NEGATIVE REFRACTION AND SUBWAVELENGTH FOCUSING USING COMPOSITE METAMATERIALS

     We have successfully demonstrated negative refraction and subwavelength focusing through left-handed metamaterials [1] (LHM). Here we present a   brief summary of the experimental results that we have obtained. We have confirmed negative refraction by using 3 different methods. One method is a   common experimental technique used  to verify negative refraction, so called wedge method [2-4]. We have also shown negative refraction by using   phase shift of successive layers and Gaussian beam shift through a slab of LHM. The structure is a two-dimensional LHM with the unit cell of  two SRRs   and two wires in x-z planes, as shown in shaded parts of Fig. 1(a).

Figure 1. (a) Schematics of 2D CMM structure (b) 2D Wedge CMM structure used for negative refraction experiment.  (c) Schematic drawing of experimental setup used for refraction experiment.

     For negative refraction experiments, a prism shaped 2D CMM structure is constructed with a  wedge angle of θ = 26° (Fig. 1(b)). Figure1(c) depicts   the schematic of the experimental setup. The source is 13 cm  away from the first interface of the wedge. Receiver antenna is mounted on a rotating arm   to obtain the angular distribution of the transmitted signal. Receiver antenna is located at a distance of 70 cm away from the second interface of the   wedge. The angular refraction spectrum is scanned by ∆θ= 2.5° steps.

Figure 2. (a) Transmission spectra as a function of frequency and refraction angle (b) The angular cross section of transmitted beam at  f = 3.92 GHz.

      Figure 2(a) displays the transmission spectrum as a function of frequency and refraction angle. It is evident from the figure that the transmitted beam is   refracted on the negative side of the normal. The refraction index is measured to be negative for the entire LH transmission band. At lower frequencies   the EM waves are refracted at higher negative refraction angles, which results in a higher negative refractive index. The refraction index is lowered if we   go to higher frequencies. To investigate the beam profile, the angular cross section at f = 3.92 GHz is plotted in Fig. 2(b). By employing Snell’s law   (nLHM sinθi = nair sinθr) an effective refractive index can be defined for the CMM. For θi = 26°, EM wave is refracted at an angle of θr = 55°,  then   from Snell’s law we obtain neff  = -1.87 ± 0.05 at 3.92 GHz.

_Figure 3. Unwrapped transmission phase data obtained from different lengths of CMM. Inset: Average phase difference between consecutive numbers of layers of CMM (a) for frequencies 5.4 - 7.0 GHz where right-handed transmission takes place, (b) for frequencies 3.73 - 4.05 where left-handed transmission occurs.

     The transmitted phase of LHMs is measured to investigate the phase velocity within both the left-handed (3.73-4.05 GHz) and right-handed (5.4-7.0   GHz) transmission bands [5]. Phase measurements are performed on rectangular slabs of LHMs, with various numbers of layers. Figure 3(a) shows the   transmitted phase of CMMs (with varying number of layers) between frequencies 5.4-7.0 GHz, where LHM acts as a right-handed medium. As shown   in Fig. 3(a), the phase of the transmitted EM wave increases, when a longer CMM is used, which is a typical right-handed behavior. On the other hand,   increasing the number of layers decreases the phase of the transmitted EM wave at the left-handed frequency region (Fig.3(b)). As shown in the inset of   Fig. 3, the average phase shift is negative for the relevant frequency range, which indicates that the phase velocity is negative.

  One can find the value of refractive index by using the phase shift between consecutive numbers of layers of LHM. Phase velocity is defined as vph =   c/n, and also given by vph = ω/k. Then, refraction index can be defined as n = k.c/ω, where k = ΔΦ/ΔL. We then obtain the refraction index as n =  (Δ Φ/ΔL).(c/ω). At f = 3.92 GHz, the average phase shift between CMM layers is ΔΦ = -0.41 ± 0.05 π. By employing Eq.1, neff is obtained to be -1.78 ±   0.22, which is in good agreement with the value of -1.87 ± 0.05 obtained from the refraction experiment. The measured phase velocity at 3.92 GHz is   negative and equal to -0.51 c.

     Then we have performed transmission and reflection measurements on a 2D LHM structure which is composed of Nx = 5, Ny = 20, and Nz = 40 unit   cells, with lattice spacings ax = ay = az = 9.3 mm. Transmission and reflection measurements are performed in free space. The experimental   measurement setup consists of a HP 8510C network analyzer, and microwave horn antennas.

     Figure 4 depicts the measured transmission (blue) and reflection (red) spectra of a 2D LHM between 3.0-5.5 GHz. The SRR structure is responsible   for the negative permeability at the frequency range 3.55-4.05 GHz [5]. The periodic wire medium has a plasma frequency at 8.0 GHz, below which the   effective dielectric permittivity takes negative values. In our case, a transmission band is observed between 3.75 - 4.05 GHz (Fig. 2). At this frequency   range the effective parameters of the material (i.e. e and μ) posses negative values, therefore the transmission band is indeed left-handed. The   transmission peak measures -9.9 dB at 3.86 GHz.

