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Basic Detection Techniques
Quasi-Optical techniques
Andrey Baryshev
Lecture on 18 Oct 2011
Basic Detection Techniques – Submm receivers (Part 4) 2
Outline
• What is quasi – optics (diffraction)• Gaussian beam and its properties• What is far? (confocal distance), far field, radiation pattern• Gaussian beam coupling
• Concept• Lens/elliptical mirror
• Gaussian beam launching• Corrugated horn
• Polarization elements• Wire grid• Roof top Mirror
• Quasi-optical components and systems
Basic Detection Techniques – Submm receivers (Part 4) 3
A to B
A (source)
B (detector)
Basic Detection Techniques – Submm receivers (Part 4) 4
A to B
A (source)
B (detector)
Basic Detection Techniques – Submm receivers (Part 4) 5
A to B optical
A (source)
B (detector)
Basic Detection Techniques – Submm receivers (Part 4) 6
A to B diffraction
A (source)
A (detector)
Basic Detection Techniques – Submm receivers (Part 4) 7
Quasi - optics
Lens
Antenna
GeometricalOptics D
Radio D D Quasi - optics
• Both, Lens and Antenna
• Simplification of physical optics
Basic Detection Techniques – Submm receivers (Part 4) 8
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: λ 0, no diffractionQuasi-optics: finite λ, diffraction
Quasi-optics was developed in 1960’s as a result of interest in laser resonators.
Basic Detection Techniques – Submm receivers (Part 4) 9
Why quasi-optics is of interest
Task: Propagate submm beams / signals in a suitable way
Could use - Cables high loss, narrow band- Waveguides high loss, cut-off freq- Optics 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.
Basic Detection Techniques – Submm receivers (Part 4) 10
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
• Stays Gaussian passing optical elements
• Laser beams• Submm beams• Radio telescope illumination
Basic Detection Techniques – Submm receivers (Part 4) 11
Gaussian beam – properties I
A Gaussian beam begins as a perfect plane wave at waist but – due to its finite diameter – increases in diameter (diffraction) and changes into a wave with curved wave front.
Beam waist
Basic Detection Techniques – Submm receivers (Part 4) 12
Gaussian beam properties II
Solution of Helmholtz equation
2 ( , , ) 0k E x y z
In cylindrical coordinates
2 2
02( )
( )( )
2
2( , )
( )
r j rj k z j z
R zw zE r z ew z
0 20
zArcTan
w
0w Waist size
2k
Phase
Basic Detection Techniques – Submm receivers (Part 4) 13
Gaussian beam – properties III
Gaussian beam diameter (= the distance between 1/e points) varies along the propagation direction as
with λ = free space wavelengthz = distance from beam waist (“focus”)w0 = beam waist radius
Radius of phase front curvature is given by
2
0 20
( ) 1z
w z ww
220( ) 1w
R z zz
Basic Detection Techniques – Submm receivers (Part 4) 14
Gaussian beam propagation
Beam waist withradius wo
Beam profile variation of the fundamental Gaussian beam mode along the propagation direction z
Beam diameter 2w at distance z
Basic Detection Techniques – Submm receivers (Part 4) 15
Gaussian beam - phase front curvature
Beam profile variation of the fundamental Gaussian beam mode along the propagation direction z
Curvature of phase front
Far field divergence angle
00w
Basic Detection Techniques – Submm receivers (Part 4) 16
Confocal (Rayleigh) distance
20
c
wz
Quasi-optics becomes geometricalBorder between far and near field
Waist
cz Far fieldof ALMAAntenna
377 km
Basic Detection Techniques – Submm receivers (Part 4) 17
Launching Gaussian beam from fiber
Basic Detection Techniques – Submm receivers (Part 4) 18
Corrugated horn coupling principle
Basic Detection Techniques – Submm receivers (Part 4) 19
Quasi-optical components – Feedhorn (cont’d)
Often used in submm: Corrugated feedhorn
500 GHz horn
• 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.
• This allows determining the characteristics of a receiving antenna by measuring its emission properties.
