Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/016
J. Solhaug, J. Stamnes, K. Oughstun
We study the behaviour of a plane-wave delta-function pulse that is diffracted at an edge in a dispersive medium. In particular, we show that the edge-diffraction process by itself is dispersive and adds to the dispersion induced by the medium in such a way as to completely change the behaviour of the Brillouin precursor. The dispersion associated with edge diffraction manifests itself through the appearance of a new algebraic singularity near the origin. Since the Sommerfeld precursor field is due to asymptotic contributions from saddle points that always stay far from the origin, the character of this field is not changed by the new singularity induced by edge diffraction. The Brillouin precursor field, however, is due to asymptotic contributions from saddle points that are close to the origin, and therefore the new singularity changes its behaviour dramatically. Numerical illustrations of the evolution of the edge-diffracted pulse are given and the behaviour of the Brillouin precursor field is explained both mathematically and physically.
{"title":"Diffraction of electromagnetic pulses in a single-resonance Lorentz model dielectric","authors":"J. Solhaug, J. Stamnes, K. Oughstun","doi":"10.1088/0963-9659/7/5/016","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/016","url":null,"abstract":"We study the behaviour of a plane-wave delta-function pulse that is diffracted at an edge in a dispersive medium. In particular, we show that the edge-diffraction process by itself is dispersive and adds to the dispersion induced by the medium in such a way as to completely change the behaviour of the Brillouin precursor. The dispersion associated with edge diffraction manifests itself through the appearance of a new algebraic singularity near the origin. Since the Sommerfeld precursor field is due to asymptotic contributions from saddle points that always stay far from the origin, the character of this field is not changed by the new singularity induced by edge diffraction. The Brillouin precursor field, however, is due to asymptotic contributions from saddle points that are close to the origin, and therefore the new singularity changes its behaviour dramatically. Numerical illustrations of the evolution of the edge-diffracted pulse are given and the behaviour of the Brillouin precursor field is explained both mathematically and physically.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90455248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/030
S. Nicola, D. Anderson, M. Lisak
We study the propagation characteristics of focused, apertured radially symmetric beams and show that the axial point at which the mean-square radius of the diffracted beam is a minimum tends to be displaced towards the aperture plane depending on the Fresnel number associated with the aperture and the Fresnel number associated with the radius of the incident beam. The magnitude of this effect can be determined by a simple and general formula in terms of the amplitude distribution of the incident beam across the aperture and of the two Fresnel numbers. We investigate the focal shift effects for the case of a focused, apertured Gaussian beam. The irradiance and the encircled-power distributions in the plane at which the mean-square radius of the diffracted beam is minimum are calculated and compared with those corresponding to a uniform beam.
{"title":"Focal shift effects in diffracted focused beams","authors":"S. Nicola, D. Anderson, M. Lisak","doi":"10.1088/0963-9659/7/5/030","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/030","url":null,"abstract":"We study the propagation characteristics of focused, apertured radially symmetric beams and show that the axial point at which the mean-square radius of the diffracted beam is a minimum tends to be displaced towards the aperture plane depending on the Fresnel number associated with the aperture and the Fresnel number associated with the radius of the incident beam. The magnitude of this effect can be determined by a simple and general formula in terms of the amplitude distribution of the incident beam across the aperture and of the two Fresnel numbers. We investigate the focal shift effects for the case of a focused, apertured Gaussian beam. The irradiance and the encircled-power distributions in the plane at which the mean-square radius of the diffracted beam is minimum are calculated and compared with those corresponding to a uniform beam.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72631186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/012
P. Pääkkönen, P. Vahimaa, A. Friberg, J. Turunen
An iterative method is developed to find exact solutions of wave propagation problems in Kerr media, taking into account backscattering effects. The method is based on the TE-mode Fourier-expansion eigenmode technique in the rigorous diffraction theory of gratings, but it permits an accurate treatment of non-periodic geometries as well. Self-focusing by a slab of Kerr medium is used to demonstrate the method and to compare it with the propagating-beam solution of the nonlinear Helmholtz equation, which ignores backscattering. The latter is shown to fail completely in many geometries, in particular, if the index modulation is high.
