Abstract

This paper applies rigorous diffraction theory to evaluate the minimum mass sensitivity of a confocal optical microscope designed to excite and detect surface plasmons operating on a planar metallic substrate. The diffraction model is compared with an intuitive ray picture which gives remarkably similar predictions. The combination of focusing the surface plasmons and accurate phase measurement mean that under favorable but achievable conditions detection of small numbers of molecules is possible, however, we argue that reliable detection of single molecules will benefit from the use of structured surfaces. System configurations needed to optimize performance are discussed.

© 2014 Optical Society of America

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References

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  1. P. P. Markowicz, W. C. Law, A. Baev, P. N. Prasad, S. Patskovsky, and A. Kabashin, “Phase-sensitive time-modulated surface plasmon resonance polarimetry for wide dynamic range biosensing,” Opt. Express 15(4), 1745–1754 (2007).
    [Crossref] [PubMed]
  2. S.-Y. Wu and H.-P. Ho, “Single-beam self-referenced phase-sensitive surface plasmon resonance sensor with high detection resolution,” Chin. Opt. Lett. 6(3), 176–178 (2008).
    [Crossref]
  3. P. Kvasnička, K. Chadt, M. Vala, M. Bocková, and J. Homola, “Toward single-molecule detection with sensors based on propagating surface plasmons,” Opt. Lett. 37(2), 163–165 (2012).
    [Crossref] [PubMed]
  4. M. Piliarik and J. Homola, “Self-referencing SPR imaging for most demanding high-throughput screening applications,” Sens. Actuators B Chem. 134(2), 353–355 (2008).
    [Crossref]
  5. S. Pechprasarn and M. G. Somekh, “Surface plasmon microscopy: Resolution, sensitivity and crosstalk,” J. Microsc. 246(3), 287–297 (2012).
    [Crossref] [PubMed]
  6. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Quantitative plasmonic measurements using embedded phase stepping confocal interferometry,” Opt. Express 21(9), 11523–11535 (2013).
    [Crossref] [PubMed]
  7. ICX NOMADICS, “Overview of Surface Plasmon Resonance,” http://www.sensiqtech.com/uploads/file/support/spr/Overview_of_SPR.pdf (accessed 28th Nov 2013).
  8. F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
    [Crossref] [PubMed]
  9. Photonics Research Group University of Gent, “Gent rigorous optical diffration software (RODIS),” http://www.photonics.intec.ugent.be/research/facilities/design/rodis (accessed 28th Nov 2013).
  10. I. Richter, P. Kwiecien, and J. Ctyroky, “Advanced photonic and plasmonic waveguide nanostructures analyzed with Fourier modal methods,” in Transparent Optical Networks (ICTON), 2013 15th International Conference on (2013), pp. 1–7.
    [Crossref]
  11. B. Zhang, S. Pechprasarn, J. Zhang, and M. G. Somekh, “Confocal surface plasmon microscopy with pupil function engineering,” Opt. Express 20(7), 7388–7397 (2012).
    [Crossref] [PubMed]
  12. A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express 17(23), 21191–21204 (2009).
    [Crossref] [PubMed]
  13. R. P. Feynman, R. B. Leighton, and M. Sands, “The origin of refractive index,” in The Feynman Lectures on Physics: Mainly Mechanics, Radiation, and Heat (Basic Books, 2011), Chap. 21.
  14. K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Technical limitations to homodyne detection at audio frequencies,” Appl. Opt. 46(17), 3389–3395 (2007).
    [Crossref] [PubMed]
  15. M. A. van Dijk, M. Lippitz, D. Stolwijk, and M. Orrit, “A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles,” Opt. Express 15(5), 2273–2287 (2007).
    [Crossref] [PubMed]
  16. S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011).
    [Crossref] [PubMed]

2013 (1)

2012 (3)

2011 (1)

S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011).
[Crossref] [PubMed]

2009 (1)

2008 (2)

M. Piliarik and J. Homola, “Self-referencing SPR imaging for most demanding high-throughput screening applications,” Sens. Actuators B Chem. 134(2), 353–355 (2008).
[Crossref]

S.-Y. Wu and H.-P. Ho, “Single-beam self-referenced phase-sensitive surface plasmon resonance sensor with high detection resolution,” Chin. Opt. Lett. 6(3), 176–178 (2008).
[Crossref]

2007 (3)

2001 (1)

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Baev, A.

Bocková, M.

Chadt, K.

Chung, T.

S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011).
[Crossref] [PubMed]

Elwing, H.

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Fant, C.

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Gray, M. B.

Grigorenko, A. N.

Ho, H.-P.

Homola, J.

P. Kvasnička, K. Chadt, M. Vala, M. Bocková, and J. Homola, “Toward single-molecule detection with sensors based on propagating surface plasmons,” Opt. Lett. 37(2), 163–165 (2012).
[Crossref] [PubMed]

M. Piliarik and J. Homola, “Self-referencing SPR imaging for most demanding high-throughput screening applications,” Sens. Actuators B Chem. 134(2), 353–355 (2008).
[Crossref]

Höök, F.

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Kabashin, A.

Kabashin, A. V.

Kasemo, B.

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Kvasnicka, P.

Lam, P. K.

Law, W. C.

Lee, B.

S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011).
[Crossref] [PubMed]

Lippitz, M.

Markowicz, P. P.

McClelland, D. E.

McKenzie, K.

Nylander, T.

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Orrit, M.

Patskovsky, S.

Pechprasarn, S.

Piliarik, M.