 Figure 4. Measured (a) transmission (blue), and (b) reflection (red) spectra of a two-dimensional left-handed metamaterial structure between 3.0-5.5 GHz

     A dip in the reflection spectrum is observed at 3.86 GHz, corresponding to a dip value of -38 dB. At this specific frequency, the impedance is   matched to the free space. Therefore, almost all of the EM waves enter inside the LHM structure without being reflected at the surface. If the real parts   of ε and μ are equal, the impedance of LHM will be equal to that of free space. As seen in Fig. 2, the impedance matched frequency region is very   narrow. It is not surprising to have such a small range for an impedance matched frequency region, since μ is known to vary rapidly between the   resonance and magnetic plasma frequency, although ε varies slowly.

     Impedance matching at the surface of a metamaterial is desired, since it reduces the complications of front face reflection, and assures that the   negatively refracted beam is not a result of any experimental artifacts. Much more energy is transferred into the medium at impedance matched   frequencies. Therefore, the higher transmission (-9.9 dB) can be explained by better impedance matching between the free space and LHM for our   particular design. Additionally, the matched impedance at the surface assures the validity of the previously reported phase shift experiments for the same   structures.

     Then we have performed Gaussian beam shifting method at the second interface of LHM to validate the negative refraction. The refraction spectrum is   measured by a standard high gain microwave horn antenna as the transmitter, and a monopole antenna as the receiver (Fig. 5(a)). The size of the   monopole antenna is 3.9 cm, which is half of the wavelength (λ@7.77cm) of the EM wave at a working frequency of f= 3.86 GHz. The top view of the   experimental setup is given in Fig. 5(a), the x and z directions are shown in the figure, whereas the y is directed to the out of page.

Figure 5.  Schematic drawings of the top view of the experimental setup used for verifying (a) negative refraction, and (b) flat lens focusing.

     As seen in Fig. 5(a), the horn antenna is placed on the negative side (-x) of the LHM structure with respect to its central axis. The horn antenna is 125   mm (1.6λ) away from the first interface of the LHM slab. The EM wave is sent through the LHM slab with an incident angle of θi = 15°. The intensity   distribution of the refracted EM wave is scanned by a monopole antenna mounted to a 2D scanning table with Dx = Dz = 2.5 mm steps.  At f = 3.86   GHz our 2D LHM is shown to have the highest transmission and lowest reflection values. We have set 3.86 GHz as our working frequency, to assure   that the effect of the reflections on our results is kept at minimum, including losses due to reflection.

     Figure 6(a) displays the measured refraction spectrum at 3.86 GHz. The intensities are normalized with respect to maximum intensity. The incident EM   wave has a Gaussian beam profile centered at x = 0. Therefore, by measuring the shift of the outgoing beam, one can easily deduce whether the _structure   has a positive or negative index of refraction. As clearly seen in Fig. 6(a), the center of the outgoing Gaussian beam is shifted to the left side of _the center   of the incident Gaussian beam, which due to Snell’s law, corresponds to negative refraction. The point z = 0 in Fig. 6(a) corresponds to the _second   LHM-air interface. Figure 6(b) is the cross-section of Fig. 6(a) taken at z = 0, in other words it provides the intensity distribution of an EM _wave at the   LHM-air interface. As can be seen in Fig. 6(b), the center of the refracted Gaussian beam (red dashed line) is measured at -12.5 mm _away from the   center of the incident Gaussian beam (blue dotted line).

Figure 6.  Schematic drawings of the top view of the experimental setup used for verifying (a) negative refraction, and (b) flat lens focusing.

     The refractive index of LHM is then calculated from Snell’s law as neff = -1.86.  The refractive index values by using the experimental results of   refraction through a wedge shaped LHM sample (neff = -1.95) and the phase shift between different numbers of LHM layers (neff = -2.00). The result   neff = -1.86 obtained from a Gaussian beam shifting experiment is in good agreement with the previously reported experimental results. 

     A parallel-sided slab of material made of negative index metamaterial can focus EM waves. EM waves emerging from an omni-directional source   located near such a lens will first be refracted through the first air-LHM interface and will come into focus inside the material. Then outgoing EM waves   will face refraction again at the second LHM-air interface and the refracted beam will meet the optical axis of flat lens, where the second focusing will   occur. We have employed a LHM lens with 40×20×10 layers along the x, y and z directions. Along the propagation direction (z direction) the structure   has 10 unit cells, and the thickness is t = 91.2 mm. The top view of the experimental setup for verifying focusing through a flat lens of LHM is   schematically given in Fig. 5(b). A monopole antenna is used as the point source. The source is located away from the LHM lens at two different source   distances of ds = 39 mm (0.5λ) and ds = 78 mm (λ). The intensity distribution of an EM wave is scanned by another monopole antenna with Dx = Dz =   5 mm steps.

