Abstract

Metamaterials and plasmonics potentially offer an ultimate control of light to enable a rich number of non-conventional devices and a testbed for many novel physical phenomena. However, optical loss in metamaterials and plasmonics is a fundamental challenge rendering many conceived applications not viable in practical settings. Many approaches have been proposed so far to mitigate losses, including geometric tailoring, active gain media, nonlinear effects, metasurfaces, dielectrics, and 2D materials. Here, we review recent efforts on the less explored and unique territory of “virtual gain” as an alternative approach to combat optical losses. We define the virtual gain as the result of any extrinsic amplification mechanism in a medium. Our aim is to accentuate virtual gain not only as a promising candidate to address the material challenge, but also as a design concept with broader impacts.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (2)

A. Krasnok and A. Alu, “Active nanophotonics,” Proc. IEEE 108(5), 628–654 (2020).
[Crossref]

H. Li, A. Mekawy, A. Krasnok, and A. Alù, “Virtual parity-time symmetry,” Phys. Rev. Lett. 124(19), 193901 (2020).
[Crossref]

2019 (11)

Y. Zhou, I. I. Kravchenko, H. Wang, H. Zheng, G. Gu, and J. Valentine, “Multifunctional metaoptics based on bilayer metasurfaces,” Light: Sci. Appl. 8(1), 80 (2019).
[Crossref]

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[Crossref]

J.-S. Lee, J. Bang, S. Hong, C. Lee, K. H. Seol, J. Lee, and K.-G. Lee, “Experimental demonstration of quantum learning speedup with classical input data,” Phys. Rev. A 99(1), 012313 (2019).
[Crossref]

C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller, “Self-verifying variational quantum simulation of lattice models,” Nature 569(7756), 355–360 (2019).
[Crossref]

X. Zhang, J. I. Davis, and D. O. Guney, “Ultra-thin metamaterial beam splitters,” Appl. Sci. 10(1), 53 (2019).
[Crossref]

G. Yoon, J. Jang, J. Mun, K. T. Nam, and J. Rho, “Metasurface zone plate for light manipulation in vectorial regime,” Commun. Phys. 2(1), 156 (2019).
[Crossref]

C. Stock, T. Siefke, and U. Zeitner, “Metasurface-based patterned wave plates for vis applications,” J. Opt. Soc. Am. B 36(5), D97 (2019).
[Crossref]

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[Crossref]

G. Yuan, K. S. Rogers, E. T. Rogers, and N. I. Zheludev, “Far-field superoscillatory metamaterial superlens,” Phys. Rev. Appl. 11(6), 064016 (2019).
[Crossref]

G. Chen, Z.-Q. Wen, and C.-W. Qiu, “Superoscillation: from physics to optical applications,” Light: Sci. Appl. 8(1), 56 (2019).
[Crossref]

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Günaydın, L. A. Bentolila, C. Kural, and A. Ozcan, “Deep learning enables cross-modality super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

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S. Yoo, S. Lee, and Q.-H. Park, “Loss-free negative-index metamaterials using forward light scattering in dielectric meta-atoms,” ACS Photonics 5(4), 1370–1374 (2018).
[Crossref]

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[Crossref]

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Figures (18)

