Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929387101749248 |
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| author | Kim, Seulong Kim, Kihong |
| author_facet | Kim, Seulong Kim, Kihong |
| contents | We theoretically investigate the scaling behavior of the localization length for $s$-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro-Loginov formula of differentiation, we accurately compute the localization length $ξ$ of $s$ waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter $σ^2$ and the disorder correlation length $l_c$. Away from the critical angle, $ξ$ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber $k$, $kξ$ depends on the single parameter $kl_cσ^2$, satisfying a universal equation $kξ\approx 1.3717\left(kl_cσ^2\right)^{-1/3}$ across the entire range of parameter values. Additionally, we find that $ξ$ scales as $λ^{4/3}$ for the entire range of the wavelength $λ$, regardless of the values of $σ^2$ and $l_c$. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media Kim, Seulong Kim, Kihong Optics Disordered Systems and Neural Networks We theoretically investigate the scaling behavior of the localization length for $s$-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro-Loginov formula of differentiation, we accurately compute the localization length $ξ$ of $s$ waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter $σ^2$ and the disorder correlation length $l_c$. Away from the critical angle, $ξ$ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber $k$, $kξ$ depends on the single parameter $kl_cσ^2$, satisfying a universal equation $kξ\approx 1.3717\left(kl_cσ^2\right)^{-1/3}$ across the entire range of parameter values. Additionally, we find that $ξ$ scales as $λ^{4/3}$ for the entire range of the wavelength $λ$, regardless of the values of $σ^2$ and $l_c$. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence. |
| title | Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media |
| topic | Optics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2406.08156 |