## Large positive and negative lateral shifts near pseudo-Brewster dip on reflection from a chiral metamaterial slab |

Optics Express, Vol. 19, Issue 2, pp. 1310-1323 (2011)

http://dx.doi.org/10.1364/OE.19.001310

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### Abstract

The lateral shifts from a slab of lossy chiral metamaterial are predicted for both perpendicular and parallel components of the reflected field, when the transverse electric (TE)-polarized incident wave is applied. By introducing different chirality parameter, the lateral shifts can be large positive or negative near the pseudo-Brewster angle. It is found that the lateral shifts from the negative chiral slab are affected by the angle of incidence and the chirality parameter. In the presence of inevitable loss of the chiral slab, the enhanced lateral shifts will be decreased, and the pseudo-Brewster angle will disappear correspondingly. For the negative chiral slab with loss which is invisible for the right circularly polarized (RCP) wave, we find that the loss of the chiral slab will lead to the fluctuation of the lateral shift with respect to the thickness of the chiral slab. The validity of the stationary-phase analysis is demonstrated by numerical simulations of a Gaussian-shaped beam.

© 2011 Optical Society of America

## 1. Introduction

1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. **1**, 333–346 (1947). [CrossRef]

2. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. **2**, 87–102 (1948). [CrossRef]

4. B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. **61**, 586–594 (1971). [CrossRef]

5. F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. **68**, 931–933 (1992). [CrossRef] [PubMed]

7. B. M. Jost, A. A. R. Al-Rashed, and B. E. A. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. **81**, 2233–2235 (1998). [CrossRef]

8. A. Madrazo and M. Nieto-Veperinas, “Detection of subwavelength Goos-Hänchen shifts from near-field intensities: a numerical simulation,” Opt. Lett. **20**, 2445–2447 (1995). [CrossRef] [PubMed]

9. L. G. Wang, H. Chen, N. H. Liu, and S. Y. Zhu, “Negative and positive lateral shift of a light beam reflected from a grounded slab,” Opt. Lett. **31**, 1124–1126 (2006). [CrossRef] [PubMed]

10. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. **91**, 133903–133906 (2003). [CrossRef] [PubMed]

11. M. Merano, A. Aiello, C. W. Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express **15**, 15928–15934 (2007). [CrossRef] [PubMed]

15. W. T. Dong, L. Gao, and C. W. Qiu, “Goos-Hänchen shift at the surface of chiral negative refractive media,” Prog. Electromagn. Res., PIER **104**, 255–263 (2009). [CrossRef]

16. W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A **25**, 2099–2101 (1982). [CrossRef]

18. B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express **17**, 21433–21441 (2009). [CrossRef] [PubMed]

*et al*reported that a normally incident beam reflected from an antiferromagnet can result in a lateral shift too [19

19. F. Lima, T. Dumelow, J. A. P. Costa, and E. L. Albuquerque, “Lateral shift of far infrared radiation on normal incidence reflection off an antiferromagnet,” Europhys. Lett. **83**, 17003 (2008). [CrossRef]

20. P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E **66**, 067603 (2002). [CrossRef]

22. A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability”, Electromagnetics **23**, 71–75 (2003). [CrossRef]

23. D. R. Pendry, “A chiral route to negative refraction,” Science **306**, 1353–1355 (2004). [CrossRef] [PubMed]

24. C. W. Qiu, N. Burokur, S. Zouhdi, and L. W. Li, “Chiral nihility effects on energy flow in chiral materials,” J. Opt. Soc. Am. A **25**, 53–63 (2008). [CrossRef]

25. C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and S. T. Yeo, “Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction,” Phys. Rev. B **75**, 155120 (2007). [CrossRef]

26. S. Zhang, Y. S. Park, J. S. Li, X. C. Lu, W. L. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. **102**, 023901 (2009). [CrossRef] [PubMed]

27. J. F. Zhou, J. F. Dong, N. B. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B **79**, 121104 (2009). [CrossRef]