{"title":"ITERATIVE MODEL FOR WAVE PROPAGATION IN KERR MEDIA","authors":"P. Pääkkönen, P. Vahimaa, A. Friberg, J. Turunen","doi":"10.1088/0963-9659/7/5/012","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/012","url":null,"abstract":"An iterative method is developed to find exact solutions of wave propagation problems in Kerr media, taking into account backscattering effects. The method is based on the TE-mode Fourier-expansion eigenmode technique in the rigorous diffraction theory of gratings, but it permits an accurate treatment of non-periodic geometries as well. Self-focusing by a slab of Kerr medium is used to demonstrate the method and to compare it with the propagating-beam solution of the nonlinear Helmholtz equation, which ignores backscattering. The latter is shown to fail completely in many geometries, in particular, if the index modulation is high.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83071840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/021
G. Agarwal
We discuss how one can achieve subwavelength resolution using incident and scattered evanescent waves. We develop the underlying theoretical framework. We show how radiation from a dipole near a structure serves as its probe.
{"title":"Subwavelength resolution using evanescent waves","authors":"G. Agarwal","doi":"10.1088/0963-9659/7/5/021","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/021","url":null,"abstract":"We discuss how one can achieve subwavelength resolution using incident and scattered evanescent waves. We develop the underlying theoretical framework. We show how radiation from a dipole near a structure serves as its probe.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90194660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/027
G. Gbur, P. Carney
We consider the problem of the characterization of beams by moments of the field intensity in the aperture and its moments in the far field. The well known beam propagation factor, , is considered. We give convergence criteria for these factors and also discuss a new approach to optimization of the even moments of the far-field intensity.
{"title":"Convergence criteria and optimization techniques for beam moments","authors":"G. Gbur, P. Carney","doi":"10.1088/0963-9659/7/5/027","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/027","url":null,"abstract":"We consider the problem of the characterization of beams by moments of the field intensity in the aperture and its moments in the far field. The well known beam propagation factor, , is considered. We give convergence criteria for these factors and also discuss a new approach to optimization of the even moments of the far-field intensity.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83542450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/029
S. H. Wiersma, T. Visser, P. Török
We study the problem of light focusing by a high-aperture lens through a planar interface between two media with different refractive indices. It is demonstrated how, by using annular illumination, the intensity distribution can be significantly confined. A new scanning mechanism is proposed to continuously probe the intensity peak through the second medium. This mechanism may be applied in, for example, lithography and three-dimensional imaging.
{"title":"ANNULAR FOCUSING THROUGH A DIELECTRIC INTERFACE : SCANNING AND CONFINING THE INTENSITY","authors":"S. H. Wiersma, T. Visser, P. Török","doi":"10.1088/0963-9659/7/5/029","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/029","url":null,"abstract":"We study the problem of light focusing by a high-aperture lens through a planar interface between two media with different refractive indices. It is demonstrated how, by using annular illumination, the intensity distribution can be significantly confined. A new scanning mechanism is proposed to continuously probe the intensity peak through the second medium. This mechanism may be applied in, for example, lithography and three-dimensional imaging.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76965343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/024
Bingquan Chen, J. Stamnes, A. Devaney, H. M. Pedersen, K. Stamnes
Starting from two-dimensional optical diffraction tomography (ODT) for an object embedded in a non-absorbing and non-scattering medium, we consider the case in which the object is embedded in a randomly scattering medium. We use the `effective wavenumber' K in the random medium and reasonable approximations to study both the forward problem and the inverse problem (i.e. the reconstruction of the object) and present relevant computer simulation results. For practical measurements of transmitted fields we discuss the possibility of using the coherent detection imaging (CDI) technique as a means of realizing ODT in a random medium.
