Abstract

The angles at which a light beam gets diffracted by a grating depend strongly on the direction of incidence for diffraction angles close to a right angle. Accordingly, it is possible to amplify small beam deflections by placing a grating at an optimal orientation to the light path. We use this principle to amplify small beam deviations arising out of a light beam refracting at the interface of an optically active medium, and demonstrate a new technique of enhancing the limit of detection of chiro-optical measurements.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Rohlin, “An interferometer for precision angle measurements,” Appl. Opt. 2, 762–763 (1963).
    [CrossRef]
  2. D. Malacara and O. Harris, “Interferometric measurements of angle,” Appl. Opt. 9, 1630–1633 (1970).
    [CrossRef]
  3. G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
    [CrossRef]
  4. P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
    [CrossRef]
  5. P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
    [CrossRef]
  6. P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
    [CrossRef]
  7. G. D’Emilia and F. Iaconis, “A simple fiber optic sensor for angle measurement,” in Instrumentation and Measurement Technology Conference (IEEE, 1994), pp. 295–299.
  8. C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
    [CrossRef]
  9. D. Sagrario and P. Mead, “Axial and angular displacement fiber-optic sensor,” Appl. Opt. 37, 6748–6754 (1998).
    [CrossRef]
  10. G. Margheri, A. Mannoni, and F. Quercioli, “High-resolution angular and displacement sensing based on excitation of surface plasma waves,” Appl. Opt. 36, 4521–4525 (1997).
    [CrossRef]
  11. J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
    [CrossRef]
  12. J. Guo, Z. Zhu, and W. Deng, “Small-angle measurement based on surface-plasmon resonance and the use of magneto-optical modulation,” Appl. Opt. 38, 6550–6555 (1999).
    [CrossRef]
  13. 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, 1351–1354 (1988).
    [CrossRef]
  14. P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
    [CrossRef]
  15. A. Ghosh and P. Fischer, “Chiral molecules split light: reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
    [CrossRef]
  16. R. P. Rajan and A. Ghosh, “Enhancement of circular differential deflection of light in an optically active medium,” Opt. Lett. 37, 1232–1234 (2012).
    [CrossRef]
  17. A. Ghosh, F. M. Fazal, and P. Fischer, “Circular differential double diffraction in chiral media,” Opt. Lett. 32, 1836–1838(2007).
    [CrossRef]
  18. M. Pfeifer and P. Fischer, “Weak value amplified optical activity measurements,” Opt. Express 19, 16508–16517 (2011).
    [CrossRef]
  19. A. Ghosh, W. Hill, and P. Fischer, “Observation of the Faraday effect via beam deflection in a longitudinal magnetic field,” Phys. Rev. A 76, 055402 (2007).
    [CrossRef]
  20. C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
    [CrossRef]
  21. A. Garcıa-Valenzuela, G. E. Sandoval-Romero, and C. Sanchez-Perez, “High-resolution optical angle sensors: approaching the diffraction limit to the sensitivity,” Appl. Opt. 43, 4311–4321 (2004).
    [CrossRef]
  22. J. P. Weber, “Device design using Gaussian beams and ray matrices in planar optics,” IEEE J. Quantum Electron. 30, 2407–2416 (1994).
    [CrossRef]
  23. D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
    [CrossRef]

2012 (1)

2011 (1)

2009 (2)

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

2007 (2)

A. Ghosh, F. M. Fazal, and P. Fischer, “Circular differential double diffraction in chiral media,” Opt. Lett. 32, 1836–1838(2007).
[CrossRef]

A. Ghosh, W. Hill, and P. Fischer, “Observation of the Faraday effect via beam deflection in a longitudinal magnetic field,” Phys. Rev. A 76, 055402 (2007).
[CrossRef]

2006 (1)

A. Ghosh and P. Fischer, “Chiral molecules split light: reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef]

2004 (1)

1999 (1)

1998 (2)

J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
[CrossRef]

D. Sagrario and P. Mead, “Axial and angular displacement fiber-optic sensor,” Appl. Opt. 37, 6748–6754 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (2)

1994 (1)

J. P. Weber, “Device design using Gaussian beams and ray matrices in planar optics,” IEEE J. Quantum Electron. 30, 2407–2416 (1994).
[CrossRef]

1992 (2)

C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
[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 spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

1974 (1)

1970 (1)

1963 (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 spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

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, 1351–1354 (1988).
[CrossRef]

Chapman, G. D.

