## Voigt Airy surface magneto plasmons |

Optics Express, Vol. 20, Issue 19, pp. 21187-21195 (2012)

http://dx.doi.org/10.1364/OE.20.021187

Acrobat PDF (1071 KB)

### Abstract

We present a basic theory on Airy surface magneto plasmons (SMPs) at the interface between a dielectric layer and a metal layer (or a doped semiconductor layer) under an external static magnetic field in the Voigt configuration. It is shown that, in the paraxial approximation, the Airy SMPs can propagate along the surface without violating the nondiffracting characteristics, while the ballistic trajectory of the Airy SMPs can be tuned by the applied magnetic field. In addition, the self-deflection-tuning property of the Airy SMPs depends on the direction of the external magnetic field applied, owing to the nonreciprocal effect.

© 2012 OSA

## 1. Introduction

1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. **47**(3), 264–267 (1979). [CrossRef]

2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. **99**(21), 213901 (2007). [CrossRef] [PubMed]

3. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. **32**(8), 979–981 (2007). [CrossRef] [PubMed]

3. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. **32**(8), 979–981 (2007). [CrossRef] [PubMed]

4. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics **3**(7), 395–398 (2009). [CrossRef]

5. A. Rudnick and D. M. Marom, “Airy-soliton interactions in Kerr media,” Opt. Express **19**(25), 25570–25582 (2011). [CrossRef] [PubMed]

6. G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express **20**(3), 2196–2205 (2012). [CrossRef] [PubMed]

7. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics **2**(11), 675–678 (2008). [CrossRef]

8. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. **105**(25), 253901 (2010). [CrossRef] [PubMed]

9. C. J. Zapata-Rodríguez, S. Vuković, M. R. Belić, D. Pastor, and J. J. Miret, “Nondiffracting Bessel plasmons,” Opt. Express **19**(20), 19572–19581 (2011). [CrossRef] [PubMed]

10. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. **25**(20), 1493–1495 (2000). [CrossRef] [PubMed]

11. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. **35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

12. W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. **36**(7), 1164–1166 (2011). [CrossRef] [PubMed]

13. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. **107**(11), 116802 (2011). [CrossRef] [PubMed]

14. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. **107**(12), 126804 (2011). [CrossRef] [PubMed]

15. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. **28**(22), 1455–1458 (1972). [CrossRef]

*ω*and the incident frequency

_{p}*ω*, but also by the cyclotron frequency

*ω*, which is a function of the external magnetic field. In consequence, the medium becomes highly anisotropic (the permittivity of the conductor becomes a tensor) under an external magnetic field – even though the medium is isotropic. Therefore, SMPs have some unique and intriguing features, compared with general SP waves [15

_{c}15. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. **28**(22), 1455–1458 (1972). [CrossRef]

16. M. S. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. **41**(1-8), 1–416 (2001). [CrossRef]

15. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. **28**(22), 1455–1458 (1972). [CrossRef]

17. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. **100**(2), 023902 (2008). [CrossRef] [PubMed]

18. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. **37**(11), 1895–1897 (2012). [CrossRef] [PubMed]

## 2. Theory of Airy surface magneto plasmons

*z*= 0, and propagates along the

*z*-axis. An external static magnetic field

*B*is applied uniformly on the whole structure along the

*y*-axis, forming the so called Voigt configuration.

*x*<0). It can be written, according to the Maxwell equations, aswhere

*k*

_{0}is the wave vector in free space. When

*B*is applied, the permittivity of the metal/semiconductor

17. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. **100**(2), 023902 (2008). [CrossRef] [PubMed]

19. E. D. Palik and J. K. Furdyna, “Infrared and microwave magnetoplasma effects in semiconductors,” Rep. Prog. Phys. **33**(3), 1193–1322 (1970). [CrossRef]

*ε*=

_{xx}*ε*[1 –

_{∞}*ω*

_{p}^{2}/ (

*ω*

^{2}–

*ω*

_{c}^{2})],

*ε*= –

_{xz}*iε*

_{∞}ω_{p}^{2}

*ω*/ [

_{c}*ω*(

*ω*

^{2}–

*ω*

_{c}^{2})], and

*ε*=

_{yy}*ε*(1 –

_{∞}*ω*

_{p}^{2}/

*ω*

^{2}), in which

*ω*is the angular frequency of the incident wave,

*ω*is the plasma frequency of the metal/semiconductor,

_{p}*ε*is the high-frequency permittivity, and

_{∞}*ω*=

_{c}*eB*/

*m** is the cyclotron frequency.

