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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 3 — Feb. 5, 2007
  • pp: 1115–1127
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Modulating and tuning the response of metamaterials at the unit cell level

Aloyse Degiron, Jack J. Mock, and David R. Smith  »View Author Affiliations


Optics Express, Vol. 15, Issue 3, pp. 1115-1127 (2007)
http://dx.doi.org/10.1364/OE.15.001115


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Abstract

We perform a series of simulations and experiments at microwave frequencies where we dynamically alter the magnetic resonance of one individual split ring resonator by photodoping a piece of low-doped semiconductor positioned within the gap of the resonator. We predict and experimentally achieve a complete suppression of the resonance amplitude using an 815 nm laser source and then briefly consider the problem of tuning the frequency of an SRR by the same method. We also illustrate the metamaterial approach to active electromagnetic devices by implementing a simple yet efficient optical modulator and a three channel dynamical filter.

© 2007 Optical Society of America

1. Introduction

Recently, an innovative approach has been proposed to increase the available range of electromagnetic properties in materials. The idea consists of constructing artificially structured composites, or metamaterials, that mimic the behavior of homogeneous media [1–4

1. R. M. Walser, “Electromagnetic metamaterials,” in Complex Mediums II: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, W. S. Weiglhofer, and I. J. Hodgkinson, eds.,Proc. SPIE4467,1–15 (2001). [CrossRef]

]. Typically, metamaterials are periodic structures obtained by stacking hundreds of subwavelength scattering objects in close proximity. Given that the scale of inhomogeneity of the metamaterial components is much smaller than the wavelengths of operation, the interaction of metamaterials with an applied electromagnetic field can be described to a good approximation in terms of macroscopic quantities—the electric permittivity, ε, and the magnetic permeability, μ— that are averaged over the composite [5

5. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305,788–792 (2004). [CrossRef] [PubMed]

]. By carefully designing the metamaterial unit cells, it is thus possible to construct composites that exhibit effective homogeneous properties unlike those found in naturally occurring materials. For example, it has been experimentally verified [3

3. D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “A composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett 84,4184–4187 (2000). [CrossRef] [PubMed]

] that an array of wires and split ring resonators (SRRs) possesses all the non-intuitive properties predicted by Veselago and Pendry for negative index materials [6

6. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of eand μ,” Sov. Phys. Usp 10,509–514 (1968). [CrossRef]

, 7

7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett 85,3966–3969 (2000). [CrossRef] [PubMed]

] including negative refraction, evanescent wave enhancement and reversal of phase and group velocities [8ߝ15]. In addition to facilitating the development of negative index media, the metamaterial approach has been also successfully applied to design a variety of new structures with unique electromagnetic properties. For example metamaterials can be constructed that exhibit permittivity and permeability tensors having both positive and negative values [16

16. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett 90,077405 (2003). [CrossRef] [PubMed]

]. These indefinite media have remarkable imaging and scattering properties [17

17. D. Schurig and D. R. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys 7,162 (2005). [CrossRef]

] that make them of potential interest as transitioning elements in guided wave optics [18

18. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett 84,2244–2246 (2004). [CrossRef]

, 19

19. A. Degiron, D. R. Smith, J. J. Mock, B. J. Justice, and J. Gollub, “Negative Index and Indefinite Media Waveguide Couplers,” Appl. Phys. A, in press.

]. Another natural application for metamaterials is the development of gradient index media [20

20. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71,036609 (2005). [CrossRef]

] because the value of the permittivity and permeability can be engineered at virtually any point within the structure by adjusting the scattering properties of each unit cell [21

21. R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett 87,091114 (2005). [CrossRef]

, 22

22. T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006). [CrossRef]

]. By implementing complex gradients independently in the permittivity and permeability tensor components, it has been shown that an entirely new class of materials can be realized by the process of transformation optics [23

23. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312,1780–1782 (2006). [CrossRef] [PubMed]

, 24

24. U. Leonhardt, “Optical Conformal Mapping,” Science 312,1777–1780 (2006). [CrossRef] [PubMed]

]. A recent example utilized metamaterials to form an “invisibility cloak” that was demonstrated to render an object invisible to a narrow band of microwave frequencies [25

25. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science ,314,977–980 (2006). [CrossRef] [PubMed]

].

