Christiansen Filter Research Articles

Beam profiles and radiation coherence at the output of solid-state and dye lasers with an intra-cavity immersion diffuser

Lasers on mixtures of solid particles and liquids have long been an attractive subject of research as they can serve as sources of low-coherent radiation and provide a good thermal management using a medium flow. One of such schemes is a laser with an intra-cavity cuvette-diffuser filled by a dense immersion mixture of activated solid micro-particles and a liquid (slurry), similar to the known Christiansen filter. The properties of perspective slurry lasers and features of beams formation in such media were studied in model experiments on bulk Nd:YVO4 and Nd:YAG active elements pumped by 808 nm diodes in quasi-continuous (1 ms, 10 Hz) regime, and on a Rhodamine 101 dye laser pumped by 20 ns, 532 nm light pulses. Laser media were tested in compact (7–50 mm) resonators using a diffuser on a mixture of non-doped LiF micro-particles and isobutanol. The laser spatial coherence was estimated by the contrast C of speckle patterns or by the visibility of Young interferograms γ. Near the threshold separate deformed Laguerre-Gaussian modes and concentric rings were observed at lasers’ output, indicating radiation coherence of C=0.5−0.7. At 100 W pumping Nd:YVO4 and Nd:YAG lasers with diffusers in plano-spherical (PS) resonators provided 1 ms pulses of 1–6 W multimode 1064 nm generation with smoothed beam profiles, divergence up to 0.11 rad and C=0.02−0.1. For a dye laser with a diffuser in PS resonators, 17 ns pulses of 627 nm multimode radiation with 1–3.5 mJ energy, beam divergence 60–280 mrad, γ=0.01−0.05 and up to 30% optical efficiency were obtained. Thus, an intra-cavity diffuser with an immersion mixture is a convenient and simple device to reduce the laser coherence. C and γ values, close to those for thermal light sources make it possible to use the developed lasers for speckles suppression at laser projection, in speed photography, etc. Promising solid-state and dye slurry lasers are discussed. The obtained results show the specific of beam formation in slurry media and give grounds to expect successful development and applications of low-coherent solid-state and dye slurry lasers operating in the visible and infra-red spectral regions.

Christiansen filters realized with cylindrical lenses of even symmetry

A type of Christiansen filter that takes the form of a smooth cylindrical lens of even symmetry is proposed. By varying the shape of the lens, the filter can be made to realize many common filtering responses, including the polynomial function response, the Gaussian function response, and the sinc function response. A systematic design technique based on inverse scattering is established, and a desired, prescribed response can be tailored by properly shaping the lens of the filter. Three prototypical Christiansen filters, namely, a second-order all-real-roots filter, a second-order sinc filter, and a Gaussian filter, are synthesized using the proposed method. A prescribed response at 545 nm with a FWHM of 2 nm is achieved systematically by all of the three Christiansen filters.

Lasing in a medium with the properties of a Christiansen filter.

Dye lasing in a dense slurry-like mixture, similar to the optical medium of the Christiansen filter, is first reported. A cuvette with lithium fluoride (LiF) crystal particles and an immersion liquid containing pyrromethene 567 dye was placed in a two plane mirror resonator and pumped by pulses of the second harmonic of the neodymium-doped yttrium aluminum garnet (Nd:YAG) laser. Twenty nanosecond pulses at 545-570 nm wavelengths with energies up to 0.6 mJ were obtained at the output of this slurry laser. The central part of the laser beam with a divergence of 6 mrad was usually accompanied by a ring structure of scattered radiation. The conditions of the generation development and formation of the output beam profile in a slurry laser as well as its possible applications are discussed.

Phototunable Christiansen Color Filter Using Photoisomerization of Stilbene

We report a fabrication of a phototunable color filter by combining the Christiansen filter effect and photoisomerization of stilbene. It is known that stilbene isomerizes by irradiation with light, but in that case the light absorption capacity changes only in the ultraviolet region. However, the change in the refractive index due to the isomerization is reflected in the visible light region. A system in which glass beads were dispersed in a solution containing dissolved stilbene as a photochromic dye exhibited a vivid color due to the Christiansen filter effect, in spite of the lack of pigment color. Additionally, we found that the hue of the system can be changed by the isomerization of stilbene upon irradiation with ultraviolet light.

Circular differential scattering of polarized light by a chiral random medium

Differential scattering of left- and right-handed circularly polarized waves is a general property of scattering media lacking space-inversion symmetry. We show in this paper that this scattering difference has remarkable properties in the case of an almost transparent chiral random medium. By tuning the refractive indices of the materials composing the medium, this scattering difference can be varied and even inverted. Within the limit of a dense scattering material, the difference of scattering cross sections between polarizations of opposite handedness can be largely adjusted. These properties are illustrated by measurement of the difference between the transmission of right- and left-handed polarized waves through a chiral Christiansen filter.

