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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7095–7100

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Co-sputtered SiC + Ag nanomixtures as visible wavelength negative index metamaterials

G. Nehmetallah, R. Aylo, P. Powers, A. Sarangan, J. Gao, H. Li, A. Achari, and P. P. Banerjee  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 7095-7100 (2012)
http://dx.doi.org/10.1364/OE.20.007095


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Abstract

The fabrication and characterization of a novel metamaterial that shows negative index in the visible (blue) is reported. The real part of the negative index of this metamaterial at 405 nm, comprising co-sputtered SiC + Ag nanoparticle mixture on a glass substrate, is deduced from results of double Michelson interferometry setup which shows a negative phase delay. It is numerically verified that this metamaterial can yield near-field super-resolution imaging for both TE and TM polarizations.

© 2012 OSA

1. Introduction

The imaging resolution of conventional optical systems is limited by the diffraction limit. This is due to the loss of the information from the fine features of the object that are carried by non-propagating (or evanescent) spatial frequency components of the optical field, which exponentially decay in the direction of propagation resulting in a low pass filtered image of the original object. This diffraction limit can be improved by avoiding evanescent wave decay, as demonstrated using a contact mask made of metal, to obtain 100nm resolution using a 405nm laser light [1

H. I. Smith, “Fabrication techniques for surface-acoustic wave and thin-film optical devices,” Proc. IEEE 62(10), 1361–1387 (1974). [CrossRef]

]. Also, immersion lenses, which exploit the refractive index (RI) to improve resolution, are of limited benefit owing to the paucity of high-RI materials [2

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

]. Although subwavelength imaging techniques using near-field optical microscopy, atomic force microscopy, stimulated-emission-depletion fluorescence microscopy, etc [3

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994). [CrossRef] [PubMed]

]. exist, they are limited by slow raster scanning and inability to obtain the whole image in one shot.

It has been suggested by Veselago [4

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

] that a material with a negative permittivity ε and permerability μ could have peculiar properties such as reversal of Snell's law and inverse Doppler effect. Based on this theory, it has been hypothesized that one may obtain a perfect image in one shot by capturing and enhancing all evanescent waves through a slab of such a negative index material (NIM) [5

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

], and first experimentally demonstrated at microwave frequencies [6

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

]. In the optical regime, Fang et al. [2

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

] have proposed to use a thin slab of a metal such as Ag for super-resolution “imaging” in the near field. For TM waves the negative permittivity alone is sufficient to obtain super-resolution.

In this paper, the fabrication and characterization of a novel metamaterial that shows negative index in the visible is reported. The metamaterial comprises co-sputtered SiC + Ag nanoparticle mixture of thicknesses between 50 and 100 nm on a glass substrate. The samples show a negative real part of the RI (Re(n)) in the visible (e.g., 405 nm) as deduced from double Michelson interferometry experiments, and supported by surface plasmon resonance (SPR) measurements. It is also numerically verified that this metamaterial can indeed yield near-field super-resolution imaging for both TE and TM polarizations.

2. Fabrication of SiC + Ag samples using co-sputtering

Using quasi-effective-medium theory, it has been shown that NIMs can be obtained by mixing of plasmonic and polaritonic nanoparticles [7

P. P. Banerjee, G. Nehmetallah, R. Aylo, and S. Rogers, “Nanoparticle-Dispersed Metamaterial Sensors for Adaptive Coded Aperture Imaging (ACAI) applications,” Proc. SPIE 8165, 81651G (2011).

]. In the visible range, most plasmonic metallic nanoparticles exhibit negative permittivity. The negative effective permeability of (polaritonic) SiC nanoparticles is due to the enhancement of the azimuthal component of the displacement current in the SiC spheres due to their large permittivity (εSiC>>1). This current is responsible for enhanced magnetic activity near TE resonance, finally resulting in a magnetic flux density which is opposite to the direction of the magnetic field of the electromagnetic wave, thereby creating an effective negative permeability (Re (μeff) < 0) [8

N. Limberopoulos, A. Akyurtlu, K. Higginson, A.-G. Kussow, and C. D. Merritt, “Negative refractive index metamaterials in the visible spectrum based on MgB2/SiC composites,” Appl. Phys. Lett. 95(2), 023306 (2009). [CrossRef]

