## Plasmonic beam deflector

Optics Express, Vol. 16, Issue 7, pp. 4753-4759 (2008)

http://dx.doi.org/10.1364/OE.16.004753

Acrobat PDF (376 KB)

### Abstract

The authors theoretically demonstrate a plamonic beam deflector based on the particular properties of surface plasmon polaritons in metallic nanoslits. Beam deflection ranging from 0° to 90° can be achieved by designing the deflector with appropriate structural parameters. Numerical illustrations of deflectors for variant deflection angles are presented through finite-difference time-domain simulation, showing good agreement with theoretical analysis. The efficiency and some factors influencing the deflection behavior are also discussed.

© 2008 Optical Society of America

## 1. Introduction

2. Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. **85**, 642 (2004). [CrossRef]

4. T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by the metallic slab lens with nanoslits,” Appl. Phys. Lett. **91**, 201501 (2007). [CrossRef]

6. C. J. Min, P. Wang, X. J. Jiao, Y. Deng, and H. Ming, “Beam manipulating by metallic nano-optic lens containing nonlinear media,” Opt. Express **15**, 9541 (2007). [CrossRef] [PubMed]

## 2. Principle and design for the plasmonic beam deflector

*y*-direction impinges on the metal surface, SPPs can be excited at the slit entrance. Each nanoslit can be treated as a waveguide constructed by two closely placed parallel metallic plates (inset of Fig. 1). The SPPs propagate inside the slit in the specific waveguide modes, until reaching the slit exit where they are scattered into free space. Since the slit width is assumed to be far less than the wavelength, only the fundamental mode dominates the propagation behavior. The complex propagation constant

*k*for SPPs inside the slit region can be calculated by

_{spp}*k*is the wave vector of light in free space,

_{0}*ε*and

_{m}*ε*are the permittivities for the metal and dielectric medium filled in the slit, and w is the slit width. The real and imaginary parts of

_{d}*k*determine the phase velocity and the propagation loss of SPPs inside the slit, respectively.

_{spp}*d*, we can express the phase retardation of the SPPs transmitted through the slit as the following form [8],

*Δϕ*and

_{1}*Δϕ*are the accompanied phase shift occurring at the slit entrance and exit, respectively. When the medium on the illuminated and unilluminated side of metal film are the same, such as in our design (where the material is air), the two factors have the equal value but opposite sign, and thus can be cancelled together. The last term

_{2}*Φ*originates from the multiple reflections between the entrance and exit interfaces. Further calculation indicates that when the silt width is larger than 10nm, the retardation contribution from

*Φ*is less than 1 percentage in proportion with the factor (

*k*) in Eq. (2). That is to say, the phase retardation is mainly dominated by the real part of propagation constant, which is approximated as

_{spp}d*Δϕ*=Re(

*k*). Therefore, the phase retardation

_{spp}d*Δϕ*can be tuned by varying the slit width

*w*if the other parameters (including

*k*,

_{0}*d*,

*ε*and

_{m}*ε*) are fixed.

_{d}*θ*, as shown in Fig. 1, the phase retardation of light transmitted through the slits along the

*x*direction should take the form:

*n*is an integer number. Therefore, the key point of designing a plasmonic beam deflector is to determine the width and position of each nanoslit for the desirable phase retardation calculated from Eq. (3).

*ε*=-17.36+i0.715 [9]. The medium surrounding the deflector and inside silts are assumed to be air. On the basis of Eqs. (1)–(3), slits with variant widths are designed for different deflections, as plotted in Fig. 2. The designed slits’ width ranges from 10nm to about 50nm, corresponding to phase retardation modulation range of 2π. The metal space between any two adjacent slits is larger than the skin depth, about 24nm for silver at wavelength 650nm [1], to eliminate the plasmonic interaction between neighboring slits which would deteriorate the desired phase retardation.

_{m}## 3. Simulation and discussion

*θ*=arcsin(

*Nλ/D*), where

*N*is the number of phase fringes which are close to the deflector’s exit side and confined in the simulation region, and

*D*is aperture size of the deflector. With

*N*for four deflectors approximately equal to 4.5, 6.5, 8 and 9 from Fig. 3, the calculated values show good agreement with design result.

*θ*=45°, with the deflector’s aperture ranging from 0.35µm (5 slits) to 6µm (60 slits). It is clearly shown that the better deflection behavior occurs with the wider aperture and more slits employed in the deflector. However, even when the aperture size of the deflector is close to half of incident wavelength (cyan line), there still exists obvious deflection phenomenon and the deflection angle agrees with the designed one, except for the broadened angular spectra width due to the diffraction effect.

