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Project titleGeneration of optical harmonics in nonlinear subwavelength resonators

Research area 02 - PHYSICS AND SPACE SCIENCES, 02-204 - Nano- and microstructures

Keywordshigh-Q resonators, subwavelength optics, nanoparticles, generation of optical harmonics

Annotation
The proposed project is devoted to important unresolved problem of enhancement of nonlinear optical generation efficiency in systems of subwavelength size. This problem is of high fundamental importance, since the main mechanism of nonlinear generation of signals which is based on phase matching is not applicable at the scales smaller than the wavelength. The solution of this problem is of extremal significance and has great practical importance because of a wide range of potential applications of subwavelength nonlinear optical generators, especially for information technologies, namely, optical elements for optical communication lines and optical data processing and storage systems. Nowadays, one of the main platforms for nonlinear generation of signals at subwavelength scale are resonant metallic (plasmonic) nanostructures. These resonators allow to achieve strong spatial localization of light, however their quality factor is limited by significant losses because of free carrier absorption. Moreover, plasmonic structures do not exhibit second-order bulk nonlinearity because their crystal structure contains the inversion center, which substantially limits the range of their possible applications. At the moment, the record of measured conversion efficiency in a single subwavelength plasmon resonator is only about 10^(-8) – 10^(-9). At the same time, the range of dielectric and semiconductor materials is much wider and their material losses are several orders of magnitude lower than for metallic resonators. Quality factor of dielectric resonators rapidly decreases with decreasing of resonator size, so at wavelength scales it becomes of order 20-30. Nevertheless, at the moment reported experimental data on the effectiveness of nonlinear conversion is of order of 10^(-4) – 10^(-5). This value substantially exceeds the efficiency of plasmon analogues, but such values are still not enough for many practical applications. Thus, the problem of effective nonlinear generation for subwavelength resonators requires absolutely new fundamental approaches. The goal of proposed project is theoretical analysis and development of a new class of dielectric subwavelength resonators with high efficiency of nonlinear generation which will be achieved through: (i) hybrid metal-dielectric structures which provide strong localization of light and field enhancement via plasmonic components and nonlinear generation via dielectric components ; (ii) optical nanoantennas providing efficient pumping and emission of radiation because of fulfillment of frequency matching conditions; (iii) new principles of subwavelength light localization, based on destructive interference of several modes of the system in far field. Last mechanism of localization is known in the field of quantum dynamics of open systems as the Friedrich-Wintgen mechanism of destructive interference. For enhancement of nonlinear generation efficiency in optical structures this mechanism will be studied for the first time. Nonlinear dynamics of optical resonators is very complex and remains difficult for detailed theoretical analysis. Rigorous analysis of such systems requires combination of classical electrodynamics and nonlinear dynamics methods, as well as antenna theory and group theory. The problem is even more complicated because the systems under investigation are open and should be described within the framework of non-Hermitian electrodynamics. One of project goals is development of a generalized theory of nonlinear generation of optical signals for subwavelength resonators that goes beyond the range of applicability of existing approximations. The proposed project will include full research cycle from the development of theoretical models, computer modeling and design of photonic microresonators to the fabrication of experimental samples, their characterization and analysis of possible applications and commercialization of the results. All the theoretical and experimental goals of the proposed project are new. Successful realization of project goals will pave the way towards creation of new devices for all-optical communication, signal processing and quantum computing, as well as will form a basis for new scientific directions in the field of nonlinear photonics. Project results will lead to a substantial decrease of the threshold pump power required to observe nonlinear effects, which will significantly expand the range of possible applications of such devices and lead to a notable energy consumption reduction and decrease of final product price. The scientific group chosen for this project include theoreticians, experts in numerical simulation, engineers and experimentalists, capable to carry out all stages of the project: from the extension of scientific hypothesis and theoretical analysis to the practical realization of the prototype and its comprehensive experimental study. Despite the fact that all members of the team are under 32 years, they have extensive experience in dealing with similar problems. Scientific group have all the necessary equipment required for computer modeling, prototyping and experimental study of their optical properties. The totality of scientific group experience in the implementation of large international research projects, group’s professionalism, presence of the comprehensive project plan, necessary equipment, rich scientific groundwork and international colleagues, ready to collaborate on project goals, allows us to state that formulated tasks will be fully resolved, the results will be published in the top-rated scientific journals and will be in high demand by international scientific community and high-tech industry representatives.

