Basic Detection TechniquesBasic Detection Techniques

Quasi-opticsQuasi-optics

Wolfgang Wild Wolfgang Wild

Lecture on 03 Oct 2006Lecture on 03 Oct 2006

Basic Detection Techniques – Submm receivers 2

Contents overviewContents overview

• What is quasi-optics ?What is quasi-optics ?• Why is it important ? Where is it used ?Why is it important ? Where is it used ?• Basic formulaeBasic formulae• Gaussian beamsGaussian beams• Quasi-optical components and systems (examples)Quasi-optical components and systems (examples)

• MirrorMirror• LensesLenses• GridGrid• FeedhornsFeedhorns• Quarter-wave plateQuarter-wave plate• Martin-Puplett InterferometerMartin-Puplett Interferometer

• LiteratureLiterature

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What is “quasioptics” ?What is “quasioptics” ?

““Quasi-optics deals with the propagation of a beam of Quasi-optics deals with the propagation of a beam of radiation that is reasonably well collimated but has radiation that is reasonably well collimated but has relatively small dimensions (measured in wavelenghts) relatively small dimensions (measured in wavelenghts) transverse to the axis of propagation.”transverse to the axis of propagation.”

While this may sound very restrictive, it actually applies to While this may sound very restrictive, it actually applies to many practical situations, such a submillimeter and laser many practical situations, such a submillimeter and laser optics.optics.

Main difference to geometrical optics: Main difference to geometrical optics:

Geometrical optics: Geometrical optics: λλ 0, no diffraction 0, no diffractionQuasi-optics:Quasi-optics: finite finite λλ, diffraction, diffraction

Quasi-optics was developed in 1960’s as a result of interest in Quasi-optics was developed in 1960’s as a result of interest in laser resonators.laser resonators.

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Why quasi-optics is of interestWhy quasi-optics is of interest

Task: Propagate submm beams / signals in a suitable wayTask: Propagate submm beams / signals in a suitable way

Could useCould use - Cables- Cables high loss, narrow band high loss, narrow band

- Waveguides- Waveguides high loss, cut-off freq high loss, cut-off freq

- Optics- Optics lossless free-space, lossless free-space,

broad bandbroad band

But: “Pure” (geometrical) optical systems would require But: “Pure” (geometrical) optical systems would require components much larger than components much larger than λλ..

In sub- /mm range diffraction is important, and quasi-optics In sub- /mm range diffraction is important, and quasi-optics handles this in a theorectical way.handles this in a theorectical way.

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Gaussian beam - definitionGaussian beam - definition

Most often quasi-optics deals with “Gaussian” beams, i.e. beams which have a Gaussian intensity distribution transverse to Most often quasi-optics deals with “Gaussian” beams, i.e. beams which have a Gaussian intensity distribution transverse to the propagation axis.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 IGaussian beam – properties I

A Gaussian beam begins as a perfect plane wave when emitted A Gaussian beam begins as a perfect plane wave when emitted but – due to its finite diameter – increases in diameter but – due to its finite diameter – increases in diameter (diffraction) and changes into a wave with curved wave front.(diffraction) and changes into a wave with curved wave front.

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Gaussian beam – properties IIGaussian beam – properties II

Gaussian beam diameter (= the distance between 1/e points) Gaussian beam diameter (= the distance between 1/e points) varies along the propagation direction as varies along the propagation direction as

withwith λλ = free space wavelength = free space wavelength

z = distance from beam waist (“focus”)z = distance from beam waist (“focus”)

ww0 0 = beam waist radius= beam waist radius

Radius of phase front curvature is given byRadius of phase front curvature is given by

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Gaussian beam propagationGaussian 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

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Gaussian beam - phase front curvatureGaussian 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 - MirrorsQuasi-optical components - Mirrors

• Use of flat and curved mirrorsUse of flat and curved mirrors

• Curved mirrors (elliptical, parabolic) for focusingCurved mirrors (elliptical, parabolic) for focusing

• Material: mostly machined metal (non-optical quality). Surface Material: mostly machined metal (non-optical quality). Surface roughness ~few micron sufficient for submmroughness ~few micron sufficient for submm

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Quasi-optical components - LensesQuasi-optical components - Lenses

• For focusing of beamFor focusing of beam• In quasi-optics: no focus “point”, but a “beam waist”In quasi-optics: no focus “point”, but a “beam waist”• Material: HDPE, Teflon (“plastic”)Material: HDPE, Teflon (“plastic”)• Refractive index n ≈ 1.5 in submillimeter rangeRefractive index n ≈ 1.5 in submillimeter range

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QO Lens with antireflection “coating”QO Lens with antireflection “coating”

• Refractive index for antireflection coating nRefractive index for antireflection coating nARAR = n = n1/21/2, , λλ/4 thick /4 thick

• Optical lenses: special material with correct nOptical lenses: special material with correct nARAR

• Submillimeter lenses: grooves of width dSubmillimeter lenses: grooves of width dgg « « λλ

