Skip to main content
SpringerLink
Log in

Plasmonic Response of Nano-C-apertures: Polarization Dependent Field Enhancement and Circuit Model

  • Published:
Plasmonics Aims and scope Submit manuscript

Abstract

The plasmonic response of C-shaped nano-apertures is investigated. Full-field numerical simulations are presented that show how the resonance condition depends on the wavelength and polarization of the incident light. Effects of dimension scaling are also discussed. A circuit model is proposed that relates geometrical and material parameters to equivalent inductive and capacitive circuit elements. The topological profile of the induced surface currents is used to find the representative inductance and capacitance values. The equivalent impedance of the circuit model is found to be correlated to the resonance behavior of the actual C-aperture. Comparison between the numerical simulations and the circuit model analysis shows agreement in predicting the resonant wavelength and bandwidth variations with C-aperture dimensions. The presented analysis can be useful in designing C-apertures for applications such as photonic metasurfaces, optical trapping, and fluorescence microscopy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Availability of Data and Materials

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Sun L, Batra R, Shi X, Hesselink L (2004) Topology visualization of the optical power flow through a novel c-shaped nano-aperture. Soc, IEEE Comput. https://doi.org/10.1109/visual.2004.106

    Book  Google Scholar 

  2. Li L, Yao K, Wang Z, Liu Y (2020b) Harnessing evanescent waves by bianisotropic metasurfaces. 14(12):1900244. https://doi.org/10.1002/lpor.201900244

  3. Song EY, Lee GY, Park H, Lee K, Kim J, Hong J, Kim H, Lee B (2017) Compact generation of airy beams with c-aperture metasurface 5(10):1601028. https://doi.org/10.1002/adom.201601028

    Article  CAS  Google Scholar 

  4. Wang Z, Yao K, Chen M, Chen H, Liu Y (2016) Manipulating smith-purcell emission with babinet metasurfaces 117(15):157401. https://doi.org/10.1103/physrevlett.117.157401

    Article  Google Scholar 

  5. Fore S, Yuen Y, Hesselink L, Huser T (2007) Pulsed-interleaved excitation FRET measurements on single duplex DNA molecules inside c-shaped nanoapertures. Nano Lett 7(6):1749–1756. https://doi.org/10.1021/nl070822v

    Article  CAS  Google Scholar 

  6. Tang L, Miller DA, Okyay AK, Matteo JA, Yuen Y, Saraswat KC, Hesselink L (2006) C-shaped nanoaperture-enhanced germanium photodetector. Opt Lett 31(10):1519. https://doi.org/10.1364/ol.31.001519

    Article  Google Scholar 

  7. Ashkin A (1970) Acceleration and trapping of particles by radiation pressure. Phys Rev Lett 24(4):156. https://doi.org/10.1103/physrevlett.24.156

    Article  CAS  Google Scholar 

  8. Ashkin A, Dziedzic J (1987) Optical trapping and manipulation of viruses and bacteria. Science 235(4795):1517–1520. https://doi.org/10.1126/science.3547653

    Article  CAS  Google Scholar 

  9. Guo H, Meyrath TP, Zentgraf T, Liu N, Fu L, Schweizer H, Giessen H (2008) Optical resonances of bowtie slot antennas and their geometry and material dependence 16(11):7756. https://doi.org/10.1364/oe.16.007756

    Article  Google Scholar 

  10. Rindzevicius T, Alaverdyan Y, Dahlin A, Höök F, Sutherland DS, Käll M (2005) Plasmonic sensing characteristics of single nanometric holes 5(11):2335–2339. https://doi.org/10.1021/nl0516355

    Article  CAS  Google Scholar 

  11. Wen K, Luo XQ, Chen Z, Zhu W, Guo W, Wang X (2019) Enhanced optical transmission assisted near-infrared plasmonic optical filter via hybrid subwavelength structures 14(6):1649–1657. https://doi.org/10.1007/s11468-019-00963-4

    Article  Google Scholar 

  12. Tsai WY, Huang JS, Huang CB (2014) Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral. Nano Lett 14(2):547–552. https://doi.org/10.1021/nl403608a

    Article  CAS  Google Scholar 

  13. Ziegler JI, Haglund RF (2013) Complex polarization response in plasmonic nanospirals. Plasmonics 8(2):571–579. https://doi.org/10.1007/s11468-012-9436-3

    Article  CAS  Google Scholar 

  14. Kubo W, Fujikawa S (2010) Au double nanopillars with nanogap for plasmonic sensor. Nano Lett 11(1):8–15. https://doi.org/10.1021/nl100787b

    Article  CAS  Google Scholar 

  15. Juan ML, Righini M, Quidant R (2011) Plasmon nano-optical tweezers. Nat Photonics 5(6):349–356. https://doi.org/10.1038/nphoton.2011.56

