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.

© 1998 Optical Society of America

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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 and V.A. Kiselyev, “Proper Frequencies of a Rotating Ring Resonator,” Zh. Eksp. Teor. Fiz. 57, 1353–1360 (1969)
  5. A.M. Volkov and V.A. Kiselyev, “Rotating Ring Cavity with a Nonreciprocal Element,” Opt. Spektrosk. 29, 365–370 (1970)
  6. A.M. Volkov and V.A. Kiselyev, “Rotating Ring Cavity with a Moving Medium as the Nonreciprocal Element,” Opt. Spektrosk. 30, 332–339 (1971)
  7. V.E. Privalov and 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 and E.M. Lifshitz, The Classical Theory of Fields (“Nauka”, Moscow, 1988)
  10. L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media (“Nauka”, Moscow, 1992)
  11. Yu.A. Anan’ev, Optical Resonators and Laser Beams (“Nauka”, Moscow, 1990)

1992 (1)

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

1990 (1)

Yu.A. Anan’ev, Optical Resonators and Laser Beams (“Nauka”, Moscow, 1990)

1977 (1)

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

1971 (1)

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

1970 (1)

A.M. Volkov and V.A. Kiselyev, “Rotating Ring Cavity with a Nonreciprocal Element,” Opt. Spektrosk. 29, 365–370 (1970)

1969 (2)

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

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

1967 (1)

E.J. Post, “Sagnac Effect,” Rev. Mod. Phys. 39, 475–493 (1967)
[Crossref]

1966 (1)

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

1964 (1)

C.V. Heer, “Resonant Frequencies of an Electromagnetic Cavity in an Accelerated System of Reference,” Phys. Rev. 134, A799–804 (1964)
[Crossref]

Anan’ev, Yu.A.

Yu.A. Anan’ev, Optical Resonators and Laser Beams (“Nauka”, Moscow, 1990)

Belonogov, A.M.

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

Filatov, Yu.V.

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

Heer, C.V.

C.V. Heer, “Resonant Frequencies of an Electromagnetic Cavity in an Accelerated System of Reference,” Phys. Rev. 134, A799–804 (1964)
[Crossref]

Khromykh, A.M.

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

Kiselyev, V.A.

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

A.M. Volkov and V.A. Kiselyev, “Rotating Ring Cavity with a Nonreciprocal Element,” Opt. Spektrosk. 29, 365–370 (1970)

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

Landau, L.D.

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

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

Lifshitz, E.M.

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

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

Post, E.J.

E.J. Post, “Sagnac Effect,” Rev. Mod. Phys. 39, 475–493 (1967)
[Crossref]

Privalov, V.E.

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

Volkov, A.M.

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

A.M. Volkov and V.A. Kiselyev, “Rotating Ring Cavity with a Nonreciprocal Element,” Opt. Spektrosk. 29, 365–370 (1970)

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

Kvant. Electron. (Moscow) (1)

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

Opt. Spektrosk. (2)

A.M. Volkov and V.A. Kiselyev, “Rotating Ring Cavity with a Nonreciprocal Element,” Opt. Spektrosk. 29, 365–370 (1970)

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

Phys. Rev. (1)

C.V. Heer, “Resonant Frequencies of an Electromagnetic Cavity in an Accelerated System of Reference,” Phys. Rev. 134, A799–804 (1964)
[Crossref]

Rev. Mod. Phys. (1)

E.J. Post, “Sagnac Effect,” Rev. Mod. Phys. 39, 475–493 (1967)
[Crossref]

Zh. Eksp. Teor. Fiz. (2)

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

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

Zh. Tekh. Fiz. (1)

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

Other (3)

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

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

Yu.A. Anan’ev, 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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