A Christiansen filter realized with a cylindrical lens

A type of Christiansen filter that takes the form of a cylindrical lens is proposed. This kindof Christiansen filter has a pass band narrower than the traditional one, with more meansof control of its performance; it could approximate arbitrary functions over a frequencyrange of interest. An inverse scattering theory for the synthesis of such a filter is developedand a systematic design technique is established. A desired, prescribed response can betailored by properly configuring the lens of the filter. A Gaussian filter centered at225 nm with a full width at half maximum of 1 nm is synthesized and is numericallymodeled on a computer using the finite difference beam propagation method.The simulation results confirm the feasibility of the proposed Christiansen filter.

Christiansen filter using cylindrical step lens of odd symmetry

A type of Christiansen filter that uses a cylindrical step lens of odd symmetry to achieve wavelength discrimination is proposed. This kind of Christiansen filter has pass band narrower than that of a traditional Christiansen filter, with more means of control for its performance. It could approximate arbitrary functions over a frequency range of interest. The filter's response is analyzed against the step parameters of the lens, and a systematic design method of inverse scattering is developed for the synthesis of such filter. The design technique uses Fourier transformation to correlate the lens' parameters with the filter's performance. With this method the lens shape can be derived from the characteristic pattern of its scattering, which is set to the prescribed filter response. This enables the synthesis of such filter from a desired, target performance. The synthesis of a desired, prescribed response by properly configuring the steps of the lens of the filter is established. It is derived that, due to the limitation of the step lens itself, only certain filter responses can be synthesized and realized physically in Christiansen filter form. Several popular filtering functions are discussed in detail. Two Christiansen filters centered at 545 nm with a full width at half maximum of 2 nm are designed with step lenses, and their selectivity is compared. When a response function cannot be realised in the Christiansen filter form, the underlying difficulty is discussed.

Christiansen filters realized with spherical lenses

We propose the use of a smooth spherical lens in the Christiansen filter cell. The realization of common filtering functions with such a filter configuration is discussed. A systematic design technique based on inverse Fourier cosine transform or inverse Laplace transform is established, with which a desired, prescribed response can be tailored by properly configuring the lens of the filter. Four Christiansen filters centered at 545 nm with a full width at half-maximum of 2 nm are analyzed in detail.

Christiansen filter realized by an odd smooth cylindrical lens

The Christiansen filter that is realized by odd smooth cylindrical lenses is analyzed in detail. Several popular filtering functions are discussed. The corresponding lens profile functions are obtained by an inverse scattering theory, which enables the filter to synthesize a desired prescribed response function. This kind of Christiansen filter has a passband narrower than that of the traditional Christiansen filter. Three Christiansen filters centered at 545 nm with full width at half-maximum of 2 nm are synthesized, and the approach to a better suppression of halos from the main transmission peak of the filters is presented in a systematic way.

Unusual Swelling of HPC in Toluene Forming a Microspherical Domain Structure that Causes Christiansen Scattering Coloration

The unusual swelling behavior of hydroxypropyl cellulose (HPC) by toluene is described. At temperatures as high as 100 degrees C, toluene molecules can enter the HPC film up to the weight fraction of 55%; however, they are segregated from the HPC matrix and form microspherical domains. The size of the spherical domain is approximately 4.5 microm in diameter on average. Such an unusual swelling behavior is due to the amphiphilic nature of the HPC; HPC polymers rearrange to contact their hydrophobic group with toluene and confine the toluene molecules in spherical domains. Because of the similarity in refractive indices of the toluene microspherical phase and the HPC continuum phase, the swollen film shows a beautiful scattering color that is called the Christiansen filter effect.

Christiansen filter synthesized with the Z-transform

The Christiansen filter using three dimensional step lens including spherical lens to achieve wavelength discrimination is analyzed. A systematic design technique based on the Z transform is developed. The synthesis of a desired, prescribed response by properly configuring the lens of the filter is established. Four Christiansen filters centered at 225 nm with a full width at half maximum of 1 nm are discussed in detail.