D’Emilia, G.

G. D’Emilia and F. Iaconis, “A simple fiber optic sensor for angle measurement,” in Instrumentation and Measurement Technology Conference (IEEE, 1994), pp. 295–299.

Deng, W.

J. Guo, Z. Zhu, and W. Deng, “Small-angle measurement based on surface-plasmon resonance and the use of magneto-optical modulation,” Appl. Opt. 38, 6550–6555 (1999).
[CrossRef]

J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
[CrossRef]

Dixon, P. B.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
[CrossRef]

Fazal, F. M.

Fischer, P.

M. Pfeifer and P. Fischer, “Weak value amplified optical activity measurements,” Opt. Express 19, 16508–16517 (2011).
[CrossRef]

A. Ghosh, W. Hill, and P. Fischer, “Observation of the Faraday effect via beam deflection in a longitudinal magnetic field,” Phys. Rev. A 76, 055402 (2007).
[CrossRef]

A. Ghosh, F. M. Fazal, and P. Fischer, “Circular differential double diffraction in chiral media,” Opt. Lett. 32, 1836–1838(2007).
[CrossRef]

A. Ghosh and P. Fischer, “Chiral molecules split light: reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef]

Garcia-Valenzuela, A.

Ghosh, A.

R. P. Rajan and A. Ghosh, “Enhancement of circular differential deflection of light in an optically active medium,” Opt. Lett. 37, 1232–1234 (2012).
[CrossRef]

A. Ghosh, F. M. Fazal, and P. Fischer, “Circular differential double diffraction in chiral media,” Opt. Lett. 32, 1836–1838(2007).
[CrossRef]

A. Ghosh, W. Hill, and P. Fischer, “Observation of the Faraday effect via beam deflection in a longitudinal magnetic field,” Phys. Rev. A 76, 055402 (2007).
[CrossRef]

A. Ghosh and P. Fischer, “Chiral molecules split light: reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef]

Greve, J.

C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Grooth, B. G. D.

C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Guo, J.

J. Guo, Z. Zhu, and W. Deng, “Small-angle measurement based on surface-plasmon resonance and the use of magneto-optical modulation,” Appl. Opt. 38, 6550–6555 (1999).
[CrossRef]

J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
[CrossRef]

Harris, O.

Hill, W.

A. Ghosh, W. Hill, and P. Fischer, “Observation of the Faraday effect via beam deflection in a longitudinal magnetic field,” Phys. Rev. A 76, 055402 (2007).
[CrossRef]

Howel, J. C.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

Howell, J. C.

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
[CrossRef]

Huang, P. S.

Hulst, N. F. V.

C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Iaconis, F.

G. D’Emilia and F. Iaconis, “A simple fiber optic sensor for angle measurement,” in Instrumentation and Measurement Technology Conference (IEEE, 1994), pp. 295–299.

Jordan, A. N.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
[CrossRef]

Kamada, O.

Kiyono, S.

Malacara, D.

Mannoni, A.

Margheri, G.

Mead, P.

Ni, J.

Pfeifer, M.

Putman, C. A. J.

C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Quercioli, F.

Rajan, R. P.

Rohlin, J.

Sagrario, D.

Sanchez-Perez, C.

Sandoval-Romero, G. E.

Shen, S.

J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
[CrossRef]

Starling, D. J.

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
[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, 1351–1354 (1988).
[CrossRef]

Weber, J. P.

J. P. Weber, “Device design using Gaussian beams and ray matrices in planar optics,” IEEE J. Quantum Electron. 30, 2407–2416 (1994).
[CrossRef]

Wu, C.

C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
[CrossRef]

Zhu, Z.

