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Basic Detection Techniques
Quasi-optics
Wolfgang Wild
Lecture on 03 Oct 2006
Contents overview
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What is quasi-optics ?
Why is it important ? Where is it used ?
Basic formulae
Gaussian beams
Quasi-optical components and systems (examples)
• Mirror
• Lenses
• Grid
• Feedhorns
• Quarter-wave plate
• Martin-Puplett Interferometer
Literature
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What is “quasioptics” ?
“Quasi-optics deals with the propagation of a beam of
radiation that is reasonably well collimated but has
relatively small dimensions (measured in wavelenghts)
transverse to the axis of propagation.”
While this may sound very restrictive, it actually applies to
many practical situations, such a submillimeter and laser
optics.
Main difference to geometrical optics:
Geometrical optics:
Quasi-optics:
λ  0, no diffraction
finite λ, diffraction
Quasi-optics was developed in 1960’s as a result of interest in
laser resonators.
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Why quasi-optics is of interest
Task: Propagate submm beams / signals in a suitable way
Could use
- Cables
- Waveguides
- Optics
 high loss, narrow band
 high loss, cut-off freq
 lossless free-space,
broad band
But: “Pure” (geometrical) optical systems would require
components much larger than λ.
In sub- /mm range diffraction is important, and quasi-optics
handles this in a theorectical way.
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Gaussian beam - definition
Most often quasi-optics deals with “Gaussian” beams, i.e. beams
which have a Gaussian intensity distribution transverse to the
propagation axis.
Gaussian beams are of great practical
importance:
• Represents fundamental mode TEM00
• Laser beams
• Submm beams
• Radio telescope illumination
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Gaussian beam – properties I
A Gaussian beam begins as a perfect plane wave when emitted but
– due to its finite diameter – increases in diameter (diffraction)
and changes into a wave with curved wave front.
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Gaussian beam – properties II
Gaussian beam diameter (= the distance between 1/e points)
varies along the propagation direction as
with
λ = free space wavelength
z = distance from beam waist (“focus”)
w0 = beam waist radius
Radius of phase front curvature is given by
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Gaussian beam propagation
Beam diameter
2w at distance z
Beam waist with
radius wo
Beam profile variation of the fundamental Gaussian beam
mode along the propagation direction z
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Gaussian beam - phase front curvature
Beam profile variation of the
fundamental Gaussian beam mode
along the propagation direction z
Curvature of phase front
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Quasi-optical components - Mirrors
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Use of flat and curved mirrors
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Curved mirrors (elliptical, parabolic) for focusing
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Material: mostly machined metal (non-optical quality). Surface
roughness ~few micron sufficient for submm
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Quasi-optical components - Lenses
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For focusing of beam
In quasi-optics: no focus “point”, but a “beam waist”
Material: HDPE, Teflon (“plastic”)
Refractive index n ≈ 1.5 in submillimeter range
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QO Lens with antireflection “coating”
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Refractive index for antireflection coating nAR = n1/2, λ/4 thick
Optical lenses: special material with correct nAR
Submillimeter lenses: grooves of width dg « λ
Effect of AR coating if height and width are chosen such that the
“mixed” refractive index between air and material = nAR
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Quasi-optical components - Grid
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For separating a beam into orthogonal polarizations
For beam combining (reflection/transmission) of orthogonal
polarizations
Polarization parallel to wire is reflected, perpendicular to wire is
transmitted
Material: thins wires over a metal frame
Also used in more complicated setups
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Quasi-optical components - Feedhorn
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A feedhorn is a type of waveguide antenna for emission or
reception of radiation
Feedhorns can produce (or receive) Gaussian beams with high
efficiency and low sidelobes.
Different designs of feedhorns: diagonal, circular, corrugated, …
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Quasi-optical components – Feedhorn (cont’d)
Often used in submm:
Corrugated feedhorn
500 GHz horn
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Lorentz’ reciprocity theorem implies that antennas work equally
well as transmitters or receivers, and specifically that an
antenna’s radiation and receiving patterns are identical.
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This allows determining the characteristics of a receiving
antenna by measuring its emission properties.
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Quasi-optical components – Quarter wave plate
Quarter-wave plate: linear pol.  circular polarisation
If linear pol. wave incident at 45o Path 1: ½ reflected by grid
Path 2: ½ transmitted by grid
and reflected by mirror
Path difference is ΔL = L1 + L2 = 2d cos θ
Phase delay Φ = k ΔL = (4πλ/d) cos θ
For linear  circular pol. we need
ΔL = λ/4  Φ = π/2 , i.e.
D = λ / (8 cos θ)
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Martin-Puplett (Polarizing) Interferometer
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Low-loss combination of two beams of different frequency and
polarization into one beam of the same polarization
Often used for LO and signal beam coupling
Use of polarization rotation by roof top mirror:
• Input beam reflected by grid
• Polarization rotated by 90o
through rooftop mirror
•Beam transmitted by grid
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Martin-Puplett Diplexer
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Consider two orthogonally polarized input beams: Signal and LO
Central grid P2 at 45o angle  both beams are split equally and
recombined
For proper pathlength difference setting in the diplexer, both
beams leave at port 3 with the same polarization (and no loss)
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Literature on Quasi-optics (examples)
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“Quasioptical Systems”, P.F. Goldsmith, IEEE Press 1998
Excellent book for (sub-)mm optics
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“Beam and Fiber Optics”, J.A. Arnaud, Academic Press 1976
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“Light Transmission Optics”, D. Marcuse, Van Nostrand-Reinhold,
1975
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“An Introduciton to Lasers and Masers”, A.E. Siegman, McGrawHill 1971
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Chapter 5 (by P.F. Goldsmith) in Infrared and Millimeter Waves,
Vol. 6, ed. K.J. Button, Academic Press 1982
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