Nature New Biology

Zhou J., Tong M.

Random couplingRandom coupling theory for multi-mode waveguidesMulti-mode waveguide and free spaceFree space propagation. The chapter studies the random coupled mode theoryCoupled mode theory, which has the coupling coefficients varies randomly and should be studied through the stochastic approach. The basic equations are given and the analytical results for the average value, as well as the 2nd and 4th order moments are studied analytically as well.

Zhou J., Tong M.

The chapter reviews the fundamental physicsPhysics for multi-mode propagation inside waveguides and in free spaceFree space. Coupled mode theoryCoupled mode theory is derived. Multimode interferenceMulti-mode interference theory is revealed.

Zhou J., Tong M.

Temporal modes and spatiotemporal modes. The chapter extends the theory of spatial beam propagation to the temporal domain, and the concept of temporal waveguides and temporal Fractional Fourier transform are proposed. Afterwards, a temporal signal processing tool, i.e., a temporal diffractive deep neural network is proposed. The concept is extended beyond the spatial domain or the temporal domain, but the 4-dimensional space-time. A new class of spatial-temporal beam is discussed and a spatial-temporal diffractive deep neural network is proposed in the end.

Zhou J., Tong M.

Coupled mode theoryCoupled mode theory for multi-mode propagation. The chapter introduces the coupled mode theoryCoupled mode theory, which is a powerful tool for multi-mode propagation analysis. The coupled mode theoryCoupled mode theory will be formulated both for the classic optics and quantum opticsQuantum optics. While the coupled mode theoryCoupled mode theory is a powerful tool for multi-mode propagation analysis in classic optics, quantum formulation of the multimode propagation is provided afterwards.

Zhou J., Tong M.

Multi-mode interferenceMulti-mode interference in waveguides and free spaceFree space. The chapter deals with the modes in the waveguides or free spaceFree space which propagates with different velocities and propagation constants. Interference is expected and can be used to design useful functional devices such as multi-mode interferenceMulti-mode interference couplers. Functional devices such as unitary transformers are designed based on the multi-mode interferenceMulti-mode interference concept. In free spaceFree space, the multi-mode interferenceMulti-mode interference is described as the Talbot effect, which can be exploited to generate spatial modes.

Zhou J., Tong M.

Multi-core fibers. The chapter studies the multi-core fibers, which are considered as a special kind of multi-mode waveguideMulti-mode waveguide while the cores are closely coupled to each other and form the super-modes. The concept is discussed and analytical solutions are given for various multi-core fibers with different core arrangement.

Zhou J., Tong M.

Mode generationMode generation and multiplexing for multi-mode waveguidesMulti-mode waveguide and free spaceFree space. The chapter studies the mode generatorMode generator and multiplexer, which are the key components for mode division multiplexingMode division multiplexing systems. The chapter discusses the novel ways to realize mode generatorsMode generator and multiplexers.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

In this chapter, we extend the Hamiltonian governing the interaction between light and molecules to incorporate external reservoirs, including the free space modes reservoir, the dephasing reservoir associated with spectral line broadening in gases, and the reservoir responsible for vibron mode relaxation. These reservoirs are essential for facilitating light emission by atoms. We demonstrate that, under the conditions of weak interaction between the reservoirs and the atom, and when the reservoirs are in thermal equilibrium, it is possible to eliminate the reservoirs’ variables from the operator equations describing the atom-vibron system. As a result, the system exhibits noise terms, leading to a set of complex equations. To tackle these intricate equations, we develop a perturbation theory, enabling us to solve them systematically. We establish that the Raman effect emerges as a consequence of the second-order perturbation within this framework, ultimately allowing us to determine the Raman spectrum.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

In this book, the phenomena of inelastically scattered light on molecules are associated with the excitation of the vibrational degrees of freedom of the molecule nuclei. The developed approach is based on the original qualitative ideas of classical physics—the modulation of the oscillation of the molecular dipole moment by vibrations of molecular nuclei.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

This chapter serves as a foundational component of the book, delving into precisely solvable scenarios involving the interaction of atoms with external electromagnetic fields. This chapter plays a crucial role in acquainting readers with the fundamental concepts essential for the book’s comprehension. In particular, we rigorously establish a critical principle: within closed Hermitian systems comprising a finite number of subsystems, stationary states are unattainable for individual subsystems. This principle lays the groundwork for our subsequent discussions. Furthermore, we meticulously demonstrate that an atom interacting with a single mode of either classical or quantum fields does not emit photons. Within this chapter, we elucidate the quantization of electromagnetic fields. Employing the rotating wave approximation, we tackle the well-known problem of Rabi oscillations, exploring the population inversion in a two-level atom. The chapter also delves into essential frameworks for describing quantum systems, such as the Schrödinger and Heisenberg pictures. We introduce notations and concepts used in the book’s narrative, including the model of a two-level atom, Dirac’s bra and ket vectors, Pauli matrices, raising and lowering operators, as well as the gauge calibration of electromagnetic fields. These foundational elements set the stage for a deeper understanding of the subsequent chapters.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

Show that in the Schrödinger picture, a TLS interacting with a single mode of a monochromatic external field is in the regime of Rabi oscillations.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

This chapter serves as the introduction, where we provide a concise overview of the theoretical underpinnings of Rayleigh scattering. We highlight the pivotal role played by quantum mechanics in advancing our understanding of this phenomenon and acknowledge the persisting challenges within the theory. Furthermore, we draw attention to the notion of virtual states, frequently invoked to elucidate scattering effects despite their absence in experimental observations. In this book, we depart from this concept, presenting an alternative approach to comprehending light-scattering phenomena. Additionally, we offer a glimpse into the broader context of the subsequent chapters, providing readers with a roadmap for the exploration of this subject matter.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

This chapter investigates the impact of nuclear vibrations in active materials characterized by strong electron-phonon coupling on the amplification properties of conventional lasers. Traditionally, this effect is regarded as negligible, even in active media with pronounced electron-phonon interaction. However, our study reveals that active mediums with significant Raman cross sections may lead to unconventional laser behavior. The presence of robust electron-phonon coupling introduces novel regimes of laser dynamics, potentially transforming a laser into a coherent optical phonon generator. The analysis of the system operation above the conventional lasing threshold unveils the emergence of a new pump rate threshold, which arises above a critical value of the Fröhlich constant. Beyond this second threshold, depending on system parameters, the system may exhibit joint self-oscillations of coherent phonons in the gain medium and photons in a cavity or even chaotic behavior. Furthermore, we identify a range of Fröhlich constant and pump rate values where multiple stable dynamical regimes coexist. In such cases, the laser’s dynamics are uniquely determined by the initial conditions.

Lisyansky A.A., Andrianov E.S., Vinogradov A.P., Shishkov V.Y.

This chapter delves into a semiclassical description of high-intensity Rayleigh scattering, employing the Heisenberg-Langevin operator equations. In this analysis, we treat the incident field as classical while considering the scatterer as quantum. Within resonant scattering, where the external field’s frequency matches the transition frequency of a two-level atom, we unveil an intriguing phenomenon in the response spectrum. Alongside the narrow Rayleigh scattering line, three new lines emerge. Among them, one aligns with the incident light’s frequency, while the other two exhibit frequency shifts corresponding to the Rabi frequency. This phenomenon is recognized as the Mollow triplet. We also explore the nonresonant scenario, where the most intense line aligns with the atom’s transition frequency, while the remaining two lines are significantly weaker. These two lines manifest in Raman scattering as background noise, often eclipsing the Raman effect and requiring careful consideration.