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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 23 — Nov. 8, 2010
  • pp: 23957–23964
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Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves

Miguel Beruete, Miguel Navarro-Cía, Diana C. Skigin, and Mario Sorolla  »View Author Affiliations


Optics Express, Vol. 18, Issue 23, pp. 23957-23964 (2010)
http://dx.doi.org/10.1364/OE.18.023957


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Abstract

Experimental evidence of phase resonances in a dual-period reflection structure comprising three subwavelength grooves in each period is provided in the millimeter-wave regime. We have analyzed and measured the response of these structures and show that phase resonances are characterized by a minimum in the reflected response, as predicted by numerical calculations. It is also shown that under oblique incidence these structures exhibit additional phase resonances not present for normal illumination because of the potentially permitted odd field distribution. A satisfactory agreement between the experimental and numerical reflectance curves is obtained. These results confirm the recent theoretical predictions of phase resonances in reflection gratings in the millimeter-wave regime, and encourage research in this subject due to the multiple potential applications, such as frequency selective surfaces, backscattering reduction and complex-surface-wave-based sensing. In addition, it is underlined here that the response becomes much more complex than the mere infinite analysis when one considers finite periodic structures as in the real experiment.

© 2010 Optical Society of America

1. Introduction

It is well known that when an infinite metallic grating is illuminated by p-polarized light, a surface plasmon polariton (SPP) can be excited along the surface [1

1. V. M. Agranovich and D. L. Mills, Surface polaritons, (North Holland, Amsterdam, 1982).

]. This excitation is accompanied by a significant power absorption [2

2. A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965). [CrossRef]

, 3

3. M. C. Hutley, “Anomalies and the electromagnetic theory of grating efficiencies,” chapter 6 in Diffraction gratings, (Academic Press, London, 1982).

], and consequently it produces a sudden change in the efficiency curves of the reflected orders. This phenomenon is particularly important when the corrugations are shallow. However, as the depth of the grooves is increased, another type of resonance can take place: the eigenmodes of each cavity can be excited, producing interesting resonant effects, such as field enhancement inside the corrugations [4

4. J. R. Andrewartha, J. R. Fox, and I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta (Lond.) 26, 69–89 (1977). [CrossRef]

, 5

5. A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985). [CrossRef]

]. Both effects manifest themselves as dips in the reflected power curves and absorption peaks, and they can even merge into one another forming hybrid resonances [6

6. T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998). [CrossRef]

, 7

7. D. C. Skigin and R. A. Depine, “Surface shape resonances and surface plasmon polariton excitations in bottle-shaped metallic gratings,” Phys. Rev. E 63, 046608 (2001). [CrossRef]

]. Based on the results for infinite periodic structures, resonances occuring in finite gratings comprising rectangular grooves have also been investigated [8

8. A. Zuniga-Segundo and O. Mata-Mendez, “Interaction of S-polarized beams with infinitely conducting grooves: enhanced fields and dips in the reflectivity,” Phys. Rev. B 46, 536–539 (1992). [CrossRef]

12

12. R. A. Depine and D. C. Skigin, “Resonant modes of a bottle-shaped cavity and their effects in the response of finite and infinite gratings,” Phys. Rev. E 61, 4479–4490 (2000). [CrossRef]

].

The study of finite compound arrays has been historically connected to the superdirective property exhibited by structures formed by an array of passive elements such as slotted cylinders [13

13. V. V. Veremey and R. Mittra, “Scattering from structures formed by resonant elements,” IEEE Trans. Antenn. Propag. 46, 494–501 (1998). [CrossRef]

] or rectangular cavities [14

14. D. C. Skigin, V. V. Veremey, and R. Mittra, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999). [CrossRef]

]. Phase resonances were first reported in such structures, and were later observed in compound infinitely periodic gratings [15

15. A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effect in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001). [CrossRef]

17

17. D. C. Skigin, A. N. Fantino, and S. I. Grosz, “Phase resonances in compound metallic gratings,” J. Opt. A, Pure Appl. Opt. 5, S129–S135 (2003). [CrossRef]

]. Le Perchec et al. analyzed the excitation of phase resonances in a two-slit system [18

18. J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at sub-wavelength scales,” Phys. Rev. Lett. 97, 036405 (2006). [CrossRef] [PubMed]

], and recently Barbara et al. investigated a new kind of resonances that arise in commensurate arrangements of deep metallic sub-wavelength grooves [19

19. A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008). [CrossRef]

].