While the possibilities offered by passive composites are already considerable and still growing, recent studies have examined how to dynamically tune or modulate the electromagnetic properties of metamaterials [26–29

26. S. Lim, C. Caloz, and T Itoh, IEEE Trans. Microw. Theory Tech52,2678–2690 (2004). [CrossRef]

]. For example, calculations and experiments performed at microwave frequencies have established that metamaterials can be controlled by incorporating variable capacitance diodes (varactors) to their inner structure. This approach has been first applied in the context of metamaterial transmission lines [26

26. S. Lim, C. Caloz, and T Itoh, IEEE Trans. Microw. Theory Tech52,2678–2690 (2004). [CrossRef]

]. In this study, a bias voltage was applied to the varactors so as to adjust the distributed transmission line capacitance and inductance that both govern the signal propagation. Varactors have been later employed to tune the resonance frequency of SRRs [27

27. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt. Express 14,9344–9349 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9344. [CrossRef] [PubMed]

]. Typically, the electromagnetic response of SRRs results from a resonant exchange of energy between the inductive currents in the rings and the electrostatic fields in the capacitive gaps. It is thus possible to gain control over the structure by altering the resonance conditions; in Ref. [27

27. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt. Express 14,9344–9349 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9344. [CrossRef] [PubMed]

], for example, the authors placed a varactor in the gap in order to dynamically change the capacitance of the resonator. SRRs can also be controlled using visible light, as demonstrated in the THz regime for a planar array of SRRs patterned on a GaAs substrate [28

28. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metama-terial Response at Terahertz Frequencies,” Phys. Rev. Lett 96,107401 (2006). [CrossRef] [PubMed]

]. In Ref. [28

28. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metama-terial Response at Terahertz Frequencies,” Phys. Rev. Lett 96,107401 (2006). [CrossRef] [PubMed]

], the metamaterial electric response was modulated by shorting the SRR gaps through photo-excitation of free carriers in the substrate. An interesting aspect of this work is that only low levels of photodoping are needed, so that the GaAs substrate remains globally nearly transparent. The SRR response, however, is easily degraded because large field enhancements occur within the SRR gaps, rendering the structure extremely sensitive to the photo-induced changes in the substrate conductivity.

Building on these earlier results, we report an alternative way to control SRRs with light. Our structures consist of individual, isolated SRRs operating at microwave frequencies and containing a piece of low doped, n-type silicon positioned within the gap. By monitoring the magnetic resonance of each SRR when the gap is illuminated with near-infrared laser light (λ = 815 nm), we show that the SRR response can be modulated in amplitude or tuned in frequency by controlling the photo-induced losses in silicon. Having restricted the active region to the gap, we have a finer and more efficient control over the SRR response, which might ultimately broaden the range of potential applications as will be explained below with specific examples.

2. Simulations

Fig. 1. General setup. A single SRR containing a small piece of silicon in its gap is loaded in a waveguide defined by two horizontal metal plates and two vertical absorbing plates. The waveguide is 5 cm large and 1.55 cm high. Only the fundamental mode is excited in the frequency range under investigation (7–10 GHz).

Figure 2 shows a first example of controllable SRR. In our simulations, the SRR is made of Cu (thickness 17 μm) deposited on an FR4 laminate substrate (having relative permittivity εFR4=4.4+0.1i). The SRR gap is 0.15 mm wide and contains a thin piece of silicon whose edges are just long enough to make electrical contact with the arms of the SRR. The silicon considered here has the characteristics of the low doped, n-type silicon used in the experiments; that is, the silicon is assumed to have a conductivity σ0 = 0.127 S.m-1, an initial electron carrier density e 0 = 5.68×1012 cm-3 and an initial hole carrier density h 0 = 3.97×107 cm-3. When the silicon is illuminated with photons of energy similar to its bandgap, an excess carrier density is generated that increases the conductivity in the SRR gap [31

