- Email: [email protected]
Viability of focusing effect by left-handed stacked subwavelength hole arrays
ARTICLE IN PRESS Physica B 405 (2010) 2950–2954
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Viability of focusing effect by left-handed stacked subwavelength hole arrays M. Navarro-Cı´a a, M. Beruete a, M. Sorolla a,, I. Campillo b a b
´ blica de Navarra, Campus Arrosadı´a, 31006 Pamplona, Spain Millimeter and Terahertz Waves Laboratory, Universidad Pu CIC nanoGUNE Consolider, Tolosa Hiribidea 76, 20018 Donostia, Spain
a r t i c l e in f o
a b s t r a c t
Keywords: Metamaterial Left-handed medium Extraordinary transmission Metallic lens
In this work we present advances in the design of lenses based on left-handed extraordinary transmission metamaterials which provide high transmission and focusing despite the subwavelength size of their constituent apertures. Due to the effective negative index of refraction of the close-stack of subwavelength hole arrays, concave profiles are required for focusing instead of the convex geometries of dielectric lenses. An analysis of the foci produced by plano- and bi-concave lens is carried out. & 2010 Elsevier B.V. All rights reserved.
1. Introduction Back to the 1960s of the last century, Veselago proposed the possibility of a negative refractive index (NRI) medium provided it exhibits simultaneous negative permittivity and permeability. A direct consequence of this was the inversion of Snell’s refraction law at the interface between a standard and a NRI medium, among other interesting properties [1]. He predicted that a slab of thickness d, made of a metamaterial with a refractive index n ¼ 1, can focus in a focal point the radiation of another point source located at a distance l od from the slab [1]. An unpredictable property of such a planar slab is its capability to behave as a perfect lens overcoming diffraction limits of propagating waves as a result of the growth of the amplitude of the evanescent waves in the direction of propagation within limited frequency range [2]. Nevertheless, as Veselago also pointed out, this lens cannot focus a bundle of rays coming from infinity [1]. Therefore, alike conventional lenses, one needs to design the geometrical lens profile in order to achieve the above desired property. Moreover, in the case of left-handed (LH) metamaterials convex and concave lenses interchange their roles since the convex lens has a diverging effect and the concave lens a converging one [1]. Since the first experimental confirmation of a double-resonance NRI medium in 2000 [3], some proposals of geometrically profiled and flat lenses exhibiting negative index of refraction or gradient index of refraction, respectively, have been made. Some of these works have been devoted to negative index split ring resonators (SRRs)-based [4] metamaterials [5] whereas others have relied on photonic crystals [6,7]. In the pursuit for optical resonance-based metamaterials [8], stacked Fishnet topologies [9,10] seem to have the best
Corresponding author. Tel.: + 34 948169324; fax: + 34 648169720.
E-mail address: [email protected] (M. Sorolla). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.01.011
performance of all realized designs up to date since classical approaches based on SRRs suffer a great deterioration in their performances as the frequency increases. Soon after the report of the Fishnet scheme as a route for NRI medium, it was shown that the Fishnet could be improved by working within the extraordinary optical transmission (EOT) [11] regime of subwavelength hole arrays, which enhance the transmittance [12].
2. Numerical analysis of the extraordinary transmission metamaterial Prior to any lens design, we characterize the propagation through extraordinary transmission metamaterials (ETM) in terms of dispersion diagram for the infinite structure alongside constitutive EM parameters for a finite number of staked plates so as to confirm the double-negative propagation of these structures. The numerical study has been performed by CST Microwave TM Studio . Then, the constitutive EM parameters are retrieved by an usual method based on S-parameters [13,14]. Notice that the present structure is anisotropic and one of the transverse periodicities is of the order of the wavelength, so that the retrieved parameters cannot be interpreted in the same way as in homogeneous continuous and isotropic media. The dimensions of the ETM unit cell are: transversal periodicities dx ¼ 3 mm, dy ¼ 5 mm, hole diameter a ¼ 2:5 mm, and metal thickness w ¼ 0:5 mm. The longitudinal lattice constant of the stack is dz ¼ 1:5 mm 0:27l, see inset Fig. 1a. With these parameters and illuminating by vertical polarization ðEy Þ the EOT for one layer falls at 57 GHz and the first propagating band of the infinite stack goes from 52.8 to 58 GHz (Fig. 1 a), despite the holes are in cut-off regime [15]. Prominent in the dispersion diagram is the negative slope, which is the characteristic of LH propagation. The LH propagation has also proven through interferometric techniques [9,10,12] and with wedge experiments [15,16].
