Search

The Born series is in principle a powerful way to solve electromagnetic scattering problems. Higherorder terms can be computed recurrently until the desired accuracy is obtained. In practice, however, the series solution often diverges, which severely limits its use. We discuss how Padé approximation can be applied to the Born series to tame its divergence. We apply it to the scalar problem of scattering by a cylinder, which has an analytical solution that we use for comparison. Furthermore, we improve our understanding of the divergence problem by analyzing the poles in the analytical solution. This helps build the case for the use of Padé approximation in electromagnetic scattering problems. Additionally, the poles reveal the region of convergence of the Born series for this problem, which agrees with actual calculations of the Born series.

In this contribution we present a method to calibrate a radiometer at high irradiance levels (18 kW/m2). The method has been developed in the frame of the ESA Technology Research Programme. The radiometer under test is used as a reference detector in solar simulators. In order to underpin that the irradiance level that is generated in the solar simulator is within the required levels of uncertainty, the performance of the reference radiometer has been validated. The concept of the calibration of the radiometer is that the radiometer cavity is exposed to a known optical flux, provided by a laser. Taking into account the area of the cavity aperture, which is measured independently with a coordinate measurement machine, the average irradiance level is determined. The reading of the radiometer is then compared to the applied irradiance level. For this calibration the challenge is not only to achieve SI traceability at high irradiance levels, but also to meet other requirements like not to exceed a pre-determined level of irradiance at any position of the radiometer cavity, to avoid potential damage. The measurement uncertainty for the calibration of the instrument is

Array spectroradiometers are attractive alternatives to scanning spectroradiometers in solar ultraviolet measurements. However, the measurement of solar spectral irradiance imposes stringent requirements for the linearity of the instruments. In this article, two array spectroradiometers were characterized for nonlinearity. Significant nonlinearities, in excess of 10%, as a function of analog-to-digital converter counts were discovered. Additional nonlinearities as a function of integration time were observed at very long integration times. No clear residual nonlinearity as a function of spectral irradiance was witnessed despite the characterization spanning four orders of magnitude of spectral irradiance. The characterizations were carried out with three measurement setups that are briefly compared.

We present a portable traceability solution for the ground-based optical calibration of earth observation (EO) instruments. Currently, traceability for this type of calibration is typically based on spectral irradiance sources (e.g. FEL lamps) calibrated at a national metrology institute (NMI). Disadvantages of this source-based traceability are the inflexibility in operating conditions of the source, which are limited to the settings used during calibration at the NMI, and the susceptibility to aging, which requires frequent recalibrations, and which cannot be easily checked on-site. The detector-based traceability solution presented in this work uses a portable filter radiometer to calibrate light sources onsite, immediately before and after, or even during instrument calibration. The filter radiometer itself is traceable to the primary standard of radiometry in the Netherlands. We will discuss the design and realization, calibration and performance verification.

It is commonly believed that the transverse spatial size of a light beam strongly affects its nonparaxiality in the sense that the more a field is localized in space the more nonparaxial its propagation will be. We show that it is not always true. In fact, interesting counterexamples can be pointed out. In particular it is proven the existence of physically realizable fields showing, under particular conditions, a reduction in their nonparaxiality when, at the same time, their transverse sizes are reduced. Such interesting effect can be verified directly by analysing the angular spectrum of such fields as well as making use of the recently introduced concept of degree of paraxiality. After revising its definition in order to include, without inconsistencies, also pseudo-nondiffracting fields, we will recall its physical meaning and we will show its ability to reveal that anomalous relationship between paraxiality and localization for the mentioned class of optical beams.

In this work we present a new and wide class of scalar, rectangular symmetrical optical fields, the free-space propagation of which can be given in a closed-form in the paraxial approximation. In particular it is shown how such fields can be expressed as a finite linear combination of the recently introduced Lorentz beams [O. El Gawhary, S. Severini, J. Opt. A: Pure Appl. Opt., 8 (2006) 409.] that, in this way, act as a basis for the newly introduced class. Because of their mathematical form, we call such fields super-Lorentzian beams. Some common features of the class are pointed out and the concept of order of the beam introduced. Moreover, by using these results, we demonstrate the existence of a new family of mutually orthogonal paraxial fields with a related new class of orthogonal polynomials.

Nijboer–Zernike’s circle polynomials are broadly used for the evaluation of aberrations of optical systems or, more generally, wavefront analysis. This is because they are orthogonal over a unit circle and are directly related to the balanced classical aberrations for imaging systems with circular pupils. However, such expansion and successive extensions of the original theory suffer from a key limitation: it does not preserve its form under propagation. This means that even if a Nijboer–Zernike expansion for a field is known on a given reference plane, as soon as another plane is considered, a new, different set of polynomials for the same field appears. The origin of this problem is to be ascribed to the fact that Nijboer–Zernike polynomials are a useful mathematical tool which, however, are not bound to the physics of the electromagnetic problem they are employed in. In this work, we show that a more appropriate modal expansion does exist that is not only orthogonal on the unit disk but is also invariant on propagation. Besides impacting the field of aberrations analysis and retrieval, the modal expansion introduced here holds an enormous potential for digital classical and quantum optical communications, optical metrology, and adaptive optics too. The practical implementation, physical interpretation, and visualization of this new modal expansion are all very straightforward.

A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. A closed-form expression of free-space propagation under the paraxial limit is derived. Moreover, as the slowly varying part of these fields fulfils the scalar paraxial wave equation, it follows that there also exist Lorentz–Gauss beams, i.e. beams obtained by multiplying the original Lorentz beam by a Gaussian apodization function. Although the existence of Lorentz–Gauss beams can be shown by using two different and independent ways obtained recently by Kiselev (2004 Opt. Spectrosc. 96 497–81) and Gutierrez-Vega and Bandres (2005 J. Opt. Soc. Am. 22 289–98), here we have followed a third different approach, which makes use of Lie's group theory, and which possesses the merit to put into evidence the symmetries present in paraxial optics.

