Abstract

The helical crystal structure in optically active media acts as the natural micro-solenoids for the electromagnetic waves passing through them, producing the longitudinal magnetic field in the direction of the axis of helices. Magnetic flux through the helical structure is quantized. The Berry phase is induced by rotation of the electrons around the helical structure. Optical rotation is related to the difference in the accumulative Berry phase between the right-, and the left-circularly polarized waves, which is proportional to the magnetic flux through the helical structure, according to the Aharonov-Bohm effect. The optical activity is the natural Faraday effect and the natural Aharonov-Bohm effect.

© 2008 Optical Society of America

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References

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  1. E. Hecht, Optics (Addison Wesley, New York, 2002).
  2. E. U. Condon, "Theories of optical rotatory power," Rev. Mod. Phys. 9, 432-457 (1937).
    [CrossRef]
  3. C. Z. Tan, "Quantum magnetic flux through helical molecules in optically active media," Appl. Phys. B 82, 633-636 (2006).
    [CrossRef]
  4. C. Z. Tan and L. Chen, "Quantum effects in the optical activity of ?-quartz," Opt. Lett. 32, 2936-2938 (2007).
    [CrossRef] [PubMed]
  5. M. V. Berry, "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. Lond. A 392, 45-57 (1984).
    [CrossRef]
  6. Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev. 115, 485-491 (1959).
    [CrossRef]
  7. B. S. Deaver, Jr., and W. M. Fairbank, "Experimental evidence for quantized flux in superconducting cylinders," Phys. Rev. Lett. 7, 43-46 (1961).
    [CrossRef]
  8. R. Doll and M. Näbauer, "Experimental proof of magnetic flux quantization in a superconducting ring," Phys. Rev. Lett. 7, 51-52 (1961).
    [CrossRef]
  9. W. L. Goodman and B. S. Deaver, Jr., "Detailed measurements of the quantized flux states of hollow superconducting cylinders," Phys. Rev. Lett. 24, 870-873 (1970).
    [CrossRef]
  10. D. Yu. Sharvin and Yu. V. Sharvin, "Magnetic-flux quantization in cylindrical film of a normal metal," JETP Lett. 34, 272-275 (1981).
  11. R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
    [CrossRef] [PubMed]
  12. A. D. Stone and Y. Imry, "Periodicity of the Aharonov-Bohm effect in normal-metal rings," Phys. Rev. Lett. 56, 189-192 (1986).
    [CrossRef] [PubMed]
  13. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1999).
  14. F. Plastina, G. Liberti, and A. Carollo, "Scaling of Berry???s phase close to the Dicke quantum phase transition," Europhys. Lett. 76, 182-188 (2006).
    [CrossRef]
  15. M. P. Silverman, More Than One Mystery, Explorations in Quantum Interference (Springer-Verlag, Berlin, 1995).
    [CrossRef]
  16. P. Van Den Keybus and W. Grevendonk, "Comparison of optical activity and Faraday rotation in crystalline SiO2," Phys. Status Solidi B 136, 651-659 (1986).
    [CrossRef]
  17. J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
    [CrossRef]
  18. D. N. Nikogosyan, Properties of Optical and Laser-Related Materials A Handbook (John Wiley & Sons, New York, 1997).
  19. C. Z. Tan, "Piezoelectric lattice vibrations at optical frequencies," Solid State Commun. 131, 405-408 (2004).
    [CrossRef]
  20. C. Z. Tan, H. Li, and L. Chen, "Generation of mutual coherence of eigenvibrations in ?-quartz at infrared frequencies by incidence of randomly polarized waves," Appl. Phys. B 86, 129-137 (2007).
    [CrossRef]

2007 (2)

C. Z. Tan and L. Chen, "Quantum effects in the optical activity of ?-quartz," Opt. Lett. 32, 2936-2938 (2007).
[CrossRef] [PubMed]

C. Z. Tan, H. Li, and L. Chen, "Generation of mutual coherence of eigenvibrations in ?-quartz at infrared frequencies by incidence of randomly polarized waves," Appl. Phys. B 86, 129-137 (2007).
[CrossRef]

2006 (2)

F. Plastina, G. Liberti, and A. Carollo, "Scaling of Berry???s phase close to the Dicke quantum phase transition," Europhys. Lett. 76, 182-188 (2006).
[CrossRef]

