## General properties of dielectric optical antennas

Optics Express, Vol. 17, Issue 26, pp. 24084-24095 (2009)

http://dx.doi.org/10.1364/OE.17.024084

Acrobat PDF (324 KB)

### Abstract

Using Mie theory we derive a number of general results concerning the resonances of spherical and cylindrical dielectric antennas. Specifically, we prove that the peak scattering cross-section of radiation-limited antennas depends only on the resonance frequency and thus is independent of refractive index and size, a result which is valid even when the resonator is atomic-scale. Furthermore, we derive scaling limits for the bandwidth of dielectric antennas and describe a cylindrical mode which is unique in its ability to support extremely large bandwidths even when the particle size is deeply subwavelength. Finally, we show that higher Q antennas may couple more efficiently to an external load, but the optimal absorption cross-section depends only on the resonance frequency.

© 2009 OSA

## 1. Introduction

1. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. **94**(1), 017402 (2005). [CrossRef] [PubMed]

2. F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. **101**(15), 157403 (2008). [CrossRef] [PubMed]

3. F. Jäckel, A. A. Kinkhabwala, and W. E. Moerner, “Gold bowtie nanoantennas for surface enhanced Raman scattering under controlled electrochemical potential,” Chem. Phys. Lett. **446**(4-6), 339–343 (2007). [CrossRef]

4. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. **34**(5), 686–688 (2009). [CrossRef] [PubMed]

5. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. **21**(34), 3504–3509 (2009). [CrossRef]

6. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. **97**(1), 017402 (2006). [CrossRef] [PubMed]

7. T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics **2**(4), 234–237 (2008). [CrossRef]

8. J. Li, A. Slandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B **76**, 25403 (2007). [CrossRef]

9. R. K. Mongia and P. Bhartia, “““Dielectric resonator antennas-A review and general design relations for resonant frequency and bandwidth,” Int. J. Microwave Millimeter-Wave Comput.-Aided Eng. **4**(3), 230–247 (1994). [CrossRef]

10. R. C. J. Hsu, A. Ayazi, B. Houshmand, and B. Jalali, “All-dielectric photonic-assisted radio front-end technology,” Nat. Photonics **1**(9), 535–538 (2007). [CrossRef]

11. L. Cao, B. Nabet, and J. E. Spanier, “Enhanced Raman scattering from individual semiconductor nanocones and nanowires,” Phys. Rev. Lett. **96**(15), 157402 (2006). [CrossRef] [PubMed]

12. G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. **8**(5), 1341–1346 (2008). [CrossRef] [PubMed]

13. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. **99**(10), 107401 (2007). [CrossRef] [PubMed]

14. K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. **102**(13), 133901 (2009). [CrossRef] [PubMed]

15. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics **3**(11), 658–661 (2009). [CrossRef]

16. L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. **8**(8), 643–647 (2009). [CrossRef] [PubMed]

17. F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. **97**(20), 206806 (2006). [CrossRef] [PubMed]

*ε’/*∂

*ω*) and dissipation (

*ε*″) of the metal’s complex dielectric function (

*ε*=

*ε*′ +

*iε*″). Here, we derive a number of general properties describing the Mie resonances of spherical and cylindrical particles composed of dielectric materials. Specifically, we derive a fundamental limit on the extinction cross-section which is completely independent of particle size or refractive index and applies equally well to atomic or molecular systems. Furthermore, we prove that the peak scattering response of radiation-limited systems always reaches this maximal limit. We investigate differences in the Q factor of such antennas, and demonstrate a cylindrical mode which is unique in its ability to support extremely large bandwidths even when the particle size is deeply subwavelength. Finally, we describe a fundamental tradeoff between field enhancement and bandwidth, investigate its impact on coupling to an external load, and derive a fundamental limit on the absorption cross-section.

## 2. Fundamental limits of extinction

*m*which describes the azimuthal phase dependence (

*e*). Under normal incidence plane-wave illumination, the scattered fields can be considered purely transverse electric (TE, electric field perpendicular to the long axis of the cylinder) or transverse magnetic (TM, electric field parallel to the long axis) and are given by:where

^{imφ}*E*is the incident electric field strength and

_{0}*a*and

_{m}*b*are the size and material dependent coefficients of excitation (Mie coefficients). For spherically symmetric systems, the vector harmonics are functions of (

_{m}*r,θ,*φ) and the scattered fields are given by:where the vector harmonics for both cases have been normalized such that the radiated power is independent of the mode number,

*m*:

*x*=

*2πa/λ*) where

*a*is the particle radius and

*λ*is the excitation wavelength. For all coefficients the peaks get narrower and shift to lower

*x*as the refractive index increases. For a given value of the refractive index all coefficients exhibit multiple resonances as

*x*is increased. The TE

_{0}and TM

_{1}coefficients are identical [13

13. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. **99**(10), 107401 (2007). [CrossRef] [PubMed]

_{0}mode. Note that the maximum peak height always equals unity. As we will derive below, this constant maximal value of the Mie coefficient represents a fundamental limit on the extinction and scattering cross sections. Without loss of generality our derivation will cover the case of TM illuminated cylinders.