ARTICLE IN PRESS M. Navarro-Cı´a et al. / Physica B 405 (2010) 2950–2954
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Fig. 1. (a) Dispersion diagram corresponding to the first band associated to EOT. Inset: unit cell along with parameters. (b) Picture of the fabricated prototypes. The biconcave lens is made by simple assembling two plano-concave lenses back to back.
The physical origin of the resonances can be better understood from the retrieved effective material properties rather than from the dispersion diagram. Therefore, numerical analysis of finite stacks is also completed and compared with the infinite case. Transmission coefficient under vertical polarization for 1, 2, and 5 stacked perforated plates alongside retrieved constitutive parameters are plotted in Fig. 2. The main features of Fig. 2 are:
direction, z-direction). In other words, the stack displays a weak dispersion in terms of length from 3 layers on. Needless to say, due to tolerances in fabrication and assembly processes, the nonperfect convergence of the frequency can be neglected with respect to the deviations introduced by tolerances.
1. Due to periodicity artefacts just before the resonances, the retrieved parameters are not reliable in that bandwidth since the effective medium approximation breaks down. 2. The electric permittivity undergoes a Lorentzian dispersion in the upper frequency range of all cases. Moreover, note that electric permittivity comes always from negative values since the structure behaves as a diluted metal (Drude dispersion) for low frequencies. 3. One single subwavelength hole array does not display effective negative magnetic permeability. Specifically, the magnetic permeability remains positive and close to 1 up to 58.4 GHz. 4. The NRI is caused by double negativity, that is, simultaneous negative values of the real parts of the effective permittivity and permeability, from 2 stacked plates on.
In Refs. [17,18], we founded the explanation of the parabolic concave NRI lens on the usual formalism of geometrical optics that describes the reflection in a metal with being a material with refractive index n ¼ 1 [19]. However, the more rigorous approach based on the well-known optical path concept does not need any abstract interpretation [20]. Either the former or the latter, allow us to design a NRI lens with a focal length f ¼ 50 mm. To generate the parabolic geometry, the smooth profile is approximated by discrete steps, corresponding to the unit cell dimensions. Due to the stepped interface, the structure is susceptible of high order diffracted modes which deteriorate slightly the performance [17]. Plano-concave and bi-concave prototypes with parabolic profiles were fabricated in aluminium. The manufacture process includes two stages:
Also, it should be taken into consideration that, as shown in Ref. [13], when the transmission is low or in the vicinity of a resonance, the retrieved imaginary parts are not reliable. The effective index of refraction derived from the dispersion diagram predicts a refractive index nz ¼ 1 (design index of refraction) at 53.5 GHz, which agrees well with the one obtained from wedge experiment [15]. To compare this frequency of the infinite case with the finite geometries, the evolution of the frequency of nz ¼ 1 as a number of stacked perforated plates founded on retrieval method is depicted in Fig. 2 h. This figure can be split in two regions: first, a strong frequency shift between 2 (note that the frequency of 2 stacked layers is within the unreliable zone) and 3 layers as a result of the addition of one perforated plate, and second, a slow monotonous tendency towards 53.5 GHz from 3 layers on. This last feature brings a great advantage for the lens design since it ensures that any zone of the lens will behave almost uniform in terms of effective index of refraction around that frequency, independently of the number of layers of its row (we identify each row as the artificial waveguide defined by consecutive unit cells in the longitudinal
3. Experimental results of planoconcave and biconcave NRI lenses
1. To etch holes pattern by laser-cutting technique in aluminium wafers. 2. To remove central windows of holes by wire-cut electrical discharge machining in order to achieve the desired parabolic geometry once the different layers are assembled. The whole structure, including the frame for the assembly, has maximum dimensions of 125 mm 115 mm 24:5 mm-16 layers-/ 47 mm-31 layers-(plano-/bi-concave lens, respectively), see Fig. 1 b. In the central part, both lenses are composed of 2 layers. The measurements of the transmitted intensity were perTM Quasioptical Vector Network formed with an AB-Millimetre Analyzer which can operate from 40 up to 260 GHz. Nevertheless, we concentrate on the NRI band. This instrument is based on a solid state multiplier that generates the millimetre–submillimetre wave frequencies which are detected by harmonic mixer heterodyne downconversion. For the plano-concave lens, the free space setup consists of a corrugated horn antenna that generates a very well linearly polarized (vertical) Gaussian beam located at
