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In this paper, we study the birefringence in photonic crystal fiber lasers PCFs and in conventional fiber lasers in the bi-directional pump scheme in the linear cavity laser. We show that the value of birefringence in photonic crystal fibers is smaller than that of conventional fiber lasers [1].

Photonic crystal fibers (PCFs) are attracting increasing interests because of their unique properties such as: endlessly single-mode guiding, freedom of dispersion characteristics, and large mode area [^{3+} is surrounded by a lower index cladding, which is, surrounded by an air-clad region, in turn, surrounded by a second lower index cladding index.

We use the rate equation for finding the expressions of the temperature dependence in Regions I, II, III, and IV [

light and output laser can be expressed as follows:

where N_{b}(y) is the upper laser level population density, N_{yt} is the concentration of Yb^{3+}, _{as} and σ_{es} are the laser absorption and emission cross section, σ_{ap} and σ_{ep} are the pump light absorption and emission cross-section respectively, Γ_{p} and Γ_{s} are the power-filling factors [

In the case where the fiber end faces are free of traction

where

The length of optical fibers is much greater than that of a typical fiber outside radius (b). Thus, we can invoke the plane-strain approximation [

Therefore, the expressions in different regions of the fiber can be given by [

where

Equations (8)-(11) show that the fiber birefringence depends only on the thermally induced stresses.

Using the expressions of the temperature dependence in Regions I, II, III, and VI [

For the purposes of illustration, unless indicated otherwise, the parameters used in the simulation are λ_{p} = 975 nm, λ_{s} = 1080 nm, R_{1s} = 0.98, R_{2s} = 0.04, L = 5 m, _{A} = 0.05.

The boundary conditions for the laser propagation equation can be written as:

In addition, for the pump:

In the bidirectional pump scheme:

In the forward pump scheme:

Using analytical and numerical calculations, the finite-difference method (FDM) and a simple model of (PCFs), we have determined the distributions of pump and laser along the PCFs in the forward and bidirectional pumped YPCFs, and the birefringence in PCF laser dope ytterbium in cases the forward and bi-directional pump scheme respectively as function of the radius.

Both

In this paper, we have compared the birefringence in photonic crystal fibers (PCFs) with the birefringence in conventional fibers.

In summary, regarding the birefringence, their value in PCFs are less than that found in conventional fiber lasers [

N. Rouchdi,M. Abouricha,A. Boulezhar,M. Kriraa, (2015) Comparative Study of the Birefringence in Photonic Crystal Fiber Lasers. Optics and Photonics Journal,05,320-325. doi: 10.4236/opj.2015.511030