## An extraordinary directive radiation based on optical antimatter at near infrared |

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 (Δ*θ _{out}
* = 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

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]

*θ*= 0.06°, whereas the input beam is strongly divergent

*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) ]. 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

*n*= 3.45 for

*λ*= 1.55 µm) air holes Photonic Crystal (PhC) slab arranged in a hexagonal lattice in the (

*x,z*) plane with hole radius

*r,*lattice parameter

*a*and a ratio

*r/a*= 0.385, Fig. 1(a). This particular PhC shows at the normalized frequency

*ω*= 0.305 an almost isotropic effective index

_{n}*n*= –1 for TM polarization (the electric field directed along the holes axis). For

_{eff}*λ*= 1.55 µm, the corresponding parameters are

*r*= 180 nm and

*a*= 472 nm (see Fig. 1 Ref. 2 for details). In a previous paper [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]

*z*axis for long distance, without diffraction spread of the beam profile along

*x*transverse direction. In this experiment it has been shown that a fundamental step to obtain such a result is the managing of the PhC layer terminations [4

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]

*mm*long sample fabricated on a SOI (Silicon On Insulator), where the oxide substrate provides the low index medium for the vertical light confinement inside the higher index silicon layer on the top. The beam propagates, along the

*z-*direction, preserving an extremely well collimated shape in the absence of any lateral waveguide structure confining the beam, resulting in a strong macroscopic super-self-collimation effect [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]

**102**(13), 133902 (2009). [CrossRef] [PubMed]

*et al.*produced an extremely narrow antenna pattern for microwave [6

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]

## 3. Experiments

**102**(13), 133902 (2009). [CrossRef] [PubMed]

*R*of the m

^{th}–diffracted order from a grating, is directly proportional to the number of periods N that compose such a grating:

*± 10 pm*) we measure the spectral dispersion Δλ, fixing the observation angle of the diffracted beam to

*θ*= 21.55°, which corresponds to the

_{-1}*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*.

*θ*from the two extreme ends … of the grating”. From Eq. (1) we determine that the beam propagates inside the grating for, at least, N = 516 periods i.e. for a length of

*NΛ*= 1.265

*mm*. This is an underestimation of the propagation length. Indeed apart the considerations on the experimental limitations inherent in our experimental set-up, the previous formula (1) is derived within the fundamental assumption that the propagating wave in the grating is a plane wave. Eq. (1) is strictly connected with the classical grating equation that is obtained within the same hypothesiswhere

*θ*is the angle of the m-order diffracted out from the grating and

_{m}*θ*is the angle of the incident beam, in the incidence plane

_{i}*(y,z),*see Fig. 1(b). Analogously to the spectral resolution, a similar result can be obtained for the angular resolution

*Δθ*that, for a plane wave, essentially is the ratio between the wavelength and a fully coherent illuminated region of the grating:

*Δθ*~λ/NΛ. Then from previous spectral measurement we expect that the diffracted peaks are extremely narrow

*Δθ*~1.2

*mrad*= 0.07°. However the previous derivation is obtained in the case of an incident plane wave whereas, in our case, the incident wave is strongly focused (minimum focus size

*w*) and is far from the plane wave conditions. The grating Eq. (2), that is obtained applying the continuity to the

_{0}~2λ*z*-component of wavevector in this plane and considering that the incident beam has not

*x*-component,

*k*= 0, has to be considered for each

_{ix}*k*component. It can be shown that, if

_{ix}*k*, the directions of the diffracted orders lie on a cone [13], with a consequent broadening of the peaks from Eq. (2).

_{ix}≠0*x*and

*y*-direction is given by the apex angle of the asymptotic cone of the Gaussian beam

*θ*is probably in the middle respect to such value and the worst case arising from simple geometrical construction where the input beam from the lensed fiber has a minimum waist

_{beam}*w =*3

*μm*at

*z =*13

*μm*from the fiber (core diameter

*W*= 9 μm), with a light cone aperture

*x*and

*y*components are non-zero,

*k*and

_{ix}≠0*k*, and consequently the incident wavevector component along

_{iy}≠0*z*is reduced. For instance in the limit case of a pure grazing incidence

*θ*(

_{i}= 90°*k*= 0), the spread in the propagation plane,

_{iy}*k*, imply that

_{ix}≠0*z*-component of incident wavevector is consequently reduced

*k*Then at first insight a spread of incident k-wavevector means a spread of k-wavevector interacting with the grating and finally a spread of diffracted peaks. This is not the experimental evidence, where spectral and angular peaks are extremely narrow and for such a reason we defined such a radiation as extraordinarily collimated: an ordinary grating cannot give such a high collimation. We can expect that