ARTICLE IN PRESS 2952
M. Navarro-Cı´a et al. / Physica B 405 (2010) 2950–2954
Fig. 2. Real and imaginary parts of the effective: electric permittivity (a) and (b), magnetic permeability (c) and (d), and index of refraction (e) and (f); (g) transmission coefficient; 1 (dark curve), 2 (red curve), 5 (blue curve) and infinite number of perforated plates (dotted curve). (h) Frequency at which the index of refraction is nz ¼ -1 as a function of the number of stacked perforated plates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
900 mm from the lens positioner and an open-ended rectangular waveguide as a receiver. On the other hand, the free space setup for the bi-concave lens consists of a two open-ended waveguides with the source situated at the experimental focus of 45 mm [18]. In both cases, the receiver antenna is manually moved transversally (x- and y-directions) at z ¼ 45 mm along the image region so as to measure the transmittance intensity. Between source and detector, the different lenses are placed on an aperture in a sheet of wood. In turn, this holder is shielded by absorber. The empty aperture is the calibration of our measurements. Top panels of Fig. 3 show the transversal intensity as a function of frequency when the plano-concave lens is illuminated from the flat face. Two main foci are observed: one at 53.9 GHz (slightly
higher than the expected frequency of around 53.5 GHz) and the other at 55.8 GHz with an enhancement over the calibration of 1.81 and 1.78 times, respectively. Moreover, top panels highlight an asymmetrical focus with narrower behaviour along xz-plane than yz-plane. For instance, at the frequencies of the maxima, full width at half maximum (FWHM) is 8.8 mm ð 1:6lÞ and 15.9 mm ð 2:9lÞ for the lower and higher frequencies, respectively, along x, and 8.8 mm ð 1:6lÞ and 14.6 mm ð 2:7lÞ along y. On the contrary, for the bi-concave NRI lens, just one focus along the lens axis is recorded. It is located at 54.4 GHz and presents a transmittance enhancement of 12 times with respect to the calibration, which seems to be remarkably higher than the plano-concave lens. Nevertheless, this unexpected high
ARTICLE IN PRESS M. Navarro-Cı´a et al. / Physica B 405 (2010) 2950–2954
2953
Fig. 3. Measured transversal transmittance intensity in linear scale at z ¼ 45 mm as a function of frequency for the plano-concave lens (top panel), and bi-concave lens (bottom panel). Left panels correspond to power distribution along x, whereas right panels depict power distribution along y. The top and bottom colour scales correspond to plano- and bi-concave lenses results in that order. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
enhancement is founded intrinsically in the calibration because of the different sources and the distance of them with respect to the sample. The value of FWHM particularized to the maximum is in this case 4.6 mm ð 0:8lÞ along both x- and y-directions. Therefore, it is worth noting that the asymmetry displayed by the plano-concave lens is not observed in this bi-concave lens and the explanation of this fact may be found again in the different illumination. Apart from the previous comments about each lens result, the main features that can be deduced from all panels of Fig. 3 is that a concave geometry made of stacked subwavelength hole arrays operate as a NRI lens in accordance with the assumptions founded on numerical analysis and present a filtering frequency response, whose bandwidth is defined by the LH mode.
4. Conclusions Stacked subwavelength hole arrays or fishnet structures have been used to design metamaterial lenses in the millimetre wave range. In this stacked structure, it has been demonstrated that the frequency linked to the effective negative index of refraction nz ¼ 1 undergoes small variations with respect to the number of stacked plates from 3 layers on, which is a great advantage for the design. Under this assumption plano- and biconcave lenses have been fabricated corroborating not only this fact, but also achieving remarkable transversal FWHM ranging from 0:8l to 2:9l despite the transversal dimensions of the unit cell, which are comparable to wavelength. Furthermore, since
this type of topology has already been reported also in THz and optics, this result could open the route for the design of similar lens-based-devices in this frequency ranges.