C. Z. Tan, "Quantum magnetic flux through helical molecules in optically active media," Appl. Phys. B 82, 633-636 (2006).
[CrossRef]

2004 (1)

C. Z. Tan, "Piezoelectric lattice vibrations at optical frequencies," Solid State Commun. 131, 405-408 (2004).
[CrossRef]

1990 (1)

J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
[CrossRef]

1986 (2)

P. Van Den Keybus and W. Grevendonk, "Comparison of optical activity and Faraday rotation in crystalline SiO2," Phys. Status Solidi B 136, 651-659 (1986).
[CrossRef]

A. D. Stone and Y. Imry, "Periodicity of the Aharonov-Bohm effect in normal-metal rings," Phys. Rev. Lett. 56, 189-192 (1986).
[CrossRef] [PubMed]

1985 (1)

R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
[CrossRef] [PubMed]

1984 (1)

M. V. Berry, "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. Lond. A 392, 45-57 (1984).
[CrossRef]

1981 (1)

D. Yu. Sharvin and Yu. V. Sharvin, "Magnetic-flux quantization in cylindrical film of a normal metal," JETP Lett. 34, 272-275 (1981).

1970 (1)

W. L. Goodman and B. S. Deaver, Jr., "Detailed measurements of the quantized flux states of hollow superconducting cylinders," Phys. Rev. Lett. 24, 870-873 (1970).
[CrossRef]

1961 (2)

B. S. Deaver, Jr., and W. M. Fairbank, "Experimental evidence for quantized flux in superconducting cylinders," Phys. Rev. Lett. 7, 43-46 (1961).
[CrossRef]

R. Doll and M. Näbauer, "Experimental proof of magnetic flux quantization in a superconducting ring," Phys. Rev. Lett. 7, 51-52 (1961).
[CrossRef]

1959 (1)

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev. 115, 485-491 (1959).
[CrossRef]

1937 (1)

E. U. Condon, "Theories of optical rotatory power," Rev. Mod. Phys. 9, 432-457 (1937).
[CrossRef]

Aharonov, Y.

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev. 115, 485-491 (1959).
[CrossRef]

Berry, M. V.

M. V. Berry, "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. Lond. A 392, 45-57 (1984).
[CrossRef]

Bohm, D.

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev. 115, 485-491 (1959).
[CrossRef]

Carollo, A.

F. Plastina, G. Liberti, and A. Carollo, "Scaling of Berry???s phase close to the Dicke quantum phase transition," Europhys. Lett. 76, 182-188 (2006).
[CrossRef]

Chen, L.

C. Z. Tan and L. Chen, "Quantum effects in the optical activity of ?-quartz," Opt. Lett. 32, 2936-2938 (2007).
[CrossRef] [PubMed]

C. Z. Tan, H. Li, and L. Chen, "Generation of mutual coherence of eigenvibrations in ?-quartz at infrared frequencies by incidence of randomly polarized waves," Appl. Phys. B 86, 129-137 (2007).
[CrossRef]

Condon, E. U.

E. U. Condon, "Theories of optical rotatory power," Rev. Mod. Phys. 9, 432-457 (1937).
[CrossRef]

Cooper, D. G.

J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
[CrossRef]

Deaver, B. S.

W. L. Goodman and B. S. Deaver, Jr., "Detailed measurements of the quantized flux states of hollow superconducting cylinders," Phys. Rev. Lett. 24, 870-873 (1970).
[CrossRef]

B. S. Deaver, Jr., and W. M. Fairbank, "Experimental evidence for quantized flux in superconducting cylinders," Phys. Rev. Lett. 7, 43-46 (1961).
[CrossRef]

Dexter, J. L.

J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
[CrossRef]

Doll, R.

R. Doll and M. Näbauer, "Experimental proof of magnetic flux quantization in a superconducting ring," Phys. Rev. Lett. 7, 51-52 (1961).
[CrossRef]

Fairbank, W. M.

B. S. Deaver, Jr., and W. M. Fairbank, "Experimental evidence for quantized flux in superconducting cylinders," Phys. Rev. Lett. 7, 43-46 (1961).
[CrossRef]

Goodman, W. L.

W. L. Goodman and B. S. Deaver, Jr., "Detailed measurements of the quantized flux states of hollow superconducting cylinders," Phys. Rev. Lett. 24, 870-873 (1970).
[CrossRef]

Grevendonk, W.

