## Electrically controlled Goos-Hänchen shift of a light beam reflected from the metal-insulator-semiconductor structure |

Optics Express, Vol. 21, Issue 9, pp. 10430-10439 (2013)

http://dx.doi.org/10.1364/OE.21.010430

Acrobat PDF (2786 KB)

### Abstract

We proposed a scheme to manipulate the Goos-Hänchen shift of a light beam reflected from the depletion-type device via external voltage bias. It is shown that the lateral shift of the reflected probe beam can be easily controlled by adjusting the reverse voltage bias and the incidence angle. Using this scheme, the lateral shift can be tuned from negative to positive, without changing the original structure of the depletion-type device. Numerical calculations further indicate that the influence of structure parameters and light wavelength can be reduced via readjustment of the reverse bias. The proposed structure has the potential application for the integrated electronic devices.

© 2013 OSA

## 1. Introduction

1. B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. **61**(5), 586 (1971). [CrossRef]

4. H. M. Lai, F. C. Cheng, and W. K. Tang, “Goos-Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A **3**(4), 550–557 (1986). [CrossRef]

5. F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. **68**(7), 931–933 (1992). [CrossRef] [PubMed]

7. O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for gaussian optical beams,” Phys. Rev. Lett. **75**(8), 1511–1513 (1995). [CrossRef] [PubMed]

8. W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A **25**(4), 2099–2101 (1982). [CrossRef]

9. 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**(9), 680–682 (2002). [CrossRef] [PubMed]

10. D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. **28**(18), 1633–1635 (2003). [CrossRef] [PubMed]

11. P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **66**(6), 067603 (2002). [CrossRef] [PubMed]

12. X. Chen, R. R. Wei, M. Shen, Z. F. Zhang, and C. F. Li, “Bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration with nonlinear left-handed metamaterials,” Appl. Phys. B **101**(1-2), 283–289 (2010). [CrossRef]

13. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. **91**(13), 133903 (2003). [CrossRef] [PubMed]

14. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. **77**(2), 633–673 (2005). [CrossRef]

17. Y. Chen, X. G. Wei, and B. S. Ham, “Optical properties of an N-type system in Doppler- broadened multilevel atomic media of the rubidium D2 line,” J. Phys. B **42**(6), 065506 (2009). [CrossRef]

18. X. Chen, Y. Ban, and C.-F. Li, “Voltage-tunable lateral shifts of ballistic electrons in semiconductor quantum slabs,” J. Appl. Phys. **105**(9), 093710 (2009). [CrossRef]

19. X. Chen, X. J. Lu, Y. Wang, and C. F. Li, “Controllable Goos-Hänchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field,” Phys. Rev. B **83**(19), 195409 (2011). [CrossRef]

20. T. Hashimoto and T. Yoshino, “Optical heterodyne sensor using the Goos-Hänchen shift,” Opt. Lett. **14**(17), 913–915 (1989). [CrossRef] [PubMed]

21. X. Hu, Y. Huang, W. Zhang, D. K. Qing, and J. Peng, “Opposite Goos-Hänchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials,” Opt. Lett. **30**(8), 899–901 (2005). [CrossRef] [PubMed]

22. L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A **77**(2), 023811 (2008). [CrossRef]

25. Y. Wang, Z. Q. Cao, H. G. Li, J. Hao, T. Y. Yu, and Q. S. Shen, “Electric control of spatial beam position based on the Goos-Hanchen effect,” Appl. Phys. Lett. **93**(9), 091103 (2008). [CrossRef]

22. L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A **77**(2), 023811 (2008). [CrossRef]

24. S. Ziauddin and Qamar, “Control of the Goos-Hänchen shift using a duplicated two-level atomic medium,” Phys. Rev. A **85**(5), 055804 (2012). [CrossRef]

_{3}) into the guiding layer of the symmetrical metal cladding waveguide to control the lateral shift of the reflected beam by applying an external electric field [25

25. Y. Wang, Z. Q. Cao, H. G. Li, J. Hao, T. Y. Yu, and Q. S. Shen, “Electric control of spatial beam position based on the Goos-Hanchen effect,” Appl. Phys. Lett. **93**(9), 091103 (2008). [CrossRef]

26. X. Chen, M. Shen, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” J. Appl. Phys. **104**(12), 123101 (2008). [CrossRef]