Expected results
The main result of this project will be the experimental realisation of high-performance subwavelength dielectric and hybrid (metal-dielectric) systems for nonlinear second and third harmonics generation in nanostructures. Solutions realized in this project will be based on latest achievements in the field of nonlinear photonics, high-quality resonators, plasmonic and dielectric nanoantennas. In particular, next crucial results will be obtained: 1. The theory of nonlinear generation in subwavelength resonators considering both surface and volume effects, symmetry properties of nonlinear susceptibility tensor and specificity of open systems in terms of non-Hermitian electrodynamics formalism will be built. The theory of resonator modes interaction in terms of Feshbach’s projection technique, that is being used in quantum mechanics and nuclear physics, but has not been generalized to electrodynamic systems considering polarizing structure of wave functions until today, will be developed. 2. Effective nonlinear radiation sources on the basis of high-quality dielectric subwavelength resonators whose eigenmodes form due to the destructive interference of several modes of the system will be developed. The study of this mechanism of high-quality states formation in optical systems has begun quite recently. 3. Nonlinear subwavelength dielectric nanoantennas providing a resonant field enhancement both on the fundamental frequency and on the nonlinear signal frequency will be developed. 4. Effective subwavelength nonlinear hybrid metal-dielectric systems in which the high localization level is obtained due to the plasmonic effects and the effective nonlinear generation occurs in dielectric elements. Planned results are both of fundamental and concrete practical value. Preliminary estimates show that the solutions we propose will allow to enhance the nonlinear generation efficiency in subwavelength resonators more than by an order of magnitude compared to the existing analogs. Therefore, the planned results keep ahead of the current world level. Achievement of such efficiency level will loosen the pump level requirements significantly, widen the range of possible applications of nonlinear devices notably and will lead to a serious reduction in final production price and energy consumption. The raise of the nonlinear optical generation efficiency level will allow to perform a qualitative jump and come close to the development of the new devices for the fully optical communication, signal processing and quantum calculations, and also create new scientific directions in the nonlinear photonics area. The results of the proposed project possess a high commercialization potential and can be used in the work of such Russian Federation enterprises as CJSC ZAO “Svetlana Optoelectronics” and SP LOTIS TII. The most fundamental results obtained in progress of the project implementation will be directly used in master’s education program of the Department of Nanophotonics and Metamaterials at the ITMO University.