*per mode*. Thus:

*x*it holds that

*x*≤ 1 if

*x*≥

*x*

^{2}, we deduce a maximal value for the Mie coefficients:

**cross-sections are completely independent of particle size. In fact, even single atoms and molecules have a scattering cross-section equal to the limit of dipolar (**

*per-mode**m*= 1) Mie scattering (

19. G. Wrigge, I. Gerhardt, J. Hwang, G. Zumofen, and V. Sandoghdar, “Efficient coupling of photons to a single molecule and the observation of its resonance fluorescence,” Nat. Phys. **4**(1), 60–66 (2008). [CrossRef]

20. M. K. Tey, Z. Chen, S. A. Aljunid, B. Chng, F. Huber, G. Maslennikov, and C. Kurtsiefer, “Strong interaction between light and a single trapped atom without the need for a cavity,” Nat. Phys. **4**(12), 924–927 (2008). [CrossRef]

*m*

^{th}mode in the plane wave decomposition. For cylindrical systems each mode carries the same amount of power; for spherical systems the power contained in the

*m*

^{th}mode is proportional to 2

*m*+ 1. Furthermore, when the Mie coefficient equals unity the magnitudes of the

*m*

^{th}scattered and incident waves are equal. Physically, a finite portion of the illuminating plane wave’s energy is contained within the

*m*

^{th}moment about a point (line) centered on the spherical (cylindrical) scatterer. The derived limits correspond to particles perfectly scattering the

*m*

^{th}harmonic of the incident plane wave, and thus are size-independent.

*m*

^{th}harmonic of the incident illumination. Setting the third bracket equal to zero is identical to the condition that the Mie coefficient equals one, i.e. any maxima in the

*m*

^{th}Mie coefficient must occur when the coefficient reaches the derived fundamental limit. Therefore, we have proven that a dissipationless particle of any refractive index will scatter with perfect efficiency at all modal resonances. This result appears somewhat counter-intuitive at first glance. One might expect that high refractive index particles are better scatterers than low refractive index particles. Although the total scattering cross section is identical on resonance, the resonant particle size decreases with increasing refractive index and thus the scattering

*efficiency*increases.

## 3. Fundamental limits of bandwidth

21. L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. **19**(12), 1163 (1948). [CrossRef]

22. J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antenn. Propag. **44**(5), 672 (1996). [CrossRef]

*ω*) times the ratio of the stored energy (

*W*) divided by the radiated power (P

_{stored}*) [23]:*

_{radiated}*a*resonating in one of the cylindrical modes we calculate both the radiated power and the energy stored in the external fields and derive a lower limit on the scattering Q. The total external electromagnetic energy is given by:

*W*. We define the radiative (or far-field) field amplitudes, the stored electromagnetic energy, and the radiated power as:

_{total}*m*number) of the scattered mode. By making a series expansion about

*x*= 0, we can derive an analytical expression for the Chu limit of the 0th order modes:where

*γ*is Euler’s constant (

*γ*≈0.58). This logarithmic scaling with particle size contrasts markedly with the geometric scaling for spherical particles. Thus, exceptionally small diameter cylindrical antennas can still support large bandwidth resonant modes. Although the 0th order modes

*can potentially*exhibit large bandwidths they

*need not necessarily*exhibit large bandwidths. The Chu limit is only a lower bound on Q, and thus is still satisfied even when it underestimates the Q values.

_{0}and TE

_{0}modes calculated using Mie theory and plotted on a log-linear scale. We define the calculated Q as the full-width half maximum (FWHM) of the scattering resonance divided by the resonance frequency. The peculiar non-Lorentzian lineshape of the TM

_{0}resonance (Fig. 1) requires that we estimate the FWHM by taking the low frequency half width at half maximum (HWHM) and multiplying by two. The Chu limit correctly predicts the logarithmic scaling for the TM

_{0}mode and reasonably approximates the actual Qs. In contrast, the Chu limit severely underestimates the calculated Qs for the TE

_{0}mode. The TM

_{0}mode is particularly unique in that it nearly reaches the fundamental bandwidth limit. Considering that the effective bandwidth (the area under the curve in Fig. 1) is even larger than the bandwidth calculated using the procedure described above, the TM

_{0}antenna resonance seems particularly suited for applications requiring large bandwidths.

