Degree of coherence | EPFL Graph Search

In quantum optics, correlation functions are used to characterize the statistical and coherence properties of an electromagnetic field. The degree of coherence is the normalized correlation of electric fields; in its simplest form, termed g^{(1)}. It is useful for quantifying the coherence between two electric fields, as measured in a Michelson or other linear optical interferometer. The correlation between pairs of fields, g^{(2)}, typically is used to find the statistical character of intensity fluctuations. First order correlation is actually the amplitude-amplitude correlation and the second order correlation is the intensity-intensity correlation. It is also used to differentiate between states of light that require a quantum mechanical description and those for which classical fields are sufficient. Analogous considerations apply to any Bose field in subatomic physics, in particular to mesons (cf. Bose–Einstein correlations). Degree of first-o

Coherence properties of microcavity polaritons

Stefan Kundermann

This thesis presents the coherence properties of polaritons in semiconductor microcavities. Semiconductor microcavities are microstructures in which the exciton ground state of a semiconductor quantum well is coupled to a photonic mode of a microresonator. The strong coupling mixes the character of excitons and photons, giving rise to the lower and upper polariton branches, quasiparticles with an unusual energetic dispersion relation due to the extreme mass difference between exciton and photon. Particularly special is the dispersion of the lower polariton, which forms a dip in the 2-dimensional k-space around the lowest energy state with zero in-plane momentum. In this dip, which can be seen as a trap in momentum space, the polaritons are efficiently isolated from dephasing mechanisms involving phonons. Polaritons can be resonantly excited at desired points on the polariton dispersion by shining on the microcavity laser light at the appropriate angle and wavelength. Polaritons can interact and scatter pairwise with each other conserving energy and in plane momentum k, a process similar to parametric scattering of photons in a nonlinear crystal. One polariton from a pump reservoir scatters down to the signal state at k = 0 (corresponding to normal incidence) and a second takes away the excess energy and momentum of the first and scatters up to the idler position ({kP, kP} → {0, 2kP }). This process can be stimulated by a small amount of signal polaritons injected with a probe laser beam at normal incidence. Here the coherence properties of the polariton parametric scattering have been investigated using spectroscopy techniques sensitive to the optical phase, for example coherent control with phase-locked femtosecond probe pulses. Just above the threshold for the stimulated parametric scattering, the parametric amplification process is given by the linear superposition of the individual amplification processes of each probe pulse. The emission of signal, pump, and idler can be controlled by tuning the relative phase of the 150fs-long probe pulses, which are separated by a few picoseconds in time. Experiments are presented that deal with the real-time dynamics of the parametric scattering in the spontaneous and the stimulated regime. It is shown, that in the spontaneous regime the scattering is started by a small amount of polaritons which have relaxed to the band bottom by emitting phonons. In the regime where polariton scattering is stimulated by an external probe, the rise of the signal intensity is delayed with respect to the arrival time of both pump and probe, a feature that can be attributed to the complex phase-matching mechanism for the parametric scattering. In the second part of the thesis, the spontaneous build up of a macroscopic coherence in a CdTe microcavity under non-resonant laser excitation is analysed. The build up of a long-range spatial coherence easily exceeding the thermal wavelength of the polaritons is shown. This is the hallmark of Bose-Einstein condensation and the proof of a macroscopic wavefunction. Experimental data on the statistical distribution of the polaritons in time, the polarisation of the non-linear emission, and the quantum transition from a thermal to a coherent state1 confirm that Bose-Einstein condensation of microcavity polaritons has been observed. We regard these observations as the first bullet-proof evidence for spontaneous Bose-Einstein condensation in a solid state system, a phenomenon that has been the subject to many investigations and controversies during the past four decades. ------------------------------ 1 The data about the statistical distribution, the polarisation, and the transition from a thermal to a coherent state is by courtesy of Jacek Kasprzak of the University of Grenoble.

