Ray propagation in nonuniform random lattices. Part II

Area of Science:

• Optics and Photonics
• Statistical Physics
• Electromagnetism

Background:

• Ray propagation in complex media is crucial for understanding wave phenomena.
• Nonuniform random lattices present challenges due to their intricate structures.
• Electromagnetic wave interaction with occupied sites requires robust analytical models.

Purpose of the Study:

• To analytically evaluate the probability of electromagnetic ray penetration in nonuniform random half-plane lattices.
• To compare the efficacy of the Martingale approach against the Markov approach for ray propagation modeling.
• To present a modified Martingale approach yielding improved results for specific lattice configurations.

Main Methods:

• Analytical evaluation using the theory of Markov chains (Markov approach).
• Analytical evaluation using the theory of Martingale random processes (Martingale approach).
• Numerical validation comparing the two approaches under varying lattice densities.

Main Results:

• The Martingale approach, particularly with modifications, provides a more accurate method for analyzing ray propagation.
• The modified Martingale approach outperforms the Markov approach in dense lattices with slowly varying density profiles.
• Specular reflections on occupied lattice sites are modeled to determine penetration probability.

Conclusions:

• The Martingale approach is a powerful tool for modeling electromagnetic ray propagation in complex random media.
• The developed modifications enhance the predictive power of the Martingale approach for dense, nonuniform lattices.
• This research contributes to a deeper understanding of wave behavior in disordered optical and physical systems.