Acknowledgement This work has been supported by the Spanish Government under Contract TEC2008-06871-C02. References [1] [2] [3] [4] [5]
[6] [7] [8] [9] [10] [11] [12] [13] [14]
V.G. Veselago, Soviet Phys. Ups. 10 (1968) 509. J.B. Pendry, Phys. Rev. Lett. 85 (2000) 3966. R.A. Shelby, D.R. Smith, S. Schultz, Science 292 (2001) 77. J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, IEEE Trans. Microwave Theory Tech. 47 (1999) 2075. C.G. Parazzoli, R.B. Greegor, M.H. Taniliean, Development of negative index of refraction metamaterials with split ring resonators and wires for RF lens applications, in: C.M. Krowne, Y. Zhang (Eds.), Physics of Negative Refraction and Negative Index Material, Springer, New York, 2007, pp. 261–329. P. Vodo, P.V. Parimi, W.T. Lu, S. Sridar, Appl. Phys. Lett. 86 (2005) 201108-1. B. Gralak, S. Enoch, G. Tayeb, J. Opt. Soc. Amer. A 17 (2000) 1012. C.M. Soukoulis, S. Linden, M. Wegener, Science 315 (2007) 47. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, S.R.J. Brueck, Phys. Rev. Lett. 95 (2005) 137404-1. G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, S. Linden, Science 312 (2006) 892. T.W. Ebbesen, H.J. Lezec, H. Ghaemi, T. Thio, P.A. Wolf, Nature 391 (1998) 667. M. Beruete, M. Sorolla, I. Campillo, Opt. Express 14 (2006) 5445. X. Chen, T.M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr., J.A. Kong, Phys. Rev. E 70 (2004) 016608-1. D.R. Smith, D.C. Vier, T. Koschny, C.M. Soukoulis, Phys. Rev. E 71 (2005) 036617-1.
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[15] M. Navarro-Cı´a, M. Beruete, M. Sorolla, I. Campillo, Opt. Express 16 (2008) 560. [16] J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D.A. Genov, G. Bartal, X. Zhang, Nature 455 (2008) 376. [17] M. Beruete, M. Navarro-Cı´a, M. Sorolla, I. Campillo, Opt. Express 16 (2008) 9677.
[18] M. Navarro-Cı´a, M. Beruete, M. Sorolla, I. Campillo, Appl. Phys. Lett. 94 (2009) 144107-1-3. [19] S. Cornbleet, Microwave Optics: The Optics of Microwave Antenna Design, Academic Press, New York, 1976. [20] L. Solymar, E. Shamonina, Waves in Metamaterials, Oxford University Press, New York, 2009.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Viability of focusing effect by left-handed stacked subwavelength hole arrays M. Navarro-Cı´a a, M. Beruete a, M. Sorolla a,, I. Campillo b a b
´ blica de Navarra, Campus Arrosadı´a, 31006 Pamplona, Spain Millimeter and Terahertz Waves Laboratory, Universidad Pu CIC nanoGUNE Consolider, Tolosa Hiribidea 76, 20018 Donostia, Spain
a r t i c l e in f o
a b s t r a c t
Keywords: Metamaterial Left-handed medium Extraordinary transmission Metallic lens
In this work we present advances in the design of lenses based on left-handed extraordinary transmission metamaterials which provide high transmission and focusing despite the subwavelength size of their constituent apertures. Due to the effective negative index of refraction of the close-stack of subwavelength hole arrays, concave profiles are required for focusing instead of the convex geometries of dielectric lenses. An analysis of the foci produced by plano- and bi-concave lens is carried out. & 2010 Elsevier B.V. All rights reserved.
