Carving beams of light.

Some years after the appearance of the so-called non-diffracting beams, there was the development of methods capable of structuring them spatially, with the so-called frozen wave method being the first and, perhaps, the most efficient one. That method allows for modelling the longitudinal intensity pattern of non-diffracting beams, but it is little efficient in controlling their transverse spatial pattern, granting only the possibility of choosing their transverse dimensions, which remain invariant throughout the propagation. In this work, we have extended the frozen wave method in such a way, to control the transverse beam structure along the propagation, in addition to the longitudinal pattern. The new transversally and longitudinally structured beams can have potential applications in areas such as photonics, optical manipulation, optical atom guidance, and lithography.

Analytical method for the description of important obstructed optical beams and the Poisson-Arago spot.

In this work, we describe analytically the diffraction of some important beams due to a circular obstacle. In order to obtain the desired results, we deal with the wave equation in paraxial approximation together with the diffraction Fresnel integral and apply the analytical method proposed by Zamboni-Rached et al. [Appl. Opt.51, 3370-3379 (2012)APOPAI0003-693510.1364/AO.51.003370]. As a byproduct of our method, we notice the formation of the Poisson-Arago spot for ordinary beams (plane wave and Gaussian beam) and a reconstruction of the beam for nondiffracting beams (Bessel beam). Then, we pass to a vectorial analysis for better describing the electromagnetic beams.

Experimental optical trapping with frozen waves.

We report, to the best of our knowledge, the first optical trapping experimental demonstration of microparticles with frozen waves. Frozen waves are an efficient method to model longitudinally the intensity of nondiffracting beams obtained by superposing copropagating Bessel beams with the same frequency and order. Based on this, we investigate the optical force distribution acting on microparticles of two types of frozen waves. The experimental setup of holographic optical tweezers using a spatial light modulator has been assembled and optimized. The results show that it is possible to obtain greater stability for optical trapping using frozen waves. The significant enhancement in trapping geometry from this approach shows promising applications for optical tweezers micromanipulations over a broad range.

Arrays of spatially structured non-diffracting optical beams.

Non-diffracting optical beams and their structured versions have been extensively studied, theoretically and experimentally, over the last two decades, rendering important applications in fields such as imaging, microscopy, remote sensing, optical manipulation, free space optics, etc. In this paper, we theoretically construct arrays of non-coaxial structured non-diffracting beams by using the so-called frozen wave method. We also develop techniques based on polarization allocations and apodizations to mitigate undesirable interferences among neighboring beams. Our results can find interesting applications in all fields that benefit from the use of non-diffracting beams.

Transmission of spatial-shaped diffraction-resistant beams through stratified dielectric media: finite energy formulation.

In this paper, we describe the reflection and transmission of a normally incident Bessel-Gauss beam upon a flat and non-absorbing dielectric interface and use such results to develop an original method based on Bessel-Gauss beam superposition capable of providing diffraction-resistant beams whose longitudinal intensity pattern can be modeled on demand even after crossing an arbitrary stratified dielectric structure.

Modeling the longitudinal intensity pattern of diffraction resistant beams in stratified media.

In this paper, we study the propagation of the frozen wave (FW)-type beams through non-absorbing stratified media and develop a theoretical method capable of providing the desired spatially shaped diffraction-resistant beam in the last material medium. In this context, we also develop a matrix method to deal with stratified media with a large number of layers. Additionally, we undertake some discussion about minimizing reflection of the incident FW beam on the first material interface by using thin films. Our results show that it is indeed possible to obtain the control, on demand, of the longitudinal intensity pattern of a diffraction-resistant beam, even after it undergoes multiple reflections and transmissions at the layer interfaces. Remote sensing, medical and military applications, noninvasive optical measurements, etc., are some fields that can benefit from the method here proposed.

Structuring light under different polarization states within micrometer domains: exact analysis from the Maxwell equations.

We show the possibility of arbitrary longitudinal spatial modeling of non-diffracting light beams over micrometric regions. The resulting beams, which are highly non-paraxial, possess subwavelength spots and can acquire multiple intensity peaks at predefined locations over regions that are few times larger than the wavelength. The formulation we present here provides exact solutions to the Maxwell's equations where the linear, radial, and azimuthal beam polarizations are all considered. Modeling the longitudinal intensity pattern at small scale can address many challenges in three-dimensional optical trapping and micromanipulation.