, 9

A.-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisittpan, “MgB2-based negative refraction index metamaterial at visible frequencies: Theoretical analysis,” Phys. Rev. B 76(19), 195123 (2007). [CrossRef]

]. Based on this, a mixture of Ag (plasmonic) and SiC (polaritonic) nanoparticles has been realized using co-sputtering. Several samples of different thicknesses (e.g., between 50 nm and 100 nm) have been fabricated. SiC and Ag are co-sputtered on a glass substrate with a 2 nm flatness. As an example, to achieve a 100 nm layer thickness, the SiC is RF sputtered (@ 100W) and the Ag is DC sputtered (@ 5W) in a 4mT vacuum chamber for 40 min. Different sputtering conditions and times can yield different concentrations and particle sizes. A typical sample and typical SEM are shown in Fig. 1 below, which suggests nanoparticle formation. It has been verified that sputtering of one species, viz., Ag only, results in a very uniform Ag layer that does not contain any nanoparticles.

Fig. 1 (a) Typical SiC + Ag sample on glass using co-sputtering, showing excellent surface smoothness. Thickness of sample shown in picture is t = 51.2 nm; (b) SEM image for a (x350k) magnification for a 100nm thick sample.

3. Characterization of SiC + Ag nanoparticle metamaterial samples

A novel technique based on double Michelson type interferometry is schematically shown in Fig. 2 , which can be used to accurately measure phase delays, from which the phase velocity, and hence Re(n), can be readily deduced [10

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]

]. The advantage of a double path Michelson interferometer over a conventional single path interferometer is that it allows for the measurement of the test sample and reference substrate at the same time. Accordingly, one of the arms of the interferometer contains a glass substrate in both the paths of the beam, while the other arm contains the test sample (NIM) on the glass substrate in one path and pure glass substrate in the other path of the beam. Hence, one of the interferograms measures the interference between two pieces of glass substrate, while the other one measures the interference between glass substrate and the sample on the same substrate. Since the glass substrate is in the optical path in both of the cases, its contribution drops out when considering the difference. Furthermore, by measuring both interferograms simultaneously, we eliminate common-mode effects such as gross length changes in the interferometer arms.

Fig. 2 Schematic diagram for the setup of double Michelson interferometer.

The setup in Fig. 2 comprises a frequency doubled 100 fs output from a Tsunami laser at 405 nm that is split into two parallel beams using a Wollaston prism and supporting optics, and thereafter introduced into the two arms of the intereferometer. Light in one arm goes through the glass substrate and is retro-reflected from a static mirror. In the other arm that contains the test sample, light goes through the glass/glass-sample combination and is retro-reflected from a scanning mirror. The mirrors are placed at the focal plane of the focusing lenses, and care is taken to ensure that the scanning mirror translates over a distance much smaller than the Rayleigh range of the focused beam. The light pulses E 1,2(t)traveling through the two arms of the interferometer recombine at the Si detectors, producing a modulated interference signal i(τ)∝ 〈 E1(t) E2(t+τ)〉 T PDwhere τ is the so-called “interferometric” time delay, which is a function of the scanning path difference, and where the averaging is done over the response time TPD of the detectors. The outputs of both interferometers in the double interferometry technique are simultaneously recorded to minimize any effects from time-dependent fluctuations in the setup.

In the presence of a sample, the corresponding interferogram shifts on the time-delay axis. The time shift of its envelope is determined by the group velocity of the sample, while the time shift of the rapidly oscillating fringes contains information of its phase velocity. This in turn implies that a necessary condition for unambiguous measurement of phase change is that the sample thickness d should be less than the half the wavelength (for a wavelength 405nm in air this corresponds to d<200/ |n|) or equivalently, the time shift Δtphase should be less than 0.665 fs which is half the time period of light ( tp=1.33fs). A further condition for the sample thickness comes from the relationship for the phase delay Δtphase, discussed below.