1. Introduction Back to the 1960s of the last century, Veselago proposed the possibility of a negative refractive index (NRI) medium provided it exhibits simultaneous negative permittivity and permeability. A direct consequence of this was the inversion of Snell’s refraction law at the interface between a standard and a NRI medium, among other interesting properties [1]. He predicted that a slab of thickness d, made of a metamaterial with a refractive index n ¼ 1, can focus in a focal point the radiation of another point source located at a distance l od from the slab [1]. An unpredictable property of such a planar slab is its capability to behave as a perfect lens overcoming diffraction limits of propagating waves as a result of the growth of the amplitude of the evanescent waves in the direction of propagation within limited frequency range [2]. Nevertheless, as Veselago also pointed out, this lens cannot focus a bundle of rays coming from infinity [1]. Therefore, alike conventional lenses, one needs to design the geometrical lens profile in order to achieve the above desired property. Moreover, in the case of left-handed (LH) metamaterials convex and concave lenses interchange their roles since the convex lens has a diverging effect and the concave lens a converging one [1]. Since the first experimental confirmation of a double-resonance NRI medium in 2000 [3], some proposals of geometrically profiled and flat lenses exhibiting negative index of refraction or gradient index of refraction, respectively, have been made. Some of these works have been devoted to negative index split ring resonators (SRRs)-based [4] metamaterials [5] whereas others have relied on photonic crystals [6,7]. In the pursuit for optical resonance-based metamaterials [8], stacked Fishnet topologies [9,10] seem to have the best
Corresponding author. Tel.: + 34 948169324; fax: + 34 648169720.
E-mail address: [email protected] (M. Sorolla). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.01.011
performance of all realized designs up to date since classical approaches based on SRRs suffer a great deterioration in their performances as the frequency increases. Soon after the report of the Fishnet scheme as a route for NRI medium, it was shown that the Fishnet could be improved by working within the extraordinary optical transmission (EOT) [11] regime of subwavelength hole arrays, which enhance the transmittance [12].
2. Numerical analysis of the extraordinary transmission metamaterial Prior to any lens design, we characterize the propagation through extraordinary transmission metamaterials (ETM) in terms of dispersion diagram for the infinite structure alongside constitutive EM parameters for a finite number of staked plates so as to confirm the double-negative propagation of these structures. The numerical study has been performed by CST Microwave TM Studio . Then, the constitutive EM parameters are retrieved by an usual method based on S-parameters [13,14]. Notice that the present structure is anisotropic and one of the transverse periodicities is of the order of the wavelength, so that the retrieved parameters cannot be interpreted in the same way as in homogeneous continuous and isotropic media. The dimensions of the ETM unit cell are: transversal periodicities dx ¼ 3 mm, dy ¼ 5 mm, hole diameter a ¼ 2:5 mm, and metal thickness w ¼ 0:5 mm. The longitudinal lattice constant of the stack is dz ¼ 1:5 mm 0:27l, see inset Fig. 1a. With these parameters and illuminating by vertical polarization ðEy Þ the EOT for one layer falls at 57 GHz and the first propagating band of the infinite stack goes from 52.8 to 58 GHz (Fig. 1 a), despite the holes are in cut-off regime [15]. Prominent in the dispersion diagram is the negative slope, which is the characteristic of LH propagation. The LH propagation has also proven through interferometric techniques [9,10,12] and with wedge experiments [15,16].
ARTICLE IN PRESS M. Navarro-Cı´a et al. / Physica B 405 (2010) 2950–2954
2951
Fig. 1. (a) Dispersion diagram corresponding to the first band associated to EOT. Inset: unit cell along with parameters. (b) Picture of the fabricated prototypes. The biconcave lens is made by simple assembling two plano-concave lenses back to back.
The physical origin of the resonances can be better understood from the retrieved effective material properties rather than from the dispersion diagram. Therefore, numerical analysis of finite stacks is also completed and compared with the infinite case. Transmission coefficient under vertical polarization for 1, 2, and 5 stacked perforated plates alongside retrieved constitutive parameters are plotted in Fig. 2. The main features of Fig. 2 are:
direction, z-direction). In other words, the stack displays a weak dispersion in terms of length from 3 layers on. Needless to say, due to tolerances in fabrication and assembly processes, the nonperfect convergence of the frequency can be neglected with respect to the deviations introduced by tolerances.
1. Due to periodicity artefacts just before the resonances, the retrieved parameters are not reliable in that bandwidth since the effective medium approximation breaks down. 2. The electric permittivity undergoes a Lorentzian dispersion in the upper frequency range of all cases. Moreover, note that electric permittivity comes always from negative values since the structure behaves as a diluted metal (Drude dispersion) for low frequencies. 3. One single subwavelength hole array does not display effective negative magnetic permeability. Specifically, the magnetic permeability remains positive and close to 1 up to 58.4 GHz. 4. The NRI is caused by double negativity, that is, simultaneous negative values of the real parts of the effective permittivity and permeability, from 2 stacked plates on.