P. Van Den Keybus and W. Grevendonk, "Comparison of optical activity and Faraday rotation in crystalline SiO2," Phys. Status Solidi B 136, 651-659 (1986).
[CrossRef]

Imry, Y.

A. D. Stone and Y. Imry, "Periodicity of the Aharonov-Bohm effect in normal-metal rings," Phys. Rev. Lett. 56, 189-192 (1986).
[CrossRef] [PubMed]

Laibowitz, R. B.

R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
[CrossRef] [PubMed]

Landry, J.

J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
[CrossRef]

Li, H.

C. Z. Tan, H. Li, and L. Chen, "Generation of mutual coherence of eigenvibrations in ?-quartz at infrared frequencies by incidence of randomly polarized waves," Appl. Phys. B 86, 129-137 (2007).
[CrossRef]

Liberti, G.

F. Plastina, G. Liberti, and A. Carollo, "Scaling of Berry???s phase close to the Dicke quantum phase transition," Europhys. Lett. 76, 182-188 (2006).
[CrossRef]

Näbauer, M.

R. Doll and M. Näbauer, "Experimental proof of magnetic flux quantization in a superconducting ring," Phys. Rev. Lett. 7, 51-52 (1961).
[CrossRef]

Plastina, F.

F. Plastina, G. Liberti, and A. Carollo, "Scaling of Berry???s phase close to the Dicke quantum phase transition," Europhys. Lett. 76, 182-188 (2006).
[CrossRef]

Reintjes, J.

J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
[CrossRef]

Sharvin, D. Yu.

D. Yu. Sharvin and Yu. V. Sharvin, "Magnetic-flux quantization in cylindrical film of a normal metal," JETP Lett. 34, 272-275 (1981).

Sharvin, Yu. V.

D. Yu. Sharvin and Yu. V. Sharvin, "Magnetic-flux quantization in cylindrical film of a normal metal," JETP Lett. 34, 272-275 (1981).

Stone, A. D.

A. D. Stone and Y. Imry, "Periodicity of the Aharonov-Bohm effect in normal-metal rings," Phys. Rev. Lett. 56, 189-192 (1986).
[CrossRef] [PubMed]

Tan, C. Z.

C. Z. Tan, H. Li, and L. Chen, "Generation of mutual coherence of eigenvibrations in ?-quartz at infrared frequencies by incidence of randomly polarized waves," Appl. Phys. B 86, 129-137 (2007).
[CrossRef]

C. Z. Tan and L. Chen, "Quantum effects in the optical activity of ?-quartz," Opt. Lett. 32, 2936-2938 (2007).
[CrossRef] [PubMed]

C. Z. Tan, "Quantum magnetic flux through helical molecules in optically active media," Appl. Phys. B 82, 633-636 (2006).
[CrossRef]

C. Z. Tan, "Piezoelectric lattice vibrations at optical frequencies," Solid State Commun. 131, 405-408 (2004).
[CrossRef]

Umbach, C. P.

R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
[CrossRef] [PubMed]

Van Den Keybus, P.

P. Van Den Keybus and W. Grevendonk, "Comparison of optical activity and Faraday rotation in crystalline SiO2," Phys. Status Solidi B 136, 651-659 (1986).
[CrossRef]

Washburn, S.

R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
[CrossRef] [PubMed]

Webb, R. A.

R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
[CrossRef] [PubMed]

Appl. Phys. B (2)

C. Z. Tan, "Quantum magnetic flux through helical molecules in optically active media," Appl. Phys. B 82, 633-636 (2006).
[CrossRef]

C. Z. Tan, H. Li, and L. Chen, "Generation of mutual coherence of eigenvibrations in ?-quartz at infrared frequencies by incidence of randomly polarized waves," Appl. Phys. B 86, 129-137 (2007).
[CrossRef]

Europhys. Lett. (1)

F. Plastina, G. Liberti, and A. Carollo, "Scaling of Berry???s phase close to the Dicke quantum phase transition," Europhys. Lett. 76, 182-188 (2006).
[CrossRef]

JETP Lett. (1)

D. Yu. Sharvin and Yu. V. Sharvin, "Magnetic-flux quantization in cylindrical film of a normal metal," JETP Lett. 34, 272-275 (1981).