Basic Detection Techniques – Submm receivers (Part 4) 20
Beam coupling, lens as example
'
1 1 1
f R R
Basic Detection Techniques – Submm receivers (Part 4) 21
QO Lens with antireflection “coating”
• 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
Basic Detection Techniques – Submm receivers (Part 4) 22
Elliptical mirror
FP1 FP2 Rotationaxis
R1 R2
Basic Detection Techniques – Submm receivers (Part 4) 23
Mirror chain
Basic Detection Techniques – Submm receivers (Part 4) 24
Quasi-optical components - Mirrors
• Use of flat and curved mirrors
• Curved mirrors (elliptical, parabolic) for focusing
• Material: mostly machined metal (non-optical quality). Surface roughness ~few micron sufficient for submm
Basic Detection Techniques – Submm receivers (Part 4) 25
Quasi-optical components - Grid
• 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
Basic Detection Techniques – Submm receivers (Part 4) 26
Quasi-optical components – Quarter wave plate
Quarter-wave plate: linear pol. circular polarisationIf 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 θPhase delay Φ = k ΔL = (4πλ/d) cos θ
For linear circular pol. we needΔL = λ/4 Φ = π/2 , i.e.
D = λ / (8 cos θ)
Basic Detection Techniques – Submm receivers (Part 4) 27
Polarization transfer, roof top mirror
Basic Detection Techniques – Submm receivers (Part 4) 28
Quasi – optical components
Basic Detection Techniques – Submm receivers (Part 4) 29
Quasi optical systems example
Basic Detection Techniques – Submm receivers (Part 4) 30
Martin-Puplett (Polarizing) Interferometer
• 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
Basic Detection Techniques – Submm receivers (Part 4) 31
Martin-Puplett Diplexer
• 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)
Basic Detection Techniques – Submm receivers (Part 4) 32
QO system characterization
x
y
System to measure
Test sourceor receiverMoves in x,y
Beam pattern (PSF) measurements
• E(x,y) phase and amplitude for near field
• E2(x,y) for far field, in two planes
By fitting Gaussian beam distribution one canlocate waist position and waist size, relative to measurement XY system
Basic Detection Techniques – Submm receivers (Part 4) 33
Beam pattern examples, ALMA main beam
Basic Detection Techniques – Submm receivers (Part 4) 34
Alma beam – cross polarization
Basic Detection Techniques – Submm receivers (Part 4) 35
HIFI FPU (Focal Plane Unit)
Basic Detection Techniques – Submm receivers (Part 4) 36
Common Optics Assembly
Basic Detection Techniques – Submm receivers (Part 4) 37
Common Optics Assembly
Basic Detection Techniques – Submm receivers (Part 4) 38
Mixer Assembly
Contains two Mixer Subassemblies (MSA)
Accepts LO and signalin two polarizations
Michelson interferometer
Basic Detection Techniques – Submm receivers (Part 4) 39
Transfer function:
Cosine Fourier transfer
Interferogram
Basic Detection Techniques – Submm receivers (Part 4) 40
0.005 0.000 0.005
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Pathlength m
Power
a.usis25 05 d3 a .dat
Fourier transform (band pass)
Basic Detection Techniques – Submm receivers (Part 4) 41
400 500 600 700 800 9000.0000
0.0005
0.0010
0.0015
0.0020
Frequency GHz
Power
a.usis25 05d3 a .fts
Planck formula
Basic Detection Techniques – Submm receivers (Part 4) 42
Per unit square In all directions
Integral for gaussion beam over surface andbeam angle gives lambda^2 throughput
3
Basic Detection Techniques – Submm receivers (Part 4) 43
Literature on Quasi-optics (examples)
• “Quasioptical Systems”, P.F. Goldsmith, IEEE Press 1998Excellent book for (sub-)mm optics
• “Beam and Fiber Optics”, J.A. Arnaud, Academic Press 1976
• “Light Transmission Optics”, D. Marcuse, Van Nostrand-Reinhold, 1975
• “An Introduciton to Lasers and Masers”, A.E. Siegman, McGraw-Hill 1971
• Chapter 5 (by P.F. Goldsmith) in Infrared and Millimeter Waves, Vol. 6, ed. K.J. Button, Academic Press 1982
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