    Article  CAS  Google Scholar 

  16. Li H, Ren Y, Li Y, He M, Gao B, Qi H (2022a) Nanoparticle manipulation using plasmonic optical tweezers based on particle sizes and refractive indices. 30(19):34092. https://doi.org/10.1364/oe.468024

  17. Roxworthy BJ, Ko KD, Kumar A, Fung KH, Chow EK, Liu GL, Fang NX, Toussaint KC Jr (2012) Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting. Nano Lett 12(2):796–801. https://doi.org/10.1021/nl203811q

    Article  CAS  Google Scholar 

  18. Wang K, Schonbrun E, Steinvurzel P, Crozier KB (2011) Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink. Nat Commun 2(1):469. https://doi.org/10.1038/ncomms1480

    Article  CAS  Google Scholar 

  19. Zheng Y, Ryan J, Hansen P, Cheng YT, Lu TJ, Hesselink L (2014) Nano-optical conveyor belt, part ii: demonstration of handoff between near-field optical traps. Nano Lett 14(6):2971–2976. https://doi.org/10.1021/nl404045n

    Article  CAS  Google Scholar 

  20. Lindquist NC, Johnson TW, Nagpal P, Norris DJ, Oh SH (2013) Plasmonic nanofocusing with a metallic pyramid and an integrated c-shaped aperture. 3(1). https://doi.org/10.1038/srep01857

  21. Hussain S, Bhatia CS, Yang H, Danner AJ (2015) Characterization of c-apertures in a successful demonstration of heat-assisted magnetic recording 40(15):3444. https://doi.org/10.1364/ol.40.003444

    Article  CAS  Google Scholar 

  22. Rao Z, Matteo JA, Hesselink L, Harris JS (2007b) High-intensity c-shaped nanoaperture vertical-cavity surface-emitting laser with controlled polarization. 90(19):191110. https://doi.org/10.1063/1.2737938

  23. McKeown SJ, Goddard LL (2017) Reflective palladium nanoapertures on fiber for wide dynamic range hydrogen sensing 23(2):263–268. https://doi.org/10.1109/jstqe.2016.2617086

    Article  CAS  Google Scholar 

  24. Lopatiuk-Tirpak O, Fathpour S (2010) C-shaped subwavelength apertures for silicon photonics applications. OSA. https://doi.org/10.1364/iprsn.2010.itud3

    Article  Google Scholar 

  25. Helman J, Hesselink L (1991) Visualizing vector field topology in fluid flows 11(3):36–46. https://doi.org/10.1109/38.79452

    Article  Google Scholar 

  26. Chang K, il Kwak S, Yoon YJ (2008) Equivalent circuit modeling of active frequency selective surfaces. In: 2008 IEEE Radio and Wireless Symposium. IEEE. https://doi.org/10.1109/rws.2008.4463579

  27. D’Amore M, Santis VD, Feliziani M (2012) Equivalent circuit modeling of frequency-selective surfaces based on nanostructured transparent thin films 48(2):703–706. https://doi.org/10.1109/tmag.2011.2171922

    Article  Google Scholar 

  28. Silva BS, de Siqueira Campos ALP, Neto AG (2020) Equivalent circuit model for analysis of frequency selective surfaces with ring and double concentric ring apertures 14(7):600–607. https://doi.org/10.1049/iet-map.2019.0760

    Article  Google Scholar 

  29. Corrigan TD, Kolb PW, Sushkov AB, Drew HD, Schmadel DC, Phaneuf RJ (2008) Optical plasmonic resonances in split-ring resonator structures: an improved LC model 16(24):19850. https://doi.org/10.1364/oe.16.019850

    Article  CAS  Google Scholar 

  30. Lu H, Li L, Zhang J, Xia S, Kang X, Huang M, Shen K, Dong C, Zhang X (2019) The generalized analytical expression for the resonance frequencies of plasmonic nanoresonators composed of folded rectangular geometries. 9(1). https://doi.org/10.1038/s41598-018-37275-2

  31. Shim HB, Hahn JW (2019) Plasmonic near-field scanning nanoscope with a cross-polarization detection technique 8(10):1731–1738. https://doi.org/10.1515/nanoph-2019-0132

    Article  CAS  Google Scholar 

  32. Yu H, Wang X, Su J, Qu M, Guo Q, Li Z, Song J (2021) Ultrawideband and high-efficient polarization conversion metasurface based on multi-resonant element and interference theory 29(22):35938. https://doi.org/10.1364/oe.440542

    Article  Google Scholar 

  33. Zhu D, Bosman M, Yang JKW (2014) A circuit model for plasmonic resonators 22(8):9809. https://doi.org/10.1364/oe.22.009809

    Article  CAS  Google Scholar 

  34. Shi X, Hesselink L, Thornton RL (2003) Ultrahigh light transmission through a c-shaped nanoaperture. Opt Lett 28(15):1320–1322. https://doi.org/10.1364/ol.28.001320

    Article  Google Scholar 

  35. Hansen P, Hesselink L (2015) Accurate adjoint design sensitivities for nano metal optics 23(18):23899. https://doi.org/10.1364/oe.23.023899

