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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 8 — Apr. 12, 2010
  • pp: 7893–7898
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Multiple extraordinary optical transmission peaks from evanescent coupling in perforated metal plates surrounded by dielectrics

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez  »View Author Affiliations


Optics Express, Vol. 18, Issue 8, pp. 7893-7898 (2010)
http://dx.doi.org/10.1364/OE.18.007893


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Abstract

We study numerically and theoretically the optical transmission of nanostructured gold films embedded in dielectric claddings. We show how multiple transmission peaks appear as the claddings thickness increases. These transmission peaks come not only from surface plasmon polariton excitations but also from the excitation of Fabry-Perot modes sustained at the claddings, coupled through the metal, as long as a periodic pattern is milled in the metal film. We propose that this structure could be used as an ultracompact all-optical switch by surrounding the metal film with Kerr nonlinear dielectric layers.

© 2010 OSA

1. Introduction

2. Numerical and theoretical results

The considered structure consists of a gold metal film milled with a square array of subwavelength holes with radius a of 1μm surrounded at both sides by dielectric claddings with a variable thickness d. The lattice period, P, is 5.5μm and the gold film thickness, dm, is 100nm. A schematic picture of the structure is shown in Fig. 1(a)
Fig. 1 (Color online) (a) Schematic view of the structure under study and the corresponding reference system used. (b) Transmission through a hole array (solid red line) and an unpatterned gold film (dashed blue line) with dielectric thickness d = 4 μm obtained from numerical simulation.
. In Fig. 1(b) we show the simulated transmission spectrum corresponding to a dielectric cladding thickness d = 4μm for normal incident radiation with its electric field E pointing along the x direction obtained with the licensed software CST Microwave Studio, a general purpose electromagnetic simulator based on the finite integration technique. The relative dielectric constant of gold is fitted by the Drude model with the bulk plasma frequency ωp = 1.36x1016 rad/s and damping rate γ = 1014 Hz [7

7. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]

]. Both cladding slabs are SU8 layers with εr = 2.25. From the transmission spectrum of the periodic array (solid line) it can be seen how multiple peaks emerge showing extraordinary transmission. However, these multiple peaks are not expected to appear only from SPP theory. The transmission spectrum considering an unpatterned gold film (dashed line) reveals that these resonances are neither due to tunnelling of light by evanescent waves in the gold film nor to FP modes in the SU8 slabs coupled through opaque flat metal slabs. In addition, the transmission level is very low as expected for a flat optically thick metal film. Thus, only when the structure is periodically patterned the multiple transmission peaks are observed, showing the influence of the lattice in the transmission through subwavelength metallic hole arrays.

On the theoretical side, in order to understand the physical origin of the unexpected peaks we derive the conditions required for light transmission from FP resonances through drilled metallic films sandwiched between two surrounding dielectric claddings. Figure 2
Fig. 2 (Color online) Schematic diagram of the FP configuration for a flat metal slab (εm,dm) surrounded with dielectric claddings (εd,d).
depicts a diagram of the FP scheme. A monochromatic transverse magnetic (TM) polarized plane wave is considered as the impinging light in the x-z plane. For simplicity, we consider a flat metal slab with no holes to obtain the transmission coefficient T as a function of the frequency and the transversal wavevector (kx). Only then, we consider the periodicity in the transversal plane by forcing kx to have the values given by the reciprocal lattice vectors associated to the periodicity in the metallic hole array. Although this procedure has to be considered as an approximation because the scattering effects caused by the holes are ignored, the predictions of the model are very accurate. In that sense, in analogy with the well accepted model to predict the SPP dispersion relation for single layer hole arrays [8

8. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

10

10. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavlength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

], this model provides a simple means to predict analytically an approximate resonant frequency for the EOT peaks coming from the excitation of FP modes without requiring the use of more complex methods that consider the scattering of the holes.

Specifically, the fields in each layer considering propagating waves in the claddings slabs and evanescent in the metal film can be expressed as follows, where the common factor exp(j(kxxϖt))is omitted in all the expressions:
Hy=Al+ejklz+Alejklz,kl=(k02kx2)1/2.
(1)
for z0,
Hy=Ai+ejkdz+Aiejkdz,kd=(k02εdkx2)1/2.
(2)
for the two (i = 1,2) claddings,
Hy=Bm+ekmz+Bmekmz,km=(kx2k02εm)1/2.
(3)
for the metal film, and
Hy=At+ejktz,kt=(k02kx2)1/2.
(4)
for z2d+dm.

In the expressions (1)-(4) k0 is the free-space wave number and εd, εm are the relative permittivity of the claddings and the metal slab, respectively; An+(An) represents the complex amplitude of the forward-propagating (backward-propagating) waves in the corresponding layer; Bm+(Bm) denotes the forward-decaying (backward-decaying) evanescent wave in the metal slab. In particular, At+ corresponds to a transmission amplitude t. The square of its magnitude corresponds to the transmission T coefficient, respectively.

