Analytical Estimation of Stress-Induced Birefringence in Panda-Type Polarization-Maintaining Fibers

Abstract

An analytical model for estimating the stress -induced birefringence in true Panda-type polarization -maintaining fibers with imperfect geometry has been developed in this letter. The developed model is simpler and more accurate compared to conventional sophisticated and asymptotic formulas in reported works. Our model provides a clear and simple solution to demonstrate the periodic dependence of the birefringence on the misalignment angle between the two stress-applying parts, and the monotonic dependence on the geometric parameters of stress-applying parts. Our work also reveals the important role of the misalignment angle between the two stress-applying parts in practical Panda-type fibers.

Revisiting the Stress-Induced Birefringence in Polarization-Maintaining Fibers

“…1, the "modal birefringence" in (5) equals exactly the "stress birefringence" in (4) induced by the thermal stresses through the photo-elastic effect, as stated in early works [7], [13], [14], [16]. Then the "stress-induced birefringence" (SIB) for PMFs can be written as [15] B n n…”

“…On the other hand, there are two disagreements in [13] and [14]. Firstly, the selected stress components in calculating the SIB were not consistent with each other, while this was fundamentally related to the definition of the SIB in PMFs, as demonstrated in our recent work for the SIB in Panda-PMFs [15]. Secondly, the expressions of the Airy stress function (ASF) applied in two schemes were not consistent either.…”

“…Unfortunately, our previous analyses [15] did not completely solve the above problems, due to the use of the same ASF in the pioneering work [13] and [14]. It caused tedious and contradictory mathematical calculations.…”

“…In most PMFs, the SIB is produced through the photo-elastic effect due to the thermal stress from the stress-applying parts (SAPs) embedded in fiber cladding [13], which have different thermal expanding coefficients (TECs) from surroundings due to the dopant [14]. The stress distribution and the SIB depend on the difference between TECs of these constituting materials, which is mainly dominated by the geometry of SAPs in additional to the concentration of the dopant [15], [16]. PMFs were conventionally named Panda, Bow-tie, Elliptical-cladding, and Side-pit fibers, et.al., depending on the geometry of SAPs [6], [7], [13]- [16].…”

Theoretical analysis of the non-reciprocal phase shifts due to birefringence and topology in fiber ring interferometers

“…Unfortunately, it is not true for practical FRIs, where the coiled polarization-maintaining fibers (PMFs) have both linear and circular birefringence. The linear birefringence arises from the thermal stress established in the fiber fabrication, and this is intrinsic to PMFs [29]. The circular birefringence originates from two factors, the internal rotation (IR) of the linear birefringence axes and the external twist (ET) of the fiber.…”