Conventional fibers are known to be great light guides that can provide almost lossless transmissions for long distance propagation. However, these fibers are usually not flexible to control the fiber modal properties other than customizing the light confinement. Research work has demonstrated that some fiber modal properties of an optical fiber can be manipulated by introducing a side core to near the central core of a fiber, which can potentially provide a new way to control some fiber modal properties by taking the advantage of involving the optical angular momentum in the central core - side core mode interactions. An example of this type of fiber is called Chirally Coupled Core (CCC) fiber [1].
The FDE solver in MODE can be employed to simulate some optical properties of CCC fibers by activating the Helical Fiber solver. The helical fiber solver allows the users to design the helical shape by defining some key parameters, such as the pitch and center of the helix. Some key optical properties such as effective index, loss, as well as some optical behavior of helical fibers, for example, degeneracy breaking can be simulated.
Background
In this example, the FDE solver is used to find the modes of a Chirally Coupled Core (CCC) fiber. The CCC fiber consists of two wave-guiding cores, the central core and the side core, which are usually weakly coupled. The central core is at the center of the fiber serving as the major guide for signal similar to the core in a conventional fiber. The side core forms a helical shape that is characterized by two quantities, the helix radius and period, which can be used to control the modal properties of the central core.
An example of CCC fiber, which consists of a straight central core and a side core with a helical (twisted) shape
An untwisted fiber/waveguide can carry some degenerate modes, whereas the twisted fiber/waveguide can break the degeneracy:
where
- LP01|1 and LP01|2 are the fundamental modes in an untwisted waveguide, which are linear polarized and doubly degenerate with neff = nLP01
- HE11+1 and HE11-1 are the circularly polarized modes in a twisted waveguide when the LP01 degeneracy breaks.
- LP11|1, LP11|2, LP11|3 and LP11|4 are the first set of modes with azimuthal dependence in an untwisted waveguide, which are linear polarized and quadrubly degenerate with neff = nLP11
- HE21+2, HE21|1, HE21|2 and HE21-2 are the circularly polarized modes in a twisted waveguide when the LP11 degeneracy breaks, where HE21|1, HE21|2 are doubly degenerate.
- ᴧ is the pitch of the helix
- λ0 is the wavelength
- Δn is ratio between wavelength and helix period, which is λ0/ᴧ
Simulation setup
The FDE simulation region contains the cladding, central core, and the side core with an offset (rhelix) from the center.
A table that contains the material and structure parameters used in the FDE simulation:
ncentral = 1.45144 |
rcentral = 17.5 um |
λ0 = 1 um |
nside = 1.453 |
rside = 6.5 um |
ᴧ = 6100 um |
nclad = 1.45 |
rhelix = 27 um |
By fault, the FDE solver only finds the straight fiber/waveguide modes. To activate the Helical Waveguide solver, the users need to check the "helical waveguide" option as shown in the screenshot below. To make sure we can find the all the modes we want, users can set the "n" value to 1.4512. This allows the solver to search the modes near this neff, which is like the mid-point of all the helical fiber modes.
Results
The FDE solver in MODE is used to find the straight and helical fiber modes reported in [1]. The shapes and indices of the modes show agreements with the reference.
Straight fiber modes
Helical fiber modes
Related publications
- X. Ma, “Understanding and Controlling Angular Momentum Coupled Optical Waves in Chirally-Coupled-Core (CCC) Fibers,” Ph.D. thesis, 2011.
- X. Ma, et al, “Angular-momentum coupled optical waves in chirally-coupled-core fibers,” Optics Express, vol. 19, no. 27, 2011.