In Refs. [17,18], we founded the explanation of the parabolic concave NRI lens on the usual formalism of geometrical optics that describes the reflection in a metal with being a material with refractive index n ¼ 1 [19]. However, the more rigorous approach based on the well-known optical path concept does not need any abstract interpretation [20]. Either the former or the latter, allow us to design a NRI lens with a focal length f ¼ 50 mm. To generate the parabolic geometry, the smooth profile is approximated by discrete steps, corresponding to the unit cell dimensions. Due to the stepped interface, the structure is susceptible of high order diffracted modes which deteriorate slightly the performance [17]. Plano-concave and bi-concave prototypes with parabolic profiles were fabricated in aluminium. The manufacture process includes two stages:
Also, it should be taken into consideration that, as shown in Ref. [13], when the transmission is low or in the vicinity of a resonance, the retrieved imaginary parts are not reliable. The effective index of refraction derived from the dispersion diagram predicts a refractive index nz ¼ 1 (design index of refraction) at 53.5 GHz, which agrees well with the one obtained from wedge experiment [15]. To compare this frequency of the infinite case with the finite geometries, the evolution of the frequency of nz ¼ 1 as a number of stacked perforated plates founded on retrieval method is depicted in Fig. 2 h. This figure can be split in two regions: first, a strong frequency shift between 2 (note that the frequency of 2 stacked layers is within the unreliable zone) and 3 layers as a result of the addition of one perforated plate, and second, a slow monotonous tendency towards 53.5 GHz from 3 layers on. This last feature brings a great advantage for the lens design since it ensures that any zone of the lens will behave almost uniform in terms of effective index of refraction around that frequency, independently of the number of layers of its row (we identify each row as the artificial waveguide defined by consecutive unit cells in the longitudinal
3. Experimental results of planoconcave and biconcave NRI lenses
1. To etch holes pattern by laser-cutting technique in aluminium wafers. 2. To remove central windows of holes by wire-cut electrical discharge machining in order to achieve the desired parabolic geometry once the different layers are assembled. The whole structure, including the frame for the assembly, has maximum dimensions of 125 mm 115 mm 24:5 mm-16 layers-/ 47 mm-31 layers-(plano-/bi-concave lens, respectively), see Fig. 1 b. In the central part, both lenses are composed of 2 layers. The measurements of the transmitted intensity were perTM Quasioptical Vector Network formed with an AB-Millimetre Analyzer which can operate from 40 up to 260 GHz. Nevertheless, we concentrate on the NRI band. This instrument is based on a solid state multiplier that generates the millimetre–submillimetre wave frequencies which are detected by harmonic mixer heterodyne downconversion. For the plano-concave lens, the free space setup consists of a corrugated horn antenna that generates a very well linearly polarized (vertical) Gaussian beam located at
ARTICLE IN PRESS 2952
M. Navarro-Cı´a et al. / Physica B 405 (2010) 2950–2954
Fig. 2. Real and imaginary parts of the effective: electric permittivity (a) and (b), magnetic permeability (c) and (d), and index of refraction (e) and (f); (g) transmission coefficient; 1 (dark curve), 2 (red curve), 5 (blue curve) and infinite number of perforated plates (dotted curve). (h) Frequency at which the index of refraction is nz ¼ -1 as a function of the number of stacked perforated plates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
900 mm from the lens positioner and an open-ended rectangular waveguide as a receiver. On the other hand, the free space setup for the bi-concave lens consists of a two open-ended waveguides with the source situated at the experimental focus of 45 mm [18]. In both cases, the receiver antenna is manually moved transversally (x- and y-directions) at z ¼ 45 mm along the image region so as to measure the transmittance intensity. Between source and detector, the different lenses are placed on an aperture in a sheet of wood. In turn, this holder is shielded by absorber. The empty aperture is the calibration of our measurements. Top panels of Fig. 3 show the transversal intensity as a function of frequency when the plano-concave lens is illuminated from the flat face. Two main foci are observed: one at 53.9 GHz (slightly
