Basic Detection Techniques Quasi-Optical techniques

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


A to BA (source)

B (detector)


A to B A (source)

B (detector)


A to B opticalA (source)

B (detector)


A to B diffractionA (source)

A (detector)


Quasi - optics

Lens

Antenna

GeometricalOptics D

Radio D D Quasi - optics

• Both, Lens and Antenna

• Simplification of physical optics


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.


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.


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


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


Gaussian beam properties II

Solution of Helmholtz equation

2 ( , , ) 0k E x y z

In cylindrical coordinates2 2

02 ( )( )( )

2

2( , )( )

r j rj k z j zR zw zE r z e

w z

0 20

zArcTanw

0w Waist size

2k

Phase


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

( ) 1 zw z ww

220( ) 1w

R z zz


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


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


Confocal (Rayleigh) distance

20

cw

z

Quasi-optics becomes geometricalBorder between far and near field

Waist

cz Far fieldof ALMAAntenna

377 km


Launching Gaussian beam from fiber


Corrugated horn coupling principle


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.


Beam coupling, lens as example

'

1 1 1f R R


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


Elliptical mirror

FP1 FP2 Rotationaxis

R1 R2


Mirror chain


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


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


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)


Polarization transfer, roof top mirror


Quasi – optical components


Quasi optical systems example


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


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)


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


Beam pattern examples, ALMA main beam


Alma beam – cross polarization


HIFI FPU (Focal Plane Unit)


Common Optics Assembly


Mixer Assembly

Contains two Mixer Subassemblies (MSA)

Accepts LO and signalin two polarizations

Michelson interferometer


Transfer function:

Cosine Fourier transfer

Interferogram


0.005 0.000 0.0050.000

0.001

0.002

0.003

0.004

0.005

0.006

Pathlength m

Powe

ra.usis25 05d3 a .dat

Fourier transform (band pass)


400 500 600 700 800 9000.0000

0.0005

0.0010

0.0015

0.0020

Frequency GHz

Powe

ra.usis25 05 d3 a .fts

Planck formula


Per unit square In all directions

Integral for gaussion beam over surface andbeam angle gives lambda^2 throughput

3


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

Basic Detection Techniques Quasi-Optical techniques

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