Phase resonances take place under p-polarized incidence for subwavelength grooves and they are only permitted when the period is formed by several slits or cavities. They are usually excited within a waveguide mode resonance, and are characterized by a phase reversal of the magnetic field in adjacent slits within each period [14

14. D. C. Skigin, V. V. Veremey, and R. Mittra, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999). [CrossRef]

]. Phase resonances manifest themselves as sharp features in the reflected and transmitted responses. This kind of resonances has recently been reported for s polarization, but in this case a material with a large dielectric constant is needed to be placed within the grooves to increase their effective width [20

20. D. Crouse, E. Jacquay, A. Maikal, and A. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

].

There are a few recent works in the literature that report experimental demonstrations of phase resonances, most of them in slit transmission structures [21

21. A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006). [CrossRef] [PubMed]

23

23. M. Navarro-Cía, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009). [CrossRef]

]. For reflection gratings with dual-period, reflectance measurements have been reported in [24

24. A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002). [CrossRef]

], where the authors analyze the excitation of surface plasmons and the absorption they produce at resonance. Recently, Barbara et al. gave experimental evidence of phase resonance excitation in the infrared region [19

19. A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008). [CrossRef]

, 25

25. A. Barbara, S. Collin, C. Sauvan, J. Le Perchec, C. Maxime, J.-L. Pelouard, and P. Quémerais, “Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating,” Opt. Express 18, 14913–14925 (2010). [CrossRef] [PubMed]

].

In this work we report experimental demonstration of phase resonances in compound reflection structures comprising three grooves within each period, and highlight the complexity physics arising from finiteness issues on such gratings. Copper samples have been fabricated, and their reflectance has been measured for normal and oblique incidence in the millimeter wave regime. Strictly speaking, SPPs do not excite in this regime. Nevertheless, they are mimicked by a leaky wave [26

26. R. Ulrich, “Modes of propagation on an open periodic waveguide for the far infrared,” Proc. Symposium Opt. Acoust. Microelectronics, New York, (1974).

, 27

27. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

]. The experimental results are compared with those obtained by numerical calculations.

2. Configuration and experimental setup

We fabricated a copper sample by wire-cut electrical discharge machining in which a total of 51 rulings of rectangular cross section were practised. The grooves are distributed in 17 groups of three grooves each, so that the structure can be regarded as a finite compound grating comprising three grooves in each period (see Fig. 1). The grooves’ width and the separation between nearest grooves is c = a = 0.4mm, their nominal depth is h = 1.1mm, and the period is d = 2.8mm. The copper wafer has a total diameter of 62.4 mm. The structure is illuminated by a linearly polarized Gaussian beam of wavelength λ and frequency f, coming with an angle θ0 with the y-axis.

Fig. 1 Fabricated sample and scheme of the compound reflection grating with subwavelength rectangular grooves.

The measurements of the reflected intensity were performed with an ABmmTM Quasi Optical (QO) Vector Network Analyzer. In this solid-state instrument, the millimeter-submillimeter wave frequencies are obtained by the frequency multiplication of centimeter wave frequencies generated by an internal tunable source. Afterwards, the detection is done by harmonic mixing heterodyne down-conversion. The QO set-up consists of a corrugated horn antenna that generates a very well linearly polarized Gaussian beam which, after two ellipsoidal mirrors, is focused over the sample under test with a beamwaist of 28 mm for the frequency range of this work. The reflected beam covers the same path inversely, and is steered towards the harmonic mixer by a directional coupler placed after the corrugated horn antenna. This set-up is optimized for normal incidence. When oblique incidence angles are considered, the reflected beam is misaligned with respect to the ellipsoidal mirrors, and thus, a penalty on the recorded reflected power may be suffered. For close-to-normal angles of incidence the penalty may be minimal, and this is the reason to restrict the analysis just to θ0 = 5° [28

28. C. Dahl, P. Goy, and J. P. Kotthaus, “Magneto-optical Millimeter-Wave Spectroscopy” in Millimeter and Submillimeter Wave Spectroscopy of Solids (Topics in Applied Physics, Vol. 74), Springer-Verlag Berlin Heidelberg, Ed.: G. Gruener, 221–280 (1998). [CrossRef]

, 29

29. M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Negative refraction through an extraordinary transmission left-handed metamaterial slab,” Phys. Rev. B 79, 195107 (2009).

