Abstract

An experiment was proposed to probe quantum effects on optical activity. The helical structures in optically active media act as natural microsolenoids for the electromagnetic waves passing through them, which produces a longitudinal magnetic field in the axis of helices. Magnetic flux through a helical crystal structure is quantized. A high number of quanta in the rotatory power was probed in the optical activity of α-quartz.

© 2007 Optical Society of America

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References

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  1. E. Hecht, Optics (Addison-Wesley, 2002).
  2. E. U. Condon, Rev. Mod. Phys. 9, 432 (1937).
    [CrossRef]
  3. C. Z. Tan, Appl. Phys. B 82, 633 (2006). The induced magnetic field Bi and magnetic flux Φ in Eqs. (8)-(10) in this reference should be replaced with Bi=jℏ/(er2), and Φ=jπℏ/e, because optical activity is described by one-electron theory (see Ref. ) and Bi is determined by the radius, r.
    [CrossRef]
  4. B. S. Deaver, Jr. and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961).
    [CrossRef]
  5. R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961).
    [CrossRef]
  6. W. L. Goodman and B. S. Deaver, Jr., Phys. Rev. Lett. 24, 870 (1970).
    [CrossRef]
  7. D. Yu. Sharvin and Yu. V. Sharvin, JETP Lett. 34, 272 (1981).
  8. A. D. Stone and Y. Imry, Phys. Rev. Lett. 56, 189 (1986).
    [CrossRef] [PubMed]
  9. P. Van Den Keybus and W. Grevendonk, Phys. Status Solidi B 136, 651 (1986).
    [CrossRef]
  10. D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (Wiley, 1997).
  11. C. Z. Tan, L. Cao, and T. B. Wang, Nucl. Instrum. Methods Phys. Res. B 239, 267 (2005).
    [CrossRef]
  12. C. Z. Tan, H. Li, and L. Chen, Appl. Phys. B 86, 129 (2007).
    [CrossRef]

2007

C. Z. Tan, H. Li, and L. Chen, Appl. Phys. B 86, 129 (2007).
[CrossRef]

2006

C. Z. Tan, Appl. Phys. B 82, 633 (2006). The induced magnetic field Bi and magnetic flux Φ in Eqs. (8)-(10) in this reference should be replaced with Bi=jℏ/(er2), and Φ=jπℏ/e, because optical activity is described by one-electron theory (see Ref. ) and Bi is determined by the radius, r.
[CrossRef]

2005

C. Z. Tan, L. Cao, and T. B. Wang, Nucl. Instrum. Methods Phys. Res. B 239, 267 (2005).
[CrossRef]

1986

A. D. Stone and Y. Imry, Phys. Rev. Lett. 56, 189 (1986).
[CrossRef] [PubMed]

P. Van Den Keybus and W. Grevendonk, Phys. Status Solidi B 136, 651 (1986).
[CrossRef]

1981

D. Yu. Sharvin and Yu. V. Sharvin, JETP Lett. 34, 272 (1981).

1970

W. L. Goodman and B. S. Deaver, Jr., Phys. Rev. Lett. 24, 870 (1970).
[CrossRef]

1961

B. S. Deaver, Jr. and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961).
[CrossRef]

R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961).
[CrossRef]

1937

E. U. Condon, Rev. Mod. Phys. 9, 432 (1937).
[CrossRef]

Appl. Phys. B

C. Z. Tan, Appl. Phys. B 82, 633 (2006). The induced magnetic field Bi and magnetic flux Φ in Eqs. (8)-(10) in this reference should be replaced with Bi=jℏ/(er2), and Φ=jπℏ/e, because optical activity is described by one-electron theory (see Ref. ) and Bi is determined by the radius, r.
[CrossRef]

C. Z. Tan, H. Li, and L. Chen, Appl. Phys. B 86, 129 (2007).
[CrossRef]

JETP Lett.

D. Yu. Sharvin and Yu. V. Sharvin, JETP Lett. 34, 272 (1981).

Nucl. Instrum. Methods Phys. Res. B

C. Z. Tan, L. Cao, and T. B. Wang, Nucl. Instrum. Methods Phys. Res. B 239, 267 (2005).
[CrossRef]

Phys. Rev. Lett.

A. D. Stone and Y. Imry, Phys. Rev. Lett. 56, 189 (1986).
[CrossRef] [PubMed]

B. S. Deaver, Jr. and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961).
[CrossRef]

R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961).
[CrossRef]

W. L. Goodman and B. S. Deaver, Jr., Phys. Rev. Lett. 24, 870 (1970).
[CrossRef]

Phys. Status Solidi B

P. Van Den Keybus and W. Grevendonk, Phys. Status Solidi B 136, 651 (1986).
[CrossRef]

Rev. Mod. Phys.

E. U. Condon, Rev. Mod. Phys. 9, 432 (1937).
[CrossRef]

Other

E. Hecht, Optics (Addison-Wesley, 2002).

D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (Wiley, 1997).

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Figures (4)

Fig. 1
Fig. 1

Schematic depiction of rotation of the electric field vectors in an optically active medium and the circular motion of an electron along the helical crystal structure. The incident light is linearly polarized along the x axis at z = 0 . At position z, the plane of vibration rotates an angle of ( k r k l ) z 2 with respect to the original direction. The transmission direction p p of a polarizer is perpendicular to the resultant electric field E ( z , t ) . The intensity of the transmitted light is related to high numbers of quanta in the rotatory power.

Fig. 2
Fig. 2

Experimental setup to probe the quantum effects in the optical activity of α-quartz.

Fig. 3
Fig. 3

Rotation angles of the electric field vectors in α-quartz at different propagation distances in the z axis. The rotatory power is equal to the slope of the line, which is evaluated to be 18.5818 ± 0.0045 (degrees/mm).

Fig. 4
Fig. 4

Minimum intensity of the transmitted light and its dependence on the propagation distance in the z axis. The minimum intensity is found to be proportional to sin 2 ( 2 ρ z ) (solid curve), as depicted by Eq. (9). The quantum number in the rotatory power is therefore j = 3 for the optical activity of α-quartz.

Equations (9)

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L = m r υ = j ,
B i = j e r 2 .
Φ = π r 2 B i = j π e .
ρ j = B i V = j V e r 2 .
E r ( z , t ) = E 0 2 [ e x cos ( k r z ω t ) + e y sin ( k r z ω t ) ] ,
E l ( z , t ) = E 0 2 [ e x cos ( k l z ω t ) e y sin ( k l z ω t ) ] ,
E ( z , t ) = E 0 cos ( ( k r + k l ) z 2 ω t ) { e x cos ( ( k r k l ) z 2 ) + e y sin ( ( k r k l ) z 2 ) } .
ρ = k r k l 2 = π λ ( n r n l ) .
I j = I 0 j sin 2 [ ( j 1 ) ρ z ] ,

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