Analytical approximation for photonic array modes in 1D photonic crystal superlattices

Area of Science:

• Photonics
• Condensed Matter Physics
• Wave Phenomena

Background:

• Photonic crystal superlattices feature multiple, hierarchical periodicities.
• Understanding array modes is crucial for designing advanced photonic devices.
• Existing methods for analyzing these structures can be computationally intensive.

Purpose of the Study:

• To develop a comprehensive analytical approximation for array modes in 1D photonic crystal superlattices.
• To provide accurate, vectoral calculations for modal fields and propagation constants.
• To enable rapid computation of these parameters for both low- and high-contrast devices.

Main Methods:

• Utilized a standing wave model to analytically evaluate mode envelopes.
• Combined the standing wave model with coupled-mode formalism for infinite superlattices.
• Employed a vectorial approach considering both TE and TM polarizations.

Main Results:

• Achieved a computationally efficient analytical approximation (fraction of a second).
• Obtained results highly consistent with established, more time-consuming approaches.
• Derived the first-ever analytical expressions for modal fields and propagation constants in these structures.

Conclusions:

• The developed analytical approximation offers a fast and accurate method for analyzing 1D photonic crystal superlattices.
• This work provides novel analytical expressions, advancing the design and understanding of complex photonic devices.
• The approach is versatile, applicable to various photonic device contrasts and polarizations.