].

3. Results

The experimental results are compared with the simulations obtained with CST Microwave StudioTM, a completely numerical approach based upon finite integration time domain method. To analyze the response of finitely periodic structures, many authors [19

19. A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008). [CrossRef]

,22

22. Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. E 76, 085413 (2007). [CrossRef]

,30

30. J. Le Perchec, A. Barbara, P. Quemerais, and T. López-Ríos, “Role of commensurate arrangements in the optical response of metallic gratings,” ArXiv 0706.3843 (2007), http://arxiv.org/abs/0706.3843.

] compare the experimental results with the simulated ones obtained by applying periodic boundary conditions, i.e., those corresponding to an infinitely periodic structure. However, for analyzing the generation of phase resonances in dual-period reflection structures in the millimeter-wave regime, it is crucial to use the actual structure to simulate the response, i.e., an infinite plane with a finite number of grooves. In what follows, we call this structure “finite structure”. To illustrate this fact, in Fig. 2 we compare the reflection coefficient for an infinitely periodic compound structure and that corresponding to a finite structure with 17 groups of three grooves each, which represents more accurately the fabricated sample. The infinite case is simulated using the solver defined “unit cell” boundary conditions, reducing the infinite problem to a single cell, and the illumination is done with the zeroth-order mode, which is equivalent to a normally incident plane wave. The finite case, which is actually semi-infinite since the grooves’ length is infinite in order to simplify the simulation model, is illuminated with a plane wave (thus, illumination is uniform) and the reflected component is sensed with a magnetic field probe placed at 100 mm from the surface. It was found that the best matching between the experimental and the simulated results was obtained introducing a thickness h = 1.01mm in the numerical calculation, instead of the actual thickness of the fabricated sample. This implies a fabrication error of approximately 8% in the thickness, which is completely reasonable for the fabrication method of this kind of samples. This thickness value was used in all the results presented. The blue thick curve in Fig. 2, which corresponds to the infinite structure, exhibits a remarkable minimum at a frequency f ≈ 60 GHz on an otherwise planar reflectance of unit value. The red thin curve, which corresponds to the finite structure, has a similar dip at the same frequency, but the rest of the curve exhibits ripples in the frequency range considered. These undulations are generated by the multiple resonances supported by the structure. When the structure is infinitely periodic, only two phase resonances are allowed, i.e., the (+ + +) mode and the (+ − +) mode (the first groove is arbitrarily assigned a plus sign; for the subsequent grooves, if the phase difference is 0 (π), the sign will be the same as (opposite to) that of the preceding one) [14

14. D. C. Skigin, V. V. Veremey, and R. Mittra, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999). [CrossRef]

]. In the latter case this means that in every group of three grooves, the phase of the field within the external grooves is opposite to that of the central one. However, for a finite structure, the number of phase resonances increases with the number of grooves, producing sudden changes in the reflected response. This effect becomes even more pronounced as the groups of grooves become closer to each other, i.e., as the period of the grating is reduced while keeping the other lengths fixed. In this case, field coupling between the fields at adjacent groups of grooves is allowed, and this produces new resonant modes. Taking into account that the fabricated structure has 51 grooves, a very oscillating response must be expected, as shown in Fig. 2. Consequently, in what follows we compare the experimental results with those simulated for the actual finite structure.

Fig. 2 Comparison of the simulated reflection coefficient as a function of the frequency calculated for an infinitely periodic structure and for a finite structure comprising 17 groups of three grooves for normal incidence. The parameters of the structure are: c = a = 0.4 mm, h = 1.01 mm, d = 2.8 mm.

In Fig. 3 we compare the experimental and the numerical results for a copper structure comprising 17 groups of three grooves each, illuminated by a Gaussian beam at normal incidence [Fig. 3(a)] and at θ0 = 5° [Fig. 3(b)]. The thick blue curves correspond to the measurements and the thin red ones, to the simulations.