## 2. Formulation

### 2.1. Reflection and transmission amplitudes

*θ*upon the surface of a chiral slab with the thickness

_{i}*d*. For simplicity, time dependence exp(−

*iωt*) is applied and suppressed. The constitutive relations of the chiral slab are defined as [28] where

*κ*is the chirality parameter,

*ε*and

*μ*are the relative permittivity and permeability of the chiral medium, respectively (

*ε*

_{0}and

*μ*

_{0}are the permittivity and permeability in vacuum). The electric and magnetic fields of an incident TE wave can be written as with the wave number

*k*=

_{i}*k*

_{0}≡

*ω*/

*c*. It is known that, an electric or magnetic excitation will produce both the electric and magnetic polarizations in a chiral material simultaneously. As a consequence, the reflected wave must be a combination of both perpendicular and parallel components in order to satisfy the boundary conditions. In our paper, the linearly polarized incident wave is considered, and then we express the reflected wave in terms of the combination of the perpendicular and parallel polarized waves [12, 13, 29]. Then, the electric and magnetic fields of the reflected wave are expressed as, where

*R*

_{⊥}and

*R*

_{||}are, respectively, the reflected coefficients associated with perpendicular and parallel components. Here we note that for linearly polarized incident wave, when the angle of incidence is the Brewster angle, the reflected wave is still linearly polarized but its plane of polarization is rotated with respect to the plane of polarization of the incident wave [28,30

30. S. Bassiri, C. H. Papas, and N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab,” J. Opt. Soc. Am. A **5**, 1450–1459 (1988). [CrossRef]

31. S. Bassiri, C. H. Papas, and N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab: errata,” J. Opt. Soc. Am. A **7**, 2154–2155 (1990). [CrossRef]

*ω*/

*k*

_{1}and a left circularly polarized (LCP) wave with the phase velocity

*ω*/

*k*

_{2}. The wave numbers

*k*

_{1}and

*k*

_{2}have the form

24. C. W. Qiu, N. Burokur, S. Zouhdi, and L. W. Li, “Chiral nihility effects on energy flow in chiral materials,” J. Opt. Soc. Am. A **25**, 53–63 (2008). [CrossRef]

*z*=

*d*and the other two propagating toward the interface

*z*= 0 (see Fig. 1). The electric and magnetic fields of these waves propagating inside the chiral medium toward the interface

*z*=

*d*are written as, with

*z*= 0 are with

*A*

_{1(2)}and

*B*

_{1(2)}are the transmitted coefficients, and

*θ*

_{1(2)}denote the refracted angles of the two eigen-waves in the chiral slab, respectively.

*z*>

*d*), the total transmitted wave can be expressed as where

*θ*is the transmitted angle,

_{t}*T*

_{⊥}and

*T*

_{||}are coefficients associated with perpendicular and parallel components of the transmitted wave.

*R*

_{⊥},

*R*

_{||},

*T*

_{⊥}, and

*T*

_{||}are determined by matching the boundary conditions at two interfaces

*z*= 0 and

*z*=

*d*, and the following matrix can be obtained,

### 2.2. Stationary phase method for chiral slab

32. M. McGuirk and C. K. Carniglia, “An angular spectrum representation approach to the Goos-Hänchen shift,” J. Opt. Soc. Am **67**, 103–107 (1977). [CrossRef]

*A*(

*k*) is the amplitude angular-spectrum distribution. Then, the reflected field admits the form, For simplicity, let

_{x}*R*(

_{j}*k*) =

_{x}*ρ*(

_{j}*k*)exp[

_{x}*i*Φ

*(*

_{j}*k*)] (

_{x}*j*= ⊥, ||), where

*ρ*(

_{j}*k*) is the reflection amplitude and Φ

_{x}*(*

_{j}*k*) is the phase of the reflectance.