31. P. Bhattacharya, “Semiconductor Optoelectronic Devices,” (Prentice Hall, Upper Saddle River, 1997).

]. Because the photo-induced carriers can be considered as an electron-hole plasma, it is possible to relate the level of photodoping to the silicon permittivity εSi using Drude’s theory. We write εSi in its usual form [32

32. C. H. Lee, P. S. Mak, and A. P.De Fonzo, “Optical control of millimeter-wave propagation in dielectric waveguides,” IEEE J. Quantum. Electron 16,277–288 (1980). [CrossRef]

], which can be derived by finding the contribution of the free carriers to the polarization P, or equivalently, to the volume current J:

εSieh=11.8ωpe2ω2+ve2(1iveω)ωph2ω2+vh2(1ivhω).
(1)

In this equation, 11.8 is the relative permittivity due to the host lattice, ω is the incident angular frequency (taken as constant in this study, ω = 2π.8.5 × 109 rad.s-1), ωpe = (eq)1/2/(m*eε0)1/2 is the plasma frequency for the free electrons of density e and effective mass m*e, ωpe = (hq)1/2/(m*hε0)1/2 is the plasma frequency for the holes of density h and effective mass m*h, and ve and Vh are the electron and hole collision frequencies.

Experimentally, the photodoping is limited by optical absorption [31

31. P. Bhattacharya, “Semiconductor Optoelectronic Devices,” (Prentice Hall, Upper Saddle River, 1997).

], which causes the photon density—and hence, the probability of creating an electron-hole pair—to decrease as light penetrates deeper in the material. However this dependence is not taken into account in Eq. (1), for this expression has been obtained assuming an isotropic distribution of e and h. In order to qualitatively include the effects of optical absorption in our simulations, we model the silicon slice as a two layer structure (see inset of Fig. 2). The top layer has a thickness of 10 μm—a value comparable to the penetration depth of near-infrared light in silicon—and its permittivity varies with e and h according to Eq. (1). The bottom layer is 90 μm thick and has a constant permittivity corresponding to the initial free carrier density (i.e., e and h are replaced by e 0 and h 0 in Eq. (1)). In the following, all our results are expressed as a function of the conductivity σ = ωε0 Imsi) of the top layer.

Fig. 2. S21 parameter as a function of frequency for the controllable SRR shown in the inset. The calculations have been performed for increasing levels of photodoping as indicated in the legend box. The SRR is 3 mm long, 4 mm high, 17 μm thick; its linewidth is 0.5 mm while its gap is 0.15 mm wide. The silicon slice has the same width as the SRR gap so that there is an electrical contact between the two materials.

Figure 2 shows the spectrum of the S21 parameter for various conductivities. In the absence of photoexcitation, the transmission exhibits a sharp minimum at around 8.7 Ghz which is the signature of the magnetic resonance. As the level of photodoping increases, the off-resonance transmission remains globally constant while the peak amplitude drops dramatically—in fact, the resonance is essentially destroyed for conductivities larger than ∼ 50 S.m-1. Clearly then, the SRR gap gradually loses its primary function which is to introduce a capacitance in the structure to make it resonant. This behavior is consistent with the fact that, should the conductivity indefinitely increase, the SRR would end up being a closed metal loop which is known to be non-resonant at those frequencies (see gray curve of Fig. 2). However, Fig. 2 suggests that the resonance disappears for conductivities that are orders of magnitude smaller than those of good conductors. Hence, the question arises as to whether or not the SRR gap can be considered as electrically shorted in our simulations.

In order to clarify this point, we have repeated the simulations for a slightly larger SRR gap (0.18 mm rather than 0.15 mm) so that the silicon layer is now electrically isolated from the SRR. As can be seen from the transmission coefficient plotted in Fig. 3, this minor modification has important consequences. For the lowest levels of photodoping (σ < 75 S.m-1), the magnetic resonance essentially follows approximately the same behavior as before—it primarily decreases in amplitude while conserving its shape and position. It should be noted, however, that the structure is less sensitive than before, since higher conductivities are needed to obtain the same modulation amplitude. Then, as the conductivity further increases, the resonance distinctively shifts to a new position at smaller frequencies while gradually regaining in strength. The peak reappearance suggests that the tiny interstices between the photo-doped silicon and the SRR have enough capacitance to preserve the resonant nature of the structure. In other words, for the highest conductivities, the system begins to behave as a conducting SRR with two capacitive gaps. We have verified this supposition by replacing the top layer of our silicon slice by a piece of copper of same dimensions. The transmission spectrum (gray curve in Fig. 3) confirms that, indeed, the structure exhibits a pronounced peak at nearly the same frequency as for the SRR with photo-doped silicon.