Fig. 3 Comparison of the measured and the simulated reflection coefficient as a function of the frequency. The simulated results correspond to a finite structure comprising 17 groups of three grooves each, and the parameters of the structure are: c = a = 0.4 mm, h = 1.01 mm, d = 2.8 mm. (a) Normal incidence; (b) oblique incidence (5°).

The most striking characteristic of the reflectance curves in Fig. 3(a) is the minimum at f ≈ 60 GHz. It corresponds to a π resonance mode, which is characterized by a phase reversal of the field within adjacent grooves, as it was predicted in [14

14. D. C. Skigin, V. V. Veremey, and R. Mittra, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999). [CrossRef]

]. The π resonance is the highest quality resonance among the so called phase resonances, which are characterized by phase differences of 0 or π radians between the fields at adjacent grooves [15

15. A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effect in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001). [CrossRef]

]. One of the requirements for a phase resonance to occur is to have at least one phase reversal of the magnetic field in adjacent grooves. The number of possible configurations with at least one phase reversal in adjacent grooves is determined by the total number of grooves in the structure. The symmetry imposed by the normal illumination also restricts the number of allowed modes. In Fig. 3(a) the measured reflectance exhibits a marked minimum at the phase resonance, and the rest of the curve is rather oscillating, with no other significant features. When the structure is obliquely illuminated, new possibilities of resonant configurations open up: the symmetry condition imposed by the normal illumination is removed, thus allowing new phase configurations inside the grooves. Notice that for θ0 = 5° [Fig. 3(b)], the π resonance at f ≈ 60 GHz is still present in the measured as well as in the simulated reflectance, and there is also another minimum at f ≈ 57 GHz, which corresponds to the excitation of another, non-symmetric phase resonance [31

31. D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with sub-wavelength slits,” Phys. Rev. E 74, 046606 (2006). [CrossRef]

]. As observed, there is a good agreement between the experimental and the simulated results, and these results are in qualitative agreement with previously reported experimental data in the infrared region [19

19. A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008). [CrossRef]

, 25

25. A. Barbara, S. Collin, C. Sauvan, J. Le Perchec, C. Maxime, J.-L. Pelouard, and P. Quémerais, “Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating,” Opt. Express 18, 14913–14925 (2010). [CrossRef] [PubMed]

]. However, it is important to remark that in all cases the measured dips are wider than the simulated ones, as it is to expect due to a variety of reasons: small period changes along the fabricated structure, experimental Gaussian beam illumination, which is non-uniform, reception of power employing a horn antenna, instead of the point magnetic field probe used in the simulation. Also, out of the main resonances, the agreement between simulation and experiment is only moderately good. In both cases a strong ripple is observed out of band, but the amplitude as well as frequency peak location is different in each case. As explained above, these oscillations arise from the multiple resonances that can be excited in finite dual-period gratings. Other cause that cannot be neglected is Fabry-Perot interference, inherent and inevitable in the reflection characterization of strongly reflecting structures. Both phenomena can combine to produce the observed ripple, but again the mentioned fundamental differences between simulation and measurement set-ups can lead to different curves in each case. This probably explains the wide experimental dip at f ≈ 57 GHz, which can be the result of the overlap of two resonant dips at f ≈ 56.6 GHz and f ≈ 57.3 GHz. The excitation of phase resonances is extremely sensitive to changes in the incidence angle, and it was observed that even for θ0 = 1° (not shown) this new dip already appears in the reflected response, as it was also found for transmission structures [31

31. D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with sub-wavelength slits,” Phys. Rev. E 74, 046606 (2006). [CrossRef]

]. This implies that a very small misalignment in the measurement system can produce additional resonant features in the reflectance, that should not appear under normal illumination. It is important to recall that in the reflection measurement the dynamic range and the sensitivity of the detection is much smaller than in the transmission measurement [23

23. M. Navarro-Cía, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009). [CrossRef]

], due to the directional coupler used to direct the reflected Gaussian beam. Besides, as the incidence angle is increased, the experimental configuration might be misaligned and this implies an additional penalty in sensitivity of the measurement.

