Abstract

To date, magnetic and negative-index metamaterials at optical frequencies were realized on bulk substrates in the form of thin films with thicknesses on the order of, or less than, optical wavelengths. In this work, we design and experimentally demonstrate, for the first time, fiber-coupled magnetic metamaterials integrated on the transverse cross-section of an optical fiber. Such fiber-metamaterials integration may provide fundamentally new solutions for photonic-on-a-chip systems for sensing, subwavelength imaging, image processing, and biomedical applications.

© 2011 OSA

1. Introduction

In the past few years, it was shown that metamaterials (MMs) can fundamentally change light-matter interactions by bringing the magnetic component of the field into play [15]. In particular, magnetism at optical frequencies is likely to lead to new fundamental physics and novel applications, including negative index of refraction [6], super-resolution [7], sub-wavelength waveguides [8], and unprecedented opportunities for manipulating light trajectories in space (e.g., cloaking) [9,10].

It is well-known that the magnetic susceptibility of most natural materials is very small in comparison with their dielectric susceptibility [11]. Moreover, magnetism is particularly weak at optical frequencies because the relaxation times of paramagnetic and ferromagnetic processes are significantly longer than the optical period, thus leaving the electron movement in atoms as the only mechanism for the magnetic response.

On the other hand, MMs such as an array of paired nanostrips were shown to enable an artificial magnetic response over a broad range of optical wavelengths. Indeed, a pair of nanostrips consisting of a dielectric layer sandwiched between two metal layers can support a symmetric resonance that leads to an artificial permittivity and an asymmetric resonance, which enables an artificial permeability [2].

To date, such nanostrip-based magnetic optical MMs were primarily demonstrated in the form of thin films, on a substrate, with thicknesses on the order of or less than the optical wavelength [12], although nanowire-based non-magnetic hyperbolic metamaterials with the thickness of ~10mm were also reported [13]. In order to use them in applications such as remote sensing and imaging, light in- and out-coupling issues need to be addressed. Thus, waveguide-coupled MMs would be desirable. In this paper, we propose and demonstrate, for the first time, a fiber-coupled magnetic MM structure schematically shown in Fig. 1 .

 

Fig. 1 (a) Schematic of a fiber MMs sample; (b) Enlarged picture of multilayerd nanostips; (d) Numerical simulations showing electric displacement and magnetic field distribution in a unit cell shown in (d), (d) Transverse cross-section of two nanostrips (the dashed box shows the unit cell used in the numerical simulations).

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Fiber optics is a mature technology that enables long-distance, low-loss light delivery [14]. Moreover, many devices such as fiber Bragg gratings, fiber tapers and directional couplers can be easily realized and placed in-line with the light transmission channel. Fibers are routinely used in sensing applications [15], e.g. to deliver light to and from the sample, or in near-field optics, e.g. near-field optical microscopy (NSOM) [16]. Therefore, merging this mature fiber optics technology with the emerging unique functionalities enabled by MMs technology would likely enable a plethora of advanced applications. Recently, first steps toward combining fiber technology with plasmonics have been reported [17,18].

2. Design

To demonstrate that MM structures can be integrated on a fiber, a standard single mode fiber (SMF-28) with a 9 µm core and a 125 µm diameter was used. The single-mode cut-off of this fiber is at ≈1260 nm. Figures 1(a) and 1(b) show a schematic of the fiber MM and a nanostrip array. Figures 1(c) and 1(d) show numerical simulations of the electric displacement and magnetic field distribution in a unit cell and a transverse cross-section of two nanostrips composed of 40 nm silver (Ag) layer, followed by a 40 nm Lithium Fluoride (LiF) layer, and by another 40 nm Ag layer.

Let’s briefly review the basic physics enabling unusual optical properties of nanostrip-based MMs. The electric field, oriented parallel to the nanostrips as shown in Fig. 1, induces parallel currents (symmetric plasmon polariton wave) in both nanostrips, leading to the excitation of an electric dipole moment. The magnetic field, oriented perpendicular to the plane of the nanostrips, excites anti-parallel currents (anti-symmetric plasmon polariton wave) in the pair of nanostrips. Combined with the displacement currents between the nanostrips, they induce a resonant magnetic dipole moment as shown in Fig. 1(c). The excited magnetic moment is co-directed with the incident magnetic field when the wavelength of an incident light is above the resonant wavelength, and it is counter-directed to the incident field at wavelengths below the resonant wavelength, leading to positive and negative magnetic permeability, respectively.