Opt. Comm. (1)

J. L. Dexter, J. Landry, D. G. Cooper, and J. Reintjes, "Ultraviolet optical isolators utilizing KDP-isomorphs," Opt. Comm. 80, 115-118 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev. 115, 485-491 (1959).
[CrossRef]

Phys. Rev. Lett. (5)

B. S. Deaver, Jr., and W. M. Fairbank, "Experimental evidence for quantized flux in superconducting cylinders," Phys. Rev. Lett. 7, 43-46 (1961).
[CrossRef]

R. Doll and M. Näbauer, "Experimental proof of magnetic flux quantization in a superconducting ring," Phys. Rev. Lett. 7, 51-52 (1961).
[CrossRef]

W. L. Goodman and B. S. Deaver, Jr., "Detailed measurements of the quantized flux states of hollow superconducting cylinders," Phys. Rev. Lett. 24, 870-873 (1970).
[CrossRef]

R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696-2699 (1985).
[CrossRef] [PubMed]

A. D. Stone and Y. Imry, "Periodicity of the Aharonov-Bohm effect in normal-metal rings," Phys. Rev. Lett. 56, 189-192 (1986).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

P. Van Den Keybus and W. Grevendonk, "Comparison of optical activity and Faraday rotation in crystalline SiO2," Phys. Status Solidi B 136, 651-659 (1986).
[CrossRef]

Proc. R. Soc. Lond. A (1)

M. V. Berry, "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. Lond. A 392, 45-57 (1984).
[CrossRef]

Rev. Mod. Phys. (1)

E. U. Condon, "Theories of optical rotatory power," Rev. Mod. Phys. 9, 432-457 (1937).
[CrossRef]

Solid State Commun. (1)

C. Z. Tan, "Piezoelectric lattice vibrations at optical frequencies," Solid State Commun. 131, 405-408 (2004).
[CrossRef]

Other (4)

E. Hecht, Optics (Addison Wesley, New York, 2002).

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1999).

D. N. Nikogosyan, Properties of Optical and Laser-Related Materials A Handbook (John Wiley & Sons, New York, 1997).

M. P. Silverman, More Than One Mystery, Explorations in Quantum Interference (Springer-Verlag, Berlin, 1995).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

The rotating electron of the charge -e around a contour C of the radius r in an uniform magnetic field B, with its velocity vector υ perpendicular to B. The motion of the electron is affected by the Lorentz force, eυB, and the centrifugal force, 2/r. In the equilibrium state, the two opposite forces are balanced. The magnetic flux Φ through the contour and the Berry phase γ are proportional to the angular momentum L. An electromotive force ε is related to a torque τ.

Fig. 2.
Fig. 2.

Relationship between the rotatory power ρ (in degree/mm) and the Verdet constant V (in degree/(tesla·mm)) of α-quartz in the wavelength range from 0.19 to 2 µm. Experimental results (symbols) are taken from Refs. [17,18]. The rotatory power is found to be proportional to the Verdet constant at different wavelengths of the incident light. This is the experimental confirmation of Eq. (10).

Fig. 3.
Fig. 3.

The sub-solenoids of the radius r in optically active media. The lengths of the sub-solenoids are λ/n r , and λ/n l for the r-, and the l-waves, respectively. The magnetic field B r induced by the r-waves is in the opposite direction of B l induced by the l-waves. In the equilibrium state, the Lorentz and the centrifugal forces are balanced: r B l = 2 r /r, and l B r = 2 l /r.

Equations (16)

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

L = mr υ = j ħ ,
B = L er 2 = j ħ er 2 .
Φ = π r 2 B = π e L = j π ħ e .
ε = Φ t = π e d L dt = π e τ ,
γ = e ħ Φ .
γ = π ħ L = j π .
θ = π ( n l n r ) d λ ,
θ = ρ d ,
θ = VB d ,
ρ = BV = j ħ V er 2 .
θ = γ ( n l n r ) d λ .
ρ = γ ( n l n r ) λ .
ρ = j π ( n l n r ) λ .
V = e A ( n l n r ) ħ λ ,
d 2 x dt 2 ± 1 r ( dy dt ) 2 + ω 0 2 x = e m E x ,
d 2 y dt 2 1 r ( dx dt ) 2 + ω 0 2 y = e m E y .

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