_{x}*A*(

*k*) should be sharply peaked around

_{x}*k*

_{x}_{0}. In the case of a wide enough beam, there will only be significant contributions to the integrals of Eq. (15) within a narrow distribution of

*k*values around

_{x}*k*

_{x}_{0}. As a consequence, we can expand

*ρ*(

_{j}*k*), Φ

_{x}*(*

_{j}*k*), and the quantity for the polarization direction

_{x}19. F. Lima, T. Dumelow, J. A. P. Costa, and E. L. Albuquerque, “Lateral shift of far infrared radiation on normal incidence reflection off an antiferromagnet,” Europhys. Lett. **83**, 17003 (2008). [CrossRef]

*k*=

_{x}*k*−

_{x}*k*

_{x}_{0}, we have and,

*y*−axis) and parallel component (in

*x*−

*z*plane) for the electric field of the reflected beam, which can be rewritten as with

*w*=

_{x}*w*

_{0}sec

*θ*,

_{i}*w*

_{0}is the beam width at the waist. As a consequence, from Eq. (14), the amplitude angular-spectrum distribution is derived to be

10. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. **91**, 133903–133906 (2003). [CrossRef] [PubMed]

*A*(

*k*) should be a sharply distributed Gaussian function around

_{x}*k*

_{x}_{0}. By comparing these two terms on the right hand of Eq. (21), it is expected that the first term dominates for a narrow distribution of

*k*values, and we can ignore the second term as a first approximation. In Fig. 2(a), it is numerically demonstrated that the second term can be regarded as a perturbation to the first term. Similarly, comparing the magnitude of

_{x}*x*is replaced by

_{⊥(||)},

2. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. **2**, 87–102 (1948). [CrossRef]

19. F. Lima, T. Dumelow, J. A. P. Costa, and E. L. Albuquerque, “Lateral shift of far infrared radiation on normal incidence reflection off an antiferromagnet,” Europhys. Lett. **83**, 17003 (2008). [CrossRef]

33. M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D **50**, 81–85 (2008). [CrossRef]

34. H. Huang, Y. Fan, B. I. Wu, and J. A. Kong, “Positively and negatively large Goos-Hänchen lateral displacement from a symmetric gyrotropic slab,” Appl. Phys. A **94**, 917–922 (2009). [CrossRef]

## 3. Results and discussion

*ε*= 0.64 + 0.01

*i*,

*μ*= 1 + 0.02

*i*,

*ω*= 2

*π*× 10 GHz, and

*d*= 1.5

*λ*[12]. Without loss of generality, we consider two types of chiral slabs: (1) a positive (conventional) chiral slab with

*κ*= 0.4, whose refraction indices of RCP and LCP waves are both positive (Re(

*n*

_{1}) = 1.2 and Re(

*n*

_{2}) = 0.4); (2) a negative chiral slab with

*κ*= 1.4 whose refraction indices of RCP wave and LCP wave are Re(

*n*

_{1}) = 2.2 and Re(

*n*

_{2}) = −0.6, respectively. For the two cases above, there are no critical angles for RCP waves, but for LCP waves, there exists the critical angle at

*θ*≃ 23.6° for a positive chiral slab and

_{c}*θ*≃ 37° for a negative chiral slab. Under such critical situations, only LCP waves in the chiral slab become evanescent waves when the angle of incidence exceeds the critical angle, while the RCP waves will still propagate through the chiral slab. Correspondingly, the angle of incidence is defined as pseudo-critical angle. However, the true total internal reflection will never arise under these parameters.

_{c}*R*| reaches the minimum. The corresponding angle of incidence is defined as the pseudo-Brewster angle. Note that the pseudo-Brewster angles for both perpendicular and parallel components are always smaller than the pseudo-critical angles. From Fig. 3(a) and 3(c), we clearly see that the behavior of the lateral shifts for perpendicular and parallel components are similar, and the shifts will be greatly enhanced near the angle of pseudo-Brewster dip. To one’s interest, there exist large negative (positive) lateral shifts near the angle of pseudo-Brewster dip for the positive (negative) chiral slab. The phenomenon can be easily explained in terms of the change of phases, as shown in Fig. 3(b) and 3(d). Near the angle of pseudo-Brewster dip, the phase of reflection experiences a distinct sharp variation, which decreases quickly for the negative chiral slab. As a result, one predicts a large positive lateral shift for a negative chiral slab. On the other hand, for the positive chiral slab, both components have negative lateral shifts near the angle of pseudo-Brewster dip, and then experience small positive shifts over other angles of incidence. We conclude that the lateral shifts of both perpendicular and parallel components can be greatly enhanced near the pseudo-Brewster angle for both the positive and negative chiral slabs, and the dependence of lateral shifts on the angle of incidence

