Abstract

We propose a new design for an optical sensor based on porous silicon structures. We present an analysis based on a pole expansion, which allows for the easy identification of the parameters important for the operation of the sensor, and the phenomenological inclusion of scattering losses. The predicted sensitivity of the sensor is much greater than detectors utilizing surface plasmon resonance.

© 2005 Optical Society of America

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References

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  1. J. Räty, K.-E. Peiponen, and T. Asakura, UV-visible reflection spectroscopy of liquids (Springer, Heidelberg, 2004).
  2. H. Räther, Surface plasmons on smooth and rough surfaces and on gratings (Springer, Berlin, 1988).
  3. E. Kretschmann, �??Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results.,�?? Opt. Comm. 6, 185�??187 (1972).
    [CrossRef]
  4. I. Pockrand, �??Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,�?? Surf. Sci. 72, 577�??588 (1978).
    [CrossRef]
  5. J. D. Swalen, �??Optical wave spectroscopy of molecules at surfaces,�?? J. Phys. Chem. 83, 1438�??1445 (1979).
    [CrossRef]
  6. H. Kano and S. Kawata, �??Surface-plasmon sensor for absorption-sensitivity enhancement,�?? Appl. Opt. 33, 5166�??5170 (1994).
    [CrossRef] [PubMed]
  7. J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, �??Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance,�?? Appl. Spectrosc. 57, 288�??292 (2003).
    [CrossRef] [PubMed]
  8. R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies, C. J. Roberts, and S. J. B. Tendler, �??Surface plasmon resonance analysis of dynamic biological interactions with biomaterials,�?? Biomaterials 21, 1823�??1835 (2000).
    [CrossRef] [PubMed]
  9. B. J. Sedlak, �??Next-generation microarray technologies - Focus is on higher sensitivity, drug discovery, and lipid cell signaling,�?? Genetic Engineering News 23, 20�??20 (2003).
  10. P. M. Fauchet, �??Silicon: Porous,�?? in Encyclopedia of applied physics, update 2, G. L. Trigg, ed. (Wiley-VCH Verlag, New York, 1999), pp. 249�??272.
  11. S. M. Weiss and P. M. Fauchet, �??Electrically tunable porous silicon active mirrors,�?? Phys. Stat. Sol. A 197, 556�??560 (2003).
    [CrossRef]
  12. J. E. Lugo, J. A. del Rio, and J. Tagüeña-Martínez, �??Influence of surface coverage on the effective optical properties of porous silicon modeled as a Si-wire array,�?? J. Appl. Phys. 81, 1923�??1928 (1997).
    [CrossRef]
  13. P. E. Schmid, �??Optical absorption in heavily doped silicon,�?? Phys. Rev. B. 23, 5531�??5536 (1981).
    [CrossRef]
  14. J. von Behren, L. Tsybeskov, and P. M. Fauchet, �??Preparation, properties and applications of free-standing porous silicon films,�?? in Microcrystalline and nanocrystalline semiconductors, Vol. 358, R. W. Collins, C. C. Tsai, M. Hirose, F. Koch, and L. Brus, eds. (Mat. Res. Proc., 1995), pp. 333�??338.
  15. J. E. Sipe, �??New Green-function formalism for surface optics,�?? J. Opt. Soc. Am. B 4, 481�??489 (1987).
    [CrossRef]
  16. J. E. Sipe, �??Surface plasmon-enhanced absorption of light by adsorbed molecules,�?? Solid State Commun. 33, 7�??9 (1980).
    [CrossRef]
  17. J. E. Sipe and J. Becher, �??Surface energy transfer enhanced by optical cavity excitation: a pole analysis,�?? J. Opt. Soc. Am. 72, 288�??295 (1982).
    [CrossRef]
  18. E. D. Palik, Handbook of optical constants of solids (Academic Press, New York, 1985).
  19. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1988).
  20. G. Amato, L. Boarino, S. Borini, and A. M. Rossi, �??Hybrid approach to porous silicon integrated waveguides,�?? Phys. Stat. Sol. (a) 182, 425�??430 (2000).
    [CrossRef]
  21. For an overlayer thickness l with an index nl the effective Fresnel coefficient �?r51 from the prism in Fig. 1a is exactly given by Eq. (9) but with r31 replaced by �?r31 = (r3l+rl1 exp(2iwll))/(1-rl3rl1 exp(2iwll)) in an obvious notation. Using Fresnel coefficient identities, that new equation can be written as �?r31 = (r31 + �?r1l)/(1+r31 �?r1l), where �?r1l = (r1l +rl1 exp(2iwll))/(1-r2 l1 exp(2iwll)). Using the pole approximation (11) for r31 in this new expression for �?r51, we predict a shift of the resonance dip due to the overlayer which deviates from an exact calculation of that shift by only 0.002.

