Abstract

A theoretical investigation was done concerning the resonant properties of a rotating Fabry-Perot cavity with dielectric media inside. The frequency splitting of orthogonal circularly-polarized modes had been predicted. Formula for the frequency splitting was obtained taking into account refractive index dispersion, dynamic-optical effect and the transversal structure of the electromagnetic field. We represent a simplified analysis, based on the geometrical optical theory, and we also present an accurate analysis on the basis of the general theory of relativity.

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References

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  1. C.V. Heer, "Resonant Frequencies of an Electromagnetic Cavity in an Accelerated System of Reference," Phys. Rev. 134, A799-804 (1964)
    [CrossRef]
  2. E.J. Post, "Sagnac Effect," Rev. Mod. Phys. 39, 475-493 (1967)
    [CrossRef]
  3. A.M. Khromykh, "Ring Generator in a Rotating Reference System," Zh. Eksp. Teor. Fiz. 50, 281-282 (1966)
  4. A. M. Volkov, V .A. Kiselyev, "Proper Frequencies of a Rotating Ring Resonator," Zh. Eksp. Teor. Fiz. 57, 1353-1360 (1969)
  5. A. M. Volkov, V. A. Kiselyev, "Rotating Ring Cavity with a Nonreciprocal Element," Opt. Spektrosk. 29, 365-370 (1970)
  6. A. M. Volkov, V. A. Kiselyev, "Rotating Ring Cavity with a Moving Medium as the Nonreciprocal Element," Opt. Spektrosk. 30, 332-339 (1971)
  7. V. E. Privalov, Yu. V. Filatov, "A Study of the Output Characteristics of the Rotating Gas Ring Laser," Kvant. Electron. (Moscow) 4, 1418-1425 (1977)
  8. A. M. Belonogov, "Electromagnetic Oscillations in a Three-Dimentional Resonator in a Rotating Reference Frame," Zh. Tekh. Fiz. 39, 1175-1179 (1969)
  9. L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Nauka, Moscow, 1988)
  10. L .D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Nauka, Moscow, 1992)
  11. Yu. A. Ananev, Optical Resonators and Laser Beams (Nauka, Moscow, 1990)

Other (11)

C.V. Heer, "Resonant Frequencies of an Electromagnetic Cavity in an Accelerated System of Reference," Phys. Rev. 134, A799-804 (1964)
[CrossRef]

E.J. Post, "Sagnac Effect," Rev. Mod. Phys. 39, 475-493 (1967)
[CrossRef]

A.M. Khromykh, "Ring Generator in a Rotating Reference System," Zh. Eksp. Teor. Fiz. 50, 281-282 (1966)

A. M. Volkov, V .A. Kiselyev, "Proper Frequencies of a Rotating Ring Resonator," Zh. Eksp. Teor. Fiz. 57, 1353-1360 (1969)

A. M. Volkov, V. A. Kiselyev, "Rotating Ring Cavity with a Nonreciprocal Element," Opt. Spektrosk. 29, 365-370 (1970)

A. M. Volkov, V. A. Kiselyev, "Rotating Ring Cavity with a Moving Medium as the Nonreciprocal Element," Opt. Spektrosk. 30, 332-339 (1971)

V. E. Privalov, Yu. V. Filatov, "A Study of the Output Characteristics of the Rotating Gas Ring Laser," Kvant. Electron. (Moscow) 4, 1418-1425 (1977)

A. M. Belonogov, "Electromagnetic Oscillations in a Three-Dimentional Resonator in a Rotating Reference Frame," Zh. Tekh. Fiz. 39, 1175-1179 (1969)

L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Nauka, Moscow, 1988)

L .D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Nauka, Moscow, 1992)

Yu. A. Ananev, Optical Resonators and Laser Beams (Nauka, Moscow, 1990)

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Equations (30)

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Δω = 2 Ω n 2
g 00 = g 11 = g 22 = g 33 = 1 , g 0 α = g α 0 = ( [ Ω × r ] c ) α
F ik ; l + F li ; k + F kl ; i = F ik x l + F li x k + F kl x i = 0
F ik ; k = 1 g g F ik x k = 4 π c j i
F ik = g il g km F lm , F ik = g il g km F lm
e α = F 0 α h α = 1 2 γ e αβγ F βγ
e ˜ α = g 00 F 0 α h ˜ α = 1 2 γ e αβγ g 00 F βγ
γ αβ = g α β + g 0 α g 0 β g 00 , γ = g g 00 ,
div h = 0 rot e = 1 c γ t ( γ h )
div e ˜ = 4 πρ rot h ˜ = 1 c γ t ( γ e ˜ ) + 4 π c s
e ˜ = e g 00 + [ h ˜ × g ] , h = h ˜ g 00 + [ g × e ]
g = [ Ω × r ] c
div B = 0 rot E = 1 c B t
div D = 4 πρ rot H = 1 c D t + 4 π c j
D = E + 4 πP + [ H × g ] , B = H + 4 π M + [ g × E ]
mc { du i ds + Γ kl i u k u l } = e c F ik u k
Γ β 0 α = Γ 0 β α = γ γ αγ e γβσ Ω σ
mc { d v cdt 2 [ v × Ω ] c } = e ( e [ v × h ] c )
g C = V 2 cn ω ħ μ B Ω
P = ε 1 4 π E + i 4 π [ g C × E ]
g C = λ ( C ) Ω
rot rot E = ε c 2 2 E t 2 i [ g C × 1 c 2 2 E t 2 ] + 1 c t { [ rot E × g ] + rot [ E × g ] }
div E = i εc g C B t + 2 εc 1 c g E t
ε c 2 2 E t 2 2 E = 2 c ( g ) t E i [ g C × 1 c 2 2 E t 2 ] 2 c 2 [ Ω × E t ] + i εc grad ( g C B t ) 2 εc grad ( )
( n ± 2 n 2 2 n ω Δ ω ± 2 n ( ) ) E + 2 i ( Ωτ ) ω ( 1 + λ ( C ) ω 2 ) [ τ × E ] = 0
n ± = n + n ω Δ ω ± n + ( ) ± ( Ωτ ) ω n ( 1 + λ ( C ) ω 2 )
Δφ = ω L c ( n + n ) = 2 ( Ωτ ) L nc ( 1 + λ ( C ) ω 2 ) ω L cn n ω ( Δ ω + Δ ω )
Δω = Δ ω + Δ ω = 2 Ω n 2 { ( 1 + λ ( C ) ω 2 ) ( 1 + ω ω n ln n 1 n ) } cos θ
u r , ± m ( ρ , φ ) ( ρ w ) m L r m ( 2 ρ 2 w 2 ) exp { i k ρ 2 2 q ± im φ }
Δ ω m = 2 Ω { ( m 1 n 2 ( 1 + λ ( C ) ω 2 ) ) ( 1 + ω ω n ln n 1 n ) } cos θ

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