Generating attenuation-resistant frozen waves in absorbing fluid.

We demonstrate a class of nondiffracting beams, called frozen waves, with a central spot that can be made to maintain a predefined intensity profile while propagating in an absorbing fluid. Frozen waves are composed of Bessel beams with different transverse and longitudinal wavenumbers, and are generated using a programmable spatial light modulator. The attenuation-resistant frozen waves demonstrated here address the problem of propagation losses in absorbing media. This development can be beneficial for many applications in particle micro-manipulation, data communications, remote sensing, and imaging.

Superluminal, luminal, and subluminal nondiffracting pulses applied to free-space optical systems: theoretical description.

In this paper, we show theoretically nondiffracting pulses with arbitrary peak velocities that are suitable for data signal transmission without distortion over long distances using different techniques of signal modulation. Our results provide closed-form analytical solutions to the wave equation describing superluminal, luminal, and subluminal ideal nondiffracting pulses with frequency spectra commonly used in the field of optical communications.

Production of dynamic frozen waves: controlling shape, location (and speed) of diffraction-resistant beams.

In recent times, we experimentally realized quite an efficient modeling of the shape of diffraction-resistant optical beams, thus generating for the first time the so-called frozen waves (FW), whose longitudinal intensity pattern can be arbitrarily chosen within a prefixed space interval of the propagation axis. In this Letter, we extend our theory of FWs, which led to beams endowed with a static envelope, through a dynamic modeling of the FWs whose shape is now allowed to evolve in time in a predetermined way. Further, we experimentally create such dynamic FWs (DFWs) in optics via a computational holographic technique and a spatial light modulator. Experimental results are presented here for two cases of DFWs, one of zeroth order and the other of higher order, the latter being the most interesting exhibiting a cylindrical surface of light whose geometry changes in space and time.

Propagation of time-truncated Airy-type pulses in media with quadratic and cubic dispersion.

In this paper, we describe analytically the propagation of Airy-type pulses truncated by a finite-time aperture when second- and third-order dispersion effects are considered. The mathematical method presented here, which is based on the superposition of exponentially truncated Airy pulses, is very effective and allows us to avoid the use of time-consuming numerical simulations. We analyze the behavior of the time-truncated ideal Airy pulse and also the interesting case of a time-truncated Airy pulse with a "defect" in its initial profile, which reveals the self-healing property of this kind of pulse solution.

Analytical approach of ordinary frozen waves for optical trapping and micromanipulation.

The optical properties of frozen waves (FWs) are theoretically and numerically investigated using the generalized Lorenz-Mie theory (GLMT) together with integral localized approximation. These waves are constructed from a suitable superposition of equal-frequency ordinary Bessel beams and are capable of providing almost any desired longitudinal intensity profile along their optical axis, thus being of potential interest in applications in which intensity localization may be used advantageously, such as in optical trapping and micromanipulation systems. In addition, because FWs are composed of nondiffracting beams, they are also capable of overcoming the diffraction effects for longer distances when compared to conventional (ordinary) beams, e.g., Gaussian beams. Expressions for the beam-shape coefficients of FWs are provided, and the GLMT is used to reconstruct their intensity profiles and to predict their optical properties for possible biomedical optics purposes.

Diffraction-resistant scalar beams generated by a parabolic reflector and a source of spherical waves.

In this work, we propose the generation of diffraction-resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long-range diffraction-resistant waves.

Exact analytic solutions of Maxwell's equations describing propagating nonparaxial electromagnetic beams.

In this paper, we propose a method that is capable of describing in exact and analytic form the propagation of nonparaxial scalar and electromagnetic beams. The main features of the method presented here are its mathematical simplicity and the fast convergence in the cases of highly nonparaxial electromagnetic beams, enabling us to obtain high-precision results without the necessity of lengthy numerical simulations or other more complex analytical calculations. The method can be used in electromagnetism (optics, microwaves) as well as in acoustics.

Analytic description of Airy-type beams when truncated by finite apertures.