*θ*for a negative chiral slab is opposite to that for a positive chiral slab.

_{i}*κ*= 2.0 are shown in Fig. 4. In this situation, there are no critical angles for both the RCP and LCP waves. It can be seen that there is only one dip in the perpendicular reflection curve, at which the reflection coefficient reaches a minimal magnitude and the corresponding phase is monotonically increasing as a function of the angle of incidence [see Fig. 4(b)]. As a consequence, one expects that the lateral shift of the reflected perpendicular component has a negative peak near the angle of the dip [see Fig. 4(a)]. In contrast, there are two dips for the parallel component, where the absolute values of the reflection coefficient are very close to zero, and the corresponding phase in the vicinity of these two dips monotonically decreases quickly [see the inset in Fig. 4(b)]. Thus the shifts of the parallel component can be greatly enhanced to be large positive near the pseudo-Brewster angles where the phase decreases. Note that the lateral shift can be one order in magnitude greater than the wavelength. By comparing Fig. 3 to Fig. 4, we find that for the negative chiral slab, as the chirality parameter becomes large, the lateral shifts for the perpendicular component can change from positive to negative, while they are always positive for the parallel component. But the number of the peaks of the enhanced lateral shifts may increase at the angles of the dips, due to the resonant conditions.

*θ*is smaller than the pseudo-critical angle (

_{i}*θ*≃ 37°), the lateral shifts of the reflected perpendicular component could reach large positive or relatively small negative values, but there exists no periodic fluctuation of the lateral shifts with respect to the thickness as shown in Fig. 5(a). Similar phenomenon can be found from the shifts of the parallel component [see Fig. 5(c)]. The large positive enhancement corresponds to the dip of the reflection coefficients, which follows previous discussions. However, when

_{c}*θ*is at the critical angle of the LCP wave, as shown in Figs. 5(b) and 5(d), the lateral shifts of both reflected components are always negative and the periodic fluctuation of the lateral shifts arises especially for the parallel component. Moreover, the fluctuations of the lateral shifts of both components first reach a maximally shifted distance, and then become saturated, keeping periodically fluctuating with respect to the thickness of the slab. In addition, if the angle of incidence

_{i}*θ*is larger than the pseudo-critical angle and keeps increasing, the lateral shifts with periodic fluctuation under the same thickness of the slab will decrease, as shown in Figs. 5(b) and 5(d).

_{i}*μ*= 1 + 0.02

*i*, Re(

*ε*) = 0.64, (b)

*ε*= 0.64 + 0.02

*i*, Re(

*μ*) = 1. The other parameters are the same:

*κ*= 1.4,

*d*= 1.5

*λ*. The dependence of the lateral shifts on the angle of incidence is shown in Fig. 6. It can be seen that when the absorption of the chiral slab is weak, for the reflected perpendicular component, the behaviors of its lateral shift with respect to the angle of incidence for different dielectric loss or hysteresis loss are similar. However, the enhanced lateral shifts at the dip of the pseudo-Brewster angle will be always damped when the dielectric loss (see Fig.6(a)) or hysteresis loss (see Fig.6(b)) increases. On the other hand, when the absorption of the chiral slab becomes strong, the pseudo-Brewster angle disappears and the lateral shift becomes larger at close-to-grazing incidence. The insets of Fig. 6 show the reflected coefficients, from which we can also predict that the pseudo-Brewster angle (corresponding to the minimum of reflected coefficients) will disappear with increasing loss of the chiral slab. Here we notice that the high dielectric loss and the high hysteresis loss will lead to the different behaviors of the lateral shifts with respect to the angle of incidence, i.e., the high dielectric loss results in the large positive lateral shift while the high hysteresis loss leads to the large negative lateral shift at close-to-grazing incidence. In addition, for reflected parallel component, the behavior of the lateral shifts in the presence of dielectric loss is analogous to that in the presence of hysteresis loss (not shown here).

