1. Basic Detection Techniques Quasi-optics Wolfgang Wild Lecture on 03 Oct 2006

2. Basic Detection Techniques – Submm receivers2 Contents 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 formulae Basic formulae Gaussian beams Gaussian beams Quasi-optical components and systems (examples) Quasi-optical components and systems (examples) Mirror Mirror Lenses Lenses Grid Grid Feedhorns Feedhorns Quarter-wave plate Quarter-wave plate Martin-Puplett Interferometer Martin-Puplett Interferometer Literature Literature

3. Basic Detection Techniques – Submm receivers3 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.

4. Basic Detection Techniques – Submm receivers4 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 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.

5. Basic Detection Techniques – Submm receivers5 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 Laser beams Submm beams Radio telescope illumination

6. Basic Detection Techniques – Submm receivers6 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.

7. Basic Detection Techniques – Submm receivers7 Gaussian beam – properties II Gaussian beam diameter (= the distance between 1/e points) varies along the propagation direction as withλ = free space wavelength z = distance from beam waist (“focus”) w 0 = beam waist radius Radius of phase front curvature is given by

8. Basic Detection Techniques – Submm receivers8 Gaussian beam propagation Beam waist with radius w o Beam profile variation of the fundamental Gaussian beam mode along the propagation direction z Beam diameter 2w at distance z

9. Basic Detection Techniques – Submm receivers9 Gaussian beam - phase front curvature Beam profile variation of the fundamental Gaussian beam mode along the propagation direction z Curvature of phase front

10. Basic Detection Techniques – Submm receivers10 Quasi-optical components - Mirrors Use of flat and curved mirrors Use of flat and curved mirrors Curved mirrors (elliptical, parabolic) for focusing Curved mirrors (elliptical, parabolic) for focusing Material: mostly machined metal (non-optical quality). Surface roughness ~few micron sufficient for submm Material: mostly machined metal (non-optical quality). Surface roughness ~few micron sufficient for submm

11. Basic Detection Techniques – Submm receivers11 Quasi-optical components - Lenses For focusing of beam For 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 range Refractive index n ≈ 1.5 in submillimeter range

12. Basic Detection Techniques – Submm receivers12 QO Lens with antireflection “coating” Refractive index for antireflection coating n AR = n 1/2, λ/4 thick Refractive index for antireflection coating n AR = n 1/2, λ/4 thick Optical lenses: special material with correct n AR Optical lenses: special material with correct n AR Submillimeter lenses: grooves of width d g « λ Submillimeter lenses: grooves of width d g « λ Effect of AR coating if height and width are chosen such that the “mixed” refractive index between air and material = n AR Effect of AR coating if height and width are chosen such that the “mixed” refractive index between air and material = n AR

13. Basic Detection Techniques – Submm receivers13 Quasi-optical components - Grid For separating a beam into orthogonal polarizations For separating a beam into orthogonal polarizations For beam combining (reflection/transmission) of orthogonal polarizations For beam combining (reflection/transmission) of orthogonal polarizations Polarization parallel to wire is reflected, perpendicular to wire is transmitted Polarization parallel to wire is reflected, perpendicular to wire is transmitted Material: thins wires over a metal frame Material: thins wires over a metal frame Also used in more complicated setups Also used in more complicated setups

14. Basic Detection Techniques – Submm receivers14 Quasi-optical components - Feedhorn A feedhorn is a type of waveguide antenna for emission or reception of radiation 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. Feedhorns can produce (or receive) Gaussian beams with high efficiency and low sidelobes. Different designs of feedhorns: diagonal, circular, corrugated, … Different designs of feedhorns: diagonal, circular, corrugated, …

15. Basic Detection Techniques – Submm receivers15 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. 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. This allows determining the characteristics of a receiving antenna by measuring its emission properties.

16. Basic Detection Techniques – Submm receivers16 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 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)

17. Basic Detection Techniques – Submm receivers17 Martin-Puplett (Polarizing) Interferometer Low-loss combination of two beams of different frequency and polarization into one beam of the same polarization 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 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 90 o through rooftop mirror Beam transmitted by grid

18. Basic Detection Techniques – Submm receivers18 Martin-Puplett Diplexer Consider two orthogonally polarized input beams: Signal and LO Consider two orthogonally polarized input beams: Signal and LO Central grid P2 at 45 o angle  both beams are split equally and recombined Central grid P2 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) For proper pathlength difference setting in the diplexer, both beams leave at port 3 with the same polarization (and no loss)

19. Basic Detection Techniques – Submm receivers19 Literature on Quasi-optics (examples) “Quasioptical Systems”, P.F. Goldsmith, IEEE Press 1998 “Quasioptical Systems”, P.F. Goldsmith, IEEE Press 1998 Excellent book for (sub-)mm optics “Beam and Fiber Optics”, J.A. Arnaud, Academic Press 1976 “Beam and Fiber Optics”, J.A. Arnaud, Academic Press 1976 “Light Transmission Optics”, D. Marcuse, Van Nostrand- Reinhold, 1975 “Light Transmission Optics”, D. Marcuse, Van Nostrand- Reinhold, 1975 “An Introduciton to Lasers and Masers”, A.E. Siegman, McGraw- Hill 1971 “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 Chapter 5 (by P.F. Goldsmith) in Infrared and Millimeter Waves, Vol. 6, ed. K.J. Button, Academic Press 1982