A concise and universal method for deriving arbitrary paraxial and d’Alembertian cylindrical Gaussian-type light modes

Radożycki, Tomasz

doi:10.1016/j.optlastec.2021.107670

Cited by 7 publications

(10 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where n − l > −1, may be applied to derive the superposition of mBG modes producing the so called Kummer-Gaussian beam introduced in [39]:…”

Section: Kummer-gaussian Beammentioning

confidence: 99%

“…Some efforts to unify the derivation and the description of the paraxial beams have been made in the past [35][36][37][38]. In our previous work [39], we proceeded along these lines, attempting to exploit the Hankel transformation [40,41] for this purpose. The present work is in a sense devoted to similar issue, albeit from a different point of view.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes

Radożycki

2023

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered. Two selected parameters characterizing these beams, with respect to which the superpositions are constructed, are the topological index n associated with the orbital angular momentum carried by the beam, and χ related to the dilation of the beam. It is shown that, from these modes, by choosing appropriate weighting factors, it is possible to create a number of well-and less-known solutions of the paraxial equation: Gaussian (shifted and non-shifted) beam, γ beam, Kummer-Gaussian beam, special hyperbolic Bessel-Gaussian beam, a certain special Laguerre-Gaussian beam, and generalized paraxial beams in hyperbolic and regular versions.

show abstract

“…where n − l > −1, may be applied to derive the superposition of mBG modes producing the so called Kummer-Gaussian beam introduced in [39]:…”

Section: Kummer-gaussian Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes

Radożycki

2023

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Gaussian beam is obtained by inserting into (2.14) the prefactor Afalse(pρfalse) in the form Afalse(pρfalse)=pρn,and performing the following integral [75]: ψ~nfalse(ρ,φ,zfalse)=∫0∞dpρpρn+1 normale−false(w02pρ2/4false) ψ^nfalse(ρ,φ,zfalse),which will be henceforth called the ‘Gaussian Paraxial Transform’ (GPT) and denoted with Gnfalse[ψ^false]. It represents some specific superposition of exact modes if the value of w0 is large enough to legitimize the use of the approximation (2.11), which in practice indicates w0≫λdB.…”

Section: Paraxial Approximations Of the Exact Beammentioning

confidence: 99%

“…Other paraxial solutions can be obtained in an analogous way but with the modification involving the prefactor Afalse(pρfalse) of the paraxial transform (2.14). In the case of the BG beam it takes the form [75] Afalse(pρfalse)=Infalse(χpρfalse),where χ is a certain parameter related to the aperture angle of the beam [76,77] and In stands for the modified Bessel function. Accordingly ψ~nfalse(ρ,φ,zfalse)=∫0∞dpρpρInfalse(χpρfalse) normale−false(w02pρ2/4false) ψ^nfalse(ρ,φ,zfalse),which might be called the ‘Bessel-Gaussian Paraxial Transform’ (BGPT) and is denoted below with BGnfalse[ψ^false].…”

Section: Paraxial Approximations Of the Exact Beammentioning

confidence: 99%

Paraxial Dirac equation

Radożycki

2023

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this manner, the paraxial Dirac beams are obtained in four cases: as Gaussian, Bessel-Gaussian, modified Bessel-Gaussian and elegant Laguerre-Gaussian beams. In the second part of the work, the paraxial Dirac equation is derived, and then its solutions in the aforementioned cases are directly obtained. All the resulting wave functions conform to those derived formerly by virtue of superpositions, except for terms that are negligible upon the assumption that the paraxial functions along the propagation axis vary only slightly over a distance equal to the de Broglie wavelength, which is the standard paraxial requirement.

show abstract

“…It may seem that expression ( 35 ) is final because the CR integrals cannot be explicitly calculated 77 , 78 . However, we can apply the condition of large wave vectors (| q |> > 1), as well as the Bessel–Gaussian model of the CR 53 , transforming expression ( 35 ) into the following form (“ Methods ”): where I m ( x ) is the modified Bessel function of the first kind of order m , and τ = ρ 0 + iq is a complex propagation parameter introduced to describe generalized Bessel-Gaussian beams 79 (the real part of propagation parameter τ specifies the beam radius in the focal plane ρ 0 , and the imaginary part determines the tilt angle q , with respect to the beam symmetry axis).…”

Section: Introductionmentioning

confidence: 99%

Partially coherent conical refraction promises new counter-intuitive phenomena

Mylnikov

Dudelev

Рафаилов

et al. 2022

Sci Rep

View full text Add to dashboard Cite

In this paper, we extend the paraxial conical refraction model to the case of the partially coherent light using the unified optical coherence theory. We demonstrate the decomposition of conical refraction correlation functions into well-known conical refraction coherent modes for a Gaussian Schell-model source. Assuming randomness of the electrical field phase of the input beam, we reformulated and significantly simplified the rigorous conical refraction theory. This approach allows us to consider the propagation of light through a conical refraction crystal in exactly the same way as in the classical case of coherent radiation. Having this in hand, we derive analytically the conical refraction intensity both in the focal plane and in the far field, which allows us to explain and rigorously justify earlier experimental findings and predict new phenomena. The last include the counterintuitive effect of narrowing of the conical refraction ring width, disappearance of the dark Poggendorff’s ring in the Lloyd’s plane, and shift of Raman spots for the low-coherent conical refraction light. We also demonstrate a universal power-law dependence of conical refraction cones coherence degree on the input correlation length and diffraction-free propagation of the low-coherent conical refraction light in the far field.

show abstract

A concise and universal method for deriving arbitrary paraxial and d’Alembertian cylindrical Gaussian-type light modes

Cited by 7 publications

References 54 publications

Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes

Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes

Paraxial Dirac equation

Partially coherent conical refraction promises new counter-intuitive phenomena

Contact Info

Product

Resources

About