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# Quantum Theory Of Optical Coherence Selected Papers And Lectures Pdf

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- Roy J. Glauber
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- Optics Express
- Physics: Quantum Theory & Mechanics

*Mohan, S. Lowen, and M. Mohan, I.*

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This website uses cookies to deliver some of our products and services as well as for analytics and to provide you a more personalized experience. Click here to learn more. By continuing to use this site, you agree to our use of cookies. We've also updated our Privacy Notice. Click here to see what's new. Partial spatial coherence is a fundamental concept in optical systems. Theoretically, the normalized mutual coherence function gives a quantitative measure for partial spatial coherence regardless of the spectral nature of the radiation.

Though not commonly appreciated, with polychromatic radiation this is not the case owing to the wavelength dependence of diffraction.

This result, which is demonstrated both theoretically and experimentally, thus restores the usefulness of the two-pinhole interferometer in the measurement of the spatial coherence of light beams of arbitrary spectral widths. The concept of optical coherence is at the root of much of the science and applications of light [ 1 ]. In scalar description, the cornerstone of optical coherence theory is the mutual coherence function [ 2 ].

However, Zernike considered only equal-time coherence of the light at the pinholes. A full description of classical optical coherence theory including time delays was subsequently introduced by Wolf [ 5 ] and the corresponding quantum coherence theory was formulated by Glauber [ 6 , 7 ].

The mutual coherence function provides a quantitative measure for the space—time coherence of light regardless of the spectral width of the radiation. Therefore polychromatic illumination leads to a mix of colored fringes on the observation screen and breaks down the connection between the complex degree of coherence and the two-beam interference fringes in the space—time domain.

Nonetheless, several types of broadband fields that are effectively stationary in time, such as thermal light [ 1 ], white-light LED and superluminescent diode SLD emission [ 9 ], and quasi-stationary supercontinuum radiation [ 10 , 11 ], are increasingly employed in various optical applications, making the characterization of their spatial coherence important in practice [ 12 ]. In such an instrument, a spectrometer with cylindrical optics would disperse the fringes in the direction perpendicular to the pinholes.

By observing the visibility across lines parallel with the pinholes, corresponding to different frequencies, values for the spectral degree of coherence in the space—frequency domain can be acquired. Combined with the knowledge of the spectra at the pinholes, the relation by Friberg and Wolf [ 13 ] may then be applied to numerically calculate the time—domain complex degree of coherence.

Diffraction is a universal dispersive property of light that can be compensated for. The approach is based on the achromatization of the fringe pattern such that the period of the intensity fringes is the same for all wavelengths. This is done in practice by using an achromatic Fresnel-transform system that consists of a diffractive lens and an achromatic doublet set in a specific geometry, a system resembling a previously introduced Fourier-achromat [ 14 — 16 ] or Fresnel-achromat [ 17 ] component.

Our configuration thus performs the Friberg—Wolf integration optically, and allows one to measure the spatial coherence of stationary light fields of arbitrary spectral widths as in the conventional quasi-monochromatic case. Pulsed and electromagnetic fields are briefly addressed in the conclusions. The situation is illustrated in Fig. Waves from the two pinholes interfere on the observation screen to form periodic intensity fringes at each frequency component of the radiation.

The period of the interference fringes depends on the pinhole separation and increases linearly with the wavelength. It is thus obvious that with polychromatic light the fringe pattern will be colored and spatially smeared out. The visibility changes along the lateral position on the observation screen, even when spatially fully coherent light sources are used, making the measurement of spatial coherence impossible.

The spherical waves emerging from the pinholes interfere creating intensity fringes. However, the periods of the fringes scale as a function of the wavelength and the visibility will obviously be low as the fringes of various frequencies mix. Such an achromatization of the diffraction pattern results in scale-invariant intensity fringes and the visibility of the fringe pattern can be utilized to measure the spatial coherence.

It is clear from Eq. We next assume, for simplicity, that the spectral response of the detector at the observation screen is constant within the frequency band involved.

Integrating both sides of Eq. Since the period of the cosine term in Eq. Denoting the maximum and minimum intensities in close vicinity of a given position by I max and I min , respectively, we find from Eq. If the optical intensities I 1 and I 2 at the pinholes are the same, the fringe visibility is equal to the modulus of the degree of spatial coherence.

We also see from Eq. We have confirmed the theoretical predictions by experiments. Our measurement setup, illustrated in Fig. Radiations from the lasers which separately can be regarded as quasi-monochromatic are combined into one polychromatic beam and directed onto the pinholes thus creating an interference pattern on the observation screen at each laser frequency component.

The periods of the intensity fringes, which otherwise would be different at each color, are corrected by the achromatic Fresnel transformer that is designed and constructed to produce frequency-independent two-dimensional Fresnel transforms.

The patterns in the observation plane are then detected by the CCD array. The beams from two diode-pumped solid-state lasers with wavelengths of nm and nm and a HeNe laser with the wavelength of nm are combined into a single polychromatic RGB beam using mirrors and non-polarizing beam splitters.

The achromatic Fresnel-transform system, shown in detail in Fig. The achromatic lens has a mm focal length and is placed directly behind the pinholes.

The diffractive lens is 6 mm in diameter and was constructed to have a focal length of The diffractive element profile, the central part of which is illustrated in Fig. The overall spectral sensitivity is shown in Fig. The element was fabricated by electron beam lithography and reactive ion etching. The system contained within the colored area is represented by system matrix M which is calculated using ray optics. Only the first few periods are presented since the physical width w of the lens is 6 mm.

