long wavelength near field microscopy
DESCRIPTION
principles. physical. Amplitude field. Evanescent term. Distance from the waveguide horizontal plane 0.22mm. The detection of evanescent fields. makes possible beating the. Abbe. diffraction limit. , which states that in. diffraction limit. optics it’s impossible to get a. subwaveleng. - PowerPoint PPT PresentationTRANSCRIPT
-
Long wavelength Near Field MicroscopySubwavelength aperture: Bethes theoryEquivalent principlesEquivalent electric and magnetic dipolesDipoles electromagnetic field: stored energyStored energy and electromagnetic field produced by both the dipole Electromagnetic fields in tapered metallic waveguideResultsReferences
H.A.Bethe, Theory of diffraction by small holes Phy. Rev. Vol. 66, pp 163-182, 1944
Collin, Foundation for microwave engennering.
S.A.Shelkunoff, Field equivalence Theorems, Comm. On Pure and Appl. Math, vol.4 pp. 43-59, 1951
Electromagnetic Field in the cutoff regime of tapered metallic waveguides. B.Knoll,F.Keilmann. Opt. Comm. 162
Physical principles, mathematical treatment and realization of a new near field microscope in the THz region (1011-1013 Hz) D.Coniglio, A.Doria ENEA, FIS-ACC via Enrico Fermi 45, 00044 Frascati (Rome) ITALY
Visible-Infrared near field microscopyWaveguide with a localised sourceWavelenght 2.6mmHole radius 0.13mm (l\20)Waveguide dimensions 1mm-4mmWaveguide fundamental modeTE 10FieldsEnergy
-
TeraHertz Gap
Wavelength l 3000 mm-15 mm
Frequency n 1011-1013 Hz
Energy E 0.4meV-80meV
-
Near Field Microscopy:
Near field microscopy is based on the detection of evanescent fields. They are confined on the object surface and related with its nanostructure. For their non propagating nature, its not possible to detect them far away from the sample (i.e. far field region). Its necessary to put very near to the objects surface (i.e.near field region) a small scattering element, the nanocollettor wich is able to capture these fields and convert them into propagating ones.The field detected preserves the informations about the object subwavelength structure.
Evanescent beamgenerated by the nanocollettor
Object surface
Evanescent beam generated the object surface
Propagating beam reemitted by the nanocollettor
Propagating wave
Incident light beam
Nanocollettor
One wavelength
-
The existing near field microscopy techniques work in the Visible-Infrared region. The general scheme of such microscopes is illustrated above: the sample can be illuminated by a laser in a direct way or through a metallic or dielectric tip; the evanescent field so generated just over the sample is collected by the tip. Thanks to a scanning system the tip is moved along the object surface and maintained at a certain distance from the sample (typically about 10 nm). The final images resolution is dictated by the tips dimensions.
-
On the left the evanescent field is captured by a metallic collector; the near field is projected onto the normal modes of this tapered waveguide and so converted in a propagating field. The resolution is dictated by holes dimensions. This configuration has been adopted for millimetric wavelenght.On the right the evanescent field is produced by a metallic tip working in the cut-off region. As in the Far-Infrared microscope technique, the resolution is given by tips dimensions.
laser
waveguide
Subwavelength hole
Hole evanescent field
collector
Object far field
laser
tip
collector
-
In 1942 the physicist H.A.Bethe solved with a mathematical theory, the problem of diffraction from a hole which dimensions are negligible respect to the incident radiation wavelength.
He wanted to estimate the effects of a small hole made on a common conductive wall of two coupled waveguides.
He supposed that in order to preserve boundary conditions on the hole and on the conductive plane, fictitious electric and magnetic dipoles have to exist instead of the hole. From this point of view the field diffused by the aperture is equivalent to the field irradiated by these dipoles; for this reason they are called equivalent dipoles.
-
The principles states that the field irradiated on the side 2 of the waveguides by a source situated on the side 1 is equivalent to that generated by an electric (transversal coupling) or magnetic (longitudinal coupling) current on the aperture. The equivalent currents are
Where and are the electric and magnetic fields produced by the source situated in region 1 when the aperture is closed by a perfect conductive wall.
-
In a waveguide an arbitrary electromagnetic field can be written as a normal modes guide series with index l through the expansion coefficients Al
Lets remember a Poynting theorems form
The integration over the guides walls is zero; that over the lateral walls gives an expression for the coefficients Al ( Zl is the waveguide impedance)
S+
S-
-
If on the guides walls, between S+ and S-, theres an aperture, (longitudinal coupling), we have to add this term in the right side of the expression for Al
If we suppose that holes dimensions are negligible respect to the wavelenght, we can expand in Taylor series the field H; unlikely from what happens when the field E is expanded, in this case the zero order term is responsible of a magnetic coupling and the first order term of an electric one. So both the dipoles moments have the magnetic and electric interactions exchanged. Using the expression for Jm , we finally can write the expressions for the equivalent dipoles.
Hole radius
Trasversal field H
-
These expressions have been derived in the near field limit (r
-
We calculate the electromagnetic fields in a tapered waveguides by solving a system of two coupled differential equations which describe the local reflection of the waveguide mode as the diameter changes gradually. The model can be applied both in the cut-off and in the propagating region.
z
H
b
d
d
i
-
K
1
z
(
)
H
b
1
a
z
(
)
z
a
z
(
)
H
b
d
d
-
1
2
K
1
z
(
)
z
K
1
z
(
)
H
b
H
f
-
(
)
d
d
-
z
H
f
d
d
i
K
1
z
(
)
H
f
1
a
z
(
)
z
a
z
(
)
H
f
d
d
-
1
2
K
1
z
(
)
z
K
1
z
(
)
H
f
H
b
-
(
)
d
d
-
-
TeraHertz configuration:the metallic tip is used in the cut-off region in order to produce an evanescent filed (plot on the left).
Millimetric configuration: the collector works in the propagating region; in these calculations dielectric losses are not included (plot on the right).
forward backward field
Coupling coefficient between near field and waveguide modes versus modes index.