M. Piliarik and J. Homola, “Self-referencing SPR imaging for most demanding high-throughput screening applications,” Sens. Actuators B Chem. 134(2), 353–355 (2008).
[Crossref]

Prasad, P. N.

Roh, S.

S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011).
[Crossref] [PubMed]

Somekh, M. G.

Sott, K.

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Stolwijk, D.

Vala, M.

van Dijk, M. A.

Wu, S.-Y.

Zhang, B.

Zhang, J.

Anal. Chem. (1)

F. Höök, B. Kasemo, T. Nylander, C. Fant, K. Sott, and H. Elwing, “Variations in coupled water, viscoelastic properties, and film thickness of a Mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study,” Anal. Chem. 73(24), 5796–5804 (2001).
[Crossref] [PubMed]

Appl. Opt. (1)

Chin. Opt. Lett. (1)

J. Microsc. (1)

S. Pechprasarn and M. G. Somekh, “Surface plasmon microscopy: Resolution, sensitivity and crosstalk,” J. Microsc. 246(3), 287–297 (2012).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Sens. Actuators B Chem. (1)

M. Piliarik and J. Homola, “Self-referencing SPR imaging for most demanding high-throughput screening applications,” Sens. Actuators B Chem. 134(2), 353–355 (2008).
[Crossref]

Sensors (Basel) (1)

S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011).
[Crossref] [PubMed]

Other (4)

ICX NOMADICS, “Overview of Surface Plasmon Resonance,” http://www.sensiqtech.com/uploads/file/support/spr/Overview_of_SPR.pdf (accessed 28th Nov 2013).

Photonics Research Group University of Gent, “Gent rigorous optical diffration software (RODIS),” http://www.photonics.intec.ugent.be/research/facilities/design/rodis (accessed 28th Nov 2013).

I. Richter, P. Kwiecien, and J. Ctyroky, “Advanced photonic and plasmonic waveguide nanostructures analyzed with Fourier modal methods,” in Transparent Optical Networks (ICTON), 2013 15th International Conference on (2013), pp. 1–7.
[Crossref]

R. P. Feynman, R. B. Leighton, and M. Sands, “The origin of refractive index,” in The Feynman Lectures on Physics: Mainly Mechanics, Radiation, and Heat (Basic Books, 2011), Chap. 21.

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of optical system showing the relationship between different planes in the system. The blue waveform indicates phase modulation in the back focal plane. (b) Shows the principal illumination paths that appear to come from focus and thus return through the pinhole.

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Fig. 2
Fig. 2 (a) Back focal plane image of objective lens for linear polarized incident wave calculated with NA of 1.65, with immersion medium with refractive index of 1.78 and incident wavelength of 633 nm, where light was illuminating a 47 nm thick uniform gold in water ambient. (b) Schematic diagram showing how surface plasmons propagation on the surface of the uniform gold substrate, note that the bright areas correspond to strong SP excitation (c) A portion of the wavefront of unfocused SP beam propagating from left to right which is slightly shifted by the analyte, giving a small average phase shift (d) shows the array structure simulated with RCWA. The position ‘M’ represents the mid-point position remote from the analyte where the size of the unit cell is adjusted to give a response similar to bare gold.

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Fig. 3
Fig. 3 Flowchart showing calculation process for microscope model based on RCWA calculation.

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Fig. 4
Fig. 4 Log scale of intensity of each diffracted order for N = 13 (white) and N = 50 (black); these were calculated with noil of 1.78 incident at 54 degrees (plasmonic angle) with 633 nm incident wavelength where the sample was a rod array (nrod = 1.5) with grating period of 10 μm, 1 nm thick and 400 nm in radius.

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Fig. 5
Fig. 5 Phase change, Δϕ, in radians as a function of thickness of analyte, where the radius of the analyte was fixed at 400 nm and the Δϕ(z) was calculated at z = −2.5 μm defocus.

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Fig. 6
Fig. 6 Phase change, Δϕ, in radians as a function of radius of analyte with fixed volume (mass), the Δϕ were calculated at z = −4.5 μm (shown in blue), z = −2.5 μm (shown in red).

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Fig. 7
Fig. 7 Shows the phase shift as a function of displacement of the beam from the optical axis at z = −2.5 μm defocus of analyte with radius of 400 nm and thickness of 1 nm (n = 1.5 in water ambient); the blue line represents the displacement of the analyte along p-polarisation and the green line represents the displacement of the analyte along s-polarisation direction.

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Fig. 8
Fig. 8 Shows number of 100kD molecules as a function of defocus accounting for the number of photons passin through the pinhole. The blue curve for pinhole radius of 50% of 0.61λ/NA and the green line for for pinhole radius of 30% of 0.61λ/NA. This were calculated with 100 μJ energy on the image plane.

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Equations (5)

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E ^ i n c ( k x , k ) y = P ( k x , k y ) exp ( i k z z )
E b f p ( k x ' , k y ' ) = ∬ a p e r t u r e E ^ i n c ( k x , k y ) S R C W A ( k x , k x ' , k y , k y ' ) exp ( i k z z + i ( k x − k x ' ) x s + i ( k y − k y ' ) y s ) d k x d k y
O u t ( z ) = ∬ p i n h o l e | ∬ b f p E b f p ( k x ' , k y ' ) exp ( i k z z + i ( k x − k x ' ) x i + i ( k y − k y ' ) y i ) | 2 d x i d y i
N m = N s p + N r e f + 2 N r e f N s p cos ( ϕ + ( m − 1 ) π 2 )
ϕ m e a s u r e d = tan − 1 ( N ~ 1 − N ~ 3 N ~ 4 − N ~ 2 )

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