Longitudinal spatial coherence applied for surface profilometry

A method of optical coherence profilometry, believed to be new, is demonstrated. This method is based on the spatial, rather than the temporal, coherence phenomenon. Therefore the proposed interferometric system is illuminated by a quasi-monochromatic spatial incoherent source instead of a broadband light source. The surface profile is measured by means of shifting the spatial degree of coherence gradually along its longitudinal axis while keeping the optical path difference between the measured surface and a reference plane constant. Experimental proof of the new principle is presented.     

Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond

We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwell's equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.     

新型相干结构光场调控及应用研究进展

结构光场的空域调控包括振幅、相位、偏振、相干度等丰富自由度,对其自由度的单一或联合调控引发了一系列新奇物理效应,在新型结构光场构建及多种领域中具有重要应用。相比于完全相干光场,部分相干光场在抵抗散斑噪声和大气湍流扰动等方面具有独特优势。近年来,具有新型相干结构的部分相干光束在大气传输、光学加密与成像、信息鲁棒传输、高质量光束整形等领域有着重要研究价值。本文详细综述了具有新型相干结构部分相干光场的理论构建与实验合成的研究进展,并重点介绍了新型相干结构光场在复杂环境中的鲁棒传输特性及其在光学加密、成像、鲁棒信息传输及光束整形中的应用研究进展。研究表明,新型相干结构光场调控不仅提供了一种有效抵抗复杂环境扰动的有效手段,而且丰富了光场调控技术在多种领域中的应用。最后,对新型相干结构调控技术发展趋势及潜在应用前景进行了展望。

     

Spatial phase information transmission through an optical fiber by coherence function synthesis

Transmission of one-dimensional spatial phase information by low-coherence light through a single-mode optical fiber is experimentally demonstrated by use of space-time conversion at a 4-f Fourier coherence function shaper and time-space conversion with spectral holography. The dispersion during the fiber propagation can be automatically compensated for with spectral holography. However, space-time coupling caused by the transmitter limits the capacity of information transmittable with one coherence function shaping. A significant advantage in the space-time-space conversion with low-coherence light is that an infinite number of signal channels can be multiplexed with a newly invented delay-time division scheme, which can extend this analog transmission to two-dimensional spatial phase patterns.     

From stationary annular rings to rotating Bessel beams

In this work we use a phase-only spatial light modulator (SLM) to mimic a ring-slit aperture, containing multiple azimuthally varying phases at different radial positions. The optical Fourier transform of such an aperture is currently known and its intensity profile has been shown to rotate along its propagation axis. Here we investigate the near-field of the ring-slit aperture and show, both experimentally and theoretically, that although the near-field possesses similar attributes to its Fourier transform, its intensity profile exhibits no rotation as it propagates.     

Call for Papers

Abstract

An expression is found for the propagation of the radiance function for light in any state of coherence through a concentrator which can be represented by a linear, stationary optical system. For light from a quasi-homogeneous source this expression can be somewhat simplified by an approximation. It is shown that the radiance function is invariant for a large class of optical systems. Finally it is shown that fundamental limitations for the concentration of light follow from the uncertainty principle and the second law of thermodynamics, which apply quite generally. These relations show why quasi-homogeneous light (i.e. light from thermal sources) cannot be concentrated as well as light from some other sources (such as light from a laser).     

The Spatial Coherence Properties of Gaussian Schell-model Beams

The transverse and longitudinal spatial coherence properties of the light beams generated by planar gaussian Schell-model sources are discussed. It is found that for all gaussian Schell-model beams the ratio of the transverse coherence length to the beam width remains invariant upon propagation. An examination of the longitudinal coherence for both on-axis and off-axis pairs of points indicates that the longitudinal coherence will not, in general, die out as the separation between the points is increased. Rather, the degree of longitudinal coherence will approach a finite (non-zero) value as long as the source contains a finite coherence area, regardless of how small this area may be. Gaussian quasihomogeneous beams are studied as a limiting case. The relation of the present work to the analysis of speckle size is briefly discussed.     

Efficient numerical representation of the optical field for the propagation of partially coherent radiation with a specified spatial and temporal coherence function

We propose a method to narrow the gap between the rigorous methods for the propagation of partially coherent light, which require excessive computational capacity, and the numerical methods used in practical engineering applications, where it is not clear how to handle spatial and temporal coherence in a statistically correct manner. As is the case for the latter methods, the numerical method described can deal with fields with a large spatial and temporal extent, which is necessary in practical applications such as laser fusion or optical lithography. However, the method also takes a few steps toward a more rigorous, yet efficient, representation of the optical field, which depends on detailed specified coherence properties of the radiation. The described method uses a set of independent monochromatic fields at different oscillation frequencies. The frequencies are chosen such that the statistical properties of the integrated intensity closely resemble those from a full-time trace treatment. Finally, we demonstrate the capabilities and limitations of the method with a few numerical examples of the propagation of a large field with a specified spatial and temporal coherence.     

The effects of temporal and longitudinal spatial coherence in a disbalanced-arm interferometer

During the interference of optical fields possessing broad frequency and angular spectra in an oscillating-mirror Michelson interferometer, the presence of a film introducing an additional optical path increment in one of the arms leads to a mutual shift (recession) of the signals of temporal and longitudinal spatial coherence. This phenomenon leads to breakage of the mutual coherence of the interfering fields. In the presence of two light sources, this effect can be used for the independent determination of the thickness and refractive index of the film.     

