Characteristics Of F-P Interferometric Cavity Formed By Two Types Of Fiber Bragg Gratings

Dynamic population Bragg gratings can be formed by inputting two counter-propagating coherent light waves to rare earth doped fiber.Due to the periodic saturation absorption/gain effect of the coherent lights in doped fiber,the dynamic population grating is eventually formed.Since the early 1990s,dynamic gratings have been experimental observed by Frisken and Fischer et al,and its applications have received wide attention.Such as applications in fiber amplifiers,single-frequency fiber lasers and tunable narrow-band fiber filters.In recent years,the applications in optical fiber sensors,adaptive interferometers and slow light have also been proposed and demonstrated.In this paper,we summarize the basic principles,forming mechanism,experimental observation methods and application fields of dynamic grating in erbium-doped fiber,and expound on the theory and tools of atomic coherence,transfer matrix theory and coupled-mode theory in spatial periodic media.On this basis,we propose and demonstrate a scheme to realize a dynamic grating in erbium-doped fiber by an incoherent pump.This dynamic grating consists of an erbium-doped fiber and a high-reflectivity Bragg grating,by injecting a forward probe field into the erbium doped fiber,and choosing the wavelength of the forward probe field equal to the reflected peak wavelength of the Bragg grating,so the forward probe field can be reflected by the Bragg grating to form a backward probe field.If the Bragg grating reflection is close to 1,the standing wave which formed by forward wave and backward wave is the perfect standing wave.So the real and imaginary parts of the refractive index in erbium-doped fiber can be spatial periodically modulated at the same time,this is the basis for the formation of dynamic grating.But usually the reflection of the dynamic grating is too low to formation the Fabry-Perot cavity,so we use the incoherent pump.The incoherent pumping is used to amplify the relatively lower reflection and reduce the absorption of erbium ions in the dynamic grating without pumping.The three-level model of erbium ion was used as the object of study.Two counter-propagating traveling waves ?p-and ?p-drive transition from the ground level 4I15/2 to the metastable level 4I13/2 of the erbium ion,the refractive index and absorption of the erbium-doped fiber can be spatial periodically modulated from the standing wave which formed by the two traveling waves.In order to amplify the reflection of the dynamic grating,an auxiliary Incoherent pump with the wavelength of 980nm is added between the ground level 4I15/2 and the excited level 4I11/2 of the erbium ion.In the framework of semi-classical theory,we solve the density matrix equations of the above proposed three-level model under the interaction picture,the density operator under steady state can be obtained,and then we can obtain the polarization and the refractive index of the model which is periodically modulated by the standing wave field,finally,we can obtain reflection and transmission of the probe field by transmission matrix theory in spatial periodic medium.We carry out theoretical fitting to reflection spectrum of the dynamic grating,discuss the relation between the reflection spectrum of the dynamic grating and the Rabi frequency of the probe field or the length of the erbium-doped fiber when the Incoherent pump is zero,and the relation between the reflection spectrum of the dynamic grating and the Rabi frequency of the probe field or the pumping rate when the Incoherent pump is not zero.Dynamic grating is transient and dynamic tunable,and it will disappear with the removal of the standing wave field,the spectrum characteristic of the dynamic Bragg grating can be tunable by modulating both the wavelength and intensity of the probe field and the incoherent pump.On the basis of the above erbium-doped fiber dynamic grating,we have proposed a Fabry-Perot cavity based on the dynamic grating and the traditional Bragg grating.The fiber Fabry-Perot cavity composes of three parts:The dynamic grating recorded in erbium-doped fiber,a conventional Bragg grating and the interval part of bare fiber.The dynamic gratings are created by a forward probe field in an Er3+ doped fiber and a backward reflected beam due to connection with a high reflection fiber Bragg grating at one end.A Fabry-Perot cavity can be generated by choosing appropriate parameters of the dynamic grating,the Bragg grating and the length between them.We can obtain the reflection and transmission of the Fabry-Perot cavity by using the transfer matrix method?reflection and transmission coefficient of the dynamic grating and Bragg grating.In the following,we draw the reflection spectra and transmission spectra of the Fabry-Perot cavity,discuss the relation between the reflection(transmission)spectrum of the Fabry-Perot cavity and Rabi frequency of the probe field?pumping rate of the incoherent pump?refractive index modulation depth of the Bragg grating and cavity length of the Fabry-Perot cavity.In order to obtain the best reflection or transmission of the resonant spectrum,the intensity of the probe field should be close to but less than the saturation absorption intensity of erbium-doped fiber,the pump intensity should be higher than the threshold intensity of erbium-doped fiber,and it should increase with the doped concentration and length of the erbium-doped fiber increasing to get the best gain.The spacing between the adjacent resonance lines and the spectral compression width relate to the cavity length L of Fabry-Perot cavity,so we can select proper cavity length as needed.An important feature of the proposed Fabry-Perot cavity is that its output spectra can be dynamically tunable by modulating the Rabi frequency,the wavelength of the probe field and other parameters.This tunable Fabry-Perot cavity is more flexible comparing with the Fabry-Perot cavity based on two fiber Bragg gratings,and it can overcome the asymmetrical drawback of the two fiber Bragg gratings in Fabry-Perot cavity(such as different center wavelengths,refractive index modulation depths of Bragg grating),this tunable Fabry-Perot cavity is more beneficial for mode selection.The proposed Fabry-Perot cavity has potential applications in fiber-optic communication and fiber sensors.