In order to verify the above arguments related to the origin of the negative magnetic response, we performed a detailed study of electromagnetic wave transmission in three types of nanostrip arrays. Figure 2 shows the results of the numerical simulation and experiment confirming that the nanostrip pattern consisting of three (metal-dielectric-metal) layers is responsible for the formation of the magnetic response in our structure. Figure 2 compares three cases: (a) the three layer metal-dielectric-metal structure, in which the TM polarized wave is expected induce a resonant response; (b) and (c) two and one layer structures with the same dimensions that do not lead to any resonant response. The numerical simulations were performed using a commercial finite element analysis based COMSOL Mutiphysics solver. Transmission spectra were calculated using a 2-dimensional unit cell consisting (for the case shown in Fig. 2(a)) of a single metal-dielectric-metal nanostructure and assuming the nanostrips are infinitely long in the longitudinal direction. Periodic boundary conditions were applied to simulate the periodic structure. In order to accurately represent the experimental configuration where light is delivered through the fiber, a plane wave was launched from the bottom in the simulations. Subsequently, transmission and reflection coefficients were calculated as functions of wavelength.

 

Fig. 2 Numerical simulations and experimental results confirming the origin of the magnetic response in the magnetic metamaterial. Transmission spectra under TM polarization are plotted for sample A and two control groups.

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Our simulation used for designing and modeling of the actual experimental results took into account the facts that (i) the actual fabricated nanostrips were trapezoidal in shape as shown in Fig. 1(c), and (ii) approximately 80 nm of fiber core was also removed in the process of patterning using focused ion beam. Therefore, the structure used in the numerical simulations consisted of four layers: two layers of Ag with LiF (εLiF = 1.4) in between and a layer of silica glass with refractive index of 1.44. The dielectric permittivity of silver was taken into account using the Drude-Lorentz model with five oscillators

ε=ε1ωp2ω2+iΓpω+m=1nfmωm2ωm2ω2iΓmω,
where in the Drude term, ε1 = 2.1485 is the static dielectric constant, ωp = 9.1821 eV is the plasma frequency, and Γp (0.0210 eV) is the damping rate for the Drude term (taken from Nanohub.org). Note that the contribution of the Drude term dominates in the metal at optical frequencies. The Lorentz terms mainly contribute to the loss at wavelengths shorter than 400 nm.

3. Fabrication

3.1 Deposition

The magnetic MMs structure was fabricated on the transverse cross section of a SMF-28 fiber. 10cm long pieces of fiber were cleaved using a high precision fiber cleaver (CT-32) with a typical cleave angle of ± 0.5þ. Well cleaved fibers were cleaned under a standard acetone-methanol-deionized water ultrasonic cleaning procedure. The metal-dielectric-metal layers were deposited in a customized Angstrom evaporation system. In order to improve the adhesion of the Ag layers, a two nanometer thick Titanium (Ti) layer was deposited on the fiber cross-section surface by electron beam evaporation. Standard electron beam evaporation was used to deposit the two 40 nm Ag layers, between which 40nm LiF was deposited by thermal evaporation.

3.2 Patterning

The fibers with Ag-LiF-Ag layers were mounted on the 45þ side of a standard 45þ stub by using carbon tape. Alignment markers were put on the jacket of each fiber to indicate the nanostrips' direction for future experiments. These markers made it easier to determine TE and TM polarization mode for the propagating light. The nanostrips were patterned on the Ag-LiF-Ag multilayered stack by focus ion beam (FIB) in a Zeiss AURIGA CrossBeam Workstation (FIB-SEM). A pattern area of 16 µm × 16 µm ensured that the entire core area of the SMF was covered (Fig. 3 ). The parameters of the resulting nanostrips were then measured using scanning electron microscopy (SEM) before the sample was removed from the AURIGA.

 

Fig. 3 SEM images of magnetic metamaterials on SMF. (a) The overview of the transverse cross section of a SMF with pattern in the center, imaged under 54þ tilt; (b) The SEM image of nanostrips covering the core of the fiber, which can be seen in the center; (c) Top view of nanostrips used to obtain the parameters; (d) The 54þ tilt image of nanostrips, showing 3-layer structure of each nanostrip.

