The Effect Of Vectoriality, Nonparaxiality And Aberration Of Optical Field On Spectral Shifts And Spectral Switches

It is well known that the spectral analysis of radiation is one of the mostimportant analytic methods in science. Implicit in its use is the assumption that thespectrum of light does not change as the radiation propagation in free space. Onlyrecently has it been called into question. Apparently, this assumption is important todetect the spectrum of light source. Otherwise, the spectral detector is usually placedin a distance from the source. Therefore, before the light reaches the detector, it hasactually experienced some processes such as propagation in free space, focused bylenses, diffracted by aperture etc. Studying the spectral changes of beams passingthrough the optical systems not only has a theoretical meaning, but also has anapplied one.The assumption, which it is refered to as the assumption of spectral invariance onpropagation in free space, has proven by experiment to be justified in the vastmajority of circumstance. In 1986, the first theoretical prediction that the spectrum oflight may differ from the spectrum of the source, and that may change on propagationeven in free space, was made by professor Wolf. He showed that only when thespectral degree of coherence of a source satisfies the so-called scaling law, does thespectrum of the radiation from the source keep the spectral invariance during itspropagation. Conversely, when the source does not satisfy the scaling law, the spectrum of the radiation from the source will change. Since then, the extensivetheoretical and experimental studies have been made on this subject. In 1999, Pu andhis collaborators found a new phenomenon that is defined as a spectral switchtheoretically. In 2002, the study of singular optics was extended to the spectralanomalies of spatially fully coherent polychromatic beams, and the spectral switchwas regarded as a new effect in singular optics. These results broaden the developingfield of singular optics. Based on the work at home and abroad, some original studieshave been done in this dissertation. They are summarized as follows:By using Zemike polynomials to discribe the wavefront distortion of beams, thespectral behaviors of spherically aberrated polychromatic Gaussian beams diffractedat an aperture and polychromatic GSM beams passing through an aperture lens withaberration are studied based on the propagation law of the cross-spectral densityfunction in the space-frequency. Emphasis is given on the influence of aberration onthe spectral shifts and spectral switches. The aberration-free results are obtained asspecial cases treated in our papers. Detailed numerical calculations and physicalanalysis are presented. It is shown that the spectrum of aberrated polychromaticbeams may be redshifted and blueshifted in comparison with the aberration-free case,and the spectral switch may also take place. At the geometrical focal plane ofpolychromatic GSM beams diffracted at an aperture lens with aberration, theaberration affects the behavior of spectral switches. The spectral minimum S_minincreases as spherical aberration coefficient C₄ and astigmatic coefficient C₆ increase,the transition heightâ–³decreases with increasing C₄ and C₆, the spectral switchvanishes when C₄ and C₆ are greater than a certain value, respectively. As usual,S_min≠0, only for the spatially fully coherent and aberration-free case we have S_min=0.However, for the case of the on-axis spectrum of spherically aberratedpolychromatic Gaussian beams diffracted at an aperture, S_min=0 andâ–³reachesmaximum corresponding with a apt C₄. The results would be useful for understandingsome discrepancies between the experimentally measured spectral behavior andnumerical calculation results without consideration of phase aberrations. On the basis of the polarization matrix and propagation equation of the cross-spectral density matrix, the spectral changes including the spectral shifts and spectralswitches of vector GSM beams passing through an aperture lens are studied. Theattention has been focused on the influence of correlation and polarizer on thebehavior of the spectral switch at the focal plane. In comparison with the previouspublications, it has been found that the auto-correlation of vector GSM beams affectsthe spectral switch, but the cross-correlation does not if there is no polarizer. Thecritical position u_c shifts toward the z axis, the spectral minimum S_min decreases andtransition heightâ–³increases as the relative auto-correlationσ_a/σ₁ increases.Specifically, for the spatially fully coherent caseσ_a/σ₁=∞, S_min equals to zero andâ–³reaches its maximum value. On the other hand, the polarizer affects the spectralswitch of vector GSM beams, whereas it does not affect the spectral behavior ofscalar GSM beams. In the presence of a polarizer both auto- and cross- correlations ofvector GSM beams affects u_c, S_min andâ–³. There exists a certain value of the rotatingangleθof the polarizer, at the corresponding critical position u_c, S_min takes itsminimum value andâ–³reaches its maximum value. The above conclusions would beuseful for understanding the spectral behavior of vector GSM beams anddistinguishing it from scalar GSM beams. Otherwise, a detailed study of the focalshift and focal switch of polychromatic vector GSM beams passing through asystemwith the aperture and lens separated is also performed. Before inserting a polarizer thefocal shift appears, there is no focal switch, and after inserting the polarizer the focalswitch can take place. By rotating the polarization angle, the behavior of the focalswitch can be cont rolled.As we all know, the lens is a usual component in optical system, and sphericalaberration of a single lens is unavoidable, so it is very important to research theinfluencxe of spherical aberration of the lens on the spectral