25. Y. Wang, Z. Q. Cao, H. G. Li, J. Hao, T. Y. Yu, and Q. S. Shen, “Electric control of spatial beam position based on the Goos-Hanchen effect,” Appl. Phys. Lett. **93**(9), 091103 (2008). [CrossRef]

26. X. Chen, M. Shen, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” J. Appl. Phys. **104**(12), 123101 (2008). [CrossRef]

## 2. Model and theory

_{0.3}Ga

_{0.7}As layer,

*d*= 75nm) is included to reduce leakage current and control the depletion depth (see Fig. 1(a)). We consider a TE-polarized probe light beam (

_{2}*λ*= 10µm), which is incident on the metal control electrode of the MIS structure from vacuum with an angle

*θ*. As shown in Fig. 1(b), the MIS structure consists of four layers of materials: metal control electrode, insulating barrier, depletion region, and n + doped GaAs substrate. By applying a voltage bias to change the depletion depth

*d*in the substrate (the sum of the depletion width and n-doped substrate width is a fixed constant), we can tune the phase of the reflected light, and thus can obtain the dynamic adjustable GH shift.

_{3}28. Y. C. Jun, E. Gonzales, J. L. Reno, E. A. Shaner, A. Gabbay, and I. Brener, “Active tuning of mid-infrared metamaterials by electrical control of carrier densities,” Opt. Express **20**(2), 1903–1911 (2012). [CrossRef] [PubMed]

*ε*is the high frequency dielectric constant (

_{∞}*ε*= 10.86 for GaAs),

_{∞}*ω*is the angular frequency. Here, the relaxation frequency

*Γ*(i.e. damping term) and the plasma frequency

*ω*are given byandrespectively, where

_{p}*τ*is the scattering time,

*μ*is the electron mobility,

*m**is the electron effective mass,

*q*is the electron charge, and

*n*is the electron density.

*μ*and the electron effective mass

*m**also vary with the carrier density

*n*. We can obtain the theoretical values of the carrier concentration dependent effective mass and mobility of GaAs at

*T =*300

*K*[29]:andIn Eqs. (4) and (5),

*n*is the carrier density, here its unit is cm

^{−3},

*n*is the reference electron concentration(When the electron concentration in GaAs is equal to

_{ref}*n*, the electron mobility is half of sum of maximum and minimum of electron mobility),

_{ref}*µ*= 500 cm

_{min}^{2}/vs,

*µ*= 9400 cm

_{max}^{2}/vs,

*n*= 6.0 × 10

_{ref}^{16}cm

^{−3}, and

*n*= 3.9 × 10

^{17}cm

^{−3}and

*T =*300

*K*.

32. N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **65**(44 Pt 2B), 046607 (2002). [CrossRef] [PubMed]

*j*th layer can be expressed as [22

22. L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A **77**(2), 023811 (2008). [CrossRef]

32. N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **65**(44 Pt 2B), 046607 (2002). [CrossRef] [PubMed]

*ω*is angular frequency of the probe beam on incident angles

*θ*,

*y*component of the wave number (

*k*=

*ω/c*) in vacuum, and

*c*is the light speed in vacuum,

*z*component of the wave number in the

*j*th layer,

*j*th layer. The total transfer matrix for the MIS structure is given by

*r*is given by [22

**77**(2), 023811 (2008). [CrossRef]

*z*component of the wave number in vacuum), and

## 3. Numerical results and discussion

### 3.1. The control of the GH shift with an applied voltage

*d2*to be 900nm, and the electron density in n + GaAS

*n*= 3.9 × 10

^{17}cm

^{−3}. From Eqs. (1)-(5), we know that the dielectric constant of the n-doped GaAs is 10.313254 + j0.023701 at

*d*at different reverse bias from Eqs. (6) and (7). Then we calculated the lateral shift of MIS structure in accordance to Eqs. (8)-(11).