higher than the expected frequency of around 53.5 GHz) and the other at 55.8 GHz with an enhancement over the calibration of 1.81 and 1.78 times, respectively. Moreover, top panels highlight an asymmetrical focus with narrower behaviour along xz-plane than yz-plane. For instance, at the frequencies of the maxima, full width at half maximum (FWHM) is 8.8 mm ð 1:6lÞ and 15.9 mm ð 2:9lÞ for the lower and higher frequencies, respectively, along x, and 8.8 mm ð 1:6lÞ and 14.6 mm ð 2:7lÞ along y. On the contrary, for the bi-concave NRI lens, just one focus along the lens axis is recorded. It is located at 54.4 GHz and presents a transmittance enhancement of 12 times with respect to the calibration, which seems to be remarkably higher than the plano-concave lens. Nevertheless, this unexpected high
ARTICLE IN PRESS M. Navarro-Cı´a et al. / Physica B 405 (2010) 2950–2954
2953
Fig. 3. Measured transversal transmittance intensity in linear scale at z ¼ 45 mm as a function of frequency for the plano-concave lens (top panel), and bi-concave lens (bottom panel). Left panels correspond to power distribution along x, whereas right panels depict power distribution along y. The top and bottom colour scales correspond to plano- and bi-concave lenses results in that order. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
enhancement is founded intrinsically in the calibration because of the different sources and the distance of them with respect to the sample. The value of FWHM particularized to the maximum is in this case 4.6 mm ð 0:8lÞ along both x- and y-directions. Therefore, it is worth noting that the asymmetry displayed by the plano-concave lens is not observed in this bi-concave lens and the explanation of this fact may be found again in the different illumination. Apart from the previous comments about each lens result, the main features that can be deduced from all panels of Fig. 3 is that a concave geometry made of stacked subwavelength hole arrays operate as a NRI lens in accordance with the assumptions founded on numerical analysis and present a filtering frequency response, whose bandwidth is defined by the LH mode.
4. Conclusions Stacked subwavelength hole arrays or fishnet structures have been used to design metamaterial lenses in the millimetre wave range. In this stacked structure, it has been demonstrated that the frequency linked to the effective negative index of refraction nz ¼ 1 undergoes small variations with respect to the number of stacked plates from 3 layers on, which is a great advantage for the design. Under this assumption plano- and biconcave lenses have been fabricated corroborating not only this fact, but also achieving remarkable transversal FWHM ranging from 0:8l to 2:9l despite the transversal dimensions of the unit cell, which are comparable to wavelength. Furthermore, since
this type of topology has already been reported also in THz and optics, this result could open the route for the design of similar lens-based-devices in this frequency ranges.
Acknowledgement This work has been supported by the Spanish Government under Contract TEC2008-06871-C02. References [1] [2] [3] [4] [5]
[6] [7] [8] [9] [10] [11] [12] [13] [14]
V.G. Veselago, Soviet Phys. Ups. 10 (1968) 509. J.B. Pendry, Phys. Rev. Lett. 85 (2000) 3966. R.A. Shelby, D.R. Smith, S. Schultz, Science 292 (2001) 77. J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, IEEE Trans. Microwave Theory Tech. 47 (1999) 2075. C.G. Parazzoli, R.B. Greegor, M.H. Taniliean, Development of negative index of refraction metamaterials with split ring resonators and wires for RF lens applications, in: C.M. Krowne, Y. Zhang (Eds.), Physics of Negative Refraction and Negative Index Material, Springer, New York, 2007, pp. 261–329. P. Vodo, P.V. Parimi, W.T. Lu, S. Sridar, Appl. Phys. Lett. 86 (2005) 201108-1. B. Gralak, S. Enoch, G. Tayeb, J. Opt. Soc. Amer. A 17 (2000) 1012. C.M. Soukoulis, S. Linden, M. Wegener, Science 315 (2007) 47. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, S.R.J. Brueck, Phys. Rev. Lett. 95 (2005) 137404-1. G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, S. Linden, Science 312 (2006) 892. T.W. Ebbesen, H.J. Lezec, H. Ghaemi, T. Thio, P.A. Wolf, Nature 391 (1998) 667. M. Beruete, M. Sorolla, I. Campillo, Opt. Express 14 (2006) 5445. X. Chen, T.M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr., J.A. Kong, Phys. Rev. E 70 (2004) 016608-1. D.R. Smith, D.C. Vier, T. Koschny, C.M. Soukoulis, Phys. Rev. E 71 (2005) 036617-1.
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