nanoslits perforated in a gold slab, and supports transverse-electric (TE) waveguide modes under linearly polarized illumination along the long axis of the slits. Numerical results illustrate that exciting such TE waveguide modes can modulate not only optical phase but also evanescent waves. Consequently, some high-spatial-frequency waves can contribute to the focusing of the superlens, leading to the quasi-far-field super-resolution focusing of light. Under 405 nm illumination and oil immersion, the fabricated superlens shows a focus spot of 98 nm (i.e. λ/4.13) at a focal distance of 1.49 μm (i.e. 3.68λ) using an oil immersion objective, breaking the diffraction limit of λ/2.38 in the quasi-far field regime. The developed metasurface optical superlens with such extraordinary capabilities promises exciting avenues to nanolithography and ultra-small optoelectronic devices.
$\frac{w}{2}\sqrt {{ε_{\rm{d}}}{k^2} - {\beta ^2}} = \frac{{{{m}}{\rm{π}} }}{2} + {\rm{arctan}} \frac{{\sqrt {{\beta ^2} - {ε_{\rm{m}}}{k^2}} }}{{\sqrt {{ε_{\rm{d}}}{k^2} - {\beta ^2}} }}\;,$(1)

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${E_{ix}}\left( {y,z} \right) = \left[ {{A_i}{{\rm{e}}^{{\rm{j}}{\beta _i}z}} + {B_i}{{\rm{e}}^{ - {\rm{j}}{\beta _i}z}}} \right]{f_i}\left( y \right)\;,$(2)

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$ \begin{array}{l} {E_x}\left( {{k_y},z} \right) = \dfrac{1}{{2{\rm{π}} }}{{\rm{e}}^{{\rm{j}}\sqrt {{k^2}{ε_{\rm{d}}} - k_y^2} \left( {z - d} \right)}}\sum\limits_{i = - N}^N {{E_i}{W_i}\left( {{k_y}} \right)} ,\\ {E_x}\left( {y,z} \right){\rm{ = }}\dfrac{1}{{2{\rm{π}} }}\sum\limits_{i = - N}^N {{E_i}\int\limits_{ - \infty }^{ + \infty } {{{\rm{e}}^{{\rm{j}}\sqrt {{k^2}{ε_{\rm{d}}} - k_y^2} \left( {z - d} \right)}}{W_i}\left( {{k_y}} \right){{\rm{e}}^{{\rm{j}}{k_y}y}}} } {\rm{d}}{k_y}\;, \end{array}$(3)

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${W_i}\left( {{k_y}} \right) = {{\rm{e}}^{ - {\rm{j}}{k_y}{a_i}}}\int\limits_{ - {w_i}/2}^{ + {w_i}/2} {{{\rm{e}}^{ - {\rm{j}}{k_y}y}}{f_i}\left( y \right){\rm{d}}y} \;,$(4)

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${\rm{\Delta}} \varphi (y) - {\rm{\Delta}} \varphi (0) = 2p{\rm{π}} + \frac{{2{\rm{π}} {n_{\rm{d}}}f}}{\lambda } - \frac{{2{\rm{π}} {n_{\rm{d}}}\sqrt {{f^2} + {y^2}} }}{\lambda }\;,$(5)

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$\frac{w}{2}\sqrt {{ε_{\rm{d}}}{k^2} - {\beta _0}^2} = {\rm{arctan}} \frac{{\sqrt {{\beta _0}^2 - {ε_{\rm{m}}}{k^2}} }}{{\sqrt {{ε_{\rm{d}}}{k^2} - {\beta _0}^2} }}\;.$(6)

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$\frac{{2{\rm{arctan}} \sqrt {{{ - {ε_{\rm{m}}}} / {{ε_{\rm{d}}}}}} }}{{k\sqrt {{ε_{\rm{d}}}} }} < w < \frac{{{\rm{π}} + 2{\rm{arctan}} \sqrt {{{ - {ε_{\rm{m}}}} / {{ε_{\rm{d}}}}}} }}{{k\sqrt {{ε_{\rm{d}}}} }}\;.$(7)

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Yechuan Zhu, Xiaolin Chen, Weizheng Yuan, Zhiqin Chu, Kwok-yin Wong, Dangyuan Lei, Yiting Yu. A waveguide metasurface based quasi-far-field transverse-electric superlens[J]. Opto-Electronic Advances, 2021, 4(10): 210013-1
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