arXiv subjects

Subrata Manna

Publications and source records attributed to Subrata Manna.

6 recordsLinked to original sources

arXiv2026

Observation of Higher-Order Hybrid Bright-Dark Soliton Complexes in an NPR Mode-Locked Fiber Laser

Hybrid bright-dark soliton complexes offer profound insights into multi-component nonlinear wave dynamics, yet their systematic generation via artificial saturable absorbers remains unexplored. Here, we experimentally demonstrate a comprehensive hierarchy of higher-order hybrid soliton architectures within a single nonlinear polarization rotation (NPR)-based erbium-doped fiber laser. Continuous tuning of intracavity polarization states and pump power enables reproducible access to soliton structures, with stable mode-locking confirmed at 8 MHz and a signal-to-noise ratio exceeding 72 dB. Cross-phase modulation (XPM)-mediated inter-component coupling and birefringence-induced polarization evolution collectively govern the observed soliton multiplicity, with NPR's inherent tunability proving decisive in accessing higher-order hybrid soliton regimes unexplored in prior studies. These findings expand the fundamental taxonomy of dissipative solitons and establish NPR-based fiber lasers as a reconfigurable platform for complex nonlinear wave engineering.

physics.optics↗

arXiv2026

Functional codes arising from rank $n$ Hermitian varieties and hypersurfaces in low dimensions

We study the functional code $C_d(\mathcal{X})$, introduced by G. Lachaud in 1996, in the case where $\mathcal{X}$ is a rank $n$ degenerate Hermitian variety $P\mathcal{U}_{n-1}$ in $\mathbb{P}^n(\mathbb{F}_{q^2})$ and $d\leq q$. We establish an upper bound for the maximum number of $\mathbb{F}_{q^2}$-rational points in the intersection of $P\mathcal{U}_{n-1}$ with an $\mathbb{F}_{q^2}$-hypersurface of degree at most $q$ in $\mathbb{P}^n$. Using this bound, we determine the parameters of the codes $C_d(P\mathcal{U}_{n-1})$ in the cases $n=2,3,4$. We also characterize the hypersurfaces that correspond to the minimum distance of these codes in the cases $n=2,3,4$.

math.AG↗

arXiv2026

Engineering Multi-wavelength Emission in All-Fiber Laser Mode-Locked Through Nonlinear Polarization Rotation

The increasing demand for multi-wavelength optical sources to support dense wavelength-division multiplexing (DWDM) channels has driven the development of compact and reconfigurable multi-wavelength fiber lasers. Here, we demonstrate a continuously tunable and deterministically switchable multi-wavelength erbium-doped fiber laser based on nonlinear polarization rotation (NPR) in a compact all-fiber ring cavity. By controlling the intracavity birefringence, NPR acts as a reconfigurable comb filter that enables flexible wavelength selection without modifying the cavity architecture. The laser supports stable spectral states ranging from single- to seven-wavelength mode-locking, enabling reversible wavelength switching and activation/suppression of individual channels. The selectable spectral states can be mapped to binary bit operations, where each wavelength channel represents a controllable logical state. The behavior arises from the interplay between NPR-induced birefringent comb filtering and nonlinear phase modulation, providing a simple and compact platform for reconfigurable multi-channel ultrafast sources for DWDM and photonic signal processing.

physics.optics↗

arXiv2025

Maximum number of points of intersection of a non-degenerate Hermitian variety and a cubic hypersurface

Edoukou, Ling and Xing in 2010, conjectured that in \mathbb{P}^n(\mathbb{F}_{q^2}), n \geq 3, the maximum number of common points of a non-degenerate Hermitian variety \mathcal{U}_n and a hypersurface of degree d is achieved only when the hypersurface is a union of d distinct hyperplanes meeting in a common linear space \Pi_{n-2} of codimension 2 such that \Pi_{n-2} \cap \mathcal{U}_n is a non-degenerate Hermitian variety. Furthermore, these d hyperplanes are tangent to \mathcal{U}_n if n is odd and non-tangent if n is even. In this paper, we show that the conjecture is true for d = 3 and q \geq 7.

math.AG↗

arXiv2024

Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold

It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in $\mathbb{P}^4 (\mathbb{F}_{q^2})$ has at most $d(q^5+q^2) + q^3 + 1$ points in common with a threefold of degree $d$ defined over $\mathbb{F}_{q^2}$. He proved the conjecture for $d=2$. In this paper, we show that the conjecture is true for $d = 3$ and $q \ge 7$.

math.AG↗

arXiv2021

A generalization of Gerzon's bound on spherical s-distance sets

We Use the method of linearly independent polynomials to derive an upper bound for the cardinality of a spherical s-distance set F where the sum of distinct inner products of any two elements from F is zero. Our result generalizes the well-known Gerzon's bound for the cardinality of an equiangular spherical set to a significantly broader class of spherical s-distance sets.

math.CO↗