Proceedings - Viện Vật lý

Advances _________________________________________________________________________________in Optics, Photonics, Spectroscopy and Applications. Aug. 2006, Cantho, Vietnamfield only, and then the Raman laser operates at Stokes wavelength and this lasercan be called the “Stokes laser”. In previous work [7], L.S.Meng has investigetedthe stable regime of the Raman laser by solving a set of equations for amplitudes inone-dimentional approach, only.In this paper, we develop a semi-classical theory for the far-off-resonanceRaman laser in three-dimentional approach by providing the set of equations forpower of intracavity interacting fields. The time-dependent solution to thecontinuous-wave Stokes laser is numerically solved and discussed.2. Field amplitude equation of the stokes laserWe assume that the optical field inside the cavity will be in single spatial modeand can be written as:E r, t E t u r(1)q qwhere subscript q will denote the various frequency components inside the cavity(length L) such as, the pump and the Stokes. Every mode is orthogonal:u r u * r dxdydz V(2)cavityqq q qwhere Vqis the mode volume occupied by the q-th spatial mode.Using the Maxwell’s wave equation with slowly-varying envelopeapproximation, the density matrix equation with adiabatic elimination (for all timethe upper levels J are in steady state), we have the intracavity field equations [7]ppkp2 Eepp( r)tEp( t)t GEs( t)Ep( t)tEp( t)2sks2(3)2sEs( t) Es( t) G Ep( t)Es( t)2where2cep T1p , (4)n Lpc ps ln R1 psR2 ps(5)n Lpresent the intracavity energy decay rate due to primarily the loss of the mirrors(transmitance T, reflectance R), relating to external pump field, intracavity pumpfield and Stokes field, respectively, and2 1ptan L/ bq2G c 0g(6)8 p sL / bqis difined as a gain term, with1224 1 0ab1 1g g(7) 22 1 4 / ab ab ab abababis the plane-wave gain coefficient, and2 s 2sNds Dg0(8)2n n c 2 p ssp0ab1357