Fig. 1.
Fig. 1. A conceptual structure for the implementation of plasmon injection scheme. The surface plot corresponds to the magnetic field at magnetic resonance. The field amplitude is magnified $4$ times to clearly illustrate the mode profile in the middle part of the metamaterial. The red rectangle indicates the unit cell. See text for details. Reprinted with permission from [46] © 2018 American Physical Society.
Fig. 2.
Fig. 2. Retrieved real ($n^\prime$) and imaginary ($n^{\prime \prime }$) parts of the effective refractive index of the plasmonic metamaterial structure in Fig. 1 under plasmon injection with the total auxiliary power $6$ times the input power. Reprinted with permission from [46] © 2018 American Physical Society.
Fig. 3.
Fig. 3. Compensation of losses in a superlens with virtual gain approach (i.e., $\Pi$ scheme). See text for details. Reprinted with permission from [46] © 2018 American Physical Society.
Fig. 4.
Fig. 4. (a) Magnetic field magnitude for an original object (blue), truncated object (black), raw image (red), and deconvolution-based loss compensated image (green) for hyperlens under coherent illumination. (b) Comparison of the images obtained by the deconvolution (green) and the $\Pi$ scheme (black) using the total input (blue), which is a coherent superposition of the original object with an auxiliary object. Reproduced from courtesy of The Electromagnetics Academy [56].
Fig. 5.
Fig. 5. (a) The original object (black), image resulting from the total input field (green) and the deconvolution with no auxiliary source (red) are compared for a non-ideal Pendry’s NIFL under coherent illumination. The raw image (blue) is also shown. (b) Auxiliary source. The fine structure of the auxiliary source is shown in the inset. © 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Reproduced with permission from IOP [58] CC BY.
Fig. 6.
Fig. 6. Results from nonlinear Richardson-Lucy deconvolution for noisy data from double-slit objects and a silver superlens under incoherent illumination. The slit width and separation is $\Delta x$. (a) $\Delta x=60nm$, (b) $\Delta x=30nm$, and (c) $\Delta x=20nm$. Clearly, resolution better than $20nm$ can be achieved with the deconvolution. Reprinted with permission from [59] © The Optical Society.
Fig. 7.
Fig. 7. (a) Total object distribution (i.e., superposition of the original object and auxiliary source) for $\Delta x=60nm$. A DC offset is used to make all the intensity levels positive. (b) Image resulting from (a). The DC offset is removed for comparison with the image reconstructed with linear deconvolution. Reprinted with permission from [59] © The Optical Society.
Fig. 8.
Fig. 8. Fourier spectra of the reconstructed images for Pendry’s non-ideal NIFL under coherent illumination, comparing the active and passive compensation. The latter significantly amplifies the noise. Reprinted with permission from [60] © The Optical Society.
Fig. 9.
Fig. 9. Fourier spectra of the (a) raw images with and without added physical noise under a reference weak coherent illumination case, (b) raw images with and without added physical noise displaying the contribution of the signal-dependent and signal-independent noise to the image under the strong coherent illumination case, (c) convolved images with and without added physical noise illustrating the contribution of the signal-dependent and signal-independent noise to the total image under the coherent structured illumination case. The convolved images are produced physically with a type of structured illumination in the $\Pi$ scheme. Significant amount of information about the object is obtained in (c) compared to (a) and (b). Reprinted with permission from [60] © The Optical Society.
Fig. 10.
Fig. 10. Fourier spectra of the raw image coherently superimposed with several auxiliaries uncorrelated with the object. The red and black lines are the raw images without and with added physical noise, respectively. The uncorrelated superposition does not provide useful information about the object. Reprinted with permission from [60] © The Optical Society.
Fig. 11.
Fig. 11. Schematic of the imaging systems (a) with and (b) without an integrated hyperbolic metamaterial (HMM) acting as a near-field spatial filter (not to scale). The imaging system in (a) with a high intensity illumination is used for a physical implementation of the coherent active $\Pi$ scheme. PML: perfectly matched layers. Reprinted with permission from [64] © The Optical Society.
Fig. 12.
Fig. 12. Comparison of active and passive $\Pi$ scheme, based on (a) Fourier spectra and (b) spatial field distributions of the reconstructed images. The active $\Pi$ scheme using the imaging system in Fig. 11(a) is capable of resolving objects, which is not otherwise possible with the superlens alone. Reprinted with permission from [64] © The Optical Society.
Fig. 13.
Fig. 13. Passive transfer function $T(k_y)$ of the lossy metamaterial and the active transfer function $T_A(k_y)$ of the lossy metamaterial integrated with the $Al-TiO_2$ HMM [see Fig. 11(a)]. The active transfer function provides selective amplification around $5.5k_0$. Reprinted with permission from [65] © 2018 American Physical Society.
Fig. 14.
Fig. 14. Implementations of the active $\Pi$ scheme with (a) coherently superimposed auxiliary and object fields, and (b) an integrated HMM-superlens imaging system. See text for details. Reprinted with permission from [65] © 2018 American Physical Society.
Fig. 15.
Fig. 15. (a) Source distribution at the object plane of a superlens under incoherent light. (b) Intensity distribution of the image plane. (c) Passive Richardson-Lucy deconvolution of the image in (b). The objects with the smallest separation (i.e., $25nm$) cannot be resolved even after the deconvolution. Reprinted with permission from ACS Photonics 2018, 5, 1294. © 2018 American Chemical Society.
Fig. 16.
Fig. 16. (a) “Active” images of the objects in Fig. 15 obtained by incoherent ACI before the deconvolution step. (b) Fully resolved objects (with below $25nm$ resolution), under about $60dB$ SNR, after the deconvolution of the active image. Reprinted with permission from ACS Photonics 2018, 5, 1294. © 2018 American Chemical Society.
Fig. 17.
Fig. 17. Coherent amplification of pulses with a passive optical cavity. The repetition period of the external pulse train is matched to cavity round-trip time to coherently add the pulses inside the cavity. Reprinted with permission from [68] © The Optical Society.
Fig. 18.
Fig. 18. Propagation in transmission line with uniform loss coefficient $\alpha$ and excited by a decaying signal with complex frequency $\Omega =\omega ^{\prime }+j \omega ^{\prime \prime }$. (a) $\omega ^{\prime \prime }=0$, (b) $\omega ^{\prime \prime }=\alpha$, virtual transparency, and (c) $\omega ^{\prime \prime }>\alpha$, virtual gain. Reprinted with permission from [45] © 2020 American Physical Society.

Equations (8)

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o ( y ) = k y O ( k y ) e 2 k y d 0.04 + e 2 k y d e i k y y ,
o ( y ) = k y O ( k y ) f ( k y ) e 2 k y d 0.04 + e 2 k y d e i k y y .
o ( y ) = k y O ( k y ) f p ( k y ) e 2 k y d 0.04 p + e 2 k y d e i k y y ,
f 1 2 ( k y ) = 0.04 + e 2 k y d 0.02 + e 2 k y d .
o ( y ) = k y O ( k y ) e 2 k y d 0.02 + e 2 k y d e i k y y ,
I A ( k y ) = [ O ( k y ) + A 0 O ( k y ) G ( k y ) ] T ( k y ) ,
I A ( k y ) = O ( k y ) { [ 1 + A 0 G ( k y ) ] T ( k y ) } ,
O ~ n , A ( k y ) = I n , A ( k y ) { T ( k y ) [ 1 + A 0 G ( k y ) ] } 1 ,

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