Annotation of the results obtained in 2020
All work was completed in full, and all planned results were achieved. The results obtained for the third year of the project were published in 10 papers (4 articles from the first quartile [Q1] and 6 conference proceedings). Also, two articles have been prepared, which are now under review in journals from the first quartile of Q1. Article preprints are uploaded at http://arxiv.org/. The results of the second stage of the project were presented in the form of 10 reports at prestigious Russian and international conferences (1 plenary, 2 invited reports, 7 oral reports). The results obtained within this stage were also included in one master's and one bachelor's final qualifying work. The project manager (A. Bogdanov) and the main contractor (K. Koshelev) organized a special section on the project topic at the V international conference on nanophotonics and metamaterials MetaNano 2020 (Tbilisi, Georgia [online]): https://metanano.itmo.ru / 2020 / Among the most important results, the following are worth highlighting: 1. An analytical model has been developed for the excitation of a photonic resonance structure with losses by a pulse of finite length in the framework of the model of coupled modes in the time domain. Calculated dependences of the efficiency of generation of the second and third optical harmonics on the value of parasitic losses in the case of geometric disorder and scattering from the ends of the sample. 2. The dependences of the efficiency of generation of the second and third optical harmonics on the duration and shape of the excitation pulse in structures with parasitic losses and absorption losses are obtained numerically. 3. The dependences of the efficiency of generation of high optical harmonics (seventh and higher) in the regime of excitation of bound states in the continum are found analytically and numerically. The dependence of the optimal pulse duration for the maximum efficiency of generation of high optical harmonics is calculated. 4. Samples of silicon metasurfaces with an asymmetric unit cell, which support quasi-bound states in the continuum, have been prepared. The generation of odd optical harmonics from the 3rd to 11th orders is demonstrated and their polarization dependence is investigated. 5. An algorithm was developed for the classification of eigenmodes according to irreducible representations in resonators of the simplest form, depending on their symmetry group. For each type of eigenmode, its multipole composition was found and the effect of the substrate on the change in the multipole composition was analyzed. Tables are constructed with the classification of eigenmodes and their multipole composition for the symmetry groups of a cylinder, a cone and a triangular prism, a cube, as well as for chiral resonators. 6. A numerical model has been built that allows one to find the scattering spectra for objects of cylindrical symmetry, as well as the spectra of the second harmonic generation. The three-dimensional problem is reduced to two-dimensional by separating the azimuthal variable. The constructed model makes it possible to determine the second harmonic generation spectra from cylindrically symmetric resonators with an arbitrary crystal lattice and the corresponding second-order nonlinear susceptibility tensor. 7. Theoretically and experimentally, we studied whisker nanocrystals (NWCs) with a Bragg-type resonator based on two semiconductor materials GaP and Si. Due to the deposition of Bragg reflectors using a focused ion beam, the Q-factor of resonators based on NWCs varied from 220 to 290 depending on the type of substrate: plasmonic or dielectric. The spectra of generation of the second harmonic were also obtained from the fabricated resonant structures, and the radiation pattern for the second harmonic was measured.

Publications

1. Grégoire Saerens, Iek Tang, Mihail I. Petrov, Kristina Frizyuk, Claude Renaut,Flavia Timpu, Marc Reig Escalé, Igor Shtrom, Alexey Bouravleuv, George Cirlin,Rachel Grange, and Maria Timofeeva Engineering of the Second‐Harmonic Emission Directionality with III–V Semiconductor Rod Nanoantennas LASER & PHOTONICS REVIEWS, Том: 14 Выпуск: 9 Номер статьи: 2000028 (year - 2020) https://doi.org/10.1002/lpor.202000028

2. Kirill Koshelev and Yuri Kivshar Dielectric Resonant Metaphotonics ACS Photonics, - (year - 2020) https://doi.org/10.1021/acsphotonics.0c01315

3. Mingsong Wang, Alex Krasnok, Sergey Lepeshov, Guangwei Hu, Taizhi Jiang, Jie Fang, Brian A. Korgel, Andrea Alù, Yuebing Zheng Suppressing material loss in the visible and near-infrared range for functional nanophotonics using bandgap engineering Nature Communication, Nat Commun 11, 5055 (2020) (year - 2020) https://doi.org/10.1038/s41467-020-18793-y

4. Sergey Lepeshov and Alex Krasnok Virtual optical pulling force OPTICA, Том: 7 Выпуск: 8 Стр.: 1024-1030 (year - 2020) https://doi.org/10.1364/OPTICA.391569

5. George Zograf, Kirill Koshelev, Viacheslav Korolev, Anastasia Zalogina, Duk-Yong Choi, Richard Hollinger, Barry Luther-Davies, Michael Zürch, Daniil Kartashov, Christian Spielmann, Sergey Makarov, Sergey Kruk, Yuri Kivshar Efficient High-order Optical Harmonics Generation from Resonant Semiconductor Metasurfaces Supporting Bound States in the Continuum Frontiers in Optics / Laser Science, Frontiers in Optics / Laser Science, paper FTh5D.4 (year - 2020) https://doi.org/10.1364/FIO.2020.FTh5D.4

6. Gladyshev S., Frizyuk, K, Bogdanov, A. Analysis of multipolar contributions to eigenmodes in resonators of various shapes Proceedings of SPIE - The International Society for Optical Engineering, Volume 11345, 2020, Номер статьи 113451L (year - 2020) https://doi.org/10.1117/12.2555709