EPFL2006

Broadband Digital Holographic Camera for Microscopy

Zahra Monemhaghdoust

In this thesis, we explore a combination of analog and digital holographic techniques to demonstrate high speed quantitative phase imaging (QPI) using low coherence (broad bandwidth) light sources. Off-axis digital holographic microscopy is inherently a coherent method of phase quantification and thus suffers from coherent noise. However, only one measurement is required to retrieve field information which gives an advantage in term of image acquisition speed. While incoherent methods of phase quantification remove the problem of coherent noise, they require acquiring several measurements which is sometimes not acceptable in the study of dynamical systems. Therefore, this thesis is an attempt to extend off-axis digital holographic microscopy from the coherent to the incoherent regime to maintain the benefit of high speed measurement capability of off-axis holography while reducing the coherent noise. First, we demonstrate that by using a suitable combination of holographic gratings, off-axis digital holographic microscopy can work with spectrally broadband illumination sources. Holographic gratings introduce a tilt in the coherence plane of one of the reference or object arms of an off-axis digital holographic microscope to expand the interference area to the whole field of view of the camera. Although QPI provides useful information in addition to state-of-the-art intensity-based microscopic imaging, its use has not permeated yet far beyond research laboratories. One potential reason is the need for a stand-alone dedicated microscope system, which is expensive and not back-compatible to the existing wide-field microscopes. In this Regard, the second part of this thesis explores an add-on camera module which can be attached to the camera port of any standard intensity microscope. The techniques developed to extend the off-axis DHM in the first part of the thesis will be used to demonstrate a proof-of-concept camera module which operates with broadband light sources. Overall, through the combination of analog and digital holography, the goal of this work is to extend full-field off-axis holography to incoherent regime to benefit from real-time speckle-free measurements, optical sectioning and realization of a digital holographic camera which can be placed in the image plane of a standard optical microscope.

EPFL2015

High power ultraviolet LED illumination systems: coherence properties and applications in photolithography

Johana Bernasconi

Mask-aligner photolithography is a technology used to replicate patterns from a mask to a photosensitive substrate. It is widely used in the fabrication of MEMS and micro-optical components, and for other applications with dimensions in the micrometer range. Traditionally, the light sources used for mask-aligners are high-pressure mercury arc lamps, which emit in the ultraviolet range with peaks at 365nm, 405nm and 435nm, the so-called g-, h- and i- lines. These lamps suffer from several disadvantages, such as a low efficiency, bulkiness, a short lifetime, and the toxicity of mercury. Finding an alternative to mercury arc lamps would be highly beneficial. In addition, specific techniques in mask-aligner technologies like Talbot lithography, multiple exposures, mask-source optimization or optical proximity correction lithography require high power sources with an increased control over the angular distribution and the spatial coherence. This is not easily done with a mercury arc lamp illumination. A method to easily measure the angular distribution and the spatial coherence in the mask-plane would be of great interest. In recent years, high power ultraviolet LEDs at the same wavelengths have appeared on the market. LEDs possess a smaller Etendue, they can be electronically driven at high frequencies and have a superior lifetime. This makes them ideal candidates to overcome the limitations of the mercury arc lamp illumination systems. The work focuses on the development and study of a novel LED-based illumination system for mask aligner lithography. This illumination system consists of an array of 7x7 LEDs, with individual reflectors. They form a modular 250W source which can replace a 1kW mercury arc lamp. The light is collected by the reflectors and brought onto a fly¿s eye integrator with two subsequent lenses which shape and homogenize the light field. Different patterns can be created by the source, determining the angles and the spatial coherence in the mask plane. The first part of the work presents the design and a complete set of characterizations of the final prototype. The achieved irradiance uniformity in the mask-plane of a MA/BA8 Gen3 SUSS mask-aligner is within ±1.2-2%. Prints tests in proximity printing, with a gap of 30µm, demonstrate a resolution of 3.5µm. In the second part of the thesis, the development of a method to measure the spatial coherence, which is based on a double slit approach and backed up by simulation, is described. The link between the spatial coherence length and the angular extent is made and the measurements show a good agreement with the analytical expression. A compact system is described, which enables the measurement of the spatial coherence in the mask plane, where only a little space is available. An original method is put into practice in order to measure the directional spatial coherence in two dimensions in the mask plane of a mask-aligner. This is achieved by using a circular double slits system. Prints are also made which illustrate the importance of the angular distribution and the spatial coherence. This novel LED-based illumination system is implementable in current, commercial, mask-aligners. It enables a greater efficiency, more functionalities and a longer lifetime compared to standard mercury arc lamp illumination systems. In particular, the spatial coherence properties of the source can be precisely managed and monitored thanks to the directional spatial coherence measurement.

EPFL2018