By: Behzad Khanaliloo, Application Engineer at Lumerical Solutions, Inc.
Different techniques can be employed to couple light from an external laser to on-chip devices. Bragg gratings, edge couplers, and evanescent waveguide couplers are the most common techniques to achieve this goal.
In a study published in Physical Review X, authors demonstrated an evanescent waveguide coupling between a fiber taper and a diamond waveguide. Fiber taper is made by heating a commercial fiber to its melting point while simultaneously stretching it. The fiber taper, with a diameter of 1.1 um, is then mounted on motorized stages to provide a three dimensional access to its position. Diamond waveguides with cross section of (w, t) = (460, 250) nm are made on synthetic single crystal diamond (optical index of ~2.4).
Coupling strength in the coupled waveguide system is studied as a function of wavelength and gap distance between diamond waveguide and fiber taper. This can be analyzed by monitoring transmission in fiber taper (see Eq.(1) of the paper).
Simulation methodology and results:
In the first part of simulation, we will study the effective index of coupled system as a function of wavelength for a fixed fiber taper position (300nm above the diamond waveguide). Figure1c.lsf runs three different simulations: First, effective index of fiber taper and diamond waveguide are studied as an individual systems. Then, super modes, symmetric and anti symmetric modes, of the coupled system are calculated for a gap distance of 300nm:
While optical index of diamond (~2.4) is different than glass (~1.4), evanescent modes in these two waveguides possess same effective index at λ~1.55um and thus are phase matched. This means that TE polarized mode of the fiber can be coupled with 100% efficiency to diamond waveguide modes.
The symmetric and antisymmetric modes of coupled waveguides system is shown below:
For the second part of simulations, we will study the propagation constant (β = 2π*neff / λ) of the symmetric and antisymmetric modes of the coupled waveguide system as a function of gap distance. Figure7.lsf modifies the fiber position and outputs β for two different wavelength:
These values are then used to calculate the total optical force between the diamond waveguide and fiber taper which is out of the scope of this topic.
Advanced notes and tips:
A convergence test is required if a user wants to obtain exact results for the effective index of the system. You can increase the FDE simulation region to make sure electric fields has decayed enough before reaching the FDE boundaries. A finer mesh also can be employed to obtain more accurate result. The goal of convergence test is to make sure that results are not changing with simulation parameters such as mesh size, boundary condition, or simulation span.