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0COMPARATIVE ANALYSIS OF IONIZATION MODELS IN DIAMOND UNDER STRONG PULSED LASER IMPACT
1Ruzieva M.J, 2Xolboyeva.M.N, 3Xudoyberdiyeva O', 4Yusupov E, 5Ruziev Z.J
1,2,3,4Denau Institute of Entrepreneurship and Pedagogy, 5Tashkent State Technical University
https://doi.org/10.5281/zenodo.11115412
Abstract. In recent decades, the field of laser-material interaction has witnessed remarkable advancements, particularly in understanding the intricate processes underlying ionization in solid-state materials. Among these materials, diamond stands out as a fascinating subject due to its unique properties and potential applications in various fields such as optoelectronics, quantum computing, and high-power electronics. Understanding the ionization dynamics of diamond under strong pulsed laser irradiation is crucial for optimizing its performance in these applications [1.2].
Keywords: Diamond, laser, ionization, model.
Anotatsiya. So'nggi o'n yilliklarda lazer-materialning o'zaro ta'siri sohasida, ayniqsa qattiq holatdagi materiallarda ionlanishning murakkab jarayonlarini tushunishda ajoyib yutuqlarga guvoh bo'ldi. Ushbu materiallar orasida olmos o'zining noyob xususiyatlari va optoelektronika, kvant hisoblash va yuqori quvvatli elektronika kabi turli sohalarda potentsial qo'llanilishi tufayli ajoyib mavzu sifatida ajralib turadi. Kuchli impulsli lazer nurlanishi ostida olmosning ionlanish dinamikasini tushunish uning ushbu ilovalardagi ish faoliyatini optimallashtirish uchun juda muhimdir [1.2].
Kalit so'zlar: Olmos, lazer, ionlanish, model.
Аннотация. За последние десятилетия в области взаимодействия лазеров с материалами произошли значительные успехи, особенно в понимании сложных процессов, лежащих в основе ионизации в твердотельных материалах. Среди этих материалов алмаз выделяется как интересный объект благодаря своим уникальным свойствам и потенциальным применениям в различных областях, таких как оптоэлектроника, квантовые вычисления и мощная электроника. Понимание динамики ионизации алмаза при сильном импульсном лазерном облучении имеет решающее значение для оптимизации его характеристик в этих приложениях [1.2].
Ключевые слова; Алмаз, лазер, ионизация, модель.
Ionization, the process of creating charged particles (ions) from neutral atoms or molecules, plays a pivotal role in laser-material interactions. Various theoretical models have been developed to describe ionization processes in solids, each offering insights into different aspects of the phenomenon. In this study, we focus on three prominent ionization models: the Multifoton Ionization Model, the Ivanov Yudin (IY) Model, and the Ammosov-Delone-Krainov (ADK) Model [2].
The Multifoton Ionization Model, rooted in quantum mechanics, describes ionization as a result of the absorption of multiple photons by the target material. It provides a comprehensive framework for understanding ionization dynamics under pulsed laser excitation and has been widely applied in various materials.
The Ivanov Yudin (IY) Model offers a semi-classical approach to ionization dynamics, incorporating both tunneling and multiphoton ionization processes. Developed specifically for
strong-field laser interactions, the IY model provides insights into the ionization mechanism under intense laser fields [3.4].
The Ammosov-Delone-Krainov (ADK) Model, another semi-classical approach, focuses on tunneling ionization, where electrons escape from the potential well of the material through quantum tunneling. This model has been successful in describing ionization in a wide range of materials and laser parameters.
While each of these models offers valuable insights into ionization processes, their applicability and accuracy in describing ionization in diamond under strong pulsed laser irradiation remain to be systematically evaluated. Therefore, the primary objective of this thesis is to conduct a comparative analysis of these ionization models to determine which one provides the most accurate description of ionization dynamics in diamond under intense laser fields [1.4].
By elucidating the strengths and limitations of each model, this study aims to contribute to a deeper understanding of the ionization processes in diamond and provide valuable guidance for future research and technological applications in laser-material interactions.
The Multifoton Ionization Model is rooted in quantum mechanics and describes ionization as a result of the absorption of multiple photons by the target material. The probability of ionization is determined by considering the interaction between the incident laser field and the electronic states of the material. In this model, the multiphoton ionization rate can be expressed using perturbation theory, where the transition probability between the initial and final states is calculated by considering the matrix elements of the interaction Hamiltonian.
The multiphoton ionization rate WMPIcan be expressed using perturbation theory as follows:
( 1 \N WMPi = (H
Where rMPI is multiphoton ionization rate, I is an intensity of impacted laser pulse lDT damage threshold, N stands for the minimum number of photons in the pump pulse with adequate energy to surpass the bandgap, and a normalization coefficient independent of the field is applied
The ionization probability in the IY model combines tunneling and multiphoton ionization processes. It's often represented as:
The tunneling ionization rate in the ADK model is given by
Maxwell's equations serve as the cornerstone of classical electromagnetism, providing a comprehensive framework for understanding the behavior of electric and magnetic fields in various physical systems. However, their intricate nature often necessitates advanced computational methods for accurate analysis and prediction of electromagnetic phenomena [3].