    Article  CAS  Google Scholar 

  36. Shi X, Hesselink L (2004) Design of a c aperture to achieve \(\lambda\)/10 resolution and resonant transmission. JOSA B 21(7):1305–1317. https://doi.org/10.1364/josab.21.001305

  37. Cheng YT, Takashima Y, Yuen Y, Hansen PC, Leen JB, Hesselink L (2011) Ultra-high resolution resonant c-shaped aperture nano-tip 19(6):5077. https://doi.org/10.1364/oe.19.005077

    Article  Google Scholar 

  38. Rao Z, Hesselink L, Harris JS (2007a) High transmission through ridge nano-apertures on vertical-cavity surface-emitting lasers. 15(16):10427. https://doi.org/10.1364/oe.15.010427

  39. Leen JB, Hansen P, Cheng YT, Hesselink L (2008) Improved focused ion beam fabrication of near-field apertures using a silicon nitride membrane 33(23):2827. https://doi.org/10.1364/ol.33.002827

    Article  CAS  Google Scholar 

  40. Li Y (2017) Plasmonic optics: Theory and applications. SPIE. http://doi.org/10(1117/3):2263757

  41. Ordal MA, Bell RJ, Alexander RW, Long LL, Querry MR (1985) Optical properties of fourteen metals in the infrared and far infrared: Al Co. Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W 24(24):4493. https://doi.org/10.1364/ao.24.004493

    Article  CAS  Google Scholar 

  42. Olmon RL, Slovick B, Johnson TW, Shelton D, Oh SH, Boreman GD, Raschke MB (2012) Optical dielectric function of gold 86(23):235147. https://doi.org/10.1103/physrevb.86.235147

    Article  Google Scholar 

  43. Blaber MG, Arnold MD, Ford MJ (2010) A review of the optical properties of alloys and intermetallics for plasmonics 22(14):143201. https://doi.org/10.1088/0953-8984/22/14/143201

    Article  CAS  Google Scholar 

  44. Zaman MA, Padhy P, Hansen PC, Hesselink L (2017) Dielectrophoresis-assisted plasmonic trapping of dielectric nanoparticles. Phys Rev A 95(2):023840. https://doi.org/10.1103/physreva.95.023840

    Article  CAS  Google Scholar 

  45. Zaman MA, Padhy P, Hansen PC, Hesselink L (2018) Extracting the potential-well of a near-field optical trap using the helmholtz-hodge decomposition. Appl Phys Lett 112(9):091103. https://doi.org/10.1063/1.5016810

    Article  CAS  Google Scholar 

  46. Zaman MA, Padhy P, Hesselink L (2019a) Near-field optical trapping in a non-conservative force field. Sci Rep 9(1):649

  47. Globus A, Levit C, Lasinski T (1991) A tool for visualizing the topology of three-dimensional vector fields. In: Proceeding Visualization ’91, IEEE Comput Soc Press https://doi.org/10.1109/visual.1991.175773

  48. Zaman MA, Padhy P, Hesselink L (2019b) Solenoidal optical forces from a plasmonic archimedean spiral. Phys Rev A 100(1). https://doi.org/10.1103/physreva.100.013857

  49. Wheeler H (1982) Inductance formulas for circular and square coils 70(12):1449–1450. https://doi.org/10.1109/proc.1982.12504

    Article  Google Scholar 

  50. Alabastri A, Tuccio S, Giugni A, Toma A, Liberale C, Das G, Angelis F, Fabrizio E, Zaccaria R (2013) Molding of plasmonic resonances in metallic nanostructures: Dependence of the non-linear electric permittivity on system size and temperature 6(11):4879–4910. https://doi.org/10.3390/ma6114879

    Article  CAS  Google Scholar 

  51. Huggard PG, Cluff JA, Moore GP, Shaw CJ, Andrews SR, Keiding SR, Linfield EH, Ritchie DA (2000) Drude conductivity of highly doped GaAs at terahertz frequencies 87(5):2382–2385. https://doi.org/10.1063/1.372238

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge the support of Max Yuen, Yao-Te Cheng, and Paul C. Hansen.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Stanford University, 350 Jane Stanford Way, Stanford, 94305, CA, USA

    Mohammad Asif Zaman & Lambertus Hesselink

Authors
  1. Mohammad Asif Zaman
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.A.Z. and L.H. came up with the idea. Simulations and manuscript preparation were done by M.A.Z. Supervision was provided by L.H.

Corresponding author

Correspondence to Mohammad Asif Zaman.

Ethics declarations

Ethical Approval

Not applicable

Competing Interests

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaman, M.A., Hesselink, L. Plasmonic Response of Nano-C-apertures: Polarization Dependent Field Enhancement and Circuit Model. Plasmonics 18, 155–164 (2023). https://doi.org/10.1007/s11468-022-01735-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11468-022-01735-3

Keywords

Search

Navigation