*ε*= 0.2,

*μ*= 0.2, and

*κ*= 0.8 in Fig. 7(a) and (b). In this situation, the wave number matching condition

*k*

_{1}=

*k*

_{0}and the wave impedance matching condition

*η*=

*η*

_{0}are satisfied simultaneously. Therefore the RCP wave is transmitted through the chiral medium without either reflection or refraction. Thus, the medium is invisible for RCP wave [35

35. Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “An invisible medium for circularly polarized electromagnetic waves,” Opt. Express **16**, 20869–20875 (2008). [CrossRef] [PubMed]

*k*

_{2}= −0.6

*k*

_{0}, the critical angle for LCP wave is

*θ*= arcsin0.6 ≃ 37°. Therefore, LCP wave is totally reflected with

_{c}*θ*> 37° and it is easy to see that both reflected components have the same negative lateral shift. This is due to the fact that the reflected wave only has LCP wave, and the RCP wave contributes to the transmitted wave. Hence the perpendicular and the parallel reflection coefficients have the same absolute values, while their phases are different. We further find the lateral shifts will fluctuate with respect to the thickness of the slab when the angle of incidence is smaller than the critical angle of the LCP wave (

_{i}*θ*<

_{i}*θ*), while for

_{c}*θ*≥

_{i}*θ*, the lateral shifts will vary with the thickness monotonously. We believe that the difference of the behavior of the lateral shifts is caused by the change of the properties of the LCP wave, i.e, the LCP wave changes from the transmitted wave to an evanescent wave. Meanwhile, when the angle of incidence is close to the critical angle of the LCP wave, the lateral shifts are large and increase as the slab thickness increases. If the angle of incidence is greater than

_{c}*θ*, the lateral shifts will increase quickly and then gradually approach to an asymptotic negative value with increasing the slab thickness(see Fig. 7(b)). In this connection, the phenomenon that the lateral shifts become saturated as the thickness increases is due to the Hartman effect.

_{c}*ε*= 0.2 + 0.01

*i*,

*μ*= 0.2 + 0.02

*i*, and

*κ*= 0.8, as shown in Fig. 7(c) and 7(d). The results show that: (1) both reflected components almost have the same lateral shifts; (2) the lateral shifts of both reflected components will fluctuate strongly with respect to the thickness of the slab for

*θ*<

_{i}*θ*. Moreover, for

_{c}*θ*>

_{i}*θ*, the larger the angle of incidence is, the stronger the periodic fluctuation becomes along the lossy chiral slab.

_{c}10. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. **91**, 133903–133906 (2003). [CrossRef] [PubMed]

*w*

_{0}= 20

*λ*, the peaks of the numerical shifts are: −4.5

*λ*for the perpendicular reflected field; and 16.5

*λ*(dip I), and 18

*λ*(dip II) for the parallel reflected field. The peaks of the theoretical shifts are about −4.54

*λ*for the perpendicular field and 24.25

*λ*(19.66

*λ*) for dip I (dip II) of the parallel field. It is noted that the discrepancy between theoretical and numerical results is due to the distortion of the reflected beam, especially when the waist of the incident beam is narrow [36

36. C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos-Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E **69**, 055601 (2004). [CrossRef]

## 4. Conclusion

*R*| reaches a minimum. In addition, at a given incident angle, the dependence of the lateral shifts on the slab thickness for a negative chiral slab has also been studied. It is shown that, when the angle of incidence is at the critical angle of the LCP wave, the lateral shifts of both reflected components oscillate. Along with the increasing thickness of the slab, the shifted distance is increasing first, experiences a maximum value, and then arrive at the saturation (i.e., the periodic fluctuation of the lateral shifts when the slab’s thickness is sufficiently big). Moreover, when the angle of incidence is larger than the critical angle and keeps increasing, the lateral shifts of both reflected components will decrease along with slab’s thickness. In addition, we calculate the lateral shifts of an invisible chiral medium with and without loss. In order to demonstrate the validity of the stationary-phase approach, numerical simulations are made for a Gaussian-shaped beam.