Fig. 3. S21 parameter as a function of frequency for the controllable SRR shown in the inset. The calculations have been performed for increasing levels of photodoping as indicated in the legend box. The structure is almost identical as in Fig. 2 except that the SRR gap has been widened from 0.15 to 0.18 mm. Thus, in this case, there is no electrical contact between the silicon slice and the SRR gap.

Figure 3 shows that, although the SRR gap cannot be short-circuited, there is an intermediate range of photodoping (σ ∼ 75 S.m-1) for which the magnetic resonance is significantly attenuated. To interpret this behavior, we have plotted the real part of the permittivity as well as the dielectric loss tangent against the photoconductivity (0 < σ < 150 S.m -1) using Eq. (1). Figure 4 reveals that ReSi) is essentially constant and positive, thus indicating that the silicon remains non-conducting over the whole conductivity range. The dielectric loss tangent, in contrast, increases by four orders of magnitude so it is likely that the structure loses its resonant behavior because the photo-doped silicon layer acts to damp the strongly localized fields in the SRR gap. This conclusion has an important consequence for our understanding of the curves of Fig. 2, for the modulation was achieved with the same levels of photodoping. It means that the origin of the changes cannot be attributed to a short circuit of the SRR gap because εSi remains positive long after the magnetic resonance has disappeared—in fact, εSi does not become negative until σ reaches 300 S.m-1. In this case also, the SRR behavior seems therefore primarily governed by the photo-induced losses in silicon.

Fig. 4. Evolution of the real part of the silicon permittivity and dielectric loss tangent as a function of the conductivity.

In summary, the initial resonance can be degraded for free carrier densities that are well below those of a conducting state, which renders the controllable SRRs highly sensitive to photoexcitation. This sensitivity is however limited by the fact that the photodoping is restricted to a small volume just under the silicon surface. Figure 5 illustrates this point by comparing the response of a controllable SRR for three photodoping schemes. The SRR parameters as well as the silicon dimensions are the same as in Fig. 2. In case (i), an isotropic conductivity σ = 15 S.m-1 is assumed for the entire semiconductor layer. This configuration appears as the most favorable of all three because the SRR magnetic resonance is completely destroyed. For case (ii), the same level of photodoping is considered but the photodoped region is restricted to a 10 μm thick layer that is in contact with the SRR arms. As discussed earlier, this bilayer approximation constitutes a more realistic description of photodoping in silicon. In this case, the transmission minimum is significantly attenuated but not entirely suppressed, which means that higher conductivities are needed to achieve the same level of modulation as in (i). To gain more insight on that matter, we systematically compared the response of SRRs (i) and (ii) as a function of photodoping (results not shown here). We found that the scattering parameters for both structures systematically superimpose when:

σ(ii)=0.5σ(i)
(2)

In this relation, 〈σ(ii)〉 is the averaged conductivity over the entire silicon bilayer of SRR (ii), whereas σ(i) is the conductivity of the homogeneous silicon considered in (i). This strict proportionality relation indicates that for case (ii), the effect of photodoping is in fact counterbalanced and averaged with the contribution of the passive silicon region. It should be noted, however, that averaging the conductivity over the entire silicon slice clearly overestimates the influence of the passive layer—otherwise the proportionality factor between 〈σ(ii)〉 and σ(i) would have been equal to 1. Thus, given the respective locations of the photodoped and passive regions, it can be inferred that the conductivity averaging is only effective in a volume close to the SRR gap. This is confirmed with structure (iii), for which the silicon slice is identical to case (ii) except that the photodoped layer is now on the far side with respect to the SRR arms. In this situation, the magnetic resonance is almost unperturbed despite the fact that the photodoped layer is only 90 μm away from the SRR gap. This result is consistent with the fact that, for the SRR geometry, the microscopic fields are maximum in the gap and decay rapidly outside the structure. A practical consequence is that the sensitivity of actual controllable SRRs critically depends on how well the silicon surface facing the illumination source is adjusted in the gap.

