Abstract

We report the implementation of a highly sensitive tunable beam displacer based on the concept of weak value amplification, that allows to displace the centroid of a Gaussian beam a distance much smaller than its beam width without the need to deflect the direction of propagation of the input beam with movable optical elements. The beam’s centroid position can be displaced by controlling the linear polarization of the output beam, and the dependence between the centroid’s position and the angle of polarization is linear.

© 2015 Optical Society of America

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References

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  1. G. R. Fowles, Introduction to Modern Optics (Dover, 1975).
  2. A. J. Fowler and J. Schlafer, “A survey of laser beam deflection techniques,” Appl. Opt. 5, 1675–1682 (1966).
    [Crossref] [PubMed]
  3. Y. Li and J. Katz, “Laser beam scanning by rotary mirrors. I. Modeling mirror-scanning devices,” Appl. Opt. 34, 6403–6416 (1995).
    [Crossref] [PubMed]
  4. E. J. Galvez, “Achromatic polarization-preserving beam displacer,” Opt. Lett. 26, 971–973 (2001).
    [Crossref]
  5. L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Rev. Sci. Instrum. 86, 033109 (2015).
    [Crossref] [PubMed]
  6. For example, the tweaker plate from Thorlabs model XYT-A is a 2. 5mm thick plane-parallel plate that allows sub-mm level precision beam displacement.
  7. II-VI UK LTD offers thin film polarizers made of either ZnSe or Ge that can be used to split or combine an input beam into two components with orthogonal polarizations.
  8. For instance, Edmund Optics plate beam splitter model #49-684 is a 3mm thick N-BK7 splitter that transmits 70% of the input power and operates in the visible regime.
  9. Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a 1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351 (1988).
    [Crossref] [PubMed]
  10. I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a “weak measurement” of a spin 1/2 particle’s spin component yields a value of 100,” Phys. Rev. D 40, 2112 (1989).
    [Crossref]
  11. M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
    [Crossref]
  12. J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
    [Crossref]
  13. A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).
  14. J. P. Torres, G. Puentes, N. Hermosa, and L. J. Salazar-Serrano, “Weak interference in the high-signal regime,” Opt. Express 20, 18869–18875 (2012).
    [Crossref] [PubMed]

2015 (1)

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Rev. Sci. Instrum. 86, 033109 (2015).
[Crossref] [PubMed]

2014 (2)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

2012 (1)

2006 (1)

M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
[Crossref]

2001 (1)

1995 (1)

1989 (1)

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a “weak measurement” of a spin 1/2 particle’s spin component yields a value of 100,” Phys. Rev. D 40, 2112 (1989).
[Crossref]

1988 (1)

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

1966 (1)

Aharonov, Y.

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

Boyd, R. W.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Dressel, J.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Duck, I. M.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a “weak measurement” of a spin 1/2 particle’s spin component yields a value of 100,” Phys. Rev. D 40, 2112 (1989).
[Crossref]

El-Amawy, A.

M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
[Crossref]

Feldman, M.

M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
[Crossref]

Fowler, A. J.

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Dover, 1975).

Galvez, E. J.

Hermosa, N.

Howell, J. C.

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

Jordan, A. N.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

Katz, J.

Li, Y.

Malik, M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Martínez-Rincón, J.

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

Miatto, F. M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Puentes, G.

Salazar-Serrano, L. J.

Schlafer, J.

Srivastava, A.

M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
[Crossref]

Stevenson, P. M.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a “weak measurement” of a spin 1/2 particle’s spin component yields a value of 100,” Phys. Rev. D 40, 2112 (1989).
[Crossref]

Sudarhshan, E. C. G.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a “weak measurement” of a spin 1/2 particle’s spin component yields a value of 100,” Phys. Rev. D 40, 2112 (1989).
[Crossref]

Torres, J. P.

Vaidman, L.

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

Vaidyanathan, R.

M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
[Crossref]

Valencia, A.

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Rev. Sci. Instrum. 86, 033109 (2015).
[Crossref] [PubMed]

Appl. Opt. (2)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. D (1)

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a “weak measurement” of a spin 1/2 particle’s spin component yields a value of 100,” Phys. Rev. D 40, 2112 (1989).
[Crossref]

Phys. Rev. Lett. (1)

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

Phys. Rev. X (1)

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4, 011031 (2014).

Rev. Mod. Phys. (1)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: understanding quantum weak values: basics and applications,” Rev. Mod. Phys. 86, 307 (2014).
[Crossref]

Rev. Sci. Instrum. (2)

M. Feldman, A. El-Amawy, A. Srivastava, and R. Vaidyanathan, “Adjustable Wollaston-like prisms,” Rev. Sci. Instrum. 77, 066109 (2006).
[Crossref]

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Rev. Sci. Instrum. 86, 033109 (2015).
[Crossref] [PubMed]

Other (4)

For example, the tweaker plate from Thorlabs model XYT-A is a 2. 5mm thick plane-parallel plate that allows sub-mm level precision beam displacement.

II-VI UK LTD offers thin film polarizers made of either ZnSe or Ge that can be used to split or combine an input beam into two components with orthogonal polarizations.

For instance, Edmund Optics plate beam splitter model #49-684 is a 3mm thick N-BK7 splitter that transmits 70% of the input power and operates in the visible regime.

G. R. Fowles, Introduction to Modern Optics (Dover, 1975).

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Figures (4)

Fig. 1
Fig. 1 (a) General scheme of the tunable beam displacer. A polarization-dependent beam displacement is introduced by a TBD set at an angle θ. Input and output polarizers (POL) control the corresponding polarizations. (b) Beam displacement before traversing the second polarizer for the horizontal (solid line) and vertical (dashed line) components of the optical beam a function of the rotation angle θ. The shaded region indicates the region where the beams with orthogonal polarizations still overlap.
Fig. 2
Fig. 2 Beam profile after traversing the second polarizer for three different output polarizations (β = 30°, β = 45° and β = 60°). The insets shows more clearly the small beam displacements for different post-selections of the output state of polarization.
Fig. 3
Fig. 3 (a) Centroid position as a function of the polarization selected of the output beam, given by the post-selection angle β. (b) Insertion loss as a function of the post-selection angle β. Data: Δx = 120μm, γ = 0.9 and ϕ = 0°.
Fig. 4
Fig. 4 (a) Measurement (dots) of the beam’s centroid position as a function of the postselection angle β. The solid line corresponds to a linear fit given by 〈x〉 = −2.45β +113 μm with correlation coefficient R = 0.998. (b) Measured insertion loss (dots) and theory (solid line) obtained from Eq. (4) with Φ = 54° as fitting parameter.

Equations (4)

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E out ( x ) = E 0 { cos β exp ( ( x Δ x ) 2 / 2 w 2 + i ϕ ) + sin β exp ( ( x + Δ x ) 2 / 2 w 2 ) } ,
I out ( x ) = I 0 2 { cos 2 β exp ( ( x Δ x ) 2 / w 2 ) + sin 2 β exp ( ( x + Δ x ) 2 / w 2 ) + sin 2 β exp ( Δ x 2 / w 2 ) exp ( x 2 / w 2 ) cos ϕ } .
x = cos 2 β 1 + γ sin 2 β cos ϕ Δ x ,
L = 10 log 10 [ 1 2 ( 1 + γ sin 2 β cos ϕ ) ] .

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