Modeling and experimental observation of an on-chip two-dimensional far-field interference pattern

Area of Science:

• Photonics and Wave Propagation
• Optical Engineering
• Nanophotonics

Background:

• Far-field radiation analysis is crucial for optical device design.
• Standard far-field approximations are typically for three-dimensional (3D) systems.
• Two-dimensional (2D) waveguide systems present unique challenges for far-field analysis.

Purpose of the Study:

• To model and experimentally observe far-field radiation from interfering beams in 2D slab waveguides.
• To establish the conditions under which standard far-field approximations are valid for 2D systems.
• To demonstrate the generation of a 2D far-field pattern from an array of on-chip radiators.

Main Methods:

• Utilized a transmission-line analogy to model 2D beam propagation.
• Derived theoretical conditions for applying far-field approximations in 2D.
• Experimentally investigated far-field patterns from a 1×3 multimode interference (MMI) coupler on a silicon nanomembrane.
• Observed far-field radiation at the edge of a slab silicon waveguide connected to the MMI coupler.

Main Results:

• Successfully modeled and experimentally observed the 2D far-field radiation pattern.
• Established criteria for the validity of far-field approximations in 2D waveguide scenarios.
• Demonstrated that an MMI coupler acts as an array of on-chip radiators producing a 2D far-field pattern.

Conclusions:

• The study provides a framework for understanding and predicting far-field radiation in 2D photonic integrated circuits.
• Experimental validation confirms the theoretical models for 2D far-field approximations.
• The findings are applicable to the design and characterization of novel on-chip optical systems and antenna arrays.