Fig. 4 Magnetic field (phase and modulus) at the bottom of the grooves for two resonant situations: (a) Phase and (b) modulus for θ0 = 0° and f = 59.67 GHz; (c) phase and (d) modulus for θ0 = 5° and f = 59.78 GHz.

4. Conclusion

In conclusion, we have demonstrated experimentally the recent theoretical predictions of phase resonances in a dual-period reflection structure comprising three subwavelength grooves of rectangular cross section, in the millimeter wave regime. A copper sample was fabricated and its reflectance has been measured under normal and oblique incidence. It was shown that the reflected response exhibits minima that are associated with the excitation of phase resonances in the structure. In particular, for oblique incidence there appear additional resonant modes that cannot be excited under normal illumination. The experimental curves have been compared with numerical results obtained by a commercial software based upon finite integration time domain method, and a satisfactory agreement was obtained. In addition, aided by the software, we have been able to catch more details arising from the finiteness of the structure than those manifested on previously reported infinite compound grating analysis. We have shown that a groove width of roughly λ/10 is sufficiently subwavelength to excite phase resonances. This is an attractive fact if we think of applying this property for the design of selective devices. The results here presented confirm the common nature of π resonances of reflection gratings in frequency regimes where metals have very different behavior such as nearly perfect conductors as is the case in this paper or plasmonic models as in Refs. [19

19. A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008). [CrossRef]

] and [25

25. A. Barbara, S. Collin, C. Sauvan, J. Le Perchec, C. Maxime, J.-L. Pelouard, and P. Quémerais, “Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating,” Opt. Express 18, 14913–14925 (2010). [CrossRef] [PubMed]

].

Acknowledgments

D.S. gratefully acknowledges partial support from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET PIP 112-200801-01880), Universidad de Buenos Aires (UBA X208) and Agencia Nacional de Promoción Científica y Tecnológica (ANPCYT-BID 1728 /OC-AR06-01785). This work was also supported by Consolider “ENGINEERING METAMATERIALS” CSD2008-00066.

References and links

1.

V. M. Agranovich and D. L. Mills, Surface polaritons, (North Holland, Amsterdam, 1982).

2.

A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965). [CrossRef]

3.

M. C. Hutley, “Anomalies and the electromagnetic theory of grating efficiencies,” chapter 6 in Diffraction gratings, (Academic Press, London, 1982).

4.

J. R. Andrewartha, J. R. Fox, and I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta (Lond.) 26, 69–89 (1977). [CrossRef]

5.

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985). [CrossRef]

6.

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998). [CrossRef]

7.

D. C. Skigin and R. A. Depine, “Surface shape resonances and surface plasmon polariton excitations in bottle-shaped metallic gratings,” Phys. Rev. E 63, 046608 (2001). [CrossRef]

8.

A. Zuniga-Segundo and O. Mata-Mendez, “Interaction of S-polarized beams with infinitely conducting grooves: enhanced fields and dips in the reflectivity,” Phys. Rev. B 46, 536–539 (1992). [CrossRef]

9.

A. A. Maradudin, A. V. Shchegrov, and T. A. Leskova, “Resonant scattering of electromagnetic waves from a rectangular groove on a perfectly conducting surface,” Opt. Commun. 135, 352–360 (1997). [CrossRef]

10.

O. Mata-Mendez and J. Sumaya-Martinez, “Scattering of TE-polarized waves by a finite grating: giant resonant enhancement of the electric field within the grooves,” J. Opt. Soc. Am. A 14, 2203–2211 (1997). [CrossRef]

11.

D. C. Skigin and R. A. Depine, “Resonant enhancement of the field within a single cavity in a ground plane: comparison for different rectangular shapes,” Phys. Rev. E 59, 3661–3668 (1999). [CrossRef]

12.

R. A. Depine and D. C. Skigin, “Resonant modes of a bottle-shaped cavity and their effects in the response of finite and infinite gratings,” Phys. Rev. E 61, 4479–4490 (2000). [CrossRef]

13.

V. V. Veremey and R. Mittra, “Scattering from structures formed by resonant elements,” IEEE Trans. Antenn. Propag. 46, 494–501 (1998). [CrossRef]

14.