Appl. Opt.

Appl. Spectrosc.

Biomaterials

R. J. Green, R. A. Frazier, K. M. Skakesheff, M. C. Davies, C. J. Roberts, and S. J. B. Tendler, �??Surface plasmon resonance analysis of dynamic biological interactions with biomaterials,�?? Biomaterials 21, 1823�??1835 (2000).
[CrossRef] [PubMed]

Genetic Engineering News

B. J. Sedlak, �??Next-generation microarray technologies - Focus is on higher sensitivity, drug discovery, and lipid cell signaling,�?? Genetic Engineering News 23, 20�??20 (2003).

J. Appl. Phys.

J. E. Lugo, J. A. del Rio, and J. Tagüeña-Martínez, �??Influence of surface coverage on the effective optical properties of porous silicon modeled as a Si-wire array,�?? J. Appl. Phys. 81, 1923�??1928 (1997).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. Chem.

J. D. Swalen, �??Optical wave spectroscopy of molecules at surfaces,�?? J. Phys. Chem. 83, 1438�??1445 (1979).
[CrossRef]

Mat. Res. Proc., 1995

J. von Behren, L. Tsybeskov, and P. M. Fauchet, �??Preparation, properties and applications of free-standing porous silicon films,�?? in Microcrystalline and nanocrystalline semiconductors, Vol. 358, R. W. Collins, C. C. Tsai, M. Hirose, F. Koch, and L. Brus, eds. (Mat. Res. Proc., 1995), pp. 333�??338.

Opt. Comm.

E. Kretschmann, �??Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results.,�?? Opt. Comm. 6, 185�??187 (1972).
[CrossRef]

Phys. Rev. B

P. E. Schmid, �??Optical absorption in heavily doped silicon,�?? Phys. Rev. B. 23, 5531�??5536 (1981).
[CrossRef]

Phys. Stat. Sol. (a)

G. Amato, L. Boarino, S. Borini, and A. M. Rossi, �??Hybrid approach to porous silicon integrated waveguides,�?? Phys. Stat. Sol. (a) 182, 425�??430 (2000).
[CrossRef]

Phys. Stat. Sol. A

S. M. Weiss and P. M. Fauchet, �??Electrically tunable porous silicon active mirrors,�?? Phys. Stat. Sol. A 197, 556�??560 (2003).
[CrossRef]

Solid State Commun.

J. E. Sipe, �??Surface plasmon-enhanced absorption of light by adsorbed molecules,�?? Solid State Commun. 33, 7�??9 (1980).
[CrossRef]

Surf. Sci.

I. Pockrand, �??Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,�?? Surf. Sci. 72, 577�??588 (1978).
[CrossRef]

Other

J. Räty, K.-E. Peiponen, and T. Asakura, UV-visible reflection spectroscopy of liquids (Springer, Heidelberg, 2004).

H. Räther, Surface plasmons on smooth and rough surfaces and on gratings (Springer, Berlin, 1988).

P. M. Fauchet, �??Silicon: Porous,�?? in Encyclopedia of applied physics, update 2, G. L. Trigg, ed. (Wiley-VCH Verlag, New York, 1999), pp. 249�??272.

E. D. Palik, Handbook of optical constants of solids (Academic Press, New York, 1985).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1988).

For an overlayer thickness l with an index nl the effective Fresnel coefficient �?r51 from the prism in Fig. 1a is exactly given by Eq. (9) but with r31 replaced by �?r31 = (r3l+rl1 exp(2iwll))/(1-rl3rl1 exp(2iwll)) in an obvious notation. Using Fresnel coefficient identities, that new equation can be written as �?r31 = (r31 + �?r1l)/(1+r31 �?r1l), where �?r1l = (r1l +rl1 exp(2iwll))/(1-r2 l1 exp(2iwll)). Using the pole approximation (11) for r31 in this new expression for �?r51, we predict a shift of the resonance dip due to the overlayer which deviates from an exact calculation of that shift by only 0.002.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagrams of (a) Kretschmann’s SPR configuration and (b) optical sensor based on porous silicon.

Fig. 2.
Fig. 2.

Comparison of the reflectivity dip for SPR sensor with the optical constants given in the text. Dashed line, pole approximation; solid line, exact calculation.

Fig. 3.
Fig. 3.

