Abstract

The spatial and the angular variants of the Imbert-Federov (IF) beam shifts and the angular Goos-Hänchen (GH) shift contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the two variants of the IF effects can be decoupled and separately observed by weak value amplification and subsequent conversion of spatial ↔angular nature of the beam shifts using appropriate pre and post selection of polarization states. Such optimized weak measurement schemes also enable one to nullify one effect (either the GH or the IF) and exclusively observe the other. We experimentally demonstrate this and illustrate various other intriguing manifestations of optimized weak measurements in elliptical and / or linear polarization basis. We also present a Poincare sphere based analysis on conversion / retention of the angular or spatial nature of the shifts with pre and post selection of states in weak measurement. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their applications in sensing and precision metrology.

© 2016 Optical Society of America

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
    [Crossref]
  2. C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).
    [Crossref]
  3. A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
    [Crossref]
  4. K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
    [Crossref]
  5. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [Crossref] [PubMed]
  6. J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for Giant Transverse Optical Beam Shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
    [Crossref] [PubMed]
  7. 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 3(6), 337–340 (2009).
    [Crossref]
  8. 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]
  9. Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
    [Crossref] [PubMed]
  10. F. Töppel, M. Ornigotti, and A. Aiello, “Goos–Hanchen and Imbert–Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15(11), 113059 (2013).
    [Crossref]
  11. J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
    [Crossref]
  12. M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14(7), 073013 (2012).
    [Crossref]
  13. S. Goswami, M. Pal, A. Nandi, P. K. Panigrahi, and N. Ghosh, “Simultaneous weak value amplification of angular Goos-Hänchen and Imbert-Fedorov shifts in partial reflection,” Opt. Lett. 39(21), 6229–6232 (2014).
    [Crossref] [PubMed]
  14. G. Jayaswal, G. Mistura, and M. Merano, “Observing angular deviations in light-beam reflection via weak measurements,” Opt. Lett. 39(21), 6257–6260 (2014).
    [Crossref] [PubMed]
  15. G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
    [Crossref] [PubMed]
  16. G. Jayaswal, G. Mistura, and M. Merano, “Observation of the Imbert-Fedorov effect via weak value amplification,” Opt. Lett. 39(8), 2266–2269 (2014).
    [Crossref] [PubMed]
  17. A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
    [Crossref] [PubMed]

2014 (4)

2013 (3)

G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
[Crossref] [PubMed]

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

F. Töppel, M. Ornigotti, and A. Aiello, “Goos–Hanchen and Imbert–Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15(11), 113059 (2013).
[Crossref]

2012 (3)

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14(7), 073013 (2012).
[Crossref]

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
[Crossref]

2009 (2)

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[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. Photonics 3(6), 337–340 (2009).
[Crossref]

2008 (2)

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]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

1972 (1)

C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).
[Crossref]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

Aiello, A.

F. Töppel, M. Ornigotti, and A. Aiello, “Goos–Hanchen and Imbert–Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15(11), 113059 (2013).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
[Crossref]

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 3(6), 337–340 (2009).
[Crossref]

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[Crossref] [PubMed]

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]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

Dennis, M. R.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for Giant Transverse Optical Beam Shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14(7), 073013 (2012).
[Crossref]

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

Ghosh, N.

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Goswami, S.

Götte, J. B.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for Giant Transverse Optical Beam Shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14(7), 073013 (2012).
[Crossref]

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

Imbert, C.

C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).
[Crossref]

Jayaswal, G.

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

Löffler, W.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for Giant Transverse Optical Beam Shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

Merano, M.

Mistura, G.

Nandi, A.

Ornigotti, M.

F. Töppel, M. Ornigotti, and A. Aiello, “Goos–Hanchen and Imbert–Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15(11), 113059 (2013).
[Crossref]

Pal, M.

Panigrahi, P. K.

Töppel, F.

F. Töppel, M. Ornigotti, and A. Aiello, “Goos–Hanchen and Imbert–Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15(11), 113059 (2013).
[Crossref]

Vaidman, L.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

van Exter, M. P.

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 3(6), 337–340 (2009).
[Crossref]

Woerdman, J. P.