Fig. 5. S21 parameter as a function of frequency for three photodoping schemes. The schematics show the cross-sections perpendicular to the SRR plane (the aspect ratio is different from the actual models). In each case, the gold regions represent the SRR arms; the red box is the silicon slice inside which the photodoped region is highlighted by a hatched pattern. The calculations have been performed using the same level of photodoping in all three configurations (σ = 15 S.m-1).

3. Experiments

In practice, such a configuration restricts the choice of illumination sources that can be used for photodoping the structure: on one hand, the light source cannot be located inside the waveguide because the presence of another scattering object beside the SRR would needlessly complicate the experimental data; on the other hand, the waveguide walls are not transparent and so the silicon contained in the SRR gap cannot be directly illuminated from outside. We therefore opted to use an external laser diode (wavelength 815 nm, variable power between 0 and 1 W) coupled to a multimode optical fiber which enters the waveguide through a small aperture and ends a few microns away from the silicon.

To hold the fiber in position, we adhered it to the dielectric substrate of the SRR according to the following procedure. First, we fabricated the SRR on a FR4 laminate substrate using a high precision micromilling machine [20

20. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71,036609 (2005). [CrossRef]

]. During the machining process, we created a 0.2 mm gap in the middle of which we drilled a 150 μm diameter through hole in the FR4 substrate.

Fig. 6. (a) From left to right: rear view showing the fiber glued in the hole of the substrate; SRR gap with the hole and fiber in place; SRR gap with the fiber coupled to a 632 nm laser diode; SRR gap with the silicon slice covering the hole; SRR gap with silver epoxy at the junction of the silicon and the SRR. (b) Experimental S21 parameters when the SRR is controlled with an 815 nm laser diode. The SRR dimensions are listed in Fig. 2.

The function of this hole was to enable the illumination of the gap region from the bottom side of the FR4 substrate, that is, in our case, by inserting the tip of the multimode fiber in the hole (see Fig. 6(a)). Once the fiber was in place, we froze its position with a tiny drop of epoxy and then covered the SRR gap with a 0.2 mm × 0.2 mm silicon square diced from a n-type silicon wafer (σ0 = 0.127 S.m-1, thickness 100 μm). Finally, an electrical contact between the Si slice and the SRR arms was created by coating the junctions of the two materials with conductive silver epoxy (last picture of Fig. 6(a)). The silver epoxy reduces the width of the SRR gap to approximately 0.15 mm, which was the value used in the simulations. It should be noted that the fiber core diameter (105 μm) is smaller than the lateral size of the silicon slice. However we allowed a small separation between the fiber tip and the semiconductor surface so as to ensure that the laser spot would be large enough to provide a fairly constant illumination over the gap region. A photograph of the fabricated SRR can be seen in Fig. 6. Aside from the fiber and the cubic holder made of expanded polystyrene foam—a material that does not scatter the microwaves—the structure constitutes the practical realization of the simulated SRR of Fig. 2. We note however that we did not try to carefully adjust the position of the silicon in the gap so as to maximize the effect of photodoping (cf. discussion around Fig. 5).

Figure 6(b) shows the spectrum of the S21 parameter of the SRR with the laser power as parameter. In this figure, the laser power represents the total photon flux emerging from the fiber as measured before the fiber was mounted into the SRR structure. When the laser is off, the SRR magnetic resonance manifests itself by a transmission dip very similar to the minimum predicted for the simulated structure—in fact, the main difference is a shift of about 0.5 GHz towards smaller frequencies. Additional experiments and numerical work indicate that this discrepancy mainly accounts for the tape we used to maintain the SRR against the polystyrene holder and also for the optical fiber and epoxies that were not explicitly included in the model. If we now focus on the curves of Fig. 6(b) obtained while gradually increasing the laser power, we observe the modulation in amplitude we expected from our simulations. It is particularly worth noting that the magnetic resonance can be suppressed for rather low laser power—in this example, a little more than 1 mW. Since, in this case, the SRR has almost no effect on the signal, the ratio between on and off transmissions is chiefly determined by the attenuation caused by the structure in its undoped, resonant state. In Fig. 6, this ratio does not exceed 1.5 dB because the waveguide lateral dimensions are too large to funnel all the electromagnetic flux through the volume where the field substantially interacts with the subwavelength SRR. In order to increase the modulation amplitude, one has to maximize the coupling between the guided modes and the SRR, for example by increasing the field confinement around the resonator. Alternatively, good performances should be observed for controllable SRRs assembled in a bulk metamaterial that would entirely fill the waveguide cross-section.