7. Kirill Koshelev, George Zograf, Viacheslav Korolev, Anastasia Zalogina, Duk-Yong Choi, Richard Hollinger, Barry Luther-Davies, Michael Zürch, Daniil Kartashov, Christian Spielmann, Sergey Makarov, Sergey Kruk, and Yuri Kivshar Bound States in the Continuum for Enhanced Generation of High Optical Harmonics OSA Advanced Photonics Congress, - (year - 2020) https://doi.org/10.1364/NP.2020.NpM3E.1

8. Kirill Koshelev, George Zograf, Viacheslav Korolev, Anastasia Zalogina, Duk-Yong Choi, Richard Hollinger, Barry Luther-Davies, Michael Zurch, Daniil Kartashov, Christian Spielmann, Sergey Makarov, Sergey Kruk, Yuri Kivshar Silicon metasurfaces with bound states in the continuum for high-harmonic generation Proceedings of SPIE, Proc. of SPIE Vol. 11770, 117700G (year - 2021) https://doi.org/10.1117/12.2592977

9. Kirill Koshelev, Sergey Kruk, Mikhail Odit, Elizaveta Melik-Gaykazyan, Jae-Hyuck Choi, Sergey Gladyshev, Konstantin Ladutenko, Hong-Gyu Park, Andrey Bogdanov, Yuri Kivshar Observation of Supercavity Modes in Individual Subwavelength Dielectric Resonators Conference on Lasers and Electro-Optics, OSA Technical Digest, Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2020), paper FM2D.1 (year - 2020) https://doi.org/10.1364/CLEO_QELS.2020.FM2D.1

10. Sergey Krasikov, Alexander Chukhrov, Alexey Yulin, Andrey Bogdanov Excitation of a bound state in the continuum in nonlinear systems from the far field Proceedings of SPIE, Proc. of SPIE Vol. 11770 117701Q (year - 2021) https://doi.org/10.1117/12.2592977

11. - Человек года 2020 Фонтанка.Ру, https://award.fontanka.ru/person_of_the_year (year - )

12. - Ученый ИТМО стал номинантом категории «Человек года» ежегодной премии «Фонтанки.ру» ITMO.NEWS, https://news.itmo.ru/ru/university_live/achievements/news/9896/ (year - )

Annotation of the results obtained in 2018
A method for describing light scattering for subwavelength structures was developed, based on the resonant state expansion method. An expression for calculating the light scattering cross section depending on the polarization of the incident light and its orientation was derived. A program code implementing the developed theory was realized by means of high-level programming language Python. By means of the Mie theory, the efficiency of the second harmonic generation from dielectric nanoparticles with a nonzero intrinsic volume tensor of a nonlinear dielectric susceptibility of the second order was calculated. The benefits of dielectric platforms in comparison with plasmonic nanoparticles was shown. The dependence of the radiation pattern on the orientation of the crystal lattice of the nanoparticles was investigated. A theory of nonlinear light generation due to high-Q states of subwavelength resonators realized in the regime of the destructive mode interference was developed. An expression for the Green’s function for subwavelength systems of arbitrary geometry was derived. A universal formula for the generation efficiency of the second optical harmonic in nanoresonators was derived, showing how the generation efficiency depends on the properties of the eigenmodes at the frequencies of the first and second harmonics. A theoretical model of bi-resonant systems describing the generation of the second harmonic was developed, and the optimal parameters for achieving maximum generation efficiency were determined. A method for numerical simulation of the generation of the second and third harmonics from dielectric and hybrid subwavelength resonators based on the COMSOL Multiphysics physical modeling full-wave package was developed. The generation of the second harmonic by a nanoparticle with cylindrical symmetry was calculated, and the dependence of the radiation pattern on symmetry using truncation of the cylinder was investigated. The second harmonic generation was studied numerically with an efficiency up to 1% in a wide class of dielectric metasurfaces consisting of asymmetric meta-atoms that support high-quality states formed due to destructive mode interference. A general method for the development of subwavelength resonators with a given geometry of the radiation pattern, based on the analysis of the eigenmodes at the first and second harmonic frequencies, and the structuring of the pump beam to ensure maximum overlap with the resonator mode were proposed. A design of AlGaAs disk on a glass substrate and of a silicon disk on an SOI substrate with predetermined geometrical sizes, demonstrating the effective generation of the second and third optical harmonics, respectively, was developed, which is based on the excitation of high-quality states, formed due to the destructive interference of several system modes. A set of samples of AlGaAs disks on a glass substrate and silicon disks on a SOI substrate, supporting high-Q states, which are formed due to the destructive interference of several modes of the system, was fabricated using the electron beam lithography based on the proposed design. Optical characterization of the linear elastic scattering spectra of fabricated silicon disks on SOI substrate by dark field microscopy was performed. Based on the measurements, an estimate was made of the position of the frequencies of the natural resonances of the system and their Q-factors. Nonlinear optical characterization of the spectra of nonlinear second-harmonic signals of fabricated AlGaAs disc samples on a glass substrate under pumping by structured vector beams was performed. It is shown that excitation in the mode of azimuthal polarization of the pump is more efficient than in the mode of radial polarization. The maximum generation efficiency of the second harmonic of the order of 0.1% is shown.