Ann. Phys. (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

J. Opt. (1)

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

Nat. Photonics (1)

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 3(6), 337–340 (2009).
[Crossref]

New J. Phys. (4)

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14(1), 013058 (2012).
[Crossref]

F. Töppel, M. Ornigotti, and A. Aiello, “Goos–Hanchen and Imbert–Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15(11), 113059 (2013).
[Crossref]

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14(7), 073013 (2012).
[Crossref]

Opt. Lett. (6)

Phys. Rev. D Part. Fields (1)

C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972).
[Crossref]

Phys. Rev. Lett. (2)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref] [PubMed]

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for Giant Transverse Optical Beam Shifts,” Phys. Rev. Lett. 112(23), 233901 (2014).
[Crossref] [PubMed]

Science (1)

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Pictorial representation of the post-selection schemes (a) and (b) in Poincare sphere. In both cases, the pre-selected state is LCP (South Pole). The eigen-states of GH (p and s linear polarization) and angular IF ( + 45°/-45° linear polarizations) shift (black arrows) and the post-selected elliptical polarization states (red arrows) are shown. Two separate planes, one containing the pre-selected state and the eigen-states of GH (blue shadow), the other containing the pre-selected state and the eigen-states of angular IF (green shadow) are marked in both the figures
Fig. 2
Fig. 2 A generalized schematic of the experimental system for the weak measurement of the angular GH and IF shifts in partial reflection. P1, P2: rotatable Glan-Thompson linear polarizers mounted on precision rotation mount; QWP1, QWP2 removable quarter waveplates L: Lens. The prism mounted on a precision rotation stage act as the weak measuring device.
Fig. 3
Fig. 3 Selective weak value amplification of angular GH and angular IF shifts in partial reflection, employing pre and post-selection in circular (elliptical) polarization basis (Scheme 1). Two different elliptical post-selection schemes (scheme 1a and 1b) are shown in (a) and (b) respectively. Longitudinal GH (along x-direction, in (a)) and transverse IF (along y-direction, in (b)) shifts in beam’s centroid between the two post selected states + ε (left panel) and -ε (right panel) away from the orthogonal state are apparent. In (a), angular GH shift is amplified by nullifying the IF effects. In (b), angular IF effect (having diagonal linear polarizations as eigen modes) is amplified by decoupling it from the spatial IF effect and also by nullifying the GH shift.
Fig. 4
Fig. 4 The dependence of the shift of the beam centroid representing (a) the angular GH shift Δx GH and (b) the angular IF shift Δy IF on the angle of incidence θ for weak measurement schemes 1a and 1b, respectively. In both the figures, symbols (open circle) represent experimental data and the corresponding theoretical predictions (Eq. (6a) and (6b), for ε = 0.7 rad) are shown by black lines. The agreement between the theory and experiment is seen to be excellent on either side of the Brewster angle (θB ~56.6°).
Fig. 5
Fig. 5 The angular dependence of the weak value amplified shift of the beam centroid representing the angular IF shift Δy IF for weak measurement schemes 2a, 2b and 2c. The results are shown for pre-selection with (a) p-linear polarization and (b) s-linear polarization. In both cases, the experimental IF shifts for post selections in linear polarization (scheme 2a: black circle) and two different elliptical polarizations (scheme 2b: blue triangle, scheme 2c: red square) are shown. The corresponding theoretical predictions (Eqs. (7), 8 for ε = 0.7 rad, and Eq. (9) for ε = 0.17 rad respectively) are shown by black, blue and red lines respectively.

Equations (13)

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GH=[ Ωp(θ) 0 0 Ωs(θ) ]IF=[ 0 Ωl(θ) Ωr(θ) 0 ]
Ωp(θ)=i lnrp θ ,Ωs(θ)=i lnrs θ Ωl(θ)=i( 1+ rp rs )cotθ,Ωr(θ)=i( 1+ rs rp )cotθ
A W GH = ψ post |GH| ψ pre ψ post | ψ pre and A W IF = ψ post |IF| ψ pre ψ post | ψ pre
| ψ post [ 1ε i(1±ε) ]
A w a,GH =±i ( r p r p r s r s ) 2ε i 2 ( r p r p + r s r s ), A w a,IF =± ( r p r s r s r p ) 2ε cotθ 1 2 ( r s r p + r p r s +2 )cotθ
| ψ post [ (1+i)±ε(1i) (1i)±ε(1+i) ]
A w b,GH = 1 2ε ( r p r p r s r s ) i 2 ( r p r p + r s r s ), A w a,IF =± i 2ε ( r p r s r s r p )cotθ 1 2 ( r s r p + r p r s +2 )cotθ
Δθ w a,GH = λ πε z 0 ( r p r p r s r s ), Δx a GH =z Δθ w a,GH
Δθ w b,IF = λ πε z 0 ( r p r s r s r p )cotθ, Δy b IF =z Δθ w b,IF
ΔA w,p/s a,IF = 2i ε ( 1+ r s/p r p/s )cotθ
ΔA w,p/s b,IF = (1±i)i ε ( 1+ r s/p r p/s )cotθ
ΔA w,p/s c,IF = 2 ε ( 1+ r s/p r p/s )cotθ
Δθ w,p/s b,IF = 1 2 Δθ w,p/s a,IF , Δθ w,p/s c,IF =0, Δy w,p/s IF =z Δθ w,p/s IF

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