The time of each scan is 0.04s, the distance scanned is 0.2mm, and the velocity of the stage is v=5mm/s. Now tp is related to the temporal period T on the oscilloscope (see Fig. 3 ) through the relation tp=λ/c=1.33fs= 2vT/c=3.33× 10 −11T, where c is the velocity of light in vacuum. There are about 200 data samples over one period T. This information is useful in determining the time delay Δtphase from the oscilloscope scans. The relation between the phase delay, phase velocity, and Re(n) for a sample of thickness d is given by [10

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]

]:
Δ t phase=2d/ v phase−2d/c=> v phase=2d/[Δ t phase+2d/c],  Re(n)=c/ v phase,
(1)
from which Re(n) can be readily calculated once Δtphase is measured.

Fig. 3 (a) Typical interferograms when both arms of the interferometer have glass slides only; (b) a blow up of (a) showing the phasefronts; (c) interferograms in the case when there is a SiC + Ag sample of thickness 50nm. The SiC + Ag sample is inserted in the path of one of the beams in one arm of the double interferometer. The taller envelope is the interferogram between glass slides, while the shorter envelope (superposed) is in the presence of the SiC + Ag sample due to attenuation in the sample; (d) a blow up of (c) showing the phasefronts. The double sided arrow in (d) indicates the amount of time delay due to SiC + Ag sample.

Test experiments have been first performed between two plane glass slides (of surface flatness 2 nm) to calibrate the system. Figure 3(a) below shows a typical result where there are two glass slides only in both arms of the double interferometer. Care is taken to ensure that the phasefronts shown in Fig. 3(b) (a blowup of Fig. 3(a) around the maxima of the two envelopes), shows no shift between the arms in the absence of any samples deposited on the glass substrate. A second test experiment has been conducted using a 2 nm flatness glass partially coated with 50 nm Ag (see Fig. 2 for experimental setup). In this case, it is found from experiment that Δtphase = −0.27 fs, from which, using (1), it follows that Re(n) = 0.18, which is in excellent agreement with the published RI of Ag at 405nm: n = 0.1743 + 2.0076i.

Double interferometry experiments have then been conducted using our samples of SiC + Ag. From Eq. (1), a second and stronger condition on sample thickness for unambiguously determining the phase shift can be derived as follows. From (1), for v phase<0, Δ t phase<0with 2d/c< | Δ t phase|; also, | Δ t phase|< tp/2for the time shift to be identified as a time delay instead of a time advance. Hence, 2d/c< tp/2from which it follows that d<100nm, which justifies the sample thicknesses fabricated. Multiple sets of data have been collected at several positions on multiple SiC + Ag samples with thicknesses between 50nm and 100 nm, fabricated with different sputtering conditions. It is verified the measured values of Δtphase, consistent with the two conditions mentioned above, do indeed yield negative values for Re(n). For instance, for a certain sample where 30 measurements each at 3 different spots have been taken, the mean Δtphase = −0.42863 fs which gives Re(n) = −0.26. A second sample yields Re(n) = −0.6. Based on this trend, it is readily inferred that all of our co-sputtered SiC + Ag samples should indeed yield a negative RI. In Figs. 3(c,d)), results are shown from a SiC + Ag sample that yields the highest value for the negative RI. Again, 30 measurements have been taken and averaged. The average Δtphase = −0.693 fs, implying Re(n) = −1.08. Note that although the second condition is not exactly satisfied, the value of Re(n) can be unambiguously determined based on the trend of our samples as mentioned above.

In passing, the group velocity vgroup can be negative or positive for a NIM since it is related to the dispersion as vgroup = dω/dk = c/[(c/vphase) + ωd(c/vphase)/dω]. It is readily seen that for vphase <0, if the second term in the denominator is larger (smaller) than the absolute value of the first term, one can have a NIM with a positive (negative) vgroup. However, the energy velocity should be positive even in a NIM. For our SiC + Ag sample, there is a negative shift in the location of the peak of the envelope in the presence of the sample. The overall shift of the envelope of the pulse can be used to experimentally determine vgroup using the relation vgroup = 2d/(Δtgroup + 2d/c). In our case, Δ t group<0with | Δ t group|>2d/c, implying vgroup <0.