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For control experiments corresponding to the cases shown in Fig. 2(b) and 2(c), two additional groups of fibers were fabricated using the same process. One group of fibers was coated by a single 40 nm silver layer and a 40 nm LiF layer, while the second group contained fibers coated only by a single 40 nm silver layer. Ti was also used as an adhesion layer between fiber and silver layer. The milling depth of these two groups of fibers was the same as in the case of the three-layer fiber MMs samples per the same milling dose. The purpose of the control experiment is to prove that the resonant features that we observed in our three-layer fiber MM samples are indeed the signatures of magnetic resonance predicted in numerical simulations as opposed to diffraction features corresponding to the nanostrip patterns shown in Fig. 2(b) and 2(c), or resonant features of a single-layer nanostrip pattern shown in Fig. 2(c).

4. Experiments

4.1 Measurement setup

Figure 4 shows a schematic of the experimental setup for polarization sensitive transmission measurements used for characterization of magnetic fiber MMs. The unpatterned end of a fiber MMs sample was spliced with a piece of standard SMF patch-cord connected with a broad-band and axis-adjustable polarizer (Dichroic-Crystal lens), which is directly connected to a white light source (Ando/Yokogawa AQ4305). The patterned end was butt-coupled to another SMF connected to the Optical Spectrum Analyzer (Ando AQ6317B). Precise fiber alignment was performed using a nano-positioner and observed with a digital camera. It was estimated that if a short piece of an SMF following the polarizer is kept straight, it would maintain the polarization within ± 5þ [8].

 

Fig. 4 A schematic of the experimental setup for polarization sensitive transmission measurements used for characterization of the magnetic fiber metamaterials. The inset shows the image of the actual laboratory setup.

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The unpolarized light beam from the white light source was first sent through a polarizer to ensure that the beam propagating through the fiber MM sample is TM polarized (with electric field along the x direction and magnetic field along the y direction as shown in Fig. 1(b)). The polarization angle of the polarizer was adjusted according to the alignment marker on the jacket and the transmission spectrum was recorded. Then the polarizer was rotated clockwise in steps of 15þ and transmission spectra were recorded for a range of angles from 0þ to 180þ. From the theoretical predictions and numerical simulations we expect that the TM polarized wave spectrum will show a transmission minimum corresponding to the magnetic resonance; while the spectrum corresponding to the TE polarization should not possess any resonant features.

Based on these theoretical predictions, the angles close to TE and TM polarization were determined from the transmission spectrum measurements. Then fine tuning was performed using a similar procedure but with smaller rotation angle steps to more accurately determine the TE and TM polarization angles (with precision of ~5þ). As a result, the angles of the polarizer corresponding to the TE and TM polarizations were determined and recorded. Typically, the error in the alignment marker is less than ± 15þ compared to the angles found using the above described procedure. Since there is no significant transmission minimum for the control group samples, the alignment marker was used to define the TM polarization, where the TE polarization was defined as a 90þ rotation with respect to the TM. In addition, the TE and TM polarization can be distinguished in this case by observing the transmission spectrums’ general power level and phase shift, where the power in the TM case should be slightly higher than the TE case due to the interaction between the gratings and the polarization. The transmission spectra were recorded by the OSA with the span of wavelengths from 1000nm to 1650nm”, with 2000 (sample) points and 0.3dB accuracy.

4.2 Reference measurement

Next, reference spectra were measured to normalize the results. The fiber MMs sample was replaced by an ordinary SMF with the same length as fiber MMs. This reference fiber was butt-coupled to the SMF connected to the OSA. The same output SMF that was used in the measurement of the fiber MMs was used for the reference SMF-coupling. The transmission spectra were recorded for the same angles that corresponded to the TM and TE polarization for the fiber MMs, respectively. The transmission measurements were taken for all the fiber MMs samples. Note that as the butt-coupling efficiency depends on many factors such as fiber surface roughness, coupling distance, temperature variations and mechanical vibrations, a measurement error for the power level was anticipated. From our measurement, we estimate this error to be approximately 2dB.

5. Results

Both experimental measurements and numerical simulations were performed for 5 different fiber MMs samples. Structural dimensions of each sample were measured immediately after patterning. The standard 45þ stub was tilted by 45þin the opposite direction, so that the cross-section of the fiber MMs sample was perpendicular to the e-beam of the SEM. For each sample, the bottom width, top width and period were measured at 10 different positions. The average values of these measurements are presented in Table 1 .Both experimental and simulated transmission plots for all the samples are shown in Fig. 5 . All fiber MMs samples show transmission minima corresponding to magnetic resonance between 1000 nm and 1500 nm wavelength under TM polarization, which is close to the simulated magnetic resonant wavelengths. Although the resonant wavelengths of sample B and D have 50 nm and 120 nm shifts, respectively, as compared to the simulation plots, they are still within the expected error range, which is discussed in next section. In addition, the experimentally observed transmission minima are typically broader than those in the simulations due to 11.7 nm average standard deviation for all the averaged parameters used in the numerical simulation. The experimental spectra for TE polarization are slightly different from the simulated ones. Transmission minima can be observed at about 1400 nm, which may come from the reduced extinction ratio for the wavelength outside the center operation bandwidth (970 nm-1100 nm).