• Effect of AR coating if height and width are chosen such that the Effect of AR coating if height and width are chosen such that the “mixed” refractive index between air and material = n“mixed” refractive index between air and material = nARAR

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Quasi-optical components - GridQuasi-optical components - Grid

• For separating a beam into orthogonal polarizationsFor separating a beam into orthogonal polarizations• For beam combining (reflection/transmission) of orthogonal For beam combining (reflection/transmission) of orthogonal

polarizations polarizations • Polarization Polarization parallel to wire is reflected, perpendicular to wire is parallel to wire is reflected, perpendicular to wire is

transmittedtransmitted• Material: thins wires over a metal frameMaterial: thins wires over a metal frame• Also used in more complicated setupsAlso used in more complicated setups

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Quasi-optical components - FeedhornQuasi-optical components - Feedhorn

• A feedhorn is a type of waveguide antenna for emission or A feedhorn is a type of waveguide antenna for emission or reception of radiationreception of radiation

• Feedhorns can produce (or receive) Gaussian beams with high Feedhorns can produce (or receive) Gaussian beams with high efficiency and low sidelobes.efficiency and low sidelobes.

• Different designs of feedhorns: diagonal, circular, corrugated, …Different designs of feedhorns: diagonal, circular, corrugated, …

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Quasi-optical components – Feedhorn (cont’d)Quasi-optical components – Feedhorn (cont’d)

Often used in submm: Corrugated feedhorn

500 GHz horn

• Lorentz’ Lorentz’ reciprocity theoremreciprocity theorem implies that antennas work equally implies that antennas work equally well as transmitters or receivers, and specifically well as transmitters or receivers, and specifically that an that an antenna’s radiation and receiving patterns are identical.antenna’s radiation and receiving patterns are identical.

• This allows determining the characteristics of a receiving This allows determining the characteristics of a receiving antenna by measuring its emission properties.antenna by measuring its emission properties.

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Quasi-optical components – Quarter wave plateQuasi-optical components – Quarter wave plate

Quarter-wave plate: linear pol. Quarter-wave plate: linear pol. circular polarisation circular polarisation

If linear pol. wave incident at 45If linear pol. wave incident at 45oo Path 1: ½ reflected by gridPath 1: ½ reflected by grid

Path 2: ½ transmitted by grid Path 2: ½ transmitted by grid

and reflected by and reflected by mirrormirror

Path difference is Path difference is ΔΔL = L1 + L2 = 2d cos L = L1 + L2 = 2d cos θθ

Phase delay Phase delay ΦΦ = k = k ΔΔL = (4L = (4πλπλ/d) cos /d) cos θθ

For linear For linear circular pol. we need circular pol. we need

ΔΔL = L = λλ/4 /4 ΦΦ = = ππ/2 , i.e./2 , i.e.

D = D = λλ / (8 cos / (8 cos θθ))

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Martin-Puplett (Polarizing) InterferometerMartin-Puplett (Polarizing) Interferometer

• Low-loss combination of two beams of different frequency and Low-loss combination of two beams of different frequency and polarization into one beam of the same polarizationpolarization into one beam of the same polarization

• Often used for LO and signal beam coupling Often used for LO and signal beam coupling • Use of polarization rotation by roof top mirror: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 DiplexerMartin-Puplett Diplexer

• Consider two orthogonally polarized input beams: Signal and LOConsider two orthogonally polarized input beams: Signal and LO• Central grid P2 at 45Central grid P2 at 45oo angle angle both beams are split equally and both beams are split equally and

recombinedrecombined• For proper pathlength difference setting in the diplexer, both For proper pathlength difference setting in the diplexer, both

beams leave at port 3 with the same polarization (and no loss)beams leave at port 3 with the same polarization (and no loss)

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Literature on Quasi-optics (examples)Literature on Quasi-optics (examples)

• ““Quasioptical Systems”, P.F. Goldsmith, IEEE Press 1998Quasioptical Systems”, P.F. Goldsmith, IEEE Press 1998

Excellent book for (sub-)mm opticsExcellent book for (sub-)mm optics

• ““Beam and Fiber Optics”, J.A. Arnaud, Academic Press 1976Beam and Fiber Optics”, J.A. Arnaud, Academic Press 1976

• ““Light Transmission Optics”, D. Marcuse, Van Nostrand-Light Transmission Optics”, D. Marcuse, Van Nostrand-Reinhold, 1975Reinhold, 1975

• ““An Introduciton to Lasers and Masers”, A.E. Siegman, McGraw-An Introduciton to Lasers and Masers”, A.E. Siegman, McGraw-Hill 1971Hill 1971

• Chapter 5 (by P.F. Goldsmith) in Chapter 5 (by P.F. Goldsmith) in Infrared and Millimeter Waves, Infrared and Millimeter Waves, Vol. 6Vol. 6, ed. K.J. Button, Academic Press 1982, ed. K.J. Button, Academic Press 1982