10. S. J. Walker, J. Jahns, L. Li, W. M. Mansfiekd, P. Mulgrew, D. M. Tennant, C. W. Roberts, L. C. West, and N. K. Ailawadi, “Design and fabrication of high-efficiency beam splitters and beam deflectors for integrated planar micro-optic systems,” Appl. Opt. **28**, 2494 (1993). [CrossRef]

*θ*of 30°, 45°, 60° and 80°. The efficiencies are not too high, but still acceptable for practical applications (like optical interconnects and switching etc). The energy loss mainly arises from the great reflection at the illuminating side. The propagation loss in the nano slits, however, can be omitted due to the short propagation distance (i.e. slit depth of 0.5µm) and small imaginary part of effective index in slit region determined by Eq. (1). One interesting point is that the plasmonic interaction effect occurred at the entrance and exit of slits [11

11. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature **391**, 667 (1998). [CrossRef]

*N*to the fabrication error. In Fig. 7,

_{eff}*N*and phase retardation inside the slit are calculated as a function of slit width. It is shown that only slight variance of

_{eff}*N*and phase retardation (less than 10%) can be observed with the slit width error of +/-3nm. Moreover, the variance even becomes much smaller with widening the slit. This indicates the deflector possesses acceptable tolerance for fabrication error.

_{eff}## 4. Conclusion

## Acknowledgments

## References and links

1. | H. Raether, |

2. | Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. |

3. | Z. J. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phy. Lett. |

4. | T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by the metallic slab lens with nanoslits,” Appl. Phys. Lett. |

5. | H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, “Beam manipulating by metallic nanoslits with variant widths,” Opt. Express |

6. | C. J. Min, P. Wang, X. J. Jiao, Y. Deng, and H. Ming, “Beam manipulating by metallic nano-optic lens containing nonlinear media,” Opt. Express |

7. | H. F. Shi, C. L. Du, and X. G. Luo, “Focal length modulation by based on a metallic slit surrounded with grooves in curved depths,” Appl. Phy. Lett. |

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

9. | M. J. Weber, |

10. | S. J. Walker, J. Jahns, L. Li, W. M. Mansfiekd, P. Mulgrew, D. M. Tennant, C. W. Roberts, L. C. West, and N. K. Ailawadi, “Design and fabrication of high-efficiency beam splitters and beam deflectors for integrated planar micro-optic systems,” Appl. Opt. |

11. | T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole array,” Nature |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(240.6680) Optics at surfaces : Surface plasmons

(310.0310) Thin films : Thin films

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: February 25, 2008

Revised Manuscript: March 18, 2008

Manuscript Accepted: March 18, 2008

Published: March 24, 2008

**Citation**

Ting Xu, Changtao Wang, Chunlei Du, and Xiangang Luo, "Plasmonic beam deflector," Opt. Express **16**, 4753-4759 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-7-4753

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### References

- H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer, Berlin, 1988), Chap. 2, pp. 4-7.
- Z. J. Sun and H. K. Kim, "Refractive transmission of light and beam shaping with metallic nano-optic lenses," Appl. Phys. Lett. 85, 642 (2004). [CrossRef]
- Z. J. Sun, "Beam splitting with a modified metallic nano-optic lens," Appl. Phys. Lett. 89, 26119 (2006). [CrossRef]
- T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, "Subwavelength imaging by the metallic slab lens with nanoslits," Appl. Phys. Lett. 91, 201501 (2007). [CrossRef]
- H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, H. T. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815 (2005). [CrossRef] [PubMed]
- C. J. Min, P. Wang, X. J. Jiao, Y. Deng, and H. Ming, "Beam manipulating by metallic nano-optic lens containing nonlinear media," Opt. Express 15, 9541 (2007). [CrossRef] [PubMed]
- H. F. Shi, C. L. Du, and X. G. Luo, "Focal length modulation by based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007). [CrossRef]
- M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1999), Chap.1, pp. 16-17.
- M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, pp. 352-353.
- S. J. Walker, J. Jahns, L. Li, W. M. Mansfiekd, P. Mulgrew, D. M. Tennant, C. W. Roberts, L. C. West, and N. K. Ailawadi, "Design and fabrication of high-efficiency beam splitters and beam deflectors for integrated planar micro-optic systems," Appl. Opt. 28, 2494 (1993). [CrossRef]
- T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole array," Nature 391, 667 (1998). [CrossRef]

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