Propagation of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system

Based on the generalized Huygens–Fresnel integral, analytical expressions for the mutual coherence function, the spatial complex degree of coherence, and the effective size of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system have been derived. As a numerical example, the propagation of a partially coherent higher-order cosh-Gaussian beam through an optical Fourier-transforming system with a limiting aperture is illustrated. The normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size for the partially coherent higher-order cosh-Gaussian beam are numerically demonstrated in the observation plane. The influences of the spatial coherence length and the limiting aperture on the normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size are also examined in detail.     

A variable lateral-shearing Sagnac interferometer with high numerical aperture for measuring the complex spatial coherence function of light

Abstract

We combine a telescopic imaging system with a common-path, lateral-shearing interferometer and use phase-shifting interferometry to measure the complex spatial coherence function (or mutual intensity) of a linearly-polarized optical field. Our telescopic design increases the numerical aperture of the system without distorting the shape of the wave front, and therefore without changing the phase difference between lateral positions in the optical field. Our method of generating lateral-sheared images introduces no additional astigmatism. To demonstrate the use of the interferometer we extract the information contained in the complex spatial coherence function to reconstruct the amplitude and phase of a coherent optical field, and we also show how the spatial coherence function evolves from a coherent field to a partially coherent one as light traverses a random multiple-scattering medium.     

Optical forces on small particles from partially coherent light

We put forward a theory on the optical force exerted upon a dipolar particle by a stationary and ergodic partially coherent light field. We show through a rigorous analysis that the ensemble averaged electromagnetic force is given in terms of a partial gradient of the space-variable diagonal elements of the coherence tensor. Further, by following this result we characterize the conservative and nonconservative components of this force. In addition, we establish the propagation law for the optical force in terms of the coherence function of light at a diffraction plane. This permits us to evaluate the effect of the degree of coherence on the force components by using the archetypical configuration of Young's two-aperture diffraction pattern, so often employed to characterize coherence of waves.     

Temporal transformation of periodic incoherent ultrashort light pulses by chirped fiber gratings

The analogy between free-space propagation of optical beams and light-pulse reflection from linearly chirped fiber gratings is used to analyze the Lau effect in the temporal domain. The coherence conditions that are satisfied in the spatial domain for obtaining, at certain fixed locations, periodic fringes patterns are reformulated for guided light propagation. In this analogy, spatial periodic irradiance distributions are transformed in periodic sequences of light pulses. An optical setup is proposed to produce sharp pulse trains, with minimal distortion effects, that have repetition frequencies that are different from those associated with the input periodic optical signal. Some numerical results are given to illustrate this approach.     

Propagation of the Airy beam along the optical axis of a uniaxial medium

We investigate the propagation of an Airy beam along the optical axis of a uniaxial medium, and we find that the propagation property of the Airy beam is determined by the ordinary refractive index of uniaxial crystals and is independent of the ratio of the extraordinary to ordinary refractive index. We also know that the polarization state of linearly polarized Airy beams changes gradually during the propagation. This shows that the propagation properties of the Airy beam in uniaxial crystals along the optical axis is distinctly different from that orthogonal to the optical axis.     

Radiometric theory of spatial coherence in free-space propagation

The radiometric theory of spatial coherence is presented with special attention to the validity of the approximations on which it is based. A new definition of the transverse coherence area is introduced and shown to be in general agreement with earlier definitions. In free-space propagation the product of the transverse coherence area and the intensity is shown to be constant along rectilinear rays, and, for radiation from uniform Lambert sources, a well-known paraxial formula for the transverse coherence area is extended to the extraparaxial domain. A decrease of the spatial coherence in free-space propagation takes place in regions with an increase of the intensity. For imaging systems this occurs in a finite part of image space whenever a real image of a diffusely radiating, extended object is formed at a finite distance.     

Low-coherence interferometry with synthesis of coherence function

Synthesis of a coherence function by manipulation of the spectral phase of low-coherent light with a segmented liquid-crystal phase modulator and its application in a low-coherence interferometry are described. Effects of space-time coupling caused at diffractive gratings and second-order dispersion at the spatial light modulator on the coherence function synthesis are theoretically and experimentally verified. Various coherence functions can be shaped with phase-only masks designed by simulated annealing optimization algorithm. We utilized this technique for a novel optical low-coherence reflectometry without any mechanical movement for scanning optical delay.     

Characterization of dentin and enamel by use of optical coherence tomography

Optical coherence tomographic images of human dentin and enamel are obtained by use of polarization-sensitive optical coherence tomography. A birefringence effect in enamel (lambda = 856 nm) and light propagation along dentinal tubules are observed. The group index of refraction for both dentin and enamel was measured at 1.50 +/- 0.02 and 1.62 +/- 0.02, respectively.     

Using light scattering to measure the temporal coherence of optical sources

We demonstrate a simple and robust method for characterizing the temporal coherence of statistically stationary optical sources by using dynamic light scattering. Measurement of the contrast of the fluctuating speckle pattern produced by two counterpropagating beams incident on a scattering medium is used to evaluate their mutual coherence. Important features of this method are high statistical accuracy, the ability to compensate for imperfect spatial coherence, and the possibility of characterizing milliwatt-level optical beams with a wide range of spectral widths. As an example, the squared magnitude of the field autocorrelation function for light emitted by a broadband argon-ion laser is obtained.