Fig. 7. Experimental S21 parameter for a SRR controlled with an 815 nm laser diode. This is the same structure as in Fig. 6, except that the silicon in the gap has no electrical contact with the SRR (cf. 4th picture of Fig. 6(a)).

Equally important is the fact that all photo-induced changes were fully reversible by turning the laser off. Although we did not perform any temporal measurements, it is likely that the time required to recover the original resonance is close to the recombination time of the free carriers, which is approximately 10 microseconds for silicon. In principle, it should be possible to substantially improve the switching rate by filling the SRR gap with semiconductor materials possessing much faster carrier trapping time [28

28. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metama-terial Response at Terahertz Frequencies,” Phys. Rev. Lett 96,107401 (2006). [CrossRef] [PubMed]

].

Fig. 8. Modulating the transmission amplitude between two dielectric waveguides. (a) General overview. Here the SRR dimensions are 4 mm × 4 mm, with a linewidth and gap size of 0.5 mm. The whole setup is in fact inserted between two horizontal Al plates (not shown here). (b) Experimental map of the electric field intensity recorded at 8.8 GHz when the silicon is illuminated by the laser (color scale in dB). (c) Experimental map of the electric field intensity recorded at 8.8 GHz when the silicon in the SRR gap is not illuminated by the laser (color scale in dB).

Having now an experimental confirmation that our approach for controlling SRRs is effective, we present a simple example application, in which we demonstrate optical switching between two dielectric waveguides. Figure 8(a) shows the configuration under investigation: it consists of two lengths of dielectric waveguide separated by a controllable SRR fabricated as described above. In our experiments, the dielectric waveguides are two rods of polycarbonate (n = 1.67) with a square cross-section of 1 cm × 1 cm. To further simplify the problem, the entire experimental setup is inserted between the two horizontal metal plates of a 2D scattering chamber. The distance between the two metal plates is 1.1 cm (i.e. it is only 1 mm larger than the height of the waveguides), therefore the system can be considered as nearly translationally invariant along the vertical direction. The very close separation between the horizontal metal boundaries furthermore ensures that only the fundamental mode is supported in the planar waveguide over the frequency range we consider (7–10 GHz). More specifically, the dielectric waveguides only support a TE mode for which the electric field E is parallel to and constant along the vertical axis.

While we have just seen that individual SRRs have attractive properties as individually controllable resonators, their rich potential can also be used for developing more complicated components—these include metamaterials of course, but also devices that exploit the discrete nature of these structures. We illustrate this point by considering the dynamic multichannel filter shown in Fig. 9(a). Our structure—a cluster of three controllable SRRs with distinct resonance frequencies—has been designed to control the transmission at the junction of the two polycarbonate rods previously used in the switching experiment. As before, each SRR is connected to an optical fiber that illuminates the silicon positioned within its gap, so that the transmission between the two dielectric waveguides can be independently modulated at three different frequencies. To characterize the dynamic filter, we coupled the input and output waveguides to the ports of the network analyzer and performed a series of transmission measurements in our 2D scattering chamber. In our experiments, the impedance of the network analyzer is not perfectly matched to the dielectric waveguides, leading to unstable extrema in the transmission spectra due to outgoing waves being partially reflected back to the scattering chamber. We minimize this artifact by tilting the output waveguide to an angle of 30 degrees with respect to the axis of the input waveguide. In this configuration, however, the coupling between the dielectric waveguides is both relatively weak and frequency dependent even in the absence of the controllable SRRs. Here we do not focus on this coupling aspect but rather on the response of the dynamic filter; therefore, we normalize all of the data against the transmission spectrum taken before the SRRs were inserted in the scattering chamber.

