Abstract

The model of compound oscillators, each of which consists of four identical linear harmonic oscillators, is used for the description of the pressure variation of the optical rotary power of α quartz. This model establishes the contribution of the interaction of the oscillators not only arranged along the Z axis but also those lying in the neighboring chains.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. B. Myers and K. Vedam, J. Opt. Soc. Am. 55, 1180 (1965).
    [Crossref]
  2. M. B. Myers and K. Vedam, J. Opt. Soc. Am. 56, 1741 (1966).
    [Crossref]
  3. K. Vedam and T. A. Davis, J. Opt. Soc. Am. 58, 1451 (1968).
    [Crossref]
  4. S. Chandrasekhar, Proc. Indian Acad. Sci. A37, 468 (1953).
  5. S. Chandrasekhar, Proc. Roy. Soc. (London) 259, 531 (1961).
    [Crossref]
  6. V. Vyšín, Proc. Phys. Soc. (London) 87, 55 (1966).
    [Crossref]
  7. K. Vedam and T. A. Davis, J. Opt. Soc. Am. 57, 1140 (1967).
    [Crossref]

1968 (1)

1967 (1)

1966 (2)

V. Vyšín, Proc. Phys. Soc. (London) 87, 55 (1966).
[Crossref]

M. B. Myers and K. Vedam, J. Opt. Soc. Am. 56, 1741 (1966).
[Crossref]

1965 (1)

1961 (1)

S. Chandrasekhar, Proc. Roy. Soc. (London) 259, 531 (1961).
[Crossref]

1953 (1)

S. Chandrasekhar, Proc. Indian Acad. Sci. A37, 468 (1953).

J. Opt. Soc. Am. (4)

Proc. Indian Acad. Sci. (1)

S. Chandrasekhar, Proc. Indian Acad. Sci. A37, 468 (1953).

Proc. Phys. Soc. (London) (1)

V. Vyšín, Proc. Phys. Soc. (London) 87, 55 (1966).
[Crossref]

Proc. Roy. Soc. (London) (1)

S. Chandrasekhar, Proc. Roy. Soc. (London) 259, 531 (1961).
[Crossref]

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 (1)

F. 1
F. 1

Model of four coupled oscillators.

Equations (35)

