Designing ARROW waveguides for low-loss photonic propagation in integrated optics and photonics with MODE Solutions

In this example, we analyze the polarization dependence of an ARROW (anti-resonant reflecting optical waveguide) structure in terms of propagation loss and far-field modal profiles, and examine the frequency dependence of the dispersion and the propagation loss as a function of wavelength from 600 to 650 nm. Finally, using the built-in scripting environment, we calculate the sensitivity to lateral shifts of the fiber of coupling to the low-loss TM mode using a Gaussian beam focused through a NA=0.1 objective.

Step 1: Construct the ARROW waveguide with easy-to-use CAD editor

The layout editor shows all of the simulation objects. Objects can be moved and resized with simple mouse movements.

• orange box shows the extent of the computation volume and the boundary conditions
• while symmetric or asymmetric boundary conditions can be used to selectively locate a mode with a specific polarization, we wish to compare the propagation loss for the different polarization states and so we choose to simulate the full structure

Step 2: Sweep over refractive indices to locate the low-loss TM and TE modes

MODE Solutions allows you to easily find the mode(s) of interest by scanning through a specific refractive index range.

• to find the modes of interest, scan over refractive indices between the low-index core and the high-index cladding layers
• each mode found is expressed in terms of field profile, propagation loss, and effective index
• note that the TM-like mode has a propagation loss of 2.0 dB/cm while the TE-like mode has a value of 921 dB/cm

Step 3: Determine the far-field radiation profile of the low-loss TM ARROW mode

Built-in far-field projection routines enable you to project mode profiles onto a flat screen or onto a hemispherical surface, and integrate the profile over a specified angular cone or plane.

• as expected, the mode diffracts much more strongly in the vertical direction owing to the tighter vertical confinement of mode in the vertical direction

Step 4: Calculate the dispersion and the propagation loss of low-loss TM ARROW mode as a function of wavelength

Use built-in analysis routines to render complicated analysis simple. Perform a frequency sweep and choose from a pull-down whether you wish to analyze the propagation loss, effective index, group index, group delay, group velocity or dispersion as a function of wavelength or frequency.

• a sweep versus frequency shows that there is a resonance in the total dispersion around 620 nm

• a wavelength sweep from 600 to 650 nm shows that the propagation loss increases dramatically away from the low-loss design wavelength of approximately 630nm as the wavelength is increased

Step 5: Automate simulation and analysis - determine the sensitivity of coupling a focused Gaussian beam to the TM-like ARROW mode

Extensive overlap analysis routines allow the end user to calculate the overlap integral and coupling efficiency between the mode of interest and a Gaussian beam, another waveguide mode, or data imported from another application.

• using MODE Solutions, we first calculate the near-field mode profile of a Gaussian beam focused through a 0.1 NA objective and calculate the coupling efficiency of this mode with the TM-like ARROW mode
• the plot to the left shows that a peak coupling efficiency of 32% is achieved when the two modes are perfectly aligned and this coupling efficiency falls off to about half that value for a 2 micron misalignment in the horizontal direction