arXiv subjects

Karol Karpiński

Publications and source records attributed to Karol Karpiński.

10 recordsLinked to original sources

arXiv2025

Superlens with copper and copper oxide

We investigate the imaging properties of copper-based superlens surrounded by copper oxide (Cu$_2$O). A subwavelength image resolution of the order $λ/9$ is demonstrated theoretically and verified in numerical simulations. It is shown that the existence of excitons in Cu$_2$O influence the static and dynamical optical properties of the lens. In particular, an improvement of image quality caused by absorption in the spectral region of excitonic resonances is investigated. The plasmon-exciton interaction in the system may pave the way to a tunable, highly nonlinear superlens designs.

cond-mat.mes-hall↗

arXiv2022

Nonlinear optical properties and Kerr nonlinearity of Rydberg excitons in Cu$_2$O quantum wells

The quantum confiment of Rydberg excitons (REs) in quantum structures opens the way towards considering nonlinear interactions in such systems. We present a theoretical calculation of optical functions in the case of a nonlinear coupling between REs in a quantum well with an electromagnetic wave. Using the Real Density Matrix Approach (RDMA), the analytical expressions for a linear and nonlinear absorption are derived and numerical calculations for Cu$_2$0 quantum wells are performed. The results indicate the conditions in which quantum well confinement states can be observed in linear and nonlinear optical spectra. The Kerr nonlinearity and self-phase modulation in such a system are studied. The effect of Rydberg blockade and the associated optical bleaching are also discussed and confronted with available experimental data.

cond-mat.mes-hall↗

arXiv2022

Self-Kerr effect across the yellow $\mathrm{Cu_2O}$ Rydberg series

We investigate the nonlinear refraction induced by Rydberg excitons in $\mathrm{Cu_2O}$. Using a high-precision interferometry imaging technique that spatially resolves the nonlinear phase shift, we observe significant shifts at extremely low laser intensity near each exciton resonance. From this, we derive the nonlinear index $\mathrm{n_2}$, present the $\mathrm{n_2}$ spectrum for $n\geq 5$ and report large $\mathrm{n_2}$ values of order $10^{-3}$ mm$^2$/mW. Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that the saturation intensity $\mathrm{I_{sat}}$ decreases as $n^{-7}$. We explain this with the Rydberg blockade mechanism, whereby giant Rydberg interactions limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our setup.

quant-ph↗

arXiv2021

Quantum confined Rydberg excitons in Cu$_2$O nanoparticles

The quantum confinement of Rydberg excitons is an important step towards exploiting their large nonlinearities for quantum applications. We observe Rydberg excitons in natural nanoparticles of Cu$_2$O. We resolve up to the principal quantum number $n=12$ in a bulk Cu$_2$O crystal and up to $n=6$ in nanoparticles extracted from the same crystal. The exciton transitions in nanoparticles are broadened and their oscillator strengths decrease as $\propto n^{-4}$ compared to those in the bulk (decreasing as $\propto n^{-3}$). We explain our results by including the effect of quantum confinement of exciton states in the nanoparticles. Our results provide an understanding of the physics of Cu$_2$O Rydberg excitons in confined dimensions.

cond-mat.mes-hall↗

arXiv2021

Electro-optical properties of excitons in Cu$_2$O quantum wells: I discrete states

We present theoretical results of the calculations of optical functions for Cu$_2$O quantum well (QW) with Rydberg excitons in an external homogeneous electric field of an arbitrary field strength. Two configurations of an external electric field perpendicular and parallel to the QW planes are considered in the energetic region for discrete excitonic states and continuum states. With the help of the real density matrix approach, which enables the derivation of the analytical expressions for the QW electro-optical functions, absorption spectra are calculated for the case of the excitation energy below the gap energy.

cond-mat.mes-hall↗

arXiv2021

Electro-optical properties of excitons in Cu$_2$O quantum wells: II continuum states

We present theoretically calculated optical functions for Cu$_2$O quantum well (QW) with Rydberg excitons in an external, homogeneous electric field parallel to the QW planes for the energy region above the gap, suitable to observe the Franz-Keldysh (FK) oscillations. We quantitatively describe the amplitudes and periodicity of FK modulations and the influence of both Rydberg excitons and confinement effect on this phenomenon.

cond-mat.mes-hall↗

arXiv2021

Fractional Derivative Modification of a Drude Model

A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and numerical results. The absorption coefficient and wave vector -- key parameters describing the propagation of waves in such a medium -- are shown to follow a power law in the frequency domain, which is a common phenomenon in many real life applications. The introduction of two separate parameters provides a more flexible model than some other approaches found in literature and is well suited for numerical implementation.

physics.comp-ph↗

arXiv2020

Rydberg Magnetoexcitons in Cu$_2$O Quantum Wells

We present theoretical approach that allows for calculation of optical functions for Cu$_2$O Quantum Well (QW) with Rydberg excitons in an external magnetic field of an arbitrary field strength. Both Faraday and Voigt configurations are considered, in the energetic region of p-excitons. We use the real density matrix approach and an effective e-h potential, which enable to derive analytical expressions for the QW magneto-optical functions. For both configurations, all three field regimes: weak, intermediate, and high field, are considered and treated separately. With the help of the developed approximeted method we are able to estimate the limits between the field regimes. The obtained theoretical magneto-absorption spectra show a good agreement with available experimental data.

cond-mat.mes-hall↗

arXiv2020

Excitons in Cu2O -- from Quantum Wells to Bulk Crystals and Additional Boundary Conditions for Rydberg Exciton-Polaritons

We propose a scheme for calculation of optical functions of a semiconductor with Rydberg excitons, for a wide interval of dimensions. We start with 2-dimensional structure, then going to thin films and ending on 3-dimensional bulk crystals. The calculations including the polaritons are performed, the case of large number of polariton branches is discussed and obtained theoretical absorption spectra show good agreement with experimental data.

cond-mat.mes-hall↗

arXiv2019

Nonlinear Optical Properties and Self-Kerr Effect of Rydberg Excitons in Cu$_2$O

We show how to compute the nonlinear optical functions (absorption, reflection, and transmission) for a medium with Rydberg excitons, including the effect of the coherence between the electron-hole pair and the electromagnetic field. Using the Real Density Matrix Approach the analytical expressions for nonlinear optical functions are obtained and numerical calculations for Cu$_2$0 crystal are performed. We report a good agreement with recently published experimental data. Propagation of the electromagnetic waves in Rydberg excitons media with nonliner effect is also discussed and the possibility of obtainig self-phase modulation due to Kerr nonlinearity is investigated.

cond-mat.mes-hall↗