Alexandre April

Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent.

Optical beams exhibiting a long depth of focus and a minimum spot size can be obtained with the tight focusing of a narrow annulus of radially polarized light, leading to a needle of longitudinally polarized light. Such beams are of increasing interest for their applications, for example in optical data storage, particle acceleration, and biomedical imaging. Hence one needs to characterize the needles of longitudinally polarized light obtained with different focusing optics and incident beams. In this paper, we present analytical expressions for the electric field of such a nearly nondiffracting, subwavelength beam obtained with a parabolic mirror or an aplanatic lens. Based on these results, we give expressions of the transverse and longitudinal full widths at half maximum of the focal lines as a function of the width of the incident annular beam and we compare the performances of the two focusing systems. Then, we propose a practical solution to produce a needle of longitudinally polarized light with a tunable axial extent and a transverse width reaching the theoretical limit of 0.36λ.

Nonparaxial elegant Laguerre-Gaussian beams.

Closed-form nonparaxial expressions for optical beams are useful to calculate the fields produced by tightly focused laser beams. Such expressions for elegant Laguerre-Gaussian (eLG) beams that are exact solutions of the Helmholtz equation are introduced. These solutions are expressed as linear combinations of a finite number of analytic functions that involve spherical Bessel functions and associated Legendre functions of complex arguments. In the paraxial limit, the expressions proposed have the property to reduce to the well-known eLG beams.

Nonparaxial TM and TE beams in free space

Expressions for the fields of TM and TE laser beams in free space that are rigorous solutions to Maxwells equations are given in a closed form. The electric and the magnetic fields are both expressed in terms of nonparaxial elegant Laguerre-Gaussian beams that are exact solutions of the Helmholtz equation. These solutions involve well-known functions, such as spherical Bessel and associated Legendre functions. Radially and azimuthally polarized beams of arbitrary order are considered, and the lowest-order radially polarized beam (TM(01) beam) is investigated in detail.

Electron acceleration driven by ultrashort and nonparaxial radially polarized laser pulses

Exact closed-form solutions to Maxwells equations are used to investigate the acceleration of electrons in vacuum driven by ultrashort and nonparaxial radially polarized laser pulses. We show that the threshold power above which significant acceleration takes place is greatly reduced by using a tighter focus. Moreover, electrons accelerated by tightly focused single-cycle laser pulses may reach around 80% of the theoretical energy gain limit, about twice the value previously reported with few-cycle paraxial pulses. Our results demonstrate that the direct acceleration of electrons in vacuum is well within reach of current laser technology.

Bessel–Gauss beams as rigorous solutions of the Helmholtz equation

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

4π Focusing of TM 01 beams under nonparaxial conditions

The Richards-Wolf theory and the complex point-source method are both used to express the phasor of the electric field of tightly focused beams, but the connection between these two approaches is not straightforward. In this paper, the Richards-Wolf vector field equations are used to find the electromagnetic field of a TM(01) beam in the neighborhood of the focus of a 4π focusing system, such as a parabolic mirror with infinite transverse dimensions. Closed-form solutions are found for the distribution of the fields at any point in the vicinity of the focus; these solutions are identical to the electromagnetic field obtained with the complex source-point method in which sources are accompanied by sinks. This work thus establishes a connection between the Richards-Wolf theory and the complex sink/source model. The vector magnetic potential is introduced to simplify the computation of the six electromagnetic field components. The method is then used to find analytical expressions for the electromagnetic field of strongly focused TM(01) beams affected by primary aberrations such as curvature of field, coma, astigmatism and spherical aberration.

Power carried by a nonparaxial TM beam

In paraxial optics, the power carried by an optical beam can be accurately calculated by means of the integral of the squared modulus of its electric field over a plane transverse to the propagation axis. However, for nonparaxial electromagnetic beams, it is more appropriate to define the power carried by the beam by the integral of the longitudinal component of its time-averaged Poynting vector over a plane transverse to the propagation axis. In this paper, the expression of the power carried by a high-aperture transverse magnetic (TM) beam of any order is determined. The general expression of the power carried by a TM beam, which also applies for a transverse electric (TE) beam, is given in terms of a modified Struve function of order equal to an integer plus one-half.

Focusing a TM 01 beam with a slightly tilted parabolic mirror

A parabolic mirror illuminated with an incident collimated beam whose axis of propagation does not exactly coincide with the axis of revolution of the mirror shows distortion and strong coma. To understand the behavior of such a focused beam, a detailed description of the electric field in the focal region of a parabolic mirror illuminated with a beam having a nonzero angle of incidence is required. We use the Richards-Wolf vector field equation to investigate the electric energy density distribution of a beam focused with a parabolic mirror. The explicit aberration function of this focused field is provided along with numerically calculated electric energy densities in the focal region for different angles of incidence. The location of the peak intensity, the Strehl ratio and the full-width at half-maximum as a function of the angle of incidence are given and discussed. The results confirm that the focal spot of a strongly focused beam is affected by severe coma, even for very small tilting of the mirror. This analysis provides a clearer understanding of the effect of the angle of incidence on the focusing properties of a parabolic mirror as such a focusing device is of growing interest in microscopy.

Control of spectral aberrations in a monochromator using a plane holographic chirped grating.

A method aimed to minimize the impact of spectral aberrations in a monochromator is proposed in which the spectrum of the source of radiation under study is scanned by the rectilinear translation of a plane chirped grating. The chirped grating, which has a spatially variable groove spacing, is used to diffract and to spectrally focus the radiation. Imaging properties of the chirped grating were analyzed in order to develop the expression of the aberration coefficients of the system and the expression of the width of the instrument line shape due to aberrations. The optimal rectilinear trajectory required to operate the monochromator without significant spectral aberrations in measurements has been obtained numerically and tested in the laboratory. Experimental measurements of the emission spectrum of a seven-wavelength helium-neon laser are presented, as well as the sensitivity of the monochromator performance to different geometrical parameters.

Electron acceleration in vacuum by ultrashort and tightly focused radially polarized laser pulses

Exact closed-form solutions to Maxwell’s equations are used to investigate electron acceleration driven by radially polarized laser beams in the nonparaxial and ultra-short pulse regime. Besides allowing for higher energy gains,such beams could generate synchronized counterpropagating electron bunches.