_{iy}≠0.*x*-components propagates in QZAI metamaterial only on the small scale where the periodic re-focusing is produced, whereas globally the beam is strongly collimated and in the grating plane

*(x,z)*only the

*z-*component of the wavevector transport the energy, as we previously determine by imaging measurements. Such a self-collimating effect is explained by the coupling of materials with opposite refractive index, optically annihilating each other the light propagation. In terms of transformation optics this annihilation is equivalent to a space folding of the optically opposite regions, then both regions in the transformed space optically disappear. The folding applies in the (

*x,z*) plane without considering the

*y*-direction. On the one hand, due to the thickness of the SOI structure, the negative refraction properties of the photonic crystal are correctly derived for a 2D structure considered as infinite along the

*y*-direction, putting

*k*= 0, being the effective index of the fundamental mode supported by the SOI waveguide practically coincident with the index of the bulk silicon [2

_{iy}**102**(13), 133902 (2009). [CrossRef] [PubMed]

*k*= 0 propagates in the whole structure, shrinking the light in

_{iy}*x-*and

*y*-direction. Indeed we measure the wavevector

*y*-component propagating in QZAI measuring the spread of angular peaks. Considering the divergence

*θ*into the

_{beam}*sin θ*term in grating Eq. (2) around the central value

_{i}*θ*the diffracted angle

_{i}= 90°*θ*spread of few degrees. Then an accurate measurement of the diffracted angle is also an accurate measurement of the

_{m}*k*propagating in the grating. Limiting to a grazing incidence study, sin

_{0z}*θ*and considering

_{i}= 90°,*λ*= 1.55

*μm*only three orders (m = –1, –2, –3) in Eq. (2) satisfy the condition

*θ*In Fig. 3 the peaks position

_{-1}= 21.55°, θ_{-2}= −15.38°, θ_{-3}= −63.89°.*θ*and

_{-1}*θ*are located in excellent agreement with expected values for sin

_{-2}*θ*From one side this confirms that modulus of the propagating wavevector in z-direction is equal to the free space value of the wavenumber:

_{i}= 90°.*k*. Moreover, a fine angular scan around

_{hz}= 2π/λ*θ*(inset of Fig. 3) provides a measurement of extraordinary directivity of the scattered beam Δ

_{-1}*θ*= (0.061 ± 0.003)° in excellent agreement with our previous estimation based on the spectral resolution. From former discussion we know that the spread of diffracted peaks, in angular or in spectral domain, is due to both finite propagation length in the grating and from the deviation of the coupled

_{m = −1}*z*-component from its maximum value, as a consequence of the beam spreading in vertical and lateral direction. In absence of the self-collimation and vertical confinement effects, the strong beam aperture would be projected along the grating direction and finally would broad the diffraction peaks.

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]

*o*are the observed values,

_{i}*g*are the values of the fitted Gaussian function and

_{i}15. H. Chernoff and E. L. Lehmann, “The Use of Maximum Likelihood Estimates in *χ ^{2}* 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]

*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

## References and links

1. | J. Pendry and S. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter |

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. |

3. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

4. | V. Mocella, P. Dardano, L. Moretti, and I. Rendina, “Influence of surface termination on negative reflection by photonic crystals,” Opt. Express |

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. |

6. | S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. |

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 |

8. | M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using |

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. |

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. |

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. |

12. | M. Born, and E. Wolf, |

13. | E. G. Loewen, and E. Popov, |

14. | A. Yariv, |

15. | H. Chernoff and E. L. Lehmann, “The Use of Maximum Likelihood Estimates in 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. |

**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

- J. Pendry and S. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]
- 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]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Born, and E. Wolf, Principles of optics, 7th edition, (Cambridge University Press, Cambridge, 1999).
- E. G. Loewen, and E. Popov, Diffraction gratings and applications, (Marcel Dekker inc., New York Basel, 1997).
- A. Yariv, Quantum electronics, 3th edition, John Wiley & Sons, New York (1989).
- 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]
- 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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