changes. To ourknowledge, there are only two papers dealing with the axial spectra of GSM beamspassing through an aberration-free lens and an astigmatic lens, in which the axialspectra are only blueshifted in comparison with the source spectrum. To provide a theoretical basis for the application of spectral switches, in this dissertation, spectralshift and spectral switching of the on-axis spectrum of vector GSM beams focused bya spherically aberrated lens is studied in detail. Due to oscillation of the spectralmodifier with frequency, the spectrum of vector GSM beams passing through aspherically aberrated lens may be blueshifted and redshifted, in comparison with thesource spectrum, and spectral switching may also take place at the critical positions.With the development and wide application of diode lasers and practicaltechnology, there exist optical beams of very small spot size and/or large far-fielddivergence angle, for which the paraxial theory is invalid. Starting from thegeneralized Rayleigh-Sommerfeld diffraction integral, the expression for thespectrum of polychromatic Gaussian beams diffracted at an aperture and GSM beamsin Young's experiment are derived, where the influence of nonparaxiality of opticalfield on the spectral shifts and spectral switches is first stressed. The results obtainedin our papers are in consistence with the results under the paraxial approximation.There is a spectral shift in the nonparaxial case relative to the paraxial one and thecritical position, at which the spectral switch occurs, changes. Only when W₀/λ₀ andδsatisfy certain conditions, are the paraxial approximation results of Gaussian beamsdiffracted at an aperture consistent with the nonparaxial ones. The smaller w₀/λ₀ is,the larger the difference between the nonparaxial and paraxial results appears. Theeffect of width on spectral switch of polychromatic GSM beams in Young'sexperiment is the largest of all parameters. Therefore, in studying the spectralbehavior of fully and partially coherent light with width comparable to thewavelength, the effect of beam nonparaxiality has to be taken into consideration.Within the framework of static light scattering, scattering-induced spectralchanges is studied in the forward-scattered component of polychromatic Gaussianbeams transmitted through a colourless transparent plate with a surface roughnesscomparable with the wavelength. Our main attention is focused on the effect of themaximum deviation of the surface profile from the mean surface line H, relativerefraction index n and bandwidthσ₀ on the spectral shift and spectral switch. The spectrum of the forward-scattered component may be blueshifted and redshifted, incomparison with the source spectrum, and spectral switching may also take place atthe critical positions. The effect of n on the spectral minimum S_min and transitionheightâ–³is relatively small, butâ–³decreases with decreasing bandwidthσ₀. H is thegoverning parameter in any case. Scattering-induced spectral switches belong to theeffect in singular optics in the forward-scattered component of polychromaticGaussian beams transmitted through a colourless transparent plate with a surfaceroughness.The expression for the spectral density of polychromatic Gaussian and GSMbeams propagating through double slits in Young's experiment are derived, whichenables us to study the behavior of spectral switches in Young's experimentilluminated by fully and partially coherent, polychromatic light beams and to judge iftheir spectral switches belong to the effect in singular optics. It is shown that thecriterion for the effect in singular optics with polychromatic light field should beS_min=0(S_min—minimum of the spectral density at spectral switches) rather thanI_min=0(I_min—minimum of the total intensity). In Young's experiment illuminated bypolychromatic GSM beams the spectral switches in both near and far zones are notattributed to the effect in singular optics because S_min≠0. If the double slits in Young'sexperiment are illuminated by polychromatic Gaussian beams, the spectral switchesin the far zone belong to the effect in singular optics, whereas it is not the case in thenear zone.By means of the expansion of the window function of the hard aperture into afinite sum of complex Gaussian functions, approximate closed-form propagationequations are derived, in which the successive integral calculations are replaced bythe finite elementary summation operation. For the case that the aperture number isgreater than 3, the straightforward integral of the Collins formula becomes difficulton a personal computer, whereas the method obtained in this dissertation is stillapplicable. Numerical results have found an agreement with those by straightforwardintegral of the Collins formula, but the computing time is greatly reduced. Discrepancies appear only in the vicinity of the aperture-lens caused by Wen'smethod, an improved algorithm is proposed. It is shown that the improved algorithmprovides a good trade-off between the computational accuracy and computer time,and is applicable to the far field and near field.This field concerns with the coherent theory and spectral anomalies induced byvarious physical reasons. In recent several years, people have generated considerableinterests in studying on spectral changes due to a potentially applicative viewpoint inmany realm such as spectrum-selective interconnects. Applications of these studieshave been shown for the determination of the angular diameter of the stars, angularseparation of a double star etc. The results obtained in this dissertation broaden thestudies on spectral shifts and spectral switches, it is useful to improve the accuracy ofmeasuring spectrum, understand some discrepancies between the experimentallymeasured spectral behavior and theoretically numerical calculation results, and studythe spectral changes in nonparaxial field.