Publications

1. Claude Renaut , Lukas Lang, Kristina Frizyuk, Maria Timofeeva, Filipp E. Komissarenko, Ivan S. Mukhin, Daria Smirnova, Flavia Timpu, Mihail Petrov, Yuri Kivshar, Rachel Grange Reshaping the Second-Order Polar Response of Hybrid Metal-Dielectric Nanodimers Nano Letters, - (year - 2019) https://doi.org/10.1021/acs.nanolett.8b04089

2. Koshelev, K., Bogdanov, A., Kivshar, Y. Meta-optics and bound states in the continuum Science Bulletin, - (year - 2019) https://doi.org/10.1016/j.scib.2018.12.003

3. Koshelev, K., Lepeshov, S., Liu, M., Bogdanov, A., & Kivshar, Y. Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum Physical Review Letters, - (year - 2018) https://doi.org/10.1103/PhysRevLett.121.193903

4. Melik-Gaykazyan, E. V., Koshelev, K. L., Choi, J. H., Kruk, S. S., Park, H. G., Fedyanin, A. A., & Kivshar, Y. S. Enhanced second-harmonic generation with structured light in AlGaAs nanoparticles governed by magnetic response Письма в ЖЭТФ, Vol 109, pp. 131-135 (year - 2019) https://doi.org/10.1134/S0021364019020036

5. Kirill Koshelev, Sergey Kruk, Jae-Hyuck Choi, Elizaveta V. Melik-Gaykazyan, Daria Smirnova, Hong-Gyu Park, and Yuri Kivshar Observation of Extraordinary SHG from All-Dielectric Nanoantennas Governed by Bound States in the Continuum CLEO Proceedings, Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper FW4B.3. (year - 2019) https://doi.org/10.1364/CLEO_QELS.2019.FW4B.3

6. - Physicists Discover New Way of Resonance Tuning for Nonlinear Optics ITMO.NEWS, http://news.ifmo.ru/en/science/photonics/news/8004/ (year - )

