A Helical Multicore Optical Fiber Design for Coherent Imaging
Multicore Fiber(MCF)/imaging fiber bundle is a key device of flexible optical endoscope.In imaging applications,MCFs are widely used in the non-coherent imaging which transmits the intensity distribution only.The bending sensitive distortion of phase plane and inter-core crosstalk bring challenges in the coherent imaging application.In this paper,a Helical-Core MCF(HC-MCF)is designed for the application of coherent imaging.Due to the intricate nature of HC-MCF,neither semi-analytical models nor empirical methods can fully resolve the modal properties.Consequently,a full-vector finite-element method is employed for numerical simulation of HC-MCF.By utilizing the optical transformation technique,HC-MCF in the natural space is equivalently represented in the helical coordinate maintaining the translation invariance.The original isotropic permeability and dielectric constant(both scalars)of the optical fiber material are adjusted to equivalent dielectric constant and equivalent permeability values.This simplification can effectively reduce the computational complexity of the field distribution and equivalent effective refractive index of fundamental mode in HC-MCF.By using this method,the inter-core group delay differences of HC-MCF is simulated for optimization of fiber design.Then,an optimized design of HC-MCF is proposed.In order to minimize the distortion of phase front after transmission in HC-MCF,each core of HC-MCF should have a similar optical path.An appropriate core spacing should be selected to balance between the spatial sampling density and crosstalk among fiber cores.The helix period is preferred smaller than the critical bend radius in the application.Our final design of HC-MCF are arranged in a densely stacked hexagonal configuration,comprising 6 layers with a total of 91 cores.The radii of the fiber cores are 4 μm,3.3 μm,3.1 μm,3 μm,2.9 μm and 2.8 μm from the inside to the outside,with a core pitch of 20 μm and helical pitch of 10 cm.The inter-core group delay difference per unit length of straight HC-MCF is calculated and the maximum is found to be 6 fs/m.When the bending radius is significantly larger than the wavelength,the change in mode equivalent refractive index caused by bending is disregarded,and the variation in group delay difference resulting from core bending is determined solely by changes in core geometry length.The trajectory equation of the bent core is derived to obtain its geometry length,enabling determination of the corresponding change in group delay.Calculations are performed for two different bending radii(0.5 m and 0.05 m)to assess variations in group delay difference per unit length for helical fibers under these conditions.Remarkably,similar changes are observed under both bending scenarios,indicating that alterations in bend state do not induce significant phase modifications within transmitted light fields.By carefully designing the structure of HC-MCF,excellent bend performance can be achieved.At last,the bend induced inter-core crosstalk of HC-MCF is calculated.The crosstalks between cores of adjacent layers for HC-MCF with a total length of 100 m,torsion rate of 20 π/m,and core spacing of 20 μm are calculated and compared.Due to slight variations in mode phase mismatch between different layers during bending,there exists a maximum crosstalk value when phase matching conditions are satisfied.When the bending radius is smaller than that at which phase matching occurs,inter-layer core crosstalk becomes insensitive to bending radius and maintains a consistently low level.In this design,featuring slightly varied core sizes and a helical structure within each layer,and an exceptionally low level of crosstalk(-550 dB/100 m)is achieved.This remarkably reduced crosstalk could significantly enhance the imaging quality.Due to the helical core design of the designed helical MCF,the complex random disturbance of the optical field phase transmitted by the multi-core fiber under the bending condition is reduced,and the group delay difference caused by the bending between the cores is effectively suppressed.HC-MCF can help to reduce the complexity of the coherent image restoration,which finds useful applications in fiber optic micro-imaging,ultrafast laser imaging and other fields.
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