Basic Detection Techniques Quasi-optics

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

2. Contents overview • What is quasi-optics ? • Why is it important ? Where is it used ? • Basic formulae • Gaussian beams • Quasi-optical components and systems (examples) • Mirror • Lenses • Grid • Feedhorns • Quarter-wave plate • Martin-Puplett Interferometer • Literature Basic Detection Techniques – Submm receivers

3. 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

4. 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

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

6. 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. Basic Detection Techniques – Submm receivers

7. Gaussian beam – properties II 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”) w0 = beam waist radius Radius of phase front curvature is given by Basic Detection Techniques – Submm receivers

8. Gaussian beam propagation Beam diameter 2w 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

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

10. 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

11. Quasi-optical components - Lenses • For focusing of beam • In quasi-optics: no focus “point”, but a “beam waist” • Material: HDPE, Teflon (“plastic”) • Refractive index n ≈ 1.5 in submillimeter range Basic Detection Techniques – Submm receivers

12. 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

13. 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

14. Quasi-optical components - Feedhorn • 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. • Different designs of feedhorns: diagonal, circular, corrugated, … Basic Detection Techniques – Submm receivers

15. Quasi-optical components – Feedhorn (cont’d) Often used in submm: Corrugated feedhorn • 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. 500 GHz horn Basic Detection Techniques – Submm receivers

16. Quasi-optical components – Quarter wave plate Quarter-wave plate: linear pol.  circular polarisation If 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 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

17. 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

18. 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

19. 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, 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 – Submm receivers