*e*and

*m**are the charge and the effective mass of electrons, respectively.

*B*is the applied external magnetic field. Here, it is noted that we use the Drude model to calculate the elements in Eq. (2) [19

19. E. D. Palik and J. K. Furdyna, “Infrared and microwave magnetoplasma effects in semiconductors,” Rep. Prog. Phys. **33**(3), 1193–1322 (1970). [CrossRef]

*α*

_{1}is the decay factor in

*x*-direction. For a paraxial Airy SMP,

*α*

_{1}does not change much with that of a plane SMP wave [11

11. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. **35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

*ε*is the Voigt dielectric constant, defined by

_{V}**28**(22), 1455–1458 (1972). [CrossRef]

*k*is the propagation constant of the SMPs, calculated by a transcendental equation:in which

_{smp}*ε*is the permittivity of the dielectric. Substitute Eqs. (2) and (3) into Eq. (1), and conduct the Fourier transform on the equations with respect to

_{d}*y*, we obtain where

11. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. **35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

*D*is the partial differential with respect to

*z*. The eigen values can be calculated by nontrivial solutions of Eq. (6) asin which

*k*<<

_{y}*k*

_{0}and

*k*<<

_{y}*k*, we expand Eq. (7) up to the second and the zeroth order of

_{smp}*k*/

_{y}*k*

_{0}and

*k*/

_{y}*k*, respectively. The simplified eigen values are calculated by where

_{smp}*E*=

_{x}*E*= 0) and TM modes (

_{z}*E*= 0) of a plane wave propagating in Voigt-magnetized plasma [18

_{y}18. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. **37**(11), 1895–1897 (2012). [CrossRef] [PubMed]

18. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. **37**(11), 1895–1897 (2012). [CrossRef] [PubMed]

_{2}=

*ik*. Therefore, we choose Eq. (8b) as the eigen value in our calculations to ensure

_{smp}*E*is predominant in the electric field to excite plasmons on the surface. Consequently, the solution of Eq. (6) iswhere

_{x}*C*

_{1}is a function of

*k*needing to be determined. Like other works of Airy beams [1

_{y}1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. **47**(3), 264–267 (1979). [CrossRef]

6. G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express **20**(3), 2196–2205 (2012). [CrossRef] [PubMed]

*E*component of the Airy SMPs in the metal/semiconductor layer at the input plane

_{x}*z*= 0 takes a form of [11

**35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

*w*

_{0}is the characteristic width of the first Airy beam lobe, and

*a*is the decay factor [3

3. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. **32**(8), 979–981 (2007). [CrossRef] [PubMed]

*E*of the Airy SMPs in the metal/semiconductor asin which

_{x}*y*-direction, the definition of TE and TM modes is not the same as that of an Airy beam in free space (for TE mode:

*H*= 0, TM mode:

_{y}*E*= 0). However, in the paraxial approximation, they can be divided by

_{y}*E*= 0 for TE mode and

_{z}*H*= 0 for TM mode [11

_{z}**35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

*ε*with

_{xx}*ε*,

_{d}*α*

_{1}with -

*α*

_{2}, and

*ε*= 0, where

_{xx}**E**|

^{2}distributions of Airy SMPs on both the

*x-y*plane and

*y-z*plane without the magnetic field are plotted. In order to ensure

*ε*<0 (under this condition, SMPs can exists), the incident frequency and the magnetic field are set as

_{V}*ω*= 0.8

*ω*and

_{p}*ω*= 0.1

_{c}*ω*, respectively. Without loss of generality, the characteristic width and the decay factor are chosen as