_{3}*S*on the incident angle

_{r}*V*but also on the incident angle. The lateral shift has different behaviors at different control voltage bias and incident angle. It is clear that the lateral shifts can be very large (positive or negative) at certain value of

_{g}*V*for the incident angle of the probe beam around 75°, as we predicted in Fig. 2. The largest lateral shift can be thousands of wavelengths. In Figs. 3(a)-3(c), the reflected probe beam suffers the large negative shift near the resonant condition of the MIS structure, while in Figs. 3(e)-3(f) it suffers large positive shift. The dependence of the lateral shift

_{g}*S*on

_{r}*V*is due to the fact that the MIS internal depletion deepness and n-doped substrate width both vary with

_{g}*V*(the sum of the depletion width and n-doped substrate width is a fixed constant). This variation in deepness with

_{g}*V*modifies the resonant condition of the MIS structure and we observe the manipulation effect of the control voltage on the lateral shift. Using this effect, without changing the initial structure of the MIS structure, we can easily manipulate the lateral shift of the reflected probe beam.

_{g}### 3.2. Influence of structure parameters and wavelength

*S*on the wavelength of probe beam under different applied voltage and incident angle in Fig. 4. It is shown that the lateral shift will be greatly reduced if the wavelength slightly increased or decreased when the lateral shift peak. However, it can run up to a new peak at another reverse bias if the variety on wavelength is suffered.

_{r}*d*in accordance with the Eqs. (6) and (7). Third, of course the electron concentration in the n + doped GaAs is the other vital factor, which not only can affect the depletion width, but also affect the permittivity of n + GaAs.

_{3}_{0.3}Ga

_{0.7}As (insulated barrier) layer can be grown by molecular beam epitaxy [28

28. Y. C. Jun, E. Gonzales, J. L. Reno, E. A. Shaner, A. Gabbay, and I. Brener, “Active tuning of mid-infrared metamaterials by electrical control of carrier densities,” Opt. Express **20**(2), 1903–1911 (2012). [CrossRef] [PubMed]

*S*on the insulating barrier width under different reverse bias for the incident angle θ = 75°in Fig. 5(a) and for θ = 75.2°in Fig. 5(b). We can know that the lateral shift also will be greatly reduced if the insulating barrier width slightly varied. However, the lateral shift can run up to a new peak too at another reverse bias. Due to technical reasons or in different light conditions, the electron concentration in n + doped GaAs will change a little. Figure 6 shows that there always exists an appropriate reverse bias at which the lateral shift is very large when the electron density in the n + doped GaAs varied slightly. The above analysis shows that there exists greatly influence of the structure parameters and wavelength on the controlling effect, but the influence can be greatly reduced via adjustment of the reverse bias.

_{r}### 3.3. Numerical simulations of GH shift in real system

13. C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. **91**(13), 133903 (2003). [CrossRef] [PubMed]

33. A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A **49**(5), 3283–3295 (1994). [CrossRef] [PubMed]

**77**(2), 023811 (2008). [CrossRef]

*Z =*0, the electric field of the reflected probe beam can be written as [22

**77**(2), 023811 (2008). [CrossRef]

34. L. G. Wang, H. Chen, and S. Y. Zhu, “Wave propagation inside one-dimensional photonic crystals with single-negative materials,” Phys. Lett. A **350**(5-6), 410–415 (2006). [CrossRef]

*Z =*0.

10. D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. **28**(18), 1633–1635 (2003). [CrossRef] [PubMed]

35. C. F. Li, “Unified theory for Goos-Hänchen and Imbert-Fedorov effects,” Phys. Rev. A **76**(1), 013811 (2007). [CrossRef]

*w*. It is also shown that the lateral shift of the reflected probe beam can be controlled to be positive or negative with the external voltage bias.

36. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. **33**(13), 1437–1439 (2008). [CrossRef] [PubMed]

39. A. Aiello, M. Merano, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A **80**(6), 061801 (2009). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. |

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

3. | R. H. Renard, “Total reflection: a new evaluation of the Goos-Hänchen shift,” J. Opt. Soc. Am. |

4. | H. M. Lai, F. C. Cheng, and W. K. Tang, “Goos-Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A |

5. | F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. |

6. | E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. |

7. | O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for gaussian optical beams,” Phys. Rev. Lett. |

8. | W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A |

9. | 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. |

10. | D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. |

11. | P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

12. | X. Chen, R. R. Wei, M. Shen, Z. F. Zhang, and C. F. Li, “Bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration with nonlinear left-handed metamaterials,” Appl. Phys. B |

13. | C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett. |

14. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. |

15. | S. Li, X. Yang, X. Cao, C. Xie, and H. Wang, “Two electromagnetically induced transparency windows and an enhanced electromagnetically induced transparency signal in a four-level tripod atomic system,” J. Phys. B |

16. | Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. |

17. | Y. Chen, X. G. Wei, and B. S. Ham, “Optical properties of an N-type system in Doppler- broadened multilevel atomic media of the rubidium D2 line,” J. Phys. B |

18. | X. Chen, Y. Ban, and C.-F. Li, “Voltage-tunable lateral shifts of ballistic electrons in semiconductor quantum slabs,” J. Appl. Phys. |

19. | X. Chen, X. J. Lu, Y. Wang, and C. F. Li, “Controllable Goos-Hänchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field,” Phys. Rev. B |

20. | T. Hashimoto and T. Yoshino, “Optical heterodyne sensor using the Goos-Hänchen shift,” Opt. Lett. |

21. | X. Hu, Y. Huang, W. Zhang, D. K. Qing, and J. Peng, “Opposite Goos-Hänchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials,” Opt. Lett. |

22. | L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A |

23. | S. Ziauddin, S. Qamar, and M. S. Zubairy, “Coherent control of the Goos-Hänchen shift,” Phys. Rev. A |

24. | S. Ziauddin and Qamar, “Control of the Goos-Hänchen shift using a duplicated two-level atomic medium,” Phys. Rev. A |

25. | Y. Wang, Z. Q. Cao, H. G. Li, J. Hao, T. Y. Yu, and Q. S. Shen, “Electric control of spatial beam position based on the Goos-Hanchen effect,” Appl. Phys. Lett. |

26. | X. Chen, M. Shen, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” J. Appl. Phys. |

27. | C. Kittel, |

28. | Y. C. Jun, E. Gonzales, J. L. Reno, E. A. Shaner, A. Gabbay, and I. Brener, “Active tuning of mid-infrared metamaterials by electrical control of carrier densities,” Opt. Express |

29. | Sadao Adachi, |

30. | R. F. Pierret, |

31. | M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. |

32. | N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

33. | A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A |

34. | L. G. Wang, H. Chen, and S. Y. Zhu, “Wave propagation inside one-dimensional photonic crystals with single-negative materials,” Phys. Lett. A |

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

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

37. | M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics |

38. | M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, “Demonstration of a quasi-scalar angular Goos-Hänchen effect,” Opt. Lett. |

39. | A. Aiello, M. Merano, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A |

**OCIS Codes**

(120.5700) Instrumentation, measurement, and metrology : Reflection

(130.5990) Integrated optics : Semiconductors

(240.0240) Optics at surfaces : Optics at surfaces

(260.2110) Physical optics : Electromagnetic optics

(260.3060) Physical optics : Infrared

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: January 29, 2013

Revised Manuscript: March 17, 2013

Manuscript Accepted: April 2, 2013

Published: April 22, 2013

**Citation**

Changyou Luo, Jun Guo, Qingkai Wang, Yuanjiang Xiang, and Shuangchun Wen, "Electrically controlled Goos-Hänchen shift of a light beam reflected from the metal-insulator-semiconductor structure," Opt. Express **21**, 10430-10439 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10430