Tables Icon

Table 1. Parameters of Fiber MMs Samples

 

Fig. 5 Transmission plots for the fiber MMs samples A-E. (a) Transmission spectra under TM polarization; (b) Transmission spectra under TE polarization; (c) Simulation results under TM polarization; (d) Simulation results under TE polarization.

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The transmission plots for the two control samples were also investigated. Both of these control samples have 610 nm period and 360 nm bottom width. The two samples exhibit similar transmission spectra without transmission minima under TM illumination, as shown in Fig. 2(b) and 2(c). The power under TM polarization is slightly higher than that under TE polarization. This work confirms that the minima in transmission spectra for fiber MMs samples originate from magnetic resonance.

6. Error considerations

The transmission plot minima indicate the presence of a magnetic resonance for all fiber MMs samples. However, not all the samples exhibit resonant wavelengths well matched to the simulated ones. Errors are expected to originate from the fabrication procedure itself and from the sample structural characterization. During the experiment, the maximum observed error was 10% (sample D), which was lower than the estimated maximum error introduced in the fabrication and SEM measurement. Since both FIB patterning and SEM measurements were performed while the sample stage was tilted, all angle related errors were important for widths estimations. The typical cleave angle of the fiber cleaver is ± 0.5þ, corresponding to 1% error. And, 1.5þ (2.5%) error is introduced while mounting the fiber on the 45þ stub. These errors are doubled when the stub is tilted in the reverse direction by 45þ for SEM measurement. It is relatively easy to measure the bottom widths and periods of the structures, but difficult to identify the interface between the top surface and the side edge of each strip. The top width directly read from SEM is the distance between the two interfaces of the LiF and the top silver layer on one nanostrip, not the actual top width used for simulation. We have performed a calibration step for the SEM measurement by fabricating samples on a glass substrate and measuring the resulting structures using AFM and SEM. Assuming AFM measurement is more accurate, the difference between these two measurements implies that the actual top width should be shorter than the direct SEM reading. Then we assume that measured top width is the width at 2/3 height of a perfect trapezoid shape, then calculate the top width of this trapezoid shape according to the measured bottom width and measured top width. The actual top width is longer than the width obtained from the trapezoid shape assumption. In our experiment, the middle value, which is about 10% away from these two widths, is recorded as the top width. In total, a maximum 17% error is introduced during the fabrication and SEM measurement.

Considering maximum 10% error observed, additional simulations were performed for samples A and D with varying parameters. The shortest and longest resonant wavelengths were found and plotted in Fig. 6 and compared with the experimental result. As shown in Fig. 6(b), while the experimentally determined resonance for sample A is well within the estimated error range, the experimentally measured resonant wavelength for sample D (which is 120 nm shifted from the theoretically predicted one) is at the edge of the range of the simulated spectra (between the shortest and the longest resonant wavelengths) but still within the error range.

 

Fig. 6 Comparison of experimental results and simulated results considering 10% errors for (a) sample A and (b) sample D. The black and red dashed curves show the spectra corresponding to the shortest and longest resonant wavelengths, respectively. The green solid lines correspond to experimentally measured spectra for samples A and D, respectively.

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7. Conclusion

In summary, we designed and demonstrated fiber-coupled magnetic MMs in the near-infrared wavelength range. We performed detailed theoretical and experimental studies of coupled Ag-LiF-Ag nanostrips designed and fabricated on the transverse cross-section of a SMF, which combines the advantages of fiber and MMs technologies. Such fiber-MMs integration may provide fundamentally new solutions for photonic-on-a-chip systems for sensing, biomedical applications, such as fiber-based endoscopy with subwavelength resolution enabled by MM technology, and advanced image processing.

Acknowledgments

This work was supported by US Army Research Office Award # W911NF0910075 and US Air Force Office of Scientific Research Award # FA95501010216.

References and links

1. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]  

2. N. M. Litchintser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics (2008), vol. 51, chap. 1, pp. 1–68.

3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]  

4. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef]   [PubMed]  

5. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef]   [PubMed]  

6. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]  

7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef]   [PubMed]  

8. A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microw. Theory Tech. 52(1), 199–210 (2004). [CrossRef]  

9. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef]   [PubMed]  

10. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]  

11. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), vol. 8.

