Gap surface plasmon waveguides offer ultracompact transmission and efficient coupling efficiencies

In this example, we analyze the mode structure of a gap surface plasmon waveguide, and determine the propagation loss of that structure at a wavelength of 1,550nm. In conjunction with the optimization and parameter sweep framework of FDTD Solutions, and the built-in overlap calculator in MODE Solutions, we investigate different mechanisms including end-fire coupling with high NA lens and an optical antenna structure to determine the optimum way to couple light into the gap surface plasmon waveguide, and optimize the geometry to maximize input coupling.

Design concept based on: Jing Wen, Sergei Romanov, and Ulf Peschel, "Excitation of plasmonic gap waveguides by nanoantennas," Opt. Express 17, 5925-5932 (2009)

Step 1: Construct the gap surface plasmon waveguide model within MODE Solutions

The MODE Solutions user interface shows all of the simulation objects required to calculate the response of the gap surface plasmon waveguide, including the graded mesh capability that is particularly powerful for describing the rapid field variations present in surface plasmon devices. Objects can be moved and resized with simple mouse movements, and the design can be parameterized via structure groups.

• orange grid shows the calculation locations of the graded mesh in MODE Solutions
• while symmetric or asymmetric boundary conditions can reduce computational effort, we first perform a complete calculation to find the mode of interest

Step 2: Sweep over refractive indices to locate the gap surface plasmon waveguide mode of interest

MODE Solutions allows you to easily find the mode(s) of interest by scanning through a specific refractive index range, or searching near the maximum refractive index at the wavelength of operation.

• 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 effective index, propagation loss expressed in length units as specified by the user, and the TE fraction of the mode
• the user interface allows one to quickly plot the individual electric and magnetic field components, electric and magnetic field intensities, the energy density, and the x, y, z Poynting vectors

Step 3: Calculate how the imaginary part of the gap surface plasmon waveguide propagation constant varies with waveguide width

The built-in scripting language of MODE Solutions allows users to easily automate simulation and analysis. Here, the width of the waveguide metal layers are varied from 50 to 150nm, and the imaginary part of the propagation constant is recorded. In the limit of very wide waveguides, a propagation constant of 1.65 - 0.024i is calculated, in good agreement with the work of Wen et al.

Step 4: Calculate the coupling efficiency of end-fire coupling a high NA source into the gap surface plasmon waveguide

The Overlap Analysis capabilities of MODE Solutions enables the end user to define a reference mode and perform a quick overlap calculation against the currently selected mode. In this case, a Gaussian beam focused through a high numerical aperture of NA=0.8 is scanned across the end of the gap surface plasmon waveguide.

• the figure below shows that a peak coupling efficiency of 1.8% is obtained by centering the focused beam on the center of the gap plasmon waveguide, and that coupling efficiency falls off quickly as the beam is displaced from this ideal location

Step 5: Analyze the efficiency of the optical antenna structure as an alternative in-coupler for the gap surface plasmon waveguide

To analyze the coupling efficiency of the optical antenna structure, a 3D model is constructed in FDTD Solutions. The optical antenna consists of two electrodes with 90 degree stub sections, illuminated with a high 0.8 NA beam focused on the center of the antenna.

• the polarization of the high NA source is oriented perpendicular to the direction of waveguide propagation
• a monitor plane is established at the end of the antenna to measure the power flow through that surface, which normalized to the source power provides the coupling efficiency of the antenna

The optimal antenna geometry is determined using the built in Optimization and Parameter Sweep framework in FDTD Solutions.  Here, we parametrize the antenna length, stub length, metallization width, gap width, and beam position and optimize this 5 parameter system using the particle swarm optimization method built into FDTD Solutions.  The optimization quickly converges on a design that allows for 14% of the incident light to be coupled into the gap surface plasmon waveguide, as determined by overlapping the beam incident on the end face of the gap plasmon waveguide with the mode that waveguide supports, as calculated with MODE Solutions.

Using a combination of FDTD and MODE Solutions, it is easy to compare the coupling efficiency of injecting light into the gap surface plasmon waveguide with end-fire coupling and surface normal coupling via the optical antenna. While coupling efficiencies on the order of 2% are possible with high NA objectives, the antenna allows for much larger coupling efficiencies of 14% (7X higher, and similar to those levels reported in Wen et al.) to be obtained, together with the integration benefits of coupling into the gap surface plasmon waveguide from the surface, demonstrating the promise of utilizing such optical antenna structures to achieve high-density integrated optical components.