Classical optics propagation

In classical optics, a one mode electromagnetic held of frequency co, with the propagation vector k and linear polarization, can be represented as a plane wave... 

The geometric description of the light propagation and the kinetics description of motion were closely correlated in the history of science. Among the main evidence of classical Newtonian mechanics is Euclidean geometry based on optical effects. In Newtonian physics, space has an affine structure but time is absolute. The basic idea is the inertial system, and the relations are the linear force laws. The affine structure allows linear transformations in space between the inertial coordinate systems, but not in time. This is the Galilean transformation ... 

Naturally this coincidence does not mean that the geometric optics added to the classical physics could be used for the exact description of the light propagation since the Michelson-Morley experiment refuted its validity forever. It is evident that there are possible new mathematical definitions for c+ and c instead of the ordinary speed addition mle of the classical physics seen in Eqs. (9) and (11). These can be compatible with the experimental results as well. 

Thus, conventional electromagnetic radiation propagates in a medium in accordance with the laws of classical, linear optics. This implies a lack of any interaction whatsoever between simultaneously propagating waves they propagate independently of one another, each interacting with the medium in a manner as if the other waves were not present. 

These pulse shapes can be quantitatively understood by examining the propagation of the Stokes and anti-Stokes fields through an optically dense atomic ensemble. As shown in Fig. 2 B, the results of this analysis are in an excellent agreement with experimental observations. We theoretically model the medium as N three-level A-type atoms as shown in Fig. 1 A. The two laser fields are treated classically, whereas the generation and propagation of one transverse mode of the Stokes (anti-Stokes) quantum field is described by an effective one-dimensional slowly varying operator s z, t) ( s(z. t)), which corresponds to the vacuum field at the entrance of the cell z = 0. Our model allows us to treat a small number of transverse spatial modes which evolve... 

The energy of the optical wave that propagates along axis z is proportional to the square of the amplitude of its electric vector. It is equal to /g at the entrance of the medium defined by z = 0, and to / at the output of the medium defined by z = /. In a classical absorption set-up, also called the transmission set-up, which is used in the great majority of experiments and is displayed in Figure 5.AI, the measured quantity is the absorbance A equal to the decimal logarithm of the ratio of these two energies (also called intensities). With the help of eq. (5.A6), we may write... 

Second-harmonic generation, which was observed in the early days of lasers [18] is probably the best known nonlinear optical process. Because of its simplicity and variety of practical applications, it is a starting point for presentation of nonlinear optical processes in the textbooks on nonlinear optics [1,2]. Classically, the second-harmonic generation means the appearance of the field at frequency 2co (second harmonic) when the optical field of frequency co (fundamental mode) propagates through a nonlinear crystal. In the quantum picture of the process, we deal with a nonlinear process in which two photons of the fundamental mode are annihilated and one photon of the second harmonic is created. The classical treatment of the problem allows for closed-form solutions with the possibility of energy being transferred completely into the second-harmonic mode. For quantum fields, the closed-form analytical solution of the... 

The phase mismatch which impedes the second-harmonic generation leads also to the cascading of quadratic nonlinearities and the induced phase shift. This effect has been used in continuous-wave optical devices and much effort has been devoted to the classical description of light propagation. We address the quantum theory of steady-state propagation of light and compare this formalism... 

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