Fig. 9. A dynamic three channel filter. (a) Experiment setup comprising two dielectric waveguides separated by the dynamic filter. The optical fibers that bring the laser light within each SRR gap are clearly visible in the upper part of the picture. Insets: general overview and closer view of the filter. (b) S21 parameters as a function of the frequency when the dynamic filter is left in the dark (black curve) and when the amplitude of each SRR is successively modulated with the laser diode.

4. Conclusion

We have designed and fabricated active split ring resonators whose response to microwave radiation can be dynamically altered using near-infrared light. Although we have only considered a restricted number of SRRs at a time, the main results of this study can be applied to bulk meta-material structures. In particular, the fact that we have demonstrated optical control at the unit cell level suggests that an arrangement of active SRR can be built for which the capacitance of each gap is individually addressed. This would enable the design of much more sophisticated devices such as beam steerers and other active gradient index media.

Acknowledgements

DRS acknowledges insightful conversations regarding the use of photodoping to tune metama-terials with Ron Tonucci (Naval Research Laboratory). The authors are also grateful to Shih-Yuan Wang (Hewlett-Packard Laboratories) for stimulating discussions and to Michael Garcia (Duke University) for helping us in the experimental characterization of the silicon used in this study. The laser diode used in the experimental section was a gift provided by Hewlett-Packard. Support for this work was provided by the Defense Advanced Research Projects Agency (Contract Number HR0011-05-3-0002) and by a Multidisciplinary University Research Initiative (MURI) from the Air Force Office of Scientific Research (Contract Number FA9550-04-1-0434).

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V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of eand μ,” Sov. Phys. Usp 10,509–514 (1968). [CrossRef]

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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292,77–79 (2001). [CrossRef] [PubMed]

9.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett 90,107401 (2003). [CrossRef] [PubMed]

10.

A. A. Houck, J. B. Brock, and I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett 90,137401 (2003). [CrossRef] [PubMed]

11.

J.B. Pendry, “Introduction,” Opt. Express 11,639–639 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-7-639. [CrossRef] [PubMed]

12.

A. Lakhtakia and M. McCall, “Focus on negative refraction,” New J. Phys 7 (2005). [CrossRef]

13.

V. G. Veselago, L. Braginsky, V. Shkover, and C. Hafner, “Negative refractive index materials,” J. Comput. Theoretical Nanoscience 3,189–218 (2006).

14.

A. L. Pokrovsky and A. L. Efros, “Diffraction theory and focusing of light by a slab of left-handed material,” Physica B-Cond. Mat 338,333–337 (2003). [CrossRef]

15.

W. T. Lu and S. Sridhar, “Flat lens without optical axis: Theory of imaging,” Opt. Express 13,10673–10680 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-7-639. [CrossRef] [PubMed]

16.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett 90,077405 (2003). [CrossRef] [PubMed]

17.

D. Schurig and D. R. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys 7,162 (2005). [CrossRef]

18.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett 84,2244–2246 (2004). [CrossRef]

19.

A. Degiron, D. R. Smith, J. J. Mock, B. J. Justice, and J. Gollub, “Negative Index and Indefinite Media Waveguide Couplers,” Appl. Phys. A, in press.

20.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71,036609 (2005). [CrossRef]

21.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett 87,091114 (2005). [CrossRef]

22.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006). [CrossRef]

23.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312,1780–1782 (2006). [CrossRef] [PubMed]

24.

U. Leonhardt, “Optical Conformal Mapping,” Science 312,1777–1780 (2006). [CrossRef] [PubMed]

25.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science ,314,977–980 (2006). [CrossRef] [PubMed]

26.

S. Lim, C. Caloz, and T Itoh, IEEE Trans. Microw. Theory Tech52,2678–2690 (2004). [CrossRef]

27.

I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt. Express 14,9344–9349 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9344. [CrossRef] [PubMed]

28.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metama-terial Response at Terahertz Frequencies,” Phys. Rev. Lett 96,107401 (2006). [CrossRef] [PubMed]

29.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz meta-material devices,” Nature 444,597–600 (2006). [CrossRef] [PubMed]

30.