37. Y. Jin and S. L. He, “Focusing by a slab of chiral medium,” Opt. Express **13**, 4974–4979 (2005). [CrossRef] [PubMed]

39. T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic meterials and metamaterials,” Phys. Rev. B **79**, 235121 (2009). [CrossRef]

*ε*and

*μ*). Alternatively, one can also adopt the Drude model for

*ε*and

*μ*, and the Condon model for the chirality

*κ*[40

40. C. W. Qiu, H. Y. Yao, L. W. Li, T. S. Yeo, and S. Zouhdi, “Routes to left-handed media by magnetoelectric couplings,” Phys. Rev. B **75**, 245214 (2007). [CrossRef]

^{−3}) of the semiconductor [41

41. H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. **27**, 680–682 (2002). [CrossRef]

41. H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. **27**, 680–682 (2002). [CrossRef]

42. K. Yu. Bliokh and Yu. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partical reflection and refraction of an electromagnetic wave packet, ” Phys. Rev. E **75**, 066609 (2007). [CrossRef]

44. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. **33**, 1437–1439 (2008), [CrossRef] [PubMed]

## Acknowledgments

## References and links

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2. | K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. |

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30. | S. Bassiri, C. H. Papas, and N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab,” J. Opt. Soc. Am. A |

31. | S. Bassiri, C. H. Papas, and N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab: errata,” J. Opt. Soc. Am. A |

32. | M. McGuirk and C. K. Carniglia, “An angular spectrum representation approach to the Goos-Hänchen shift,” J. Opt. Soc. Am |

33. | M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D |

34. | H. Huang, Y. Fan, B. I. Wu, and J. A. Kong, “Positively and negatively large Goos-Hänchen lateral displacement from a symmetric gyrotropic slab,” Appl. Phys. A |

35. | Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “An invisible medium for circularly polarized electromagnetic waves,” Opt. Express |

36. | C. F. Li and Q. Wang, “Prediction of simultaneously large and opposite generalized Goos-Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E |

37. | Y. Jin and S. L. He, “Focusing by a slab of chiral medium,” Opt. Express |

38. | Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B |

39. | T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic meterials and metamaterials,” Phys. Rev. B |

40. | C. W. Qiu, H. Y. Yao, L. W. Li, T. S. Yeo, and S. Zouhdi, “Routes to left-handed media by magnetoelectric couplings,” Phys. Rev. B |

41. | H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. |

42. | K. Yu. Bliokh and Yu. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partical reflection and refraction of an electromagnetic wave packet, ” Phys. Rev. E |

43. | C. F. Li, “Unified theory for Goos-Hänchen and Imbert-Fedorov effects,” Phys. Rev. A |

44. | A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. |

**OCIS Codes**

(120.5700) Instrumentation, measurement, and metrology : Reflection

(260.0260) Physical optics : Physical optics

(260.2110) Physical optics : Electromagnetic optics

(350.5500) Other areas of optics : Propagation

(160.1585) Materials : Chiral media

(160.3918) Materials : Metamaterials

**ToC Category:**

Physical Optics

**History**

Original Manuscript: December 2, 2010

Revised Manuscript: January 7, 2011

Manuscript Accepted: January 10, 2011

Published: January 11, 2011

**Citation**

Y. Y. Huang, W. T. Dong, L. Gao, and D. W. Qiu, "Large positive and negative lateral shifts near pseudo-Brewster dip on reflection from a chiral metamaterial slab," Opt. Express **19**, 1310-1323 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1310

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### References

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