{"title":"Two-dimensional optical diffraction tomography for objects embedded in a random medium","authors":"Bingquan Chen, J. Stamnes, A. Devaney, H. M. Pedersen, K. Stamnes","doi":"10.1088/0963-9659/7/5/024","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/024","url":null,"abstract":"Starting from two-dimensional optical diffraction tomography (ODT) for an object embedded in a non-absorbing and non-scattering medium, we consider the case in which the object is embedded in a randomly scattering medium. We use the `effective wavenumber' K in the random medium and reasonable approximations to study both the forward problem and the inverse problem (i.e. the reconstruction of the object) and present relevant computer simulation results. For practical measurements of transmitted fields we discuss the possibility of using the coherent detection imaging (CDI) technique as a means of realizing ODT in a random medium.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72590701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/003
D. Ambrosini, G. Spagnolo, D. Paoletti, S. Vicalvi
We propose a high-precision digital automated quantitative determination of the modulus of the complex degree of coherence. The Thompson and Wolf experiment is repeated, using a CCD and a measurement method based on the fast Fourier transform. The experimental results agree very well with the predictions of the theory.
{"title":"High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment","authors":"D. Ambrosini, G. Spagnolo, D. Paoletti, S. Vicalvi","doi":"10.1088/0963-9659/7/5/003","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/003","url":null,"abstract":"We propose a high-precision digital automated quantitative determination of the modulus of the complex degree of coherence. The Thompson and Wolf experiment is repeated, using a CCD and a measurement method based on the fast Fourier transform. The experimental results agree very well with the predictions of the theory.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85531113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/008
M. Santarsiero, S. Vicalvi, D. Paoletti, G. Spagnolo
An interferometric technique based on the use of a diffraction grating is used to recover the intensity distribution across a spatially incoherent planar source. Information about the source profile is obtained through measurements of visibility and position of the fringe pattern at transverse planes beyond the grating. Such quantities are shown to be independent of the wavelength of the radiation, so that broadband sources can be analysed without any spectral filtering. Experimental results are given.
{"title":"Experimental determination of the intensity distribution across a source with a grating interferometer","authors":"M. Santarsiero, S. Vicalvi, D. Paoletti, G. Spagnolo","doi":"10.1088/0963-9659/7/5/008","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/008","url":null,"abstract":"An interferometric technique based on the use of a diffraction grating is used to recover the intensity distribution across a spatially incoherent planar source. Information about the source profile is obtained through measurements of visibility and position of the fringe pattern at transverse planes beyond the grating. Such quantities are shown to be independent of the wavelength of the radiation, so that broadband sources can be analysed without any spectral filtering. Experimental results are given.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85548094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/015
K. Oughstun
The angular spectrum of plane-waves representation of a pulsed electromagnetic beam field propagating in a dispersive, attenuative medium occupying the half-space expresses that wave field as a superposition of both homogeneous and inhomogeneous plane waves. A generalization of the Sherman expansion for source-free wave fields in lossless media to the lossy, dispersive medium case is used to derive a spatial series representation of a pulsed, source-free electromagnetic beam field from its angular spectrum representation. This spatial series representation displays the temporal evolution of the pulsed beam field explicitly through a single-contour integral that is of the same form as that obtained in the Fourier-Laplace description of a pulsed plane-wave field that is propagating in the positive z-direction in the lossy, dispersive medium. The temporal pulse evolution is found to depend upon the transverse spatial position in the beam field through the derivatives of the field boundary values.
{"title":"The angular spectrum representation and the Sherman expansion of pulsed electromagnetic beam fields in dispersive, attenuative media","authors":"K. Oughstun","doi":"10.1088/0963-9659/7/5/015","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/015","url":null,"abstract":"The angular spectrum of plane-waves representation of a pulsed electromagnetic beam field propagating in a dispersive, attenuative medium occupying the half-space expresses that wave field as a superposition of both homogeneous and inhomogeneous plane waves. A generalization of the Sherman expansion for source-free wave fields in lossless media to the lossy, dispersive medium case is used to derive a spatial series representation of a pulsed, source-free electromagnetic beam field from its angular spectrum representation. This spatial series representation displays the temporal evolution of the pulsed beam field explicitly through a single-contour integral that is of the same form as that obtained in the Fourier-Laplace description of a pulsed plane-wave field that is propagating in the positive z-direction in the lossy, dispersive medium. The temporal pulse evolution is found to depend upon the transverse spatial position in the beam field through the derivatives of the field boundary values.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85893702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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