_{p}*w*

_{0}= 2

*λ*and

*a*= 0.1, respectively, where

*λ*is the incident wavelength. We choose

*InSb*as the semiconductor material, which is often used in the SMPs experiments [21

21. I. L. Tyler, B. Fischer, and R. J. Bell, “On the observation of surface magnetoplasmons,” Opt. Commun. **8**(2), 145–146 (1973). [CrossRef]

23. J. Gómez Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express **13**(3), 847–859 (2005). [CrossRef] [PubMed]

*InSb*are

*m** = 0.014

*m*

_{0}, (

*m*

_{0}is the free electron mass in vacuum),

*ω*= 12.6THz, and

_{p}*ε*

_{∞}= 15.68 [23

23. J. Gómez Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express **13**(3), 847–859 (2005). [CrossRef] [PubMed]

*InSb*material, keeping the diffraction-free characteristic even after propagation distance of 80

*λ*. With the increase of the propagating length, the diffraction effect becomes obvious due to the decay factor

*a*in the y-direction, which is the same as that of a free space Airy beam [2

2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. **99**(21), 213901 (2007). [CrossRef] [PubMed]

**32**(8), 979–981 (2007). [CrossRef] [PubMed]

*+ y*-axis. Figure 2(d) shows the self-bending property of Airy SMPs.

## 3. Ballistic trajectory tuning by the external magnetic field

**35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

20. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. **33**(3), 207–209 (2008). [CrossRef] [PubMed]

*w*

_{0}is set, the ballistic dynamics of the Airy SMPs is mainly determined by

*k*. In Fig. 3 , we plot the dispersion curve of SMPs under different external magnetic field intensities with

_{smp}*ω*<

*ω*. It is found that when the magnetic field is applied along the

_{p}*+ y*-axis (denoted by

*B*> 0 in the inset), the

*k*~

_{smp}*ω*curve nearly keeps unchanged. While, when the magnetic field is applied along the

*–y*-axis (denoted by

*B*<0), the dispersion curve moves toward lower frequencies side. This intriguing nonreciprocal effect can be understood by Eq. (4). When the magnetic field is applied in the opposite direction,

*ε*in the last term changes its sign. Thus the dispersion equations become different, having different cutoff frequencies [24

_{xz}24. M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B Condens. Matter **36**(11), 5960–5967 (1987). [CrossRef] [PubMed]

*B*<0,

*k*will increase for a monochromatic wave. Consequently, according to Eq. (20), the self-bending effect of the Airy SMPs will be alleviated. In Fig. 4 , the ballistic curve of Airy SMPs varying with respect to the magnetic field is plotted for an electromagnetic wave at

_{smp}*ω*= 0.85

*ω*. It can be seen that with the increase of the magnetic field, the tilting angle of the Airy SMPs decreases. However, this phenomenon cannot be observed for

_{p}*B*>0, which is clearly shown in the inset of Fig. 4. In this situation, the “gravity” in the Newtonian equation of Eq. (21) changes very little (red dashed line), compared with that in the situation

*B*<0 (blue line). In Fig. 5 , the electric field distributions of Airy SMPs are plotted without any magnetic field, and with magnetic fields such that

*ω*= 0.25

_{c}*ω*along the

_{p}*+ y*-axis and

*–y*-axis, respectively. It can be clearly seen that, when

*B*< 0, the Airy SMPs can be tuned by the magnetic field. It should also be noted that the nonreciprocal effect can be observed by changing not only the direction of the external magnetic field, but also the propagation direction of the Airy SMPs.

**35**(12), 2082–2084 (2010). [CrossRef] [PubMed]

*z*direction at

*z*= 0 plane. Due to the limitation on our PC memories, the FDTD simulation is conducted in the region (−2

*λ*<x<5

*λ*, −30

*λ*<y<30

*λ*, 0<z<50

*λ*). The analytical and FDTD-simulation results are compared in Fig. 6 . It shows that the theoretical model gives good predictions of the main lobe and the side lobes of the Airy SMPs except for a slight shift. We believe this shift is caused by the insufficient grid density. When a magnetic field is applied (

*ω*= 0.25

_{c}*ω*) along the –y-axis, the main lobe moves about 1.5

_{p}*λ*toward the –

*y*direction, calculated by the theoretical model, while the FDTD simulation gives a shift of about 1.55

*λ*.

