1. Basic Detection Techniques Quasi-Optical techniques Andrey Baryshev Lecture on 18 Oct 2011

2. Basic Detection Techniques – Submm receivers (Part 4)2 Outline What is quasi – optics (diffraction) What is quasi – optics (diffraction) Gaussian beam and its properties Gaussian beam and its properties What is far? (confocal distance), far field, radiation pattern What is far? (confocal distance), far field, radiation pattern Gaussian beam coupling Gaussian beam coupling Concept Concept Lens/elliptical mirror Lens/elliptical mirror Gaussian beam launching Gaussian beam launching Corrugated horn Corrugated horn Polarization elements Polarization elements Wire grid Wire grid Roof top Mirror Roof top Mirror Quasi-optical components and systems Quasi-optical components and systems

3. Basic Detection Techniques – Submm receivers (Part 4)3 A to B A (source) B (detector)

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

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

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

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

8. Basic Detection Techniques – Submm receivers (Part 4)8 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.

9. Basic Detection Techniques – Submm receivers (Part 4)9 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.

10. Basic Detection Techniques – Submm receivers (Part 4)10 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

11. Basic Detection Techniques – Submm receivers (Part 4)11 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

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

13. Basic Detection Techniques – Submm receivers (Part 4)13 Gaussian beam – properties III 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

14. Basic Detection Techniques – Submm receivers (Part 4)14 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

15. Basic Detection Techniques – Submm receivers (Part 4)15 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

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

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

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

19. Basic Detection Techniques – Submm receivers (Part 4)19 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.

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

21. Basic Detection Techniques – Submm receivers (Part 4)21 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

22. Basic Detection Techniques – Submm receivers (Part 4)22 Elliptical mirror FP1 FP2 Rotation axis R1 R2

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

24. Basic Detection Techniques – Submm receivers (Part 4)24 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

25. Basic Detection Techniques – Submm receivers (Part 4)25 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

26. Basic Detection Techniques – Submm receivers (Part 4)26 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)

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

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

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

30. Basic Detection Techniques – Submm receivers (Part 4)30 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

31. Basic Detection Techniques – Submm receivers (Part 4)31 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)

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

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

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

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

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

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

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

39. Michelson interferometer Basic Detection Techniques – Submm receivers (Part 4)39 Transfer function: Cosine Fourier transfer

40. Interferogram Basic Detection Techniques – Submm receivers (Part 4)40

41. Fourier transform (band pass) Basic Detection Techniques – Submm receivers (Part 4)41

42. Planck formula Basic Detection Techniques – Submm receivers (Part 4)42 Per unit square In all directions Integral for gaussion beam over surface and beam angle gives lambda^2 throughput 3

43. Basic Detection Techniques – Submm receivers (Part 4)43 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