Dispersion curve κ m/ω̃ (solid line) and pole strength parameter κs / ω ˜ (dashed line) as a function of the waveguide thickness d. For both curves λ=1.532 µm, n 1=1.00, n 2=2.213, and n 3=1.642. The pole has a maximum value when d=287.2 nm, which we choose to be the thickness of the resonator layer.

Fig. 4.
Fig. 4.

Reflectance from the proposed PS sensor as a function of the angle of incidence (a) without nanoparticles and (b) with nanoparticles filling 1% of the volume of the pores. The three curves correspond to different coupling layer thicknesses with overcoupled (dashed line), optimal coupling (bold solid line), and undercoupled (thin solid line) case.

Fig. 5.
Fig. 5.

Reflectance from the conventional SPR sensor as a function of the angle of incidence (a) in vacuum and (b) with 1 nm thick polymer film on top of the metal film. The three curves correspond to different metal thicknesses with overcoupled (dashed line), optimal coupling (bold solid line), and undercoupled (thin solid line) case. The peaks in SPR are much broader than the peaks with our proposed PS sensor. Note that here the x-axis spans an angle 10 times larger than in the Fig. 4 for the PS sensor.

Equations (27)

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w i = ( ω ˜ 2 ε i κ 2 ) 1 2
r ij s = w i w j w i + w j ; t ij s = 2 w i w i + w j ,
r ij p = w i ε j w j ε i w i ε j + w j ε i ; t ij p = 2 n i n j w i w i ε j + w j ε i .
r ij = r ji ; t ij t ji r ij r ji = 1 .
κ SPR = ω ˜ ( ε 1 ε 3 ε 1 + ε 3 ) 1 2 ,
r 31 κ s κ κ SPR .
κ s = 2 ε 1 2 ε 3 2 ( ε 1 + ε 3 ) ( ε 1 2 ε 3 2 ) ω ˜ 2 κ SPR ,
κ s = 4 ( Re { κ SPR } ω ˜ ) .
r ˜ 51 = r 53 + t 53 r 31 t 35 exp ( 2 i w 3 d ) 1 r 31 r 35 exp ( 2 i w 3 d ) = r 53 + r 31 exp ( 2 i w 3 d ) 1 r 31 r 35 exp ( 2 i w 3 d ) ,
ϕ = 2 tan 1 ( Im { w 3 } ε 5 Re { w 5 } Re { ε 3 } )
r 31 = κ s κ ( κ m + i γ ) with κ m + i γ = κ SPR .
R 51 = exp ( i ϕ ) + β r 31 1 + β r 31 exp ( i ϕ ) 2
= 1 4 β Im { r 31 } sin ϕ 1 + β 2 r 31 2 + 2 β ( cos ϕ Re { r 31 } + sin ϕ Im { r 31 } ) ,
= 1 4 β γ κ s sin ϕ ( κ κ m + β κ s cos ϕ ) 2 + ( γ + β κ s sin ϕ ) 2 ,
tan ( hd ) = q + p h ( 1 qp h 2 ) ,
r ˜ 31 κ s κ κ m ,
κ s = 2 p m h m 2 κ m ω ˜ 2 1 ε 1 ε 2 q m p m q m + p m + q m p m d ,
r ˜ 31 κ s κ ( κ m + i γ ) ,
r ˜ 51 = r 54 + t 54 r ˜ 41 t 45 exp ( i 2 w 4 s ) 1 r 45 r ˜ 41 exp ( i 2 w 4 s )
r ˜ 41 = r 43 + r ˜ 31 exp ( i 2 w 3 D ) 1 r 34 r ˜ 31 exp ( i 2 w 3 D ) .
R 51 = r 54 2 + 1 r 54 2 2 exp ( i 2 w 4 s ) 2 R 41 ,
ϕ = 2 tan 1 ( κ m 2 ω ˜ 2 ε 3 ω ˜ 2 ε 4 κ m 2 ) 1 2 .
R 41 = exp ( i ϕ ) + β r ˜ 31 1 + β r ˜ 31 exp ( i ϕ ) 2 .
R 51 = r 54 2 + 1 r 54 2 2 exp ( i 2 w 4 s ) 2 [ 1 4 β γ κ s sin ϕ ( κ κ m + β κ s cos ϕ ) 2 + ( γ + β κ s sin ϕ ) 2 ] ,
θ crit = sin 1 ( κ m β κ s cos ϕ n 4 ω ˜ )
[ R 41 ] min = [ γ β κ s sin ϕ γ + β κ s sin ϕ ] 2 ,
D opt = 1 2 p m ln [ γ κ s sin ϕ ] .

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