Basic Detection Techniques QuasiOptical techniques Andrey Baryshev Lecture

Basic Detection Techniques Quasi-Optical techniques Andrey Baryshev Lecture on 25 Sept 2006

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) 2

A to B A (source) B (detector) 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 optical A (source) B (detector) Basic Detection Techniques – Submm receivers (Part 4) 5

A to B diffraction A (source) A (detector) Basic Detection Techniques – Submm receivers (Part 4) 6

Quasi - optics Geometrical Optics Quasi - optics Radio • Both, Lens and Antenna • Simplification of physical optics Lens Antenna Basic Detection Techniques – Submm receivers (Part 4) 7

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 diffraction Quasi-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) 8

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 handles this in a diffraction is important, and quasi-optics theorectical way. Basic Detection Techniques – Submm receivers (Part 4) 9

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 TEM 00 • Stays Gaussian passing optical elements • Laser beams • Submm beams • Radio telescope illumination Basic Detection Techniques – Submm receivers (Part 4) 10

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) 11

Gaussian beam properties II Solution of Helmholtz equation In cylindrical coordinates Phase Waist size Basic Detection Techniques – Submm receivers (Part 4) 12

Gaussian beam – properties III 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”) w 0 = beam waist radius Radius of phase front curvature is given by Basic Detection Techniques – Submm receivers (Part 4) 13

Gaussian beam propagation Beam diameter 2 w at distance z Beam waist with radius wo Beam profile variation of the fundamental Gaussian beam mode along the propagation direction z Basic Detection Techniques – Submm receivers (Part 4) 14

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 Basic Detection Techniques – Submm receivers (Part 4) 15

Confocal (Rayleigh) distance Quasi-optics becomes geometrical Border between far and near field Far field of ALMA Antenna 377 km Waist Basic Detection Techniques – Submm receivers (Part 4) 16

Launching Gaussian beam from fiber Basic Detection Techniques – Submm receivers (Part 4) 17

Corrugated horn coupling principle Basic Detection Techniques – Submm receivers (Part 4) 18

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) 19

Beam coupling, lens as example Basic Detection Techniques – Submm receivers (Part 4) 20

QO Lens with antireflection “coating” Refractive index for antireflection coating n. AR = n 1/2, λ/4 thick • Optical lenses: special material with correct n. AR • 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 = n. AR • Basic Detection Techniques – Submm receivers (Part 4) 21

Elliptical mirror R 1 R 2 FP 1 FP 2 Rotation axis Basic Detection Techniques – Submm receivers (Part 4) 22

Mirror chain Basic Detection Techniques – Submm receivers (Part 4) 23

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) 24

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) 25

Quasi-optical components – Quarter wave plate Quarter-wave plate: linear pol. circular polarisation If linear pol. wave incident at 45 o Path 1: ½ reflected by grid Path 2: ½ transmitted by grid and reflected by mirror Path difference is ΔL = L 1 + L 2 = 2 d 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) Basic Detection Techniques – Submm receivers (Part 4) 26

Polarization transfer, roof top mirror Basic Detection Techniques – Submm receivers (Part 4) 27

Quasi – optical components Basic Detection Techniques – Submm receivers (Part 4) 28

Quasi optical systems example Basic Detection Techniques – Submm receivers (Part 4) 29

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 90 o through rooftop mirror • Beam transmitted by grid Basic Detection Techniques – Submm receivers (Part 4) 30

Martin-Puplett Diplexer Consider two orthogonally polarized input beams: Signal and LO • Central grid P 2 at 45 o 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) 31

QO system characterization Beam pattern (PSF) measurements • E(x, y) phase and amplitude for near field • E 2(x, y) for far field, in two planes y Test source or receiver Moves in x, y System to measure x By fitting Gaussian beam distribution one can locate waist position and waist size, relative to measurement XY system Basic Detection Techniques – Submm receivers (Part 4) 32

Beam pattern examples, ALMA main beam Basic Detection Techniques – Submm receivers (Part 4) 33

Alma beam – cross polarization Basic Detection Techniques – Submm receivers (Part 4) 34

HIFI FPU (Focal Plane Unit) Basic Detection Techniques – Submm receivers (Part 4) 35

Common Optics Assembly Basic Detection Techniques – Submm receivers (Part 4) 36

Common Optics Assembly Basic Detection Techniques – Submm receivers (Part 4) 37

Mixer Assembly Contains two Mixer Subassemblies (MSA) Accepts LO and signal in two polarizations Basic Detection Techniques – Submm receivers (Part 4) 38

Literature on Quasi-optics (examples) • “Quasioptical Systems”, P. F. Goldsmith, IEEE Press 1998 Excellent 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, Mc. Graw. 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 – Submm receivers (Part 4) 39