D. C. Skigin, V. V. Veremey, and R. Mittra, “Superdirective radiation from finite gratings of rectangular grooves,” IEEE Trans. Antennas Propag. 47, 376–383 (1999). [CrossRef]

15.

A. N. Fantino, S. I. Grosz, and D. C. Skigin, “Resonant effect in periodic gratings comprising a finite number of grooves in each period,” Phys. Rev. E 64, 016605 (2001). [CrossRef]

16.

S. I. Grosz, D. C. Skigin, and A. N. Fantino, “Resonant effects in compound diffraction gratings: influence of the geometrical parameters of the surface,” Phys. Rev. E 65, 056619 (2002). [CrossRef]

17.

D. C. Skigin, A. N. Fantino, and S. I. Grosz, “Phase resonances in compound metallic gratings,” J. Opt. A, Pure Appl. Opt. 5, S129–S135 (2003). [CrossRef]

18.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at sub-wavelength scales,” Phys. Rev. Lett. 97, 036405 (2006). [CrossRef] [PubMed]

19.

A. Barbara, J. Le Perchec, S. Collin, C. Sauvan, J.-L. Pelouard, T. López-Ríos, and P. Quémerais, “Generation and control of hot spots on commensurate metallic gratings,” Opt. Express 16, 19127–19135 (2008). [CrossRef]

20.

D. Crouse, E. Jacquay, A. Maikal, and A. Hibbins, “Light circulation and weaving in periodically patterned structures,” Phys. Rev. B 77, 195437 (2008).

21.

A. P. Hibbins, I. R. Hooper, M. J. Lockyear, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402 (2006). [CrossRef] [PubMed]

22.

Y. G. Ma, X. S. Rao, G. F. Zhang, and C. K. Ong, “Microwave transmission modes in compound metallic gratings,” Phys. Rev. E 76, 085413 (2007). [CrossRef]

23.

M. Navarro-Cía, D. C. Skigin, M. Beruete, and M. Sorolla, “Experimental demonstration of phase resonances in metallic compound gratings with subwavelength slits in the millimeter wave regime,” Appl. Phys. Lett. 94, 091107 (2009). [CrossRef]

24.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002). [CrossRef]

25.

A. Barbara, S. Collin, C. Sauvan, J. Le Perchec, C. Maxime, J.-L. Pelouard, and P. Quémerais, “Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating,” Opt. Express 18, 14913–14925 (2010). [CrossRef] [PubMed]

26.

R. Ulrich, “Modes of propagation on an open periodic waveguide for the far infrared,” Proc. Symposium Opt. Acoust. Microelectronics, New York, (1974).

27.

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

28.

C. Dahl, P. Goy, and J. P. Kotthaus, “Magneto-optical Millimeter-Wave Spectroscopy” in Millimeter and Submillimeter Wave Spectroscopy of Solids (Topics in Applied Physics, Vol. 74), Springer-Verlag Berlin Heidelberg, Ed.: G. Gruener, 221–280 (1998). [CrossRef]

29.

M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Negative refraction through an extraordinary transmission left-handed metamaterial slab,” Phys. Rev. B 79, 195107 (2009).

30.

J. Le Perchec, A. Barbara, P. Quemerais, and T. López-Ríos, “Role of commensurate arrangements in the optical response of metallic gratings,” ArXiv 0706.3843 (2007), http://arxiv.org/abs/0706.3843.

31.

D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with sub-wavelength slits,” Phys. Rev. E 74, 046606 (2006). [CrossRef]

32.

C. I. Valencia and D. C. Skigin, “Anomalous reflection in a metallic plate with subwavelength grooves of circular cross section,” Appl. Opt. 48, 5863–5870 (2009). [CrossRef] [PubMed]

OCIS Codes
(290.5820) Scattering : Scattering measurements
(350.4010) Other areas of optics : Microwaves
(240.5440) Optics at surfaces : Polarization-selective devices

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 25, 2010
Revised Manuscript: September 17, 2010
Manuscript Accepted: September 17, 2010
Published: October 29, 2010

Citation
Miguel Beruete, Miguel Navarro-Cía, Diana C. Skigin, and Mario Sorolla, "Millimeter-wave phase resonances in compound reflection gratings with subwavelength grooves," Opt. Express 18, 23957-23964 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-23-23957


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References

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