For the purpose of designing a near-field super-resolution imaging device using our SiC + Ag NIM sample, information on the imaginary part of the RI is also needed. Now, it is well-known that the permittivity (ε) of metals are usually negative at visible wavelengths; hence a p-polarized (TM) light should excite a surface plasmon (SP) [9

A.-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisittpan, “MgB2-based negative refraction index metamaterial at visible frequencies: Theoretical analysis,” Phys. Rev. B 76(19), 195123 (2007). [CrossRef]

]. On the other hand, s-polarized (TE) light can only excite a SP for materials with negative permeability (μ) [8

N. Limberopoulos, A. Akyurtlu, K. Higginson, A.-G. Kussow, and C. D. Merritt, “Negative refractive index metamaterials in the visible spectrum based on MgB2/SiC composites,” Appl. Phys. Lett. 95(2), 023306 (2009). [CrossRef]

, 9

A.-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisittpan, “MgB2-based negative refraction index metamaterial at visible frequencies: Theoretical analysis,” Phys. Rev. B 76(19), 195123 (2007). [CrossRef]

]. The presence of SPR using both p- and s- polarized light on samples containing SiC + Ag should indicate negative ε and μ . Accordingly, SPR measurements have been performed on our SiC + Ag sample with Re(n) = −1.08 from double interferometry (described above) with both p- and s- polarized light using standard prism coupling experimentation [11

B. C. Mohanty and S. Kasiviswanathan, “Two-prism setup for surface plasmon resonance studies,” Rev. Sci. Instrum. 76(3), 033103 (2005). [CrossRef]

] in a Kretschmann configuration by monitoring the reflectance for both polarizations experimentally, and subsequent careful numerical least squares fitting of the data by systematically varying the real and imaginary parts of μ and ε. It is found that n = −1.06 + 0.47i, and thus Re(n) is in excellent agreement with our double interferometry results.

4. Design of near-field super-resolution imaging device using SiC + Ag

A typical structure that can be used for testing super-resolution using a single NIM (Re(ε)<0) such as Ag has been proposed by Fang et al. [2

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

]. Such a structure, but with Ag now replaced by SiC + Ag, which is a double NIM ((Re(ε)<0, Re(µ)<0)) is shown in Fig. 4 . Specifically, our proposed structure contains a sub-wavelength object (viz., a grating of period 160 nm) etched on Cr, a layer of spacer photoresist (PR), and a layer of our SiC + Ag nanoparticle mixture. The top PR layer is optional and is needed if the imprint of the near field image on the PR is required; otherwise, a standard near-field imaging technique such as NSOM can be used. COMSOL is used to simulate the fields inside and outside the structure, using the values of the RI for the SiC + Ag obtained from our experiments reported above. Test simulations have been first performed using Ag, and shows that super-resolution is possible for TM polarization only. On the other hand, the use of SiC + Ag facilitates super-resolution for both TE and TM polarizations, as is expected from the properties of a true double NIM (see, for instance, simulation results for TE polarization in Fig. 5 ). Upon replacing the SiC + Ag or Ag with spacer PR layer only, no super-resolution is seen for any polarization, as expected. Incidentally, a perfect lossless NIM perfectly matched with the surrounding medium (viz., nair = 1, nNIM = −1) not only super-resolves the object, but also shows the presence of higher spatial harmonics in the image, suggesting super-resolution imaging, which is not possible using a metal such as Ag only.

Fig. 4 (a) Prototype for near-field imaging structure with a periodic sub-wavelength object, (b) COMSOL simulation of the electric field.
Fig. 5 Comparison between (a) Ag @ 365 nm and (b) our NIM (SiC + Ag) @ 405 nm for TE case. For the grating pattern shown with period 160 nm and duty cycle 50%, optical fields should be higher behind the regions where there is no Cr (shaded; yellow, in color). For Ag, the grating is incorrectly imaged, whereas with SiC + Ag, good super-resolution is observed. Parameters used for simulation are for (a) εCr = −3.72 + 9.9i, εspacer = 2.415, εAg = −2.4 + 0.24i, ntop PR = 1.65; for (b) εCr = −4.15 + 11i; εspacer = 2.8, nSiC + Ag = −1.06 + 0.47i, ntop PR = 1.65. The parameters used for (a) are optimized for best super-resolution results for TM case @ 365 nm. The fields are monitored at distances (a) 120 nm (b) 90 nm from the top of the Cr.

