Analytical approximation for photonic array modes in two-dimensional photonic crystal lattices

Area of Science:

• Photonics
• Optics
• Materials Science

Background:

• 2D photonic lattices are crucial for advanced optical devices.
• Accurate modeling of array modes (fields and propagation constants) is essential for device design.
• Existing methods can be computationally intensive.

Purpose of the Study:

• To develop a comprehensive and efficient analytical approximation for 2D photonic lattices.
• To provide accurate vectorial descriptions of array modes, including modal fields and propagation constants.
• To enable rapid computation for both low- and high-contrast photonic devices.

Main Methods:

• Utilized a vectorial approach accounting for TE and TM polarizations.
• Employed a standing wave membrane model for evaluating modal field envelopes.
• Combined this model with coupled-mode formalism for 2D infinite photonic lattices.
• Validated results against established computational approaches.

Main Results:

• Achieved close agreement between analytical approximation results and well-established methods.
• Demonstrated applicability to both low- and high-contrast photonic devices.
• Obtained analytical expressions for modal fields and propagation constants for the first time.
• Completed computations in mere seconds.

Conclusions:

• The developed analytical approximation offers a fast and accurate method for analyzing 2D photonic lattices.
• This work provides novel analytical expressions for key optical parameters.
• The approach is versatile, applicable to a wide range of photonic lattice designs.