The structure provides the diffraction efficiency as shown in Fig. It is seen that the total efficiency, a product of the efficiencies of the CCD and the diffractive lens at each wavelength, is sufficiently constant within the spectral regime of nm — nm. To further examine the performance of the achromatic Fresnel-transform system we need to study the wavelength dependence of the transverse scale factor. While this is not the best possible performance ideally the factor would remain unchanged as a function of the wavelength , it is sufficient in the scope of our work.

Better results could be obtained with more complex AFT systems. It is worthwhile to note that the visibility is better in a Fresnel system where any zero-order stray light will be spread out, while in a Fourier system it will be focused in the observation plane.

With three separate lasers forming a red-green-blue RGB source, the light is effectively spatially fully coherent at each frequency, i. The laser beams are naturally mutually uncorrelated, so their intensities simply add up. Now, without the achromatization, the superposition of the diffraction patterns of the three laser beams of different colors, illustrated schematically in Fig.

Visibility is low and, even at best, only the most central fringes could be used to obtain some information about spatial coherence. Now, if the laser beams are well aligned, we should get a nearly percent visibility with our achromatic setup.

The experimentally obtained value for the visibility V , measured using the first few fringe minima and maxima, is approximately 93 percent. Since the intensities at the two pinholes are essentially equal, the degree of spatial coherence has by Eq. As can be observed from Fig. It should also be noted that more accurate results could be obtained with involved and better optimized AFT systems.

The achromatic Fresnel-transform system adjusts the two-pinhole intensity fringe periods to be the same for each wavelength. Blue: nm, Green: nm, Red: nm, and Black: superposition.

To gain further insight into polychromatic spatial coherence, we subsequently placed a phase-shifting element before the double pinhole such that light passing pinhole 1 experiences a greater phase shift than light traversing pinhole 2.

We used a simple SiO 2 plate covering both pinholes, but a sufficiently large indentation dent of nm depth was fabricated on the plate by reactive ion etching and positioned in front of the second pinhole. Such an arrangement creates a wavelength-dependent phase delay between the light fields at the two openings. Figure 8 shows this effect both experimentally [ Fig.

The deviation between the values comes from various sources like fabrication errors and difficulties in positioning the gap in the laser beam but, nevertheless, the experiment shows a clear reduction of the degree of spatial coherence for the polychromatic radiation as predicted by the theory.

This leads to a lateral displacement of the interference pattern that is different in magnitude for each wavelength. The partial spatial coherence of light sources and radiation fields is a fundamental characteristic in most optical systems.

Theoretically the degree of spatial coherence is given for stationary scalar beams of arbitrary spectral widths by the normalized version of the mutual coherence function, but in the measurement practical difficulties arise with polychromatic light due to the dispersive nature of diffraction and interference. However, the spectral variation of diffraction can be balanced by suitable chromatic elements of physical optics.

Our experimental results agree well with the theoretical predictions. Besides stationary polychromatic light, short pulses such as those from Q-switched or mode-locked lasers or fs-scale supercontinuum radiation also exhibit broad spectral distributions.

For a train of fluctuating pulses the degree of spatial coherence can be measured in a similar manner where the ensemble averaging then takes over the sequence of individual pulses. For electromagnetic vectorial partially coherent and partially polarized light the situation is considerably more involved. In two-beam interference with random vector fields not only the intensity but also the polarization state shows modulation on the observation screen and both modulation contrasts must be fully accounted for to obtain the degree of spatial coherence [ 19 , 20 ].

This work was partially funded by the Academy of Finland projects , , and Mandel and E. Born and E. Wolf, Principles of Optics , 7th exp. London A , — Tervo, T. Saleh and M. Alfano, ed. Springer, Genty, M. Surakka, J. Turunen, and A. B 28 , — Hitzenberger, M. Danner, W.

Born in New York City, he was awarded one half of the Nobel Prize in Physics "for his contribution to the quantum theory of optical coherence ", with the other half shared by John L. Hall and Theodor W. In this work, published in , he created a model for photodetection and explained the fundamental characteristics of different types of light, such as laser light see coherent state and light from light bulbs see blackbody. His theories are widely used in the field of quantum optics. He then went on to do his undergraduate work at Harvard University.

Quantum Theory of Optical Coherence: Selected Papers and Lectures. Author(s):. Roy J. Glauber. First published December

Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions tomograms is presented on an example of coherent states of parametric oscillator. The integrals of motion linear in the position and momentum are used to explicitly obtain the tomogram evolution expressed in terms of trajectories of classical parametric oscillator.

A summary of the pioneering work of Glauber in the field of optical coherence phenomena and photon statistics, this book describes the fundamental ideas of modern quantum optics and photonics in a tutorial style. It is thus not only intended as a reference for researchers in the field, but also to give graduate students an insight into the basic theories of the elizabethsid.org: Roy J. Glauber auth.

*A summary of the pioneering work of Glauber in the field of optical coherence phenomena and photon statistics, this book describes the fundamental ideas of modern quantum optics and photonics in a tutorial style. It is thus not only intended as aMoreA summary of the pioneering work of Glauber in the field of optical coherence phenomena and photon statistics, this book describes the fundamental ideas of modern quantum optics and photonics in a tutorial style. It is thus not only intended as a reference for researchers in the field, but also to give graduate students an insight into the basic theories of the field.*

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*Коммандер устало опустил глаза, затем поднял их вновь. - Сьюзан, выслушай меня, - сказал он, нежно ей улыбнувшись. - Возможно, ты захочешь меня прервать, но все же выслушай до конца.*

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