It should be remarked that with this electromagnetic scheme no SPP excitation is considered as long as kd remains a real value. However, in the considered frequency range kl takes imaginary values. Consequently, the fields are evanescent in the air implying that the supported electromagnetic fields correspond to guided modes only in the dielectric cladding giving rise to FP modes. Thus, there is no possibility for incoming light to couple to the FP modes in flat metal slabs. However, the coupling is possible when the metal is drilled with a periodical pattern due to the additional momentum given by the periodicity. It has to be stressed that it is the periodicity of the hole array what enables the coupling from external light to guided modes and, as a result, the multiple EOT peaks. If the holes were randomly distributed, external light would not couple to these modes [11

11. A. Martínez and J. Martí, “Negative refraction in two-dimensional photonic crystals: role of the lattice orientation and the interface termination,” Phys. Rev. B 71(23), 235115 (2005). [CrossRef]

], and only resonances due to the features of isolated holes would be observed [12

12. Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006). [CrossRef] [PubMed]

]. Figure 3
Fig. 3 (Color online) Representation of the theoretical transmission coefficient T(f,kx) for a dielectric thickness of d = 4 μm. Insets: electric and magnetic fields for TE and TM modes respectively in a structure scaled for better representation.
shows the calculated T(f,kx) coefficient for the same dielectric thickness as in Fig. 1(b), where T was rescaled for a better representation . The insets show how the sustained modes are propagating in the dielectric and evanescent in the air (they lay between the vacuum and dielectric light lines). Now, the unexpected EOT peaks appeared in the transmission spectrum of Fig. 1(b) can be explained if we just consider the values in kx associated to the periodicity in the metallic hole array, for which light coupling can be possible. With this consideration, it is inferred from Fig. 3 that transmission is achieved at 37.77 THz, 41.21 THz, 48.16 THz and 53.2 THz, in close similarity to the ones obtained in numerical simulation at 36.07 THz, 40.88 THz, 45.58 THz and 50.33 THz. The predicted resonant frequencies are slightly larger than those obtained in simulations because the scattering effects produced by the presence of the holes are not taken into account in our model [8

8. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

]. It should be remarked that although the TM0 mode is above the dielectric light line, it becomes a SPP mode when the dielectric thickness increases.

Figure 4(a)
Fig. 4 (Color online) (a) Simulated transmission spectra vs. dielectric thickness d. (b) The same for the calculated transmission spectra T after considering the kx values associated with the periodicity.
shows the simulated light transmission spectra, as a function of the cladding thickness d, through the subwavelength metallic hole array for a normal incoming plane wave. The variations of the peaks resonant frequencies show the spectra dependence on the cladding thickness and how more transmission peaks appear when increasing d. These multiple transmission peaks are not all expected to appear only from SPPs theory. On the other hand, Fig. 4(b) shows the variation of the theorized transmission coefficient T with the cladding thickness d, after considering the periodicity of the drilled metallic hole array in the transversal wavevector component kx. The flat line around 36THz is a numerical artifact which corresponds to the trivial solution of the dielectric light line corresponding to the case when all fields are zero [13

13. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]

]. The same scale factor is also used again to represent T.

3. Application to ultrafast all-optical switching

The existence of multiple EOT peaks can be used in several applications. Here, we propose that multiple EOT phenomenon can be employed for ultrafast all-optical switching if the metal layer is surrounded by dielectric layers with high Kerr nonlinear coefficients (such as nonlinear polymers [14

14. B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008). [CrossRef]

] or silicon nanocrystals in a silica matrix [15

15. R. Spano, N. Daldosso, M. Cazzanelli, L. Ferraioli, L. Tartara, J. Yu, V. Degiorgio, E. Giordana, J. M. Fedeli, and L. Pavesi, “Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550nm,” Opt. Express 17(5), 3941–3950 (2009). [CrossRef] [PubMed]

