INTRABAND MECHANISM OF THREE-PHOTON ABSORPTION OF POLARIZED RADIATION IN DIAMOND-LIKE SEMICONDUCTORS
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2023-07-31 |
| Journal | Austrian Journal of Technical and Natural Sciences |
| Authors | Sharifa Bekmuratovna Utamuratova, Rasulov Voxob Rustamovich, Isomiddinova Umida Mamurjonova, Kodirov Nurllo Ubaidullo ogli |
| Institutions | National University of Uzbekistan, Kokand State Pedagogical Institute named after Mukimi |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis research presents a theoretical analysis of the intraband mechanism governing three-photon absorption (3PA) and associated polarization effects in diamond-like narrow-gap semiconductors (specifically InSb and GaAs).
- Core Achievement: Calculation of the polarization and frequency-polarization dependences of the three-photon light absorption coefficient (K(3)) and the linear-circular dichroism (LCD).
- Mechanism Studied: Vertical three-photon optical transitions occurring between the spin-orbit splitting band and the conduction band states.
- Modeling Approach: The multiband Kane approach (requiring 6x6 or 8x8 matrices) was employed, necessary for accurately modeling narrow-gap crystals, unlike the simpler Luttinger-Kohn approximation.
- Key Finding (Polarization): Both K(3) and LCD exhibit multiple extrema in their polarization and frequency-polarization dependences.
- Theoretical Implication: These extrema are attributed to the specificity of the Kane model, where certain off-diagonal matrix elements of the momentum operator are independent of the carrier wave vector (k).
- Practical Relevance: The results provide a foundation for engineering nonlinear optical devices that rely on precise control of absorption using polarized light in the infrared spectrum.
Technical Specifications
Section titled āTechnical SpecificationsāThe study is primarily theoretical, focusing on the application of specific quantum mechanical models to narrow-gap semiconductors.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Materials Analyzed | InSb, GaAs | Semiconductor | Diamond-like crystals of cubic symmetry. |
| Transition Type | Three-Photon (3PA) | N/A | Vertical optical transitions (intraband). |
| Initial/Final States | N/A | Transitions from Spin-Orbit splitting band ( | |
| Required Matrix Size | 6 x 6 or 8 x 8 | N/A | Minimum matrix size required for calculations using the multiband Kane approach. |
| Key Output Coefficient | K(3)(Ļ, Ī±=Ī²) | arb. units | Three-photon light absorption coefficient calculated as a function of frequency (Ļ) and polarization angles (Ī±, Ī²). |
| Polarization Effect | Linear-Circular Dichroism (LCD) | N/A | Defined as the ratio of transition probabilities for linear versus circular polarization. |
| Energy Spectrum Model | Parabolic | N/A | Used for current carriers in all bands, though nonparabolicity is noted away from Brillouin zone edges. |
| Anomalous Behavior | Spectral increase | N/A | Observed when the energy difference in the numerator of matrix elements tends to zero. |
Key Methodologies
Section titled āKey MethodologiesāThe research methodology relies on advanced quantum mechanical modeling tailored for narrow-gap semiconductor physics.
- Band Structure Selection: The multiband Kane approach was selected over the Luttinger-Kohn approximation to accurately describe the band structure of narrow-gap crystals, necessitating the use of large (6x6 or 8x8) matrix calculations.
- Transition Definition: The study focused specifically on three-photon optical transitions of the type |SO, Ā±1/2> ā |c, Ā±1/2>, originating from the spin-orbit splitting subband into the conduction band.
- Quantum Calculation: The golden rule of quantum mechanics [12] was applied to calculate the probability of these three-photon transitions.
- Polarization Integration: Polarization dependence was introduced by defining the polarization vector projections (eāx, eāy, eāz) relative to the carrier wave vector (k), using angles Ī± (for linear polarization) and Ī² (for circular polarization).
- Coefficient Calculation: The multiphoton absorption coefficient K(3) was calculated, incorporating two main terms: the sum of partial absorption coefficients and interference terms arising from the matrix elements of the 10 different possible optical transitions.
- Parameterization: Quantitative calculations utilized established numerical values for band parameters sourced from literature [13] (Vurgaftman et al.).
- Result Analysis: The frequency-polarization dependences were plotted (Figures 1 and 2) to identify extrema and confirm that the main contribution to absorption comes from transitions where initial virtual states lie in the conduction band.
Commercial Applications
Section titled āCommercial ApplicationsāThe theoretical understanding of controlled multiphoton absorption and dichroism in narrow-gap semiconductors is critical for developing advanced optical components, particularly those operating in the infrared spectrum.
- Nonlinear Optical Switching: Utilizing the strong polarization dependence of K(3) to design all-optical switches and modulators where the transmission state is controlled by the polarization angle of the incident light.
- Infrared (IR) Photonics: Applying the results to optimize components based on narrow-gap materials (like InSb) used in mid- and far-IR laser systems, detectors, and thermal imaging.
- Optical Limiting: Developing materials with tailored 3PA characteristics for high-intensity laser protection, where the absorption coefficient increases rapidly with intensity, limiting output power.
- Polarization Sensing and Imaging: Engineering advanced sensors that exploit the linear-circular dichroism (LCD) effect to analyze the polarization state of incoming radiation, useful in remote sensing and specialized microscopy.
- Quantum Information Processing: The precise control over spin states (Ā±1/2) during optical transitions, as modeled, is foundational for potential spin-based quantum computing or sensing applications in semiconductors.
View Original Abstract
The polarization and frequency-polarization dependences of the linear-circular dichroism and light absorption coefficients in semiconductors of cubic symmetry, caused by vertical three-photon optical transitions between the states of the spin-orbit splitting and conduction bands, are calculated.