5. Conclusion

The fabrication and characterization of a novel double NIM comprising co-sputtered SiC + Ag nanoparticle mixtures on a glass substrate that shows negative index in the visible (405 nm) is reported. Co-sputtering is a relatively easy technique that readily creates nanoparticle mixtures when two species of materials are involved, and yields excellent surface smoothness. The RI of this NIM at 405 nm, estimated using double interferometry, is supported by independent measurements of the complex RI through SPR experiments with TE and TM polarizations. It is numerically verified that our SiC + Ag nanoparticle mixture can yield near-field super-resolution for TE and TM polarizations at 405 nm. A detailed study of sputtering conditions that can yield different values for the negative RI, and which can be possibly used for other visible wavelengths, is currently under way.

Acknowledgment

This work is partially supported by DARPA under contract #W31P4Q-10-C-0032. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. Approved for Public Release, Distribution Unlimited.

References

1.

H. I. Smith, “Fabrication techniques for surface-acoustic wave and thin-film optical devices,” Proc. IEEE 62(10), 1361–1387 (1974). [CrossRef]

2.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

3.

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994). [CrossRef] [PubMed]

4.

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

5.

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

6.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

7.

P. P. Banerjee, G. Nehmetallah, R. Aylo, and S. Rogers, “Nanoparticle-Dispersed Metamaterial Sensors for Adaptive Coded Aperture Imaging (ACAI) applications,” Proc. SPIE 8165, 81651G (2011).

8.

N. Limberopoulos, A. Akyurtlu, K. Higginson, A.-G. Kussow, and C. D. Merritt, “Negative refractive index metamaterials in the visible spectrum based on MgB2/SiC composites,” Appl. Phys. Lett. 95(2), 023306 (2009). [CrossRef]

9.

A.-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisittpan, “MgB2-based negative refraction index metamaterial at visible frequencies: Theoretical analysis,” Phys. Rev. B 76(19), 195123 (2007). [CrossRef]

10.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006). [CrossRef] [PubMed]

11.

B. C. Mohanty and S. Kasiviswanathan, “Two-prism setup for surface plasmon resonance studies,” Rev. Sci. Instrum. 76(3), 033103 (2005). [CrossRef]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(240.6680) Optics at surfaces : Surface plasmons
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: January 4, 2012
Revised Manuscript: February 9, 2012
Manuscript Accepted: February 28, 2012
Published: March 13, 2012

Citation
G. Nehmetallah, R. Aylo, P. Powers, A. Sarangan, J. Gao, H. Li, A. Achari, and P. P. Banerjee, "Co-sputtered SiC + Ag nanomixtures as visible wavelength negative index metamaterials," Opt. Express 20, 7095-7100 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7095


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References

  1. H. I. Smith, “Fabrication techniques for surface-acoustic wave and thin-film optical devices,” Proc. IEEE62(10), 1361–1387 (1974). [CrossRef]
  2. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
  3. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett.19(11), 780–782 (1994). [CrossRef] [PubMed]
  4. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp.10, 509–514 (1968).
  5. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  6. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  7. P. P. Banerjee, G. Nehmetallah, R. Aylo, and S. Rogers, “Nanoparticle-Dispersed Metamaterial Sensors for Adaptive Coded Aperture Imaging (ACAI) applications,” Proc. SPIE8165, 81651G (2011).
  8. N. Limberopoulos, A. Akyurtlu, K. Higginson, A.-G. Kussow, and C. D. Merritt, “Negative refractive index metamaterials in the visible spectrum based on MgB2/SiC composites,” Appl. Phys. Lett.95(2), 023306 (2009). [CrossRef]
  9. A.-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisittpan, “MgB2-based negative refraction index metamaterial at visible frequencies: Theoretical analysis,” Phys. Rev. B76(19), 195123 (2007). [CrossRef]
  10. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006). [CrossRef] [PubMed]
  11. B. C. Mohanty and S. Kasiviswanathan, “Two-prism setup for surface plasmon resonance studies,” Rev. Sci. Instrum.76(3), 033103 (2005). [CrossRef]

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