Time evolution of diffusion fringes in the Christiansen effect

When laser radiation is allowed to fall at the diffusion region separating two liquids in a Christiansen filter, a new fringe pattern appears. We termed it as “diffusion fringes”. In the present work, we have studied this interference fringe pattern and its time evolution. It has been observed that there is a definite co-relation between the shape of the fringe pattern and the width of the diffusion region. The time evolution of this fringe patterns indicates that as diffusion region increases the circular fringe becomes elliptical and finally straight. It is believed that a detailed investigation of these diffusion fringes will throw much needed light not only on the theory of the Christiansen effect but also on the rate of diffusion between two molecules.

Investigations into the mid-infrared Christiansen effect of the dispersive materials

The mid-infrared Christiansen effect was found to occur in the KBr pellets in which powder of the dispersive material α-SiC was dispersed. The KBr pellet technique is commonly used for infrared transmission (or absorption) spectroscopy of powders, and when we dispersed in KBr powder a moderate amount of a dispersive material, such as α-SiC, and pressed them into a pellet, a transmission spectrum with a sharp peak was obtained. The phenomenon is very interesting, and can be explained with the well-known Lorentz dispersion model accurately. Also, it is very useful for making a new type of mid-infrared band-pass filter, e.g. a mid-infrared Christiansen filter. After performing combinations of some other dispersive materials, such as MgO, with some transparent refractive index matching matrices, such as KCl etc, another aspect of the application of this important classical effect is shown, that is, determining the refractive indices of some mid-infrared transparent materials accurately.

Nonlinear Christiansen filter

We demonstrate a nonlinear Christiansen filter in both the steady state and the transient regimes and in both the self- and the cross-modulation modes. Experiments in which a thermal nonlinearity was used agree well with predictions based on a modified scattering theory model.

Nonlinear-optical Christiansen filter as an optical power limiter

We have constructed an optical power limiter based on nonlinear induced scattering in a cell containing crushed glass and a mixture of acetone and carbon disulfide. For 30-ps-long laser pulses the transmitted energy saturates at a value of 6 microJ. We also present the results of a theoretical modeling study that shows how the operating characteristics of such a device can be optimized.

Interaction of slow neutrons with natural Rutenium, Rhodium, Cadmium and Thallium and some of their isotopes

By means of Christiansen filter technique the following bound coherent neutron scattering lengths were obtained:natRu:b=7.02 ± 0.02 fm108Cd:b=5.31 ± 0.24 fm103Rh:b=5.90 ± 0.04 fm110Cd:b=5.78 ± 0.08 fmnatTl:b=8.773 ± 0.015 fm111Cd:b=6.47 ± 0.08 fm203Tl:b=8.51 ± 0.08 fm112Cd:b=6.34 ± 0.06 fm205Tl:b=8.87 ± 0.07 fm114Cd:b=7.48 ± 0.05 fm116Cd:b=6.26 ± 0.09 fm In combination with some total cross section measurements with neutrons in the eV-energy range and with the compiled resonance parameters we deduced consistent sets of spin state scattering lengths and potential radii.

Interaction of slow neutrons with nuclides of scandium, titanium, vanadium and manganese

Total cross section measurements at various neutron energies were performed on metallic and oxide samples of natural Sc, Ti, V, and Mn. By means of the Christiansen filter technique the coherent scattering lengths were determined on natural and isotopically enriched samples of Ti-, V-, and Mn-compounds. From the measured values we deduced the following data:

Theory of a Christiansen filter composed of inhomogeneous particles (review)

Theory of a Christiansen filter composed of inhomogeneous particles (review)

Natural convection in porous media—I. Nonfreezing

The Christiansen filter concept is used to visualize natural convection in porous media. Studies are conducted with both permeable and impermeable upper boundaries. The experimental results agree well with the numerical calculations which are based upon Darcy's law. Three different permeabilities as well as different test section aspect ratios (width/height) are examined. It is found that the aspect ratio of the cells does not vary with modified Rayleigh number for the impermeable upper boundary but this ratio increases significantly with modified Rayleigh number for the permeable upper boundary.

Refined interpretation of Christiansen-filter experiments and neutron scattering lengths of the lead-isotopes

A refined interpretation of Christiansen filter experiments is described, which allows for the effects of inhomogeneities in the powder column of the filter. Using this procedure the evaluation of experiments on enriched samples of lead isotopes provided the neutron coherent scattering lengths (in fm) for the separated isotopes:b (204) =10.6 ± 2.0;b (206)=9.23 ± 0.05;b (207)=9.28 ± 0.04 andb (208)=9.50 ± 0.06. The corresponding potential scattering radius R′ was obtained by taking account of resonance contributions as earlier used in the determination of the neutron's electric polarizability. The found R′=9.74 ± 0.07 fm is in good argreement with the literature. This confirms the correctness of the used resonance contributions.