*internal*stored energy. To good approximation, we can consider all the internal field energy to be non-radiating and derive an exact analytical expression for Q. Assuming negligible dispersion, the internal energy and Q are given by:

_{0}limit now has the correct slope but still appears to slightly underestimate Q values. This discrepancy results from the fact that TM

_{0}resonances are quite asymmetric (Fig. 1) and are poorly approximated by a Lorentzian lineshape; our method of determining Q from twice the HWHM of the Mie function is not strictly accurate. For the TE

_{0}resonance, which has a much more Lorentzian line-shape, the modified limit exactly predicts the calculated Q values. Performing the same analysis for the TM

_{1}mode (Fig. 2) we see that the original Chu limit exhibits the proper scaling but underestimates the actual Qs, while our modified Chu limit exactly predicts the resonance bandwidth.

^{2}. We expect, then, thatthe external stored energy, and thus the Chu limit, are proportional to 1/x

^{2}. The analytically derived Chu limit exhibits this scaling in the limit of very small resonators. This analysis points to a fundamental trade-off between field enhancements and bandwidth. Strong near-field enhancements lead to larger values of stored electromagnetic energy and thus smaller bandwidths.

## 4. Fundamental limits of absorption

24. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photon. **1**(3), 438–483 (2009). [CrossRef]

2. F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. **101**(15), 157403 (2008). [CrossRef] [PubMed]

6. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. **97**(1), 017402 (2006). [CrossRef] [PubMed]

4. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. **34**(5), 686–688 (2009). [CrossRef] [PubMed]

16. L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. **8**(8), 643–647 (2009). [CrossRef] [PubMed]

5. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. **21**(34), 3504–3509 (2009). [CrossRef]

25. M. Kerker and E. Matijevic, “Scattering of electromagnetic waves from concentric infinite cylinders,” J. Opt. Soc. Am. **51**(5), 506 (1961). [CrossRef]

*t*(Fig. 3 ). The absorption cross-section for a TE illuminated cylinder is given by:

_{0}(red) and TE

_{1}(blue) modes of particles with refractive indices chosen such that the two normalized resonance frequencies are identical. The TE

_{1}mode has a much narrower resonance because it has significantly more energy stored both inside the particle and in the external near-fields [Fig. 3(b)]. The enhanced near-fields for this mode allow for much stronger coupling to a thin layer of absorbing material [Fig. 3(c)]. For comparison, we also plot the Mie coefficients for the fundamental (red) and second order (blue) TE

_{1}modes of particles with refractive indices chosen such that the two normalized resonance frequencies are identical [Fig. 3(d)]. In this case, the higher Q for the second order mode results

*entirely*from excess energy stored inside the particle; the external fields are identical [Fig. 3(e)]. Thus, the coupling to an external absorber is also identical [Fig. 3(f)]. A higher Q resonance is only useful to the extent that it results from concentration of electromagnetic energy at the location where one wishes to drive a load.

*Re{a*which maximizes the absorption cross-section:and derive a corresponding limit on the per-mode absorption cross-section.

_{m}}*P*is the total power removed from the incident beam (extinction) due to both scattering and absorption. The energy stored in the scattered fields is exactly proportional to

_{ext}*total*stored energy is also proportional to

## 5. Conclusion

_{0}cylindrical antenna resonance for applications where large bandwidth, subwavelength antennas are desired. Finally, we show that high-Q antennas may exhibit stronger coupling to an external load, but the optimal absorption cross-section depends only on the resonance frequency.

## Acknowledgments

## References and links

1. | P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. |

2. | F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. |

3. | F. Jäckel, A. A. Kinkhabwala, and W. E. Moerner, “Gold bowtie nanoantennas for surface enhanced Raman scattering under controlled electrochemical potential,” Chem. Phys. Lett. |

4. | J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. |

5. | R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. |

6. | S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. |

7. | T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics |

8. | J. Li, A. Slandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B |

9. | R. K. Mongia and P. Bhartia, “““Dielectric resonator antennas-A review and general design relations for resonant frequency and bandwidth,” Int. J. Microwave Millimeter-Wave Comput.-Aided Eng. |

10. | R. C. J. Hsu, A. Ayazi, B. Houshmand, and B. Jalali, “All-dielectric photonic-assisted radio front-end technology,” Nat. Photonics |

11. | L. Cao, B. Nabet, and J. E. Spanier, “Enhanced Raman scattering from individual semiconductor nanocones and nanowires,” Phys. Rev. Lett. |

