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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25068–25074
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An extraordinary directive radiation based on optical antimatter at near infrared

Vito Mocella, Principia Dardano, Ivo Rendina, and Stefano Cabrini  »View Author Affiliations


Optics Express, Vol. 18, Issue 24, pp. 25068-25074 (2010)
http://dx.doi.org/10.1364/OE.18.025068


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Abstract

In this paper we discuss and experimentally demonstrate that in a quasi- zero-average-refractive-index (QZAI) metamaterial, in correspondence of a divergent source in near infrared (λ = 1.55 μm) the light scattered out is extremely directive (Δθout = 0.06°), coupling with diffraction order of the alternating complementary media grating. With a high degree of accuracy the measurements prove also the excellent vertical confinement of the beam even in the air region of the metamaterial, in absence of any simple vertical confinement mechanism. This extremely sensitive device works on a large contact area and open news perspective to integrated spectroscopy.

© 2010 OSA

1. Introduction

Coupling the air with a metamaterial that exhibits optically opposite properties, they annihilate each other acting for light propagation as an optical antimatter [1

1. J. Pendry and S. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]

]. In such a very particular environment the light has very special properties. Indeed alternating thousands slabs of air with equal length slabs of metamaterial, with effective refractive index equal to - 1, such complementary media transmits the light in plane without diffraction, preserving the source profile of the entrance side. Using a macroscopic sample length of 4 mm, we experimentally verify [2

2. V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009). [CrossRef] [PubMed]

] this theoretical prediction that intuitively can be described as a generalization of the superlens effect [3

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

]. However in such a very special electromagnetic medium, that has a zero or quasi-zero average refractive index, other very interesting phenomena are expected. In particular a divergent beam, or an internal point source, is transformed in an extremely directive beam in medium with refractive index close to zero. We demonstrate here that, using very accurate experimental measurements, the diffracted beam along diffraction order of the grating composed by air and anti-air metamaterial has an angular dispersion as small as Δθ = 0.06°, whereas the input beam is strongly divergent (Δθ20°), due to the focused incident beam from the lensed fiber. We also determine that, with a great accuracy, the wavenumber of the beam propagating without diffraction in the QZAI plane is the wavenumber in the air: 2π/λ. Then also the vertical y-component of the beam propagating within the QZAI metamaterial is practically zero, analogously to the lateral x-component, and the beam strongly confined propagates only along the z-direction, even if the incident beam is highly divergent in lateral and vertical direction [x and y in Fig. 1(b)
Fig. 1 A sketch of the experimental set-up (a) and of the grating sample (b).
]. Analogously, fixing the angle of the detector and scanning the input wavelength, we obtain a very narrow diffracted peak with an extremely well defined Gaussian shape. These features allow to determine the peak location with an high accuracy and could find application in lab-on-chip sensing.

2. Quasi-Zero-Average-Index Metamaterials

3. Experiments

Experimental investigation has been performed in near infrared using a CW tunable laser that provides light source at λ = 1.52 ÷ 1.62 µm connected to a lensed input fiber on a 3-axis nanopositioning stages (NanoMax by Thorlabs) with a spatial resolution of 20 nm (in piezo-electrical retroaction mode) in order to align with high accuracy the injected light. A fiber coupler and collimator (resolution 0.0004 degree) mounted on a precision rotation stage (resolution 0,001 degree) in order to achieve high angular resolution on the detection system. An IR camera Xenics Xeva 185 and a high numerical aperture (NA = 0.42) objective with a long working distance was used to determine the optimal alignment and to observe the light propagating in the structure, as in [2

2. V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009). [CrossRef] [PubMed]

]. See the Fig. 1(a) for a sketch of experimental setup and Fig. 1(b) for a sketch of the grating sample. The focus size of the input beam is 3.0 μm, in excellent agreement with target value of the commercial lensed fiber, and has been measured using a knife-edge technique. Measuring the angular and the spectral width of the diffracted peaks we obtain a direct quantification of the propagation length and of the angular spreading of the mode in this virtual waveguide, which has not a physical structure for the lateral and vertical confinement. In correspondence of a propagating monochromatic plane wave, the spectral resolution (or resolving power) R of the mth–diffracted order from a grating, is directly proportional to the number of periods N that compose such a grating:

RλΔλ=|m|N
(1)

Using a tunable laser, (Ando AQ4321D, spectral range 1520-1620 nm, wavelength accuracy ± 10 pm) we measure the spectral dispersion Δλ, fixing the observation angle of the diffracted beam to θ-1 = 21.55°, which corresponds to the m = −1 peak of the wavelength λ = 1.55 μm, see Eq. (2). The Full Width at Half Maximum (FWHM) results Δλ = (3.08 ± 0.06) nm.

These measurements definitely show that a metamaterial with average refractive index close to zero produces an extremely collimated beam in correspondence of a divergent excitation [9

9. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008). [CrossRef] [PubMed]

] an extraordinary result that cannot be explained without the unusual properties of metamaterials. We underline also that peaks are not only very narrow but they also fit extremely well a Gaussian shape: in the normalized spectral dispersion of Fig. 2
Fig. 2 Measured spectral dispersion at θ-2 = –20,7, (black square) fit perfectly with a Gaussian curve (red line).
the coefficient of determination R2=1SSerr/SStot=0.99061 is very close to unity, being very small the ratio of sum of squares of residuals SSerr=iN(oigi)2 with the total sum of square SStot=iN(oio¯)2, where oi are the observed values, gi are the values of the fitted Gaussian function and o¯=1/NiNoiis the mean of observed data over the N observations [15