Annotation of the results obtained in 2019
Theoretical and experimental studies of the second harmonic generation in hybrid nanodimers, bi-resonance structures, as well as the second and third harmonic generation in high-Q states in single resonators were performed during the second stage of the project. A number of additional problems were solved, including the analysis of the radiation pattern of the second harmonic from nanoantennas based on GaAs and AlGaAs and the analysis of non-radiation losses and the duration of the pump pulse on the harmonic generation efficiency. Theoretically and experimentally, the possibility of using metasurfaces in the terahertz frequency range to realize a nonlinear response due to the excitation of bound states in the continuum was investigated. One of the most significant experimental results obtained in the framework of the second stage of the project is an experimental demonstration of the second harmonic generation in AlGaAs nanoconductors with a record high efficiency, which is two orders of magnitude higher than the data presented in the literature. These results were published in the journal Science, one of the most prestigious scientific journals in the world. This achievement has been widely announced by federal and international media (more than thirty publications). Among the most important theoretical results are the following: (i) A theoretical (dipole) model of second-harmonic generation in hybrid nanodimers consisting of a plasmon nanoparticle has been developed and dielectric nanoparticles, the material of which has a nonlinear susceptibility. The constructed model showed good agreement with the results of numerical modeling. (ii) A formalism of the Feshbach projection approach, generalized to three-dimensional electrodynamic systems, has been developed. It is shown that the developed Feshbach method allows one to correctly describe the interactions of the eigenmodes of the resonator with the continuum modes of the surrounding space. (iii) A numerical analysis of the efficiency of nonlinear processes (third-harmonic generation, four-wave mixing, cascade, and direct fifth-harmonic generation) in dielectric resonators on a substrate supporting high-Q states resulting from the destructive interference of two resonances with close frequencies is performed. The record high efficiency of generating high harmonics in such systems is predicted. (iv) Theoretical and numerical models are constructed that describe the generation of harmonics in dielectric nanostructures with allowance for the finite duration of the pump pulse. The optimal quality factor of resonances of dielectric nanostructures is determined, which ensures the maximum harmonic generation efficiency, obtained taking into account the finiteness of the pump pulse duration. Within the framework of the constructed models, various pulse shapes are considered and it is shown that the optimal pulse duration does not depend on its shape. The PI (A. Bogdanov) and the main executor (K. Koshelev) organized a special section on the project topic at the IV international conference on nanophotonics and metamaterials MetaNano 2019 (St Petersburg, Russia). All work was completed in full, and all planned results were achieved. According to the results of the work of the second stage, three articles were published in peer-reviewed scientific journals, two of which are in the first quartile (Q1). Over the entire period of the project, 8 articles have been published, of which 5 are in Q1. The list of publications includes journals such as Science, Phys. Rev. Lett., Nano Letters, Adv. Fun Materials, JETP Letters, Science Bulletin. The results of the second stage of the project were presented in the form of 12 reports at prestigious Russian and international conferences (4 invited reports, 4 oral reports, 4 poster presentations). In general, work on the project is ahead of schedule, both in terms of planned results and publications.

Publications

1. Carletti L., Kruk S. S., Bogdanov A. A., De Angelis C., Kivshar Y. High-harmonic generation at the nanoscale boosted by bound states in the continuum Physical Review Research, Т. 1. – №. 2. – С. 023016 (2019) (year - 2019) https://doi.org/10.1103/PhysRevResearch.1.023016

2. Koshelev K., Kruk S., Melik-Gaykazyan E., Choi J. H., Bogdanov A., Park H. G., Kivshar Y. Individual nanoantennas empowered by bound states in the continuum for nonlinear photonics Science, Vol. 367, Issue 6475, pp. 288-292 (year - 2020) https://doi.org/10.1126/science.aaz3985

3. Yang Q., Kruk S., Xu Y., Wang Q., Srivastava Y. K., Koshelev K., Kravchenko I., Singh R., Han J., Kivshar Y., Shadrivov I. Mie‐Resonant Membrane Huygens' Metasurfaces Advanced Functional Materials, 1906851, 1-7 (2019) (year - 2019) https://doi.org/10.1002/adfm.201906851

4. - Физики из России, Австралии и Республики Корея создали идеальную наноловушку для света ТАСС. Мировые новости, - (year - )

5. - Российские физики впервые надолго заперли свет в наноловушке News2World, - (year - )

6. - Физикам впервые удалось надолго запереть свет в нанорезонаторе ITMO.NEWS, - (year - )

7. - Свет поймали в идеальную наноловушку Seldon News, - (year - )

8. - Свет поймали в почти идеальную наноловушку Русская весна, - (year - )

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14. - Physicists trap light in nanoresonators for record time EurekaAlert!, - (year - )

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16. - Российские физики помогли поймать свет в идеальную наноловушку News.ru, - (year - )

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21. - Успешный эксперимент: физики учатся управлять светом в сверхмалом масштабе Красная Весна, - (year - )

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