In recent years, the Finite-Difference Time-Domain (FDTD) method has emerged as a powerful numerical technique for solving Maxwell's equations in complex geometries and under
diverse boundary conditions. By discretizing both space and time, FDTD allows for the direct simulation of electromagnetic wave propagation, scattering, and interaction with materials.
In this article, we explore the integration of advanced theoretical models with the FDTD method to tackle challenging problems in electromagnetics. Specifically, we focus on the incorporation of multiphoton ionization models, such as the Inouye-Yamanouchi (IY) model, and the Ammosov-Delone-Krainov (ADK) model, which describe the ionization of atoms and molecules under intense laser fields.
Multiphoton ionization phenomena play a crucial role in various applications ranging from laser-induced breakdown spectroscopy to laser machining and nonlinear optics. By incorporating these models into the FDTD framework, researchers can gain deeper insights into the dynamics of laser-matter interactions and accurately predict the evolution of electromagnetic fields in ionized media.
This work aims to provide a comprehensive overview of the theoretical foundations of multiphoton ionization models and their implementation within the FDTD method. We will discuss the fundamental principles underlying each model, their mathematical formulations, and their implications for simulating complex electromagnetic phenomena.
Furthermore, we will explore practical examples and applications where the combined approach of multiphoton ionization models and FDTD simulations has yielded valuable insights into phenomena such as high-harmonic generation, filamentation, and laser-induced plasma formation.
Below, we will delve into a detailed analysis of the results obtained using theoretical calculations. This analysis will involve scrutinizing the intricacies of the numerical simulations based on the integrated FDTD method with multiphoton ionization models, namely the Inouye-Yamanouchi (IY) model and the Ammosov-Delone-Krainov (ADK) model. We will closely examine various aspects of the simulated electromagnetic phenomena, including but not limited to the spatial and temporal evolution of electric and magnetic fields, the distribution of ionized particles, and the generation of higher-order harmonics. By dissecting these results, we aim to elucidate the underlying physical mechanisms governing the observed phenomena and to extract meaningful insights into the complex interplay between laser fields and ionized media. Moreover, we will compare our theoretical findings with experimental data wherever available, providing validation and further refinement of the theoretical models and computational methodologies employed. Through this comprehensive analysis, we endeavor to contribute to the advancement of our understanding of laser-matter interactions and to lay the groundwork for the development of novel applications in fields such as laser spectroscopy, plasma physics, and ultrafast optics.
0 1x10,s 2x10"' 3x10,s 4x10'" 5x10'
Electric field
Figure-1. Dependence of the number of fused atoms on the intensity of the laser pulse falling into the medium.
In Figure 1, we observe a graphical representation illustrating the correlation between the number of ionized atoms and the intensity of laser radiation directed onto the diamond substrate. This investigation into the degree of ionization employed three distinct methodologies: the multiphoton ionization (MI) method, the IY method, and the ADK method.
Upon meticulous examination of the acquired data, a noteworthy trend emerges. Specifically, the MI method showcases an intriguing characteristic whereby the degree of ionization appears boundless. This phenomenon manifests as the number of ionized atoms surpasses the count of atoms within a defined volume, a circumstance exacerbated by escalating laser radiation intensity. Consequently, it becomes apparent that beyond a certain threshold of intensity, the MI method loses its efficacy, rendering it unsuitable for accurate ionization assessments.
Similarly, the outcomes derived from the ADK method echo the aforementioned observations. As laser intensity increases, the degree of ionization continues to escalate without restraint, mirroring the trend observed with the MI method.
Conversely, the IY model yields a contrasting outcome that merits attention. Here, the number of ionized atoms reaches a saturation point after surpassing a specific threshold of laser intensity. This distinctive behavior signifies a crucial attribute of the IY model—its ability to accurately predict and accommodate the limitations imposed by ionization, thereby ensuring the model's reliability and efficacy in analyzing ionization processes.
Thus, while both the MI and ADK methods demonstrate unbounded ionization tendencies, rendering them susceptible to inaccuracies at higher intensities, the IY model's capacity to acknowledge and reflect ionization limitations underscores its validity and effectiveness in elucidating ionization phenomena.
In conclusion, the analysis of ionization processes on diamond substrates using the multiphoton ionization (MI), IY, and ADK methods reveals distinct behaviors in response to varying laser radiation intensities. While the MI and ADK methods exhibit unbounded ionization tendencies, leading to inaccuracies at higher intensities, the IY model demonstrates a saturation point, indicating its reliability and efficacy in predicting ionization limitations. These findings underscore the importance of selecting appropriate methodologies for accurate ionization assessments in diamond material research.
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