15. H. Chernoff and E. L. Lehmann, “The Use of Maximum Likelihood Estimates in χ2 Tests for Goodness of Fit,” Ann. Math. Stat. 25(3), 579–586 (1954). [CrossRef]

]. The goodness of such fit means that Gaussian model likely predicts future observations in particular if, after a suitable calibration, the presence of the interesting analyte to the surface of this device produces a small shift of the resonance frequency. It is outside the scope of the present paper a detailed analysis of performances of this device as an integrated spectrometer. Anyway the very high goodness of fit open to future exploration of this open structure as integrated spectrometer, with a very small lateral dimensions (few microns) and an high accuracy at least comparable with that of a compact spectrometer integrating negative refracting elements [16

16. B. Momeni, E. S. Hosseini, M. Askari, M. Soltani, and A. Adibi, “Integrated photonic crystal spectrometers for sensing applications,” Opt. Commun. 282(15), 3168–3171 (2009). [CrossRef]

]. Finally we underline that we do not expect a Gaussian shape for the diffracted peaks and also the finite size of the grating would produce a sinc function, instead of a Gaussian peak. Then Gaussian shape are determined from the optical set-up, in particular from the collimator element mounted over the rotational stage, which has a larger Gaussian shape that convolutes the diffracted peaks, smaller compared to the peaks of Fig. 2 and Fig. 3.

3. Conclusions

The extraordinary collimation of the diffracted peaks and equivalently the extremely narrow spectral resolution, demonstrate the special properties of the beam propagation in a quasi zero refractive index metamaterial on a macroscopic scale. Together with later confinement, we prove the extremely singular propagation in this metamaterial environment, where the beam propagates as in a conventional waveguide even without lateral and vertical structures that ensure such a confinement. Finally we underline that this metamaterial has an open configuration, where the air that strongly interact with external solicitations composes roughly half part of the structure. High precision sensing spectroscopy is then possible over a macroscopic region in a sample exhibiting a very large contact area with environment. The strong lateral confinement allows a probe of a very narrow region of few microns close to the interface due to the strong vertical confinement.

References and links

1.

J. Pendry and S. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]

2.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009). [CrossRef] [PubMed]

3.

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

4.

V. Mocella, P. Dardano, L. Moretti, and I. Rendina, “Influence of surface termination on negative reflection by photonic crystals,” Opt. Express 15(11), 6605–6611 (2007). [CrossRef] [PubMed]

5.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003). [CrossRef] [PubMed]

6.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

7.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-Near-Zero (ENZ) Metamaterials and Electromagnetic Sources: Tailoring the Radiation Phase Pattern,” Phys. Rev. B 75(15), 155410 (2007). [CrossRef]

8.

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006). [CrossRef] [PubMed]

9.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008). [CrossRef] [PubMed]

10.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008). [CrossRef] [PubMed]

11.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]

12.

M. Born, and E. Wolf, Principles of optics, 7th edition, (Cambridge University Press, Cambridge, 1999).

13.

E. G. Loewen, and E. Popov, Diffraction gratings and applications, (Marcel Dekker inc., New York Basel, 1997).

14.

A. Yariv, Quantum electronics, 3th edition, John Wiley & Sons, New York (1989).

15.

H. Chernoff and E. L. Lehmann, “The Use of Maximum Likelihood Estimates in χ2 Tests for Goodness of Fit,” Ann. Math. Stat. 25(3), 579–586 (1954). [CrossRef]

16.

B. Momeni, E. S. Hosseini, M. Askari, M. Soltani, and A. Adibi, “Integrated photonic crystal spectrometers for sensing applications,” Opt. Commun. 282(15), 3168–3171 (2009). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(160.3918) Materials : Metamaterials
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Metamaterials

History
Original Manuscript: August 24, 2010
Revised Manuscript: October 28, 2010
Manuscript Accepted: October 29, 2010
Published: November 16, 2010

Citation
Vito Mocella, Principia Dardano, Ivo Rendina, and Stefano Cabrini, "An extraordinary directive radiation based on optical antimatter at near infrared," Opt. Express 18, 25068-25074 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25068


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References

  1. J. Pendry and S. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]
  2. V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009). [CrossRef] [PubMed]
  3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  4. V. Mocella, P. Dardano, L. Moretti, and I. Rendina, “Influence of surface termination on negative reflection by photonic crystals,” Opt. Express 15(11), 6605–6611 (2007). [CrossRef] [PubMed]
  5. J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90(8), 083901 (2003). [CrossRef] [PubMed]
  6. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]
  7. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-Near-Zero (ENZ) Metamaterials and Electromagnetic Sources: Tailoring the Radiation Phase Pattern,” Phys. Rev. B 75(15), 155410 (2007). [CrossRef]
  8. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006). [CrossRef] [PubMed]
  9. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008). [CrossRef] [PubMed]
  10. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008). [CrossRef] [PubMed]
  11. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]
  12. M. Born, and E. Wolf, Principles of optics, 7th edition, (Cambridge University Press, Cambridge, 1999).
  13. E. G. Loewen, and E. Popov, Diffraction gratings and applications, (Marcel Dekker inc., New York Basel, 1997).
  14. A. Yariv, Quantum electronics, 3th edition, John Wiley & Sons, New York (1989).
  15. H. Chernoff and E. L. Lehmann, “The Use of Maximum Likelihood Estimates in χ2 Tests for Goodness of Fit,” Ann. Math. Stat. 25(3), 579–586 (1954). [CrossRef]
  16. B. Momeni, E. S. Hosseini, M. Askari, M. Soltani, and A. Adibi, “Integrated photonic crystal spectrometers for sensing applications,” Opt. Commun. 282(15), 3168–3171 (2009). [CrossRef]

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