J. Guo, Z. Zhu, and W. Deng, “Small-angle measurement based on surface-plasmon resonance and the use of magneto-optical modulation,” Appl. Opt. 38, 6550–6555 (1999).
[CrossRef]

J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
[CrossRef]

Appl. Opt. (10)

J. Rohlin, “An interferometer for precision angle measurements,” Appl. Opt. 2, 762–763 (1963).
[CrossRef]

D. Malacara and O. Harris, “Interferometric measurements of angle,” Appl. Opt. 9, 1630–1633 (1970).
[CrossRef]

G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
[CrossRef]

P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
[CrossRef]

P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
[CrossRef]

P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
[CrossRef]

J. Guo, Z. Zhu, and W. Deng, “Small-angle measurement based on surface-plasmon resonance and the use of magneto-optical modulation,” Appl. Opt. 38, 6550–6555 (1999).
[CrossRef]

D. Sagrario and P. Mead, “Axial and angular displacement fiber-optic sensor,” Appl. Opt. 37, 6748–6754 (1998).
[CrossRef]

G. Margheri, A. Mannoni, and F. Quercioli, “High-resolution angular and displacement sensing based on excitation of surface plasma waves,” Appl. Opt. 36, 4521–4525 (1997).
[CrossRef]

A. Garcıa-Valenzuela, G. E. Sandoval-Romero, and C. Sanchez-Perez, “High-resolution optical angle sensors: approaching the diffraction limit to the sensitivity,” Appl. Opt. 43, 4311–4321 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. P. Weber, “Device design using Gaussian beams and ray matrices in planar optics,” IEEE J. Quantum Electron. 30, 2407–2416 (1994).
[CrossRef]

J. Appl. Phys. (1)

C. A. J. Putman, B. G. D. Grooth, N. F. V. Hulst, and J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Opt. Eng. (1)

J. Guo, Z. Zhu, W. Deng, and S. Shen, “Angle measurement using surface-plasmon resonance heterodyne interferometry: a new method,” Opt. Eng. 37, 2998–3001 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

A. Ghosh, W. Hill, and P. Fischer, “Observation of the Faraday effect via beam deflection in a longitudinal magnetic field,” Phys. Rev. A 76, 055402 (2007).
[CrossRef]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803(R) (2009).
[CrossRef]

Phys. Rev. Lett. (3)

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, 1351–1354 (1988).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howel, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef]

A. Ghosh and P. Fischer, “Chiral molecules split light: reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef]

Rev. Sci. Instrum. (1)

C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
[CrossRef]

Other (1)

G. D’Emilia and F. Iaconis, “A simple fiber optic sensor for angle measurement,” in Instrumentation and Measurement Technology Conference (IEEE, 1994), pp. 295–299.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(A) Schematic of angular amplification by a diffraction grating. Two light beams are incident on a grating at angles of incidence, i+ and i, diffracting at angles ϕm+ and ϕm respectively, where m=0, 1, 2 represent the various orders of diffraction. The ratio between the angles of diffraction, Δϕm, to the difference between the angles of incidence, δ=i+i, is defined as the angular amplification (AA). (B) The dependence of the angular amplification (AA) on the average angle of incidence, i, assuming δi+, i for various diffraction orders. Note that similar angular amplification would also be possible with a reflection grating.

Fig. 2.
Fig. 2.

Schematic of the experimental setup to generate, amplify, and measure circular differential beam deflections. Light from a He–Ne laser was modulated between two circularly polarized states and transmitted through a SF11 prism (30°–60°–90°). The prism was made optically active by the application of a dc magnetic field using a Helmholtz coil. The light beams after refraction at the prism-air interface was transmitted through a grating, which could be rotated with a precision of 25 millidegrees. The differential beam deflections were measured phase synchronously by a position-sensitive detector (PSD) and a lock-in amplifier.

Fig. 3.
Fig. 3.

Theoretical (black line) and experimental (red squares, line) angular amplification for different angles of incidence. (Inset) shows the variation of the signal-to-noise ratio of the beam deflection measurements as a function of the incident direction (dotted line is a guide to the eye).

Fig. 4.
Fig. 4.

Plotted as a function of angle of incidence (degree) are, left (red squares, solid lines), beam diameter in mm, and, right (black circles, dotted lines), ratio of the angular deflection to the beam deflection, in mm1.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

d(sini+sinϕm)=mλ.
AA=ΔϕmΔi=|cosicosϕm|.

Metrics