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Fundamentals of Nonlinear Optics
Published in Yu. N. Kulchin, Modern Optics and Photonics of Nano and Microsystems, 2018
When in ordinary life we talk about the propagation of light in matter, it is initially assumed that the characteristics of the medium do not change under its influence. Indeed, the electric fields in atoms and molecules, which are the main elements determining the structure and optical properties of matter, are very large. In this connection, the light sources that existed in the pre‐laser era could provide electric fields in the light electromagnetic wave many orders of magnitude smaller than the intra‐atomic ones. Therefore, the influence of the electromagnetic field of the lightwave on the properties of the medium turned out to be negligibly small and did not manifest itself under real conditions. Since in this case the response of the medium to the external optical action is proportional to the electric field strength in the wave, the theoretical description of the phenomena arising in the interaction of light with matter is usually called linear optics.
Nonlinear and short pulse effects
Published in John P. Dakin, Robert G. W. Brown, Handbook of Optoelectronics, 2017
In most parts of this handbook, we deal with linear optical effects. Linear optics means that the optical power at the outputs of an optical device always scales linearly with input power. The device may spectrally or spatially filter the input beam; it may split the input beam into a multitude of output beams; regardless of what the device does, the output power always relates linearly to the input power. Looking through textbooks on classical optics from the prelaser era, the impression may arise that the linearity of optical phenomena is a given thing as there is no mention of any nonlinear effects. This is in strong contrast, for example, to acoustics, where nonlinearities are so widespread that the art lies more in their avoidance than in the observation of nonlinearities. One may think of a cheap set of speakers just as one simple example. Increasing the volume, these speakers will start to sound increasingly annoying with more and more audible distortion. This distortion is not related to the frequency dependence of the speaker’s transmission characteristics because this would be independent of volume. The distortion effect is related to unwanted harmonics of the input. These harmonics arise due to nonlinearities between the emitted acoustic wave and the input current to the speaker’s solenoid. Beyond a certain drive amplitude, the speaker’s membrane position does not linearly follow the current anymore. These harmonics are not necessarily bad. All musical instruments also rely on acoustic nonlinearities, giving rise to a characteristic spectrum of overtones of the excited fundamental vibration of a chord. This characteristic spectrum allows us to distinguish different musical instruments. The omnipresence of nonlinearities in acoustics is in strong contrast to optics, where similar effects could not be observed until the advent of the laser.
Study of magnetic fringe fields and interference effects on beam dynamics for proton facility gantry
Published in Journal of Nuclear Science and Technology, 2022
Manfen Han, Jinxing Zheng, Yique Cheng, Xianhu Zeng, JunSong Shen
The gantry beamline was designed to allow focus-to-focus and full achromaticity of the transport system from the coupling point to isocenter. The first-order linear optics and magnet characteristics are performed with the TRANSPORT code [2,3]. BDSIM offers a complete beamline simulation with exact results on dynamic verification and transmission efficiency based on the Monte Carlo method [4]. To obtain a circular spot with FWHM (2.355σ) = 4 mm at the isocenter, the nominal beam parameters (2σ) at the entrance of the gantry are set to a momentum spread (Δp/p) of 0.5%, beam-width (x, y) of 3.1 mm and emittance (ε) of 16π mm·mrad. Figure 2 gives the magnetic fields corresponding to each quadrupole at different energies for this optical fit. As the energy increases, the field strengths of quadrupoles increase accordingly.
Quantum theory of light in a dispersive structured linear dielectric: a macroscopic Hamiltonian tutorial treatment
Published in Journal of Modern Optics, 2020
This note derives from a quantum optics course the author taught for some years at the University of Oregon. The treatment is meant to be tutorial and accessible, using familiar mode expansions and a minimum level of advanced mathematics, such as canonical field variables, field action or Lagrangians. It begins discussing the energy density in a dispersive dielectric. It then summarizes the inverse permittivity formulation of linear optics. Then a theory of mode expansions is given, with emphasis on mode normalization and the lack of mode orthogonality in a dispersive, structured dielectric, giving a new, macroscopic derivation of these results. Next, the quantization of the polariton field is treated in the macroscopic formulation, using the derived modes. Some special limiting cases are then summarized, followed by discussion of the continuum limit. Finally, the results are applied to quantization of the field in dielectric optical waveguides, important for emerging quantum technologies.
Decay dynamics in the coupled-dipole model
Published in Journal of Modern Optics, 2018
M. O. Araújo, W. Guerin, R. Kaiser
where is the relative distance between the atoms j and , is the Rabi frequency associated to the laser drive, and is the laser detuning from the atomic resonance. Here are the time-dependent amplitudes of dipoles j. Equation (1) is valid for weak driving fields, i.e. the solution in the linear-optics regime. This amount to approximating the quantum solution to the first order in , which is valid for , where is the saturation parameter. We note that testing this assumption quantitatively, in particular in regard to the long-lived subradiant modes, would require a full quantum treatment [44]. In a quantum framework, can be considered as the optical coherence of the atom j and the wave function of the atom ensemble reads