In this paper, we have developed an analytic method for describing Airy-type beams truncated by finite apertures. This new approach is based on suitable superposition of exponentially decaying Airy beams. Regarding both theoretical and numerical aspects, the results here shown are interesting because they have been quickly evaluated through a simple analytic solution, whose propagation characteristics agree with those already published in literature through the use of numerical methods. To demonstrate the method's potentiality three different truncated beams have been analyzed: ideal Airy, Airy-Gauss and Airy-Exponential.

Frozen waves: experimental generation.

Frozen waves (FWs) are very interesting particular cases of nondiffracting beams whose envelopes are static and whose longitudinal intensity patterns can be chosen a priori. We present here for the first time (that we know of) the experimental generation of FWs. The experimental realization of these FWs was obtained using a holographic setup for the optical reconstruction of computer generated holograms (CGH), based on a 4-f Fourier filtering system and a nematic liquid crystal spatial light modulator (LC-SLM), where FW CGHs were first computationally implemented, and later electronically implemented, on the LC-SLM for optical reconstruction. The experimental results are in agreement with the corresponding theoretical analytical solutions and hold excellent prospects for implementation in scientific and technological applications.

Simple and effective method for the analytic description of important optical beams when truncated by finite apertures.

In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the three-dimensional evolution of important waves as Bessel beams, plane waves, gaussian beams, and Bessel-Gauss beams when truncated by finite apertures. One of the by-products of our mathematical method is that one can get in a few seconds, or minutes, high-precision results, which normally require quite lengthy numerical simulations. The method works in electromagnetism (optics, microwaves) as well as in acoustics.

Cherenkov radiation versus X-shaped localized waves.

Localized waves (LW) are nondiffracting ("soliton-like") solutions to the wave equations and are known to exist with subluminal, luminal, and superluminal peak velocities V. For mathematical and experimental reasons, those that have attracted more attention are the "X-shaped" superluminal waves. Such waves are associated with a cone, so that one may be tempted-let us confine ourselves to electromagnetism-to look [Phys. Rev. Lett.99, 244802 (2007)] for links between them and the Cherenkov radiation. However, the X-shaped waves belong to a very different realm: For instance, they can be shown to exist, independently of any media, even in vacuum, as localized non-diffracting pulses propagating rigidly with a peak-velocity V>c [Hernández et al., eds., Localized Waves (Wiley, 2008)]. We dissect the whole question on the basis of a rigorous formalism and clear physical considerations.

Diffraction-attenuation resistant beams: their higher-order versions and finite-aperture generations.

Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media has been developed in terms of suitable superposition of ideal zero-order Bessel beams. In this work, we show that such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Moreover, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams. Although the method is developed for scalar fields, it can be applied to paraxial vector wave fields, as well. These new beams have many potential applications, such as in free-space optics, medical apparatus, remote sensing, and optical tweezers.

Experimental demonstration of tunable refractometer based on orbital angular momentum of longitudinally structured light.

The index of refraction plays a decisive role in the design and classification of optical materials and devices; therefore, its proper and accurate determination is essential. In most refractive index (RI) sensing schemes, however, there is a trade-off between providing high-resolution measurements and covering a wide range of RIs. We propose and experimentally demonstrate a novel mechanism for sensing the index of refraction of a medium by utilizing the orbital angular momentum (OAM) of structured light. Using a superposition of co-propagating monochromatic higher-order Bessel beams with equally spaced longitudinal wavenumbers, in a comb-like setting, we generate non-diffracting rotating light structures in which the orientation of the beam's intensity profile is sensitive to the RI of the medium (here, a fluid). In principle, the sensitivity of this scheme can exceed ~2700°/RI unit (RIU) with a resolution of ~ 1 0 - 5 RIU. Furthermore, we show how the unbounded degrees of freedom associated with OAM can be deployed to offer a wide dynamic range by generating structured light that evolves into different patterns based on the change in RI. The rotating light structures are generated by a programmable spatial light modulator. This provides dynamic control over the sensitivity, which can be tuned to perform coarse or fine measurements of the RI in real time. This, in turn, allows high sensitivity and resolution to be achieved simultaneously over a very wide dynamic range, which is a typical trade-off in all RI sensing schemes. We thus envision that this method will open new directions in refractometry and remote sensing.