Figure 7.  Measured transmission spectra along the x-z plane for a point source located at (a) ds = 0.5λ, and (b) ds = λ away from the LHM lens. The x direction is parallel to the LHM lens where x = 0 is the optical axis of the flat lens, whereas the z direction is perpendicular to the LHM lens where z = 0 is the LHM-air interface.

      The measured transmission spectra are shown in Fig. 7, with the intensities normalized with respect to the maximum intensity values. The point z = 0 corresponds to the LHM-air interface. Figure 7(a) provides the transmission spectrum for the omni-directional source located at ds = 39 mm away from the LHM   lens. As seen in the figure, an image is formed at a focal length of z = 40 mm (~0.52λ). For the case where the point source is placed at ds = 78 mm, the   image is observed at z = 20 mm (~0.26 λ) (Fig. _7(b)). As the point source is moved away from the LHM flat lens, the focal length is shifted towards the   flat lens, which is consistent with the imaging _theory.

     Figure 8. Intensity profiles of the focused EM waves taken at (a) x = 0 point along longitudinal direction, and (b) focal points of each source along the   lateral direction. The graphs are for the point source located at λ/2 (black) and λ(red) away from the air-LHM interface.

     Figure 8(a) depicts the intensity distribution of the focused EM wave along the longitudinal (z) direction taken at x = 0, for the source distances of ds =   39 mm (0.5λ) and ds = 78 mm (λ). The focal length moves towards the flat lens for larger source distances. Figure 8(b) displays the lateral intensity   profile of the focused EM waves at the focal lengths z = 40 mm for ds = 39 mm and z = 20 mm for ds = 78 mm. It is evident from Figs. 8(a) and 8(b)   that the EM wave is focused in both the longitudinal and lateral directions. FWHM of the focused beams along the longitudinal direction are ~0.3λ, for   both source distances. From the intensities along the lateral direction, FWHMs are found to be 0.4λ and 0.36λ for the source distances ds = λ/2 and ds   = λ, respectively, which are below the diffraction limit. As seen in Fig. 8(b), when the focal length is closer to the lens (as the case for ds = λ), the   contribution of the evanescent waves to focusing is higher, which in turn results in better sub-wavelength resolution (0.36λ). Note that there is a single   focal point for both cases, different than the previously observed multi-focal flat lens . Since the reflections from the surface are very small in our   structure, we observed a single focal point. As indicated in ref. 28 the presence of reflections from the surface may cause multiple images and affect flat   lens imaging.

        The flat lens presented here, subsequently enables subwavelength imaging by virtue of negative refractive index. Growth of evanescent waves inside   the LHM transmission-line lens and decay of the field outside the lens was shown by Grbic et al. [6]. In our experiments we can only measure the field   outside the LHM lens. The measured time averaged intensity has both propagating and evanescent wave components. Therefore the decay of   evanescent waves could not be observed since the propagating electric field screened the decaying behavior of evanescent waves.

        LHM structures are all-angle negatively refracting materials, since the effective refractive index of these structures is determined by the effective   material parameters, dielectric permittivity and magnetic permeability. All-angle negative refraction is essential for focusing the beam diverging from a   point source. Another crucial point is that the lens should not suffer much from the reflections at the LHM-air interface. The advantages of our flat lens in   a nutshell are that: (1) The lens is constructed from an all-angle negative refractive index LHM slab, (2) it operates at a frequency where the transmission   is at the maximum and the reflection is minimum, assuring that the experimental results are not any artifact of the reflections from the surface, (3) it is   working in free space rather than an isolated waveguide environment, and (4) it enables sub-wavelength focusing by virtue of the negative refractive   index.

      REFERENCES   

  1.  D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).

  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).

  3. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. Koltenbah, and M. Tanielian, “Experimental Verification and Simulation of Negative Index of Refraction   Using Snell’s Law,”       Phys. Rev. Lett. 90, 107401 (2003).

  4. 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).

  5. K. Aydin, K. Guven, C. M. Soukoulis, and E. Ozbay, “Observation of negative refraction and negative phase velocity in left-handed metamaterials,”   Appl. Phys. Lett. 86,       124102 (2005).

  6. A. Grbic, and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92,   117403 (2004).

  Related Group Publications:

  1.  K. Aydin, K. Guven, C. M. Soukoulis, and E. Ozbay, “Observation of negative refraction and negative phase velocity in left-handed metamaterials,”   Appl. Phys. Lett. 86,         124102 (2005).

  2.  K. Aydin, and E. Ozbay, “Negative refraction through impedance matched left-handed metamaterial slab,” J. Opt. Soc. Am. B, (to be published).

  3.  K. Aydin, I. Bulu, and E. Ozbay, “Focusing of electromagnetic waves by a left-handed metamaterial flat lens” Opt. Express 13, 8753 (2005).

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