## 4. Conclusions

## Acknowledgements

## References and links

1. | M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. |

2. | G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. |

3. | G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. |

4. | T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics |

5. | A. Rudnick and D. M. Marom, “Airy-soliton interactions in Kerr media,” Opt. Express |

6. | G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express |

7. | J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics |

8. | D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. |

9. | C. J. Zapata-Rodríguez, S. Vuković, M. R. Belić, D. Pastor, and J. J. Miret, “Nondiffracting Bessel plasmons,” Opt. Express |

10. | J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. |

11. | A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. |

12. | W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett. |

13. | A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. |

14. | L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. |

15. | J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. |

16. | M. S. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. |

17. | Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. |

18. | B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. |

19. | E. D. Palik and J. K. Furdyna, “Infrared and microwave magnetoplasma effects in semiconductors,” Rep. Prog. Phys. |

20. | G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. |

21. | I. L. Tyler, B. Fischer, and R. J. Bell, “On the observation of surface magnetoplasmons,” Opt. Commun. |

22. | L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B |

23. | J. Gómez Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express |

24. | M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B Condens. Matter |

**OCIS Codes**

(230.3810) Optical devices : Magneto-optic systems

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: July 9, 2012

Revised Manuscript: August 19, 2012

Manuscript Accepted: August 19, 2012

Published: August 31, 2012

**Citation**

Bin Hu, Qi Jie Wang, and Ying Zhang, "Voigt Airy surface magneto plasmons," Opt. Express **20**, 21187-21195 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-19-21187

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### References

- M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979). [CrossRef]
- G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007). [CrossRef] [PubMed]
- G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32(8), 979–981 (2007). [CrossRef] [PubMed]
- T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3(7), 395–398 (2009). [CrossRef]
- A. Rudnick and D. M. Marom, “Airy-soliton interactions in Kerr media,” Opt. Express19(25), 25570–25582 (2011). [CrossRef] [PubMed]
- G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express20(3), 2196–2205 (2012). [CrossRef] [PubMed]
- J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008). [CrossRef]
- D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010). [CrossRef] [PubMed]
- C. J. Zapata-Rodríguez, S. Vuković, M. R. Belić, D. Pastor, and J. J. Miret, “Nondiffracting Bessel plasmons,” Opt. Express19(20), 19572–19581 (2011). [CrossRef] [PubMed]
- J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett.25(20), 1493–1495 (2000). [CrossRef] [PubMed]
- A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett.35(12), 2082–2084 (2010). [CrossRef] [PubMed]
- W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett.36(7), 1164–1166 (2011). [CrossRef] [PubMed]
- A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011). [CrossRef] [PubMed]
- L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011). [CrossRef] [PubMed]
- J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett.28(22), 1455–1458 (1972). [CrossRef]
- M. S. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep.41(1-8), 1–416 (2001). [CrossRef]
- Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100(2), 023902 (2008). [CrossRef] [PubMed]
- B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett.37(11), 1895–1897 (2012). [CrossRef] [PubMed]
- E. D. Palik and J. K. Furdyna, “Infrared and microwave magnetoplasma effects in semiconductors,” Rep. Prog. Phys.33(3), 1193–1322 (1970). [CrossRef]
- G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett.33(3), 207–209 (2008). [CrossRef] [PubMed]
- I. L. Tyler, B. Fischer, and R. J. Bell, “On the observation of surface magnetoplasmons,” Opt. Commun.8(2), 145–146 (1973). [CrossRef]
- L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B30(6), 3277–3282 (1984). [CrossRef]
- J. Gómez Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express13(3), 847–859 (2005). [CrossRef] [PubMed]
- M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B Condens. Matter36(11), 5960–5967 (1987). [CrossRef] [PubMed]

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