J. García-García, F. Martín, J. D. Baena, R. Marqués, and L. Jelinek, “On the resonances and polarizabilities of split ring resonators,” J. Appl. Phys 98,033103 (2005). [CrossRef]

31.

P. Bhattacharya, “Semiconductor Optoelectronic Devices,” (Prentice Hall, Upper Saddle River, 1997).

32.

C. H. Lee, P. S. Mak, and A. P.De Fonzo, “Optical control of millimeter-wave propagation in dielectric waveguides,” IEEE J. Quantum. Electron 16,277–288 (1980). [CrossRef]

33.

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14,8694–8705 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-19-8694. [CrossRef] [PubMed]

OCIS Codes
(230.1150) Optical devices : All-optical devices
(230.4110) Optical devices : Modulators
(350.4010) Other areas of optics : Microwaves

ToC Category:
Metamaterials

History
Original Manuscript: December 22, 2006
Revised Manuscript: January 18, 2007
Manuscript Accepted: January 19, 2007
Published: February 5, 2007

Citation
Aloyse Degiron, Jack J. Mock, and David R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-1115


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References

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  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999). [CrossRef]
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  6. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ∑ and µ," Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
  7. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  8. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a Negative Index of Refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
  9. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003). [CrossRef] [PubMed]
  10. A. A. Houck, J. B. Brock and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003). [CrossRef] [PubMed]
  11. J. B. Pendry, "Introduction," Opt. Express 11,639-639 (2003). [CrossRef] [PubMed]
  12. A. Lakhtakia and M. McCall, "Focus on negative refraction," New J. Phys. 7, 10.1088/1367-2630/7/ (2005). [CrossRef]
  13. V. G. Veselago, L. Braginsky, V. Shkover, and C. Hafner, "Negative refractive index materials," J. Comput. Theor. Nanosci. 3, 189-218 (2006).
  14. A. L. Pokrovsky and A. L. Efros, "Diffraction theory and focusing of light by a slab of left-handed material," Physica B 338, 333 - 337 (2003). [CrossRef]
  15. W. T. Lu and S. Sridhar, "Flat lens without optical axis: Theory of imaging," Opt. Express 13, 10673-10680 (2005). [CrossRef] [PubMed]
  16. D. R. Smith, D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 077405 (2003). [CrossRef] [PubMed]
  17. D. Schurig and D. R. Smith, "Sub-diffraction imaging with compensating bilayers," New J. Phys. 7, 162 (2005). [CrossRef]
  18. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 - 2246 (2004). [CrossRef]
  19. A. Degiron, D. R. Smith, J. J. Mock, B. J. Justice, and J. Gollub, "Negative Index and Indefinite MediaWaveguide Couplers," Appl. Phys. A, in press.
  20. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E. 71, 036609 (2005). [CrossRef]
  21. R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005). [CrossRef]
  22. T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006). [CrossRef]
  23. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780 - 1782 (2006). [CrossRef] [PubMed]
  24. U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-1780 (2006). [CrossRef] [PubMed]
  25. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science,  314, 977-980 (2006). [CrossRef] [PubMed]
  26. S. Lim, C. Caloz, and T Itoh, IEEE Trans. Microw. Theory Tech. 52, 2678-2690 (2004). [CrossRef]
  27. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express 14, 9344 - 9349 (2006). [CrossRef] [PubMed]
  28. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96, 107401 (2006). [CrossRef] [PubMed]
  29. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006). [CrossRef] [PubMed]
  30. J. García-García, F. Martín, J. D. Baena, R. Marqués, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005). [CrossRef]
  31. P. Bhattacharya, "Semiconductor Optoelectronic Devices," (Prentice Hall, Upper Saddle River, 1997).
  32. C. H. Lee, P. S. Mak, and A. P. De Fonzo, "Optical control of millimeter-wave propagation in dielectric waveguides," IEEE J. Quantum. Electron. 16, 277-288 (1980). [CrossRef]
  33. B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, "Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials," Opt. Express 14, 8694-8705 (2006). [CrossRef] [PubMed]

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