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Ziemkiewicz D, Knez D, Garcia EP, Zielińska-Raczyńska S, Czajkowski G, Salandrino A, Kharintsev SS, Noskov AI, Potma EO, Fishman DA. Two-photon absorption in silicon using the real density matrix approach. J Chem Phys 2024; 161:144117. [PMID: 39392143 DOI: 10.1063/5.0219329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2024] [Accepted: 09/23/2024] [Indexed: 10/12/2024] Open
Abstract
Two-photon absorption in indirect gap semiconductors is a frequently encountered, but not well-understood phenomenon. To address this, the real-density matrix approach is applied to describe two-photon absorption in silicon through the excitonic response to the interacting fields. This approach produces an analytical expression for the dispersion of the two-photon absorption coefficient for indirect-gap materials and can be used to explain trends in reported experimental data for bulk silicon both old and new with minimal fitting.
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Affiliation(s)
- David Ziemkiewicz
- Institute of Mathematics and Physics, Technical University of Bydgoszcz, Al. Prof. S. Kaliskiego 7, 85-789 Bydgoszcz, Poland
| | - David Knez
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Evan P Garcia
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Sylwia Zielińska-Raczyńska
- Institute of Mathematics and Physics, Technical University of Bydgoszcz, Al. Prof. S. Kaliskiego 7, 85-789 Bydgoszcz, Poland
| | - Gerard Czajkowski
- Institute of Mathematics and Physics, Technical University of Bydgoszcz, Al. Prof. S. Kaliskiego 7, 85-789 Bydgoszcz, Poland
| | - Alessandro Salandrino
- Department of Electrical Engineering, University of Kansas, Lawrence, Kansas 66045, USA
| | | | - Aleksei I Noskov
- Institute of Physics, Kazan Federal University, Kazan 420008, Russia
| | - Eric O Potma
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Dmitry A Fishman
- Department of Chemistry, University of California, Irvine, California 92697, USA
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Makhonin M, Delphan A, Song KW, Walker P, Isoniemi T, Claronino P, Orfanakis K, Rajendran SK, Ohadi H, Heckötter J, Assmann M, Bayer M, Tartakovskii A, Skolnick M, Kyriienko O, Krizhanovskii D. Nonlinear Rydberg exciton-polaritons in Cu 2O microcavities. LIGHT, SCIENCE & APPLICATIONS 2024; 13:47. [PMID: 38320987 PMCID: PMC10847413 DOI: 10.1038/s41377-024-01382-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2023] [Revised: 01/10/2024] [Accepted: 01/11/2024] [Indexed: 02/08/2024]
Abstract
Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu2O-filled microresonator. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as ∝ n4.4±1.8 for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly correlated photonic (polaritonic) states in a solid state system.
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Affiliation(s)
- Maxim Makhonin
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK.
| | - Anthonin Delphan
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK
| | - Kok Wee Song
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4PY, UK
| | - Paul Walker
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK
| | - Tommi Isoniemi
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK
| | - Peter Claronino
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK
| | - Konstantinos Orfanakis
- SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK
| | - Sai Kiran Rajendran
- SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK
| | - Hamid Ohadi
- SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK
| | - Julian Heckötter
- Fakultät Physik, TU Dortmund, August-Schmidt-Straße 4, 44227, Dortmund, Germany
| | - Marc Assmann
- Fakultät Physik, TU Dortmund, August-Schmidt-Straße 4, 44227, Dortmund, Germany
| | - Manfred Bayer
- Fakultät Physik, TU Dortmund, August-Schmidt-Straße 4, 44227, Dortmund, Germany
| | | | - Maurice Skolnick
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK
| | - Oleksandr Kyriienko
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4PY, UK
| | - Dmitry Krizhanovskii
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, UK
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Mohajan J, Chao P, Jin W, Molesky S, Rodriguez AW. Fundamental limits on radiative χ (2) second harmonic generation. OPTICS EXPRESS 2023; 31:44212-44223. [PMID: 38178498 DOI: 10.1364/oe.513565] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 11/20/2023] [Indexed: 01/06/2024]
Abstract
Recent advances in fundamental performance limits for power quantities based on Lagrange duality are proving to be a powerful theoretical tool for understanding electromagnetic wave phenomena. To date, however, in any approach seeking to enforce a high degree of physical reality, the linearity of the wave equation plays a critical role. In this manuscript, we generalize the current quadratically constrained quadratic program framework for evaluating linear photonics limits to incorporate nonlinear processes under the undepleted pump approximation. Via the exemplary objective of enhancing second harmonic generation in a (free-form) wavelength-scale structure, we illustrate a model constraint scheme that can be used in conjunction with standard convex relaxations to bound performance in the presence of nonlinear dynamics. Representative bounds are found to anticipate features observed in optimized structures discovered via computational inverse design. The formulation can be straightforwardly modified to treat other frequency-conversion processes, including Raman scattering and four-wave mixing.
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