Incoherent Optical Scatterometry (IOS) is a well-established technique in electronic industries for semiconductor metrology. Using this technique one is able to retrieve the properties of the scatterer using the diffracted field. In conventional optical scatterometry, light from an incoherent source is incident on the scatterer (grating) and after the interaction, the angular spectrum is recorded by a detector in the Fourier plane (called far field intensity data). The diffracted far field contains the information about the material composition and the geometrical profile (shape parameters) of the grating. Any change in either the material composition or the geometrical profile of the grating will result in a nonlinear change in the far field data. The technique has several advantages: it is fast, efficient, easy to implement and free from diffraction limit.

In this work we present an extensive study of the scaling symmetry typical of a paraxial wave theory. In particular, by means of a Lagrangian approach we derive the conservation law and the corresponding generalized charge associated with the scale invariance symmetry. In general, such a conserved charge, qs say, can take any value that remains constant during propagation. However, it is explicitly proven that for the whole class of physically realizable shape-invariant fields, that is, fields whose intensity distribution maintains its shape on propagation, qs must necessarily vanish. Finally, an interesting relation between such charge qs and the effective radius of a beam, as introduced by Siegman some years ago, is derived.

It was predicted a few years ago that a medium with negative index of refraction would allow for perfect imaging. Although no material has been found so far that behaves as a perfect lens, some experiments confirmed the theoretical predictions in the near-field, or quasi-static, regime where the behaviour of a negative index medium can be mimicked by a thin layer of noble metal, such as silver. These results are normally attributed to the excitation of surface plasmons in the metal, which only leads to the restoration of p-polarized evanescent waves. In this work, we show that the restoration of s-polarized evanescent waves and, correspondingly, sub-wavelength imaging by a single dielectric slab are possible. Specifically, we show that at ? = 632 nm a thin layer of GaAs behaves as a superlens for s-polarized waves. Replacing the single-metal slab by a dielectric is not only convenient from a technical point of view, it being much easier to deposit and control the thickness and flatness of dielectric films than metal ones, but also invites us to re-think the connection between surface plasmon excitation and the theory of negative refraction.

Providing a femtosecond optical pulse with a proper transverse spatial profile represents a fast and relatively simple method to force a quantum system to follow a prescribed temporal evolution. In the present work, we show that the quantum system presents a surprisingly high sensitivity with respect to the spatial shape of the pulse. We discuss an explicit example where differences on the order of a few nanometers in the initial pulse’s spot size induce completely different responses in the system under study.

Supported by the European Commission and EURAMET, a consortium of 10 participants from national metrology institutes, universities and companies has started a joint research project with the aim of overcoming current challenges in optical scatterometry for traceable linewidth metrology. Both experimental and modelling methods will be enhanced and different methods will be compared with each other and with specially adapted atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurement systems in measurement comparisons. Additionally novel methods for sophisticated data analysis will be developed and investigated to reach significant reductions of the measurement uncertainties in critical dimension (CD) metrology. One final goal will be the realisation of a wafer based reference standard material for calibration of scatterometers.

The nonparaxial corrections for Bessel–Gauss beams were derived recently using two different approaches [Borghi et al., J. Opt. Soc. Am. A 18, 1618 (2001) and Vaveliuk et al., J. Opt. Soc. Am. A 24, 3297 (2007)]. However, the two obtained results do not agree, so it is necessary to determine which method is correct. In the most recent of those papers, Vaveliuk et al. claimed that their method is correct while the method described by Borghi et al. is incorrect. In the present work, just by solving the rigorous propagation problem, we show that exactly the converse is true.

We introduce the degree of paraxiality as a paraxiality measure of a monochromatic light beam. Computation of this parameter is possible once the plane-wave spectrum of the field being analyzed is given for a starting source plane. On the basis of this definition, quantitative comparisons of the paraxiality of different types of fields are possible. In addition, the recently introduced paraxial estimator [Opt. Lett.32, 927 (2007)] is identified as the limiting case of the degree of paraxiality.

We report on the realization of a small optical module for inspection of dimensional and physical properties of thin films materials on a large-area scale. The device, which can measure sample sizes of about 1 m × 0.5 m, uses a structured beam as optical probe, with different polarization states across the beam section. The design, realization, physical modelling, expected performances and the first results are reported.

In our recently published Reply [Opt. Lett. 33, 3006 (2008)], we mistakenly wrote the variable βλ instead of the correct βw0.

The theory of the degree of paraxiality is correct. Very likely, the Comment [Opt. Lett.33, 3004 (2008)] on our original Letter [Opt. Lett.33, 1360 (2008)] originated from an imprecision we made in the plot included in the paper. Such imprecision induced the Comment's author to raise further objections that, as proved in the present Reply, are totally incorrect.

A linearly polarized optical field can be obtained by filtering a stochastic field through an ideal linear polarizer. The produced field possesses a given degree of paraxiality that, as proved in the present Letter, can be affected by the correlations of the original stochastic field. An example with Gaussian beams is discussed in detail.

We comment on a recent paper by Seshadri [Appl. Opt.45, 5335 (2006)]APOPAI0003-693510.1364/AO.45.005335. In the cited work the author utilized the so-named Felsen method in order to derive the full wave expression of a scalar Bessel-Gauss field, propagating in free space, originated from an assigned input distribution on the source plane z = 0. As we show, the author's obtained results do not correctly reproduce the aforesaid input field distribution, as, on the contrary, they have to do.