12. W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007). [CrossRef]   [PubMed]  

13. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008). [CrossRef]   [PubMed]  

14. G. P. Agrawal, Lightwave Technology: Telecommunication Systems, Har/Cdr edition (Wiley-Interscience, 2005).

15. E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists, 1st ed. (Wiley-Interscience, 1991).

16. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).

17. T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000). [CrossRef]  

18. E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008). [CrossRef]  

References

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  1. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  2. N. M. Litchintser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics (2008), vol. 51, chap. 1, pp. 1–68.
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  4. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
    [CrossRef] [PubMed]
  5. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
    [CrossRef] [PubMed]
  6. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [CrossRef]
  7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  8. A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microw. Theory Tech. 52(1), 199–210 (2004).
    [CrossRef]
  9. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  10. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
    [CrossRef]
  11. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), vol. 8.
  12. W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
    [CrossRef] [PubMed]
  13. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
    [CrossRef] [PubMed]
  14. G. P. Agrawal, Lightwave Technology: Telecommunication Systems, Har/Cdr edition (Wiley-Interscience, 2005).
  15. E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists, 1st ed. (Wiley-Interscience, 1991).
  16. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
  17. T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000).
    [CrossRef]
  18. E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
    [CrossRef]

2008 (2)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

2007 (3)

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2004 (3)

A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microw. Theory Tech. 52(1), 199–210 (2004).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microw. Theory Tech. 52(1), 199–210 (2004).
[CrossRef]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
[CrossRef] [PubMed]

Capasso, F.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Crozier, K. B.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

Cubukcu, E.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

de Silva, V. C.

Diehl, L.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

Drachev, V. P.

Ebbesen, T. W.

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000).
[CrossRef]

Engheta, N.

A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microw. Theory Tech. 52(1), 199–210 (2004).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
[CrossRef] [PubMed]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Lezec, H. J.

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Smythe, E. J.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Thio, T.

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Yu, N.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

Yuan, H.-K.

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1448–1461 (2008).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microw. Theory Tech. 52(1), 199–210 (2004).
[CrossRef]

Nat. Photonics (2)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Physica B (1)

T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279(1-3), 90–93 (2000).
[CrossRef]

Science (4)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Other (5)

N. M. Litchintser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics (2008), vol. 51, chap. 1, pp. 1–68.

G. P. Agrawal, Lightwave Technology: Telecommunication Systems, Har/Cdr edition (Wiley-Interscience, 2005).

E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists, 1st ed. (Wiley-Interscience, 1991).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), vol. 8.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of a fiber MMs sample; (b) Enlarged picture of multilayerd nanostips; (d) Numerical simulations showing electric displacement and magnetic field distribution in a unit cell shown in (d), (d) Transverse cross-section of two nanostrips (the dashed box shows the unit cell used in the numerical simulations).

Fig. 2
Fig. 2

Numerical simulations and experimental results confirming the origin of the magnetic response in the magnetic metamaterial. Transmission spectra under TM polarization are plotted for sample A and two control groups.

Fig. 3
Fig. 3

SEM images of magnetic metamaterials on SMF. (a) The overview of the transverse cross section of a SMF with pattern in the center, imaged under 54þ tilt; (b) The SEM image of nanostrips covering the core of the fiber, which can be seen in the center; (c) Top view of nanostrips used to obtain the parameters; (d) The 54þ tilt image of nanostrips, showing 3-layer structure of each nanostrip.

Fig. 4
Fig. 4

A schematic of the experimental setup for polarization sensitive transmission measurements used for characterization of the magnetic fiber metamaterials. The inset shows the image of the actual laboratory setup.

Fig. 5
Fig. 5

Transmission plots for the fiber MMs samples A-E. (a) Transmission spectra under TM polarization; (b) Transmission spectra under TE polarization; (c) Simulation results under TM polarization; (d) Simulation results under TE polarization.

Fig. 6
Fig. 6

Comparison of experimental results and simulated results considering 10% errors for (a) sample A and (b) sample D. The black and red dashed curves show the spectra corresponding to the shortest and longest resonant wavelengths, respectively. The green solid lines correspond to experimentally measured spectra for samples A and D, respectively.

Tables (1)

Tables Icon

Table 1 Parameters of Fiber MMs Samples

Equations (1)

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ε= ε 1 ω p 2 ω 2 +i Γ p ω + m=1 n f m ω m 2 ω m 2 ω 2 i Γ m ω ,

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