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### References

- B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am.61(5), 586 (1971). [CrossRef]
- M. McGuirk and C. K. Carniglia, “An angular spectrum representation approach to the Goos-Hänchen shift,” J. Opt. Soc. Am.67(1), 103–107 (1977). [CrossRef]
- R. H. Renard, “Total reflection: a new evaluation of the Goos-Hänchen shift,” J. Opt. Soc. Am.54(10), 1190–1196 (1964). [CrossRef]
- H. M. Lai, F. C. Cheng, and W. K. Tang, “Goos-Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A3(4), 550–557 (1986). [CrossRef]
- F. Bretenaker, A. Le Floch, and L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett.68(7), 931–933 (1992). [CrossRef] [PubMed]
- E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett.70(15), 2281–2284 (1993). [CrossRef] [PubMed]
- O. Emile, T. Galstyan, A. Le Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for gaussian optical beams,” Phys. Rev. Lett.75(8), 1511–1513 (1995). [CrossRef] [PubMed]
- W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A25(4), 2099–2101 (1982). [CrossRef]
- 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(9), 680–682 (2002). [CrossRef] [PubMed]
- D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett.28(18), 1633–1635 (2003). [CrossRef] [PubMed]
- P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(6), 067603 (2002). [CrossRef] [PubMed]
- X. Chen, R. R. Wei, M. Shen, Z. F. Zhang, and C. F. Li, “Bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration with nonlinear left-handed metamaterials,” Appl. Phys. B101(1-2), 283–289 (2010). [CrossRef]
- C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91(13), 133903 (2003). [CrossRef] [PubMed]
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77(2), 633–673 (2005). [CrossRef]
- S. Li, X. Yang, X. Cao, C. Xie, and H. Wang, “Two electromagnetically induced transparency windows and an enhanced electromagnetically induced transparency signal in a four-level tripod atomic system,” J. Phys. B40(16), 3211–3219 (2007). [CrossRef]
- Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett.99(12), 123603 (2007). [CrossRef] [PubMed]
- Y. Chen, X. G. Wei, and B. S. Ham, “Optical properties of an N-type system in Doppler- broadened multilevel atomic media of the rubidium D2 line,” J. Phys. B42(6), 065506 (2009). [CrossRef]
- X. Chen, Y. Ban, and C.-F. Li, “Voltage-tunable lateral shifts of ballistic electrons in semiconductor quantum slabs,” J. Appl. Phys.105(9), 093710 (2009). [CrossRef]
- X. Chen, X. J. Lu, Y. Wang, and C. F. Li, “Controllable Goos-Hänchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field,” Phys. Rev. B83(19), 195409 (2011). [CrossRef]
- T. Hashimoto and T. Yoshino, “Optical heterodyne sensor using the Goos-Hänchen shift,” Opt. Lett.14(17), 913–915 (1989). [CrossRef] [PubMed]
- X. Hu, Y. Huang, W. Zhang, D. K. Qing, and J. Peng, “Opposite Goos-Hänchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials,” Opt. Lett.30(8), 899–901 (2005). [CrossRef] [PubMed]
- L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A77(2), 023811 (2008). [CrossRef]
- S. Ziauddin, S. Qamar, and M. S. Zubairy, “Coherent control of the Goos-Hänchen shift,” Phys. Rev. A81(2), 023821 (2010). [CrossRef]
- S. Ziauddin and Qamar, “Control of the Goos-Hänchen shift using a duplicated two-level atomic medium,” Phys. Rev. A85(5), 055804 (2012). [CrossRef]
- Y. Wang, Z. Q. Cao, H. G. Li, J. Hao, T. Y. Yu, and Q. S. Shen, “Electric control of spatial beam position based on the Goos-Hanchen effect,” Appl. Phys. Lett.93(9), 091103 (2008). [CrossRef]
- X. Chen, M. Shen, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” J. Appl. Phys.104(12), 123101 (2008). [CrossRef]
- C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, 1995).
- Y. C. Jun, E. Gonzales, J. L. Reno, E. A. Shaner, A. Gabbay, and I. Brener, “Active tuning of mid-infrared metamaterials by electrical control of carrier densities,” Opt. Express20(2), 1903–1911 (2012). [CrossRef] [PubMed]
- Sadao Adachi, Properties of Group-IV, III–V and II–VI Semiconductors (Wiley, 2005).
- R. F. Pierret, Semiconductor Device Fundamentals (Addison Wesley, 1996).
- M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt.22(7), 1099–20 (1983). [CrossRef] [PubMed]
- N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(44 Pt 2B), 046607 (2002). [CrossRef] [PubMed]
- A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A49(5), 3283–3295 (1994). [CrossRef] [PubMed]
- L. G. Wang, H. Chen, and S. Y. Zhu, “Wave propagation inside one-dimensional photonic crystals with single-negative materials,” Phys. Lett. A350(5-6), 410–415 (2006). [CrossRef]
- C. F. Li, “Unified theory for Goos-Hänchen and Imbert-Fedorov effects,” Phys. Rev. A76(1), 013811 (2007). [CrossRef]
- A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett.33(13), 1437–1439 (2008). [CrossRef] [PubMed]
- M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009). [CrossRef]
- M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, “Demonstration of a quasi-scalar angular Goos-Hänchen effect,” Opt. Lett.35(21), 3562–3564 (2010). [CrossRef] [PubMed]
- A. Aiello, M. Merano, and J. P. Woerdman, “Duality between spatial and angular shift in optical reflection,” Phys. Rev. A80(6), 061801 (2009). [CrossRef]

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