]). The Kerr effect is an instantaneous variation of the refractive index of a dielectric medium proportional to the optical intensity (square of the electrical field). In the structure under consideration (see Fig. 5
Fig. 5 (Color online) All-optical switch based on multiple EOT through a perforated metal plates surrounded by Kerr nonlinear dielectric media. Pump and probe optical signals are tuned at two different transmission windows (λ1 and λ2). The Kerr effect is modelled by slightly increasing the dielectric refractive index n: Pump on n = 1.505, Pump off n = 1.5. Inset: Scheme of the switching structure, which is extremely compact in the longitudinal direction.
inset), high optical intensities inside the dielectric layers are expected even for moderate power levels as a consequence of the strong confinement of the field at the metal-dielectric interfaces. If we assume that there are two different transmission windows (centred at λ1 and λ2 respectively) arising from the multiple EOT phenomenon, we can use a high-power pulsed pump signal (tuned at λ1) to switch a probe signal (tuned at λ2), as depicted in Fig. 5. When the pump signal is on, the index of the dielectric layers is instantaneously increased owing to the Kerr effect, which results in a red-shift of the EOT peaks. This produces an immediate effective switching of the probe controlled by the pump signal. Compared to other all-optical switching approaches, this structure has the important advantage of being extremely compact in the longitudinal direction, being its size the total dielectric-metal-dielectric thickness. It has to be mentioned that a similar approach (a drilled metal-dielectric-metal structure) has been recently demonstrated to produce subpicosecond all-optical switching by making use of free carriers generated optically [16

16. K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. J. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009). [CrossRef] [PubMed]

].

4. Conclusion

In conclusion, through theoretical analysis and numerical simulations, we have demonstrated a mechanism for multiple extraordinary light transmission through a classically opaque material independent of conventional tunnelling transmission. The present transmission is characterized by FP modes in the claddings evanescently coupled through the drilled metallic film. Moreover, SPP excitations are also present in the transmission spectrum since the TM0 mode lies at the right of the dielectric light line for thicker dielectric claddings. Consequently, these results are of great significance as they relate the important role of the periodicity not only to surface modes, like SPPs, but also to propagating modes in the dielectric claddings in the onset of EOT resonances, and also in the design and operation of highly compact optical devices that could become important building blocks in future nano-optical systems.

Acknowledgments

Financial support by the Spanish MICINN was provided under contracts PET2007-0505, TEC2008-06871-C02-02, and CSD2008-00066. Consolider EMET is gratefully acknowledged. R. Ortuño, C. García-Meca, and F. J. Rodríguez-Fortuño also acknowledge grant programs FPI of UPV, FPU of MICINN, and FPI of GVA, respectively.

References and links

1.

R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55(10), 1117–1120 (1985). [CrossRef] [PubMed]

2.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolf, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

3.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004). [CrossRef] [PubMed]

4.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86(24), 5601–5603 (2001). [CrossRef] [PubMed]

5.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunnelling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94(24), 243905 (2005). [CrossRef]

6.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005). [CrossRef]

7.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]

8.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

9.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

10.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavlength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

11.

A. Martínez and J. Martí, “Negative refraction in two-dimensional photonic crystals: role of the lattice orientation and the interface termination,” Phys. Rev. B 71(23), 235115 (2005). [CrossRef]

12.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006). [CrossRef] [PubMed]

13.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]

14.

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008). [CrossRef]

15.

R. Spano, N. Daldosso, M. Cazzanelli, L. Ferraioli, L. Tartara, J. Yu, V. Degiorgio, E. Giordana, J. M. Fedeli, and L. Pavesi, “Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550nm,” Opt. Express 17(5), 3941–3950 (2009). [CrossRef] [PubMed]

16.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. J. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009). [CrossRef] [PubMed]

OCIS Codes
(050.2230) Diffraction and gratings : Fabry-Perot
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: January 19, 2010
Revised Manuscript: February 26, 2010
Manuscript Accepted: March 23, 2010
Published: March 31, 2010

Citation
R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, "Multiple extraordinary optical transmission peaks from evanescent coupling in perforated metal plates surrounded by dielectrics," Opt. Express 18, 7893-7898 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-7893


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References

  1. R. Dragila, B. Luther-Davies, and S. Vukovic, “High transparency of classically opaque metallic films,” Phys. Rev. Lett. 55(10), 1117–1120 (1985). [CrossRef] [PubMed]
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolf, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  3. K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004). [CrossRef] [PubMed]
  4. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86(24), 5601–5603 (2001). [CrossRef] [PubMed]
  5. L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunnelling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94(24), 243905 (2005). [CrossRef]
  6. V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005). [CrossRef]
  7. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]
  8. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
  9. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  10. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavlength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
  11. A. Martínez and J. Martí, “Negative refraction in two-dimensional photonic crystals: role of the lattice orientation and the interface termination,” Phys. Rev. B 71(23), 235115 (2005). [CrossRef]
  12. Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006). [CrossRef] [PubMed]
  13. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182(2), 539–554 (1969). [CrossRef]
  14. B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008). [CrossRef]
  15. R. Spano, N. Daldosso, M. Cazzanelli, L. Ferraioli, L. Tartara, J. Yu, V. Degiorgio, E. Giordana, J. M. Fedeli, and L. Pavesi, “Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550nm,” Opt. Express 17(5), 3941–3950 (2009). [CrossRef] [PubMed]
  16. K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. J. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009). [CrossRef] [PubMed]

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