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

r ¨ k + ω 0 2 r k + 2 π 2 j = 1 k j 4 k j r j = 0 ,
12 = 34 13 = 24 14 = 23 .
r k = A k e i λ t .
( ω 0 2 λ 2 ) A k + 2 π 2 j = 1 k j 4 k j A j = 0 .
| ( ω 0 2 λ 2 ) 2 π 2 12 2 π 2 13 2 π 2 14 2 π 2 12 ( ω 0 2 λ 2 ) 2 π 2 14 2 π 2 13 2 π 2 13 2 π 2 14 ( ω 0 2 λ 2 ) 2 π 2 12 2 π 2 14 2 π 2 13 2 π 2 12 ( ω 0 2 λ 2 ) | = 0 .
ω 1 2 = ω 0 2 + 2 π 2 ( 12 + 13 + 14 ) ω 2 2 = ω 0 2 2 π 2 ( 12 13 + 14 ) ω 3 2 = ω 0 2 2 π 2 ( 12 + 13 14 ) ω 4 2 = ω 0 2 + 2 π 2 ( 12 13 14 ) ,
q 1 = 1 2 ( r 1 + r 2 + r 3 + r 4 ) q 2 = 1 2 ( r 1 r 2 + r 3 r 4 ) q 3 = 1 2 ( r 1 r 2 r 3 + r 4 ) q 4 = 1 2 ( r 1 + r 2 r 3 r 4 ) .
q ¨ η + ω η 2 q η = 0 , η = 1 , 2 , 3 , 4 .
X r = E 0 cos ω t Y r = E 0 sin ω t X l = E 0 cos ω t Y l = E 0 sin ω t .
F 13 r = e E 0 ( A cos ω t B sin ω t )
F 24 r = ( A cos Θ B sin Θ ) e E 0 cos ( ω t Φ r ) ( A sin Θ + B cos Θ ) e E 0 sin ( ω t Φ r ) ,
R q 1 r = 1 2 ( F 1 r + F 2 r + F 3 r + F 4 r ) = ( F 1 r + F 2 r ) R q 2 r = 1 2 ( F 1 r F 2 r + F 3 r F 4 r ) = ( F 1 r F 2 r ) .
q ¨ η + ω η 2 q η = 2 ( a q η τ ) ( e / m ) f q η ,
n l 2 n r 2 = 4 π N e 2 m { [ ( a q 1 l ) 2 ( a q 1 r ) 2 ] f q 1 ω 1 2 ω 2 + [ ( a q 2 l ) 2 ( a q 2 r ) 2 ] f q 2 ω 2 2 ω 2 } .
( a q 1 r ) 2 = ( A 2 + B 2 ) ( 1 + cos Θ + Φ r sin Θ ) ( a q 2 r ) 2 = ( A 2 + B 2 ) ( 1 cos Θ Φ r sin Θ ) ( a q 1 l ) 2 = ( A 2 + B 2 ) ( 1 + cos Θ Φ l sin Θ ) ( a q 2 l ) 2 = ( A 2 + B 2 ) ( 1 cos Θ Φ l sin Θ ) ,
( a q 2 l ) 2 ( a q 2 r ) 2 = 2 ( A 2 + B 2 ) ( Φ l + Φ r ) sin Θ ( a q 1 l ) 2 ( a q 1 r ) 2 = 2 ( A 2 + B 2 ) ( Φ l + Φ r ) sin Θ
n l 2 n r 2 = ( n l n r ) ( n l + n r ) .
ρ = ( ω / 2 c ) ( n l n r )
ρ = 4 π N e 2 ( A 2 + B 2 ) R 12 sin θ ω 2 m c 2 ( f q 2 ω 2 2 ω 2 f q 1 ω 1 2 ω 2 )
ρ = 4 π N e 2 ( A 2 + B 2 ) R 12 sin θ ω 2 m c 2 × ( 2 π 2 ( f q 2 + f q 1 ) ( 12 + 14 ) ( ω 0 2 ω 2 ) 2 + 4 π 2 13 ( ω 0 2 ω 2 ) + ( f q 2 f q 2 ) [ ( ω 0 2 ω 2 ) + 2 π 2 13 ] ( ω 0 2 ω 2 ) 2 + 4 π 2 13 ( ω 0 2 ω 2 ) ) .
f q 2 + f q 1 = 2 f 0 ( 1 + π 2 13 ) f q 2 f q 1 = ( 2 f 0 / ω 0 ) π 2 ( 12 + 14 ) .
ρ = K ω ω 2 ( 2 π 2 f 0 ( 12 + 14 ) + 2 π 2 f 0 ( 12 + 14 ) ( ω 2 / ω 0 2 ) ( ω 0 2 ω 2 ) 2 + 4 π 2 13 ( ω 0 2 ω 2 ) )
ρ = K λ λ 2 ( 2 π 2 f 0 ( 12 + 14 ) [ 1 + ( λ 2 / λ 0 2 ) ] ( λ 2 λ 0 2 ) 2 + ( 13 λ 0 2 λ 2 / c 2 ) ( λ 2 λ 0 2 ) ) ,
K λ = N e 2 ( A 2 + B 2 ) R 12 λ 0 4 sin Θ / π m c 4 .
ρ = 7.19 λ 2 / { [ λ 2 ( 0.0926 ) 2 ] 2 } ,
ρ = π N e 2 R 12 sin θ λ 0 4 ( A 2 + B 2 ) f 0 m c 4 · λ 2 ( λ 2 λ 0 2 ) 2
13 λ 0 2 λ 2 ( λ 2 λ 0 2 ) / c 2 ( λ 2 λ 0 2 ) 2 .
13 ( R 12 3 / R 13 3 ) 12 .
ρ = 2 π N e 2 ( A 2 + B 2 ) R 12 f 0 ( 12 + 14 ) sin θ λ 0 4 m c 4 · λ 2 ( λ 2 λ 0 2 ) 2 .
ρ = const N ( P ) R 12 ( P ) f 0 ( P ) × [ 12 ( P ) + 14 ( P ) ] λ 0 4 ( P ) · λ 2 [ λ 2 λ 0 2 ( P ) ] 2 ,
1 ρ d ρ d P = λ 4 λ 2 λ 0 2 Π 0 + β + Γ ( R 12 ) + Γ ( f 0 ) + Γ ( 12 + 14 ) ,
Π 0 = ( 1 / λ 0 ) d λ 0 / d P β = ( 1 / N ) d N / d P Γ ( R 12 ) = ( 1 / R 12 ) d R 12 / d P Γ ( f 0 ) = ( 1 / f 0 ) d f 0 / d P
Γ ( 12 + 14 ) = [ ( 1 / 12 ) d 12 / d P + ( 1 / 14 ) d 14 / d P ] .
= ( f 0 e 2 cos Θ ) / 2 π 2 m R 12 3 ;
Γ ( f 0 ) = ( 2 / f 0 ) d f 0 / d P , Γ ( R 12 ) = ( 2 / R 12 ) d R 12 / d P .