12. | G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. |

13. | J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. |

14. | K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. |

15. | J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics |

16. | L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. |

17. | F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. |

18. | C. F. Bohren, and D. R. Huffman, |

19. | G. Wrigge, I. Gerhardt, J. Hwang, G. Zumofen, and V. Sandoghdar, “Efficient coupling of photons to a single molecule and the observation of its resonance fluorescence,” Nat. Phys. |

20. | M. K. Tey, Z. Chen, S. A. Aljunid, B. Chng, F. Huber, G. Maslennikov, and C. Kurtsiefer, “Strong interaction between light and a single trapped atom without the need for a cavity,” Nat. Phys. |

21. | L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. |

22. | J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antenn. Propag. |

23. | J. D. Jackson, |

24. | P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photon. |

25. | M. Kerker and E. Matijevic, “Scattering of electromagnetic waves from concentric infinite cylinders,” J. Opt. Soc. Am. |

**OCIS Codes**

(140.4780) Lasers and laser optics : Optical resonators

(290.4020) Scattering : Mie theory

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(280.4788) Remote sensing and sensors : Optical sensing and sensors

**ToC Category:**

Scattering

**History**

Original Manuscript: September 28, 2009

Revised Manuscript: December 5, 2009

Manuscript Accepted: December 6, 2009

Published: December 17, 2009

**Citation**

Jon A. Schuller and Mark L. Brongersma, "General properties of dielectric optical antennas," Opt. Express **17**, 24084-24095 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-24084

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### References

- P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005). [CrossRef] [PubMed]
- F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, and J. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailored nanoantenna for infrared detection,” Phys. Rev. Lett. 101(15), 157403 (2008). [CrossRef] [PubMed]
- F. Jäckel, A. A. Kinkhabwala, and W. E. Moerner, “Gold bowtie nanoantennas for surface enhanced Raman scattering under controlled electrochemical potential,” Chem. Phys. Lett. 446(4-6), 339–343 (2007). [CrossRef]
- J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through subwavelength slits,” Opt. Lett. 34(5), 686–688 (2009). [CrossRef] [PubMed]
- R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21(34), 3504–3509 (2009). [CrossRef]
- S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]
- T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008). [CrossRef]
- J. Li, A. Slandrino, and N. Engheta, “Shaping light beams in the nanometer scale: a Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76, 25403 (2007). [CrossRef]
- R. K. Mongia and P. Bhartia, “Dielectric resonator antennas-A review and general design relations for resonant frequency and bandwidth,” Int. J. Microwave Millimeter-Wave Comput.-Aided Eng. 4(3), 230–247 (1994). [CrossRef]
- R. C. J. Hsu, A. Ayazi, B. Houshmand, and B. Jalali, “All-dielectric photonic-assisted radio front-end technology,” Nat. Photonics 1(9), 535–538 (2007). [CrossRef]
- L. Cao, B. Nabet, and J. E. Spanier, “Enhanced Raman scattering from individual semiconductor nanocones and nanowires,” Phys. Rev. Lett. 96(15), 157402 (2006). [CrossRef] [PubMed]
- G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. 8(5), 1341–1346 (2008). [CrossRef] [PubMed]
- J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007). [CrossRef] [PubMed]
- K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102(13), 133901 (2009). [CrossRef] [PubMed]
- J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009). [CrossRef]
- L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009). [CrossRef] [PubMed]
- F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006). [CrossRef] [PubMed]
- C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Inter-Science, New York, 1998).
- G. Wrigge, I. Gerhardt, J. Hwang, G. Zumofen, and V. Sandoghdar, “Efficient coupling of photons to a single molecule and the observation of its resonance fluorescence,” Nat. Phys. 4(1), 60–66 (2008). [CrossRef]
- M. K. Tey, Z. Chen, S. A. Aljunid, B. Chng, F. Huber, G. Maslennikov, and C. Kurtsiefer, “Strong interaction between light and a single trapped atom without the need for a cavity,” Nat. Phys. 4(12), 924–927 (2008). [CrossRef]
- L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. 19(12), 1163 (1948). [CrossRef]
- J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antenn. Propag. 44(5), 672 (1996). [CrossRef]
- J. D. Jackson, Classical Electrodynamics (Wiley and Sons, New York, 1999).
- P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical Antennas,” Adv. Opt. Photon. 1(3), 438–483 (2009). [CrossRef]
- M. Kerker and E. Matijevic, “Scattering of electromagnetic waves from concentric infinite cylinders,” J. Opt. Soc. Am. 51(5), 506 (1961). [CrossRef]

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