Quasi-Optical Design and Analysis (MBI) Créidhe O Sullivan, J.Anthony Murphy, Marcin Gradziel, Neil Trappe, Tully Peacocke & graduate students

Transcription

1 Quasi-Optical Design and Analysis (MBI) Créidhe O Sullivan, J.Anthony Murphy, Marcin Gradziel, Neil Trappe, Tully Peacocke & graduate students

2 Outline Corrugated Horns Analysis Techniques MBI/MODAL 2

3 Analysis Techniques: Horns Principle of reciprocity: consider horns as emitters Horns must satisfy strict criteria with regard to cross-polarisation and sidelobe level (e.g. PLANCK) Corrugated horns designed to propagate HE 11 mode PSB waveguide polypropylene filter cap 2b 2a bolometer cavity z 3 L

4 Hybrid Mode (Surface Impedance) Model Treat corrugated walls as surface with different average impedance in the z and φ directions Hybrid modes (HE/EH modes) are natural eigenmodes of the system, efficient description of system with few modes and no scattering Hybrid modes propagate independently through waveguide filter and conical horns Assume several corrugations per wavelength (>3) 4

5 Dispersion characteristics for modes of azimuthal order 1 in a corrugated waveguide 10 8 r 1 /r o = 0.6 βr 1 6 EH 11 HE 11 HE EH 12 HE kr 1 Finite bandwidth for fundamental mode Fall off in horn gain (on-axis efficiency) at high frequencies 5

6 Intuitive, fast computationally Gives high- and low-frequency cut-off for hybrid modes Simple analytical expression, convenient as input to quasioptical software Bessel function approximation to a scalar horn normalised intensity (db) E-Plane H-Plane truncated Bessel Gaussian beam But 6-50 off-axis angle (degrees) It s approximate, especially when there are few corrugations per λ takes no account of profiling of horn

7 Mode Matching (Scattering Matrix) Model PLANCK and QUaD both use cylindrically symmetric horns which transmit both orthogonal polarisations profiled horns & multimoded for non-polarised PLANCK channels r o r 1 7 corrugated waveguide Electromagnetic mode-matching technique regards the corrugated structure as a sequence of smooth-walled cylindrical waveguide sections each of which can support a set of TE and TM modes. At each junction power is scattered between the guide modes.

8 Mode Matching (Scattering Matrix) Model 8 Rectangular-circular transitions, profiles etc.

9 Far field intensity at 150GHz 150 GHz Far-Field Intensity Intensity (db) Intensity(dB) E Plane H Plane -10 exp result - H plane -15 exp result - E plane Theta(degrees) off-axis angle (deg) 9

10 normalised intensity (db) measurements SCATTER prediction off-axis angle (degrees) 100 GHz Broadband beams exp result Broadband Intensity Approximate Model Total Intensity GHz +/-30%

11 primarymirror Gaussian focal plane secondary mirror SCATTER angle (degrees) angle (degrees) Gaussian vs mode-matching description of a PLANCK horn

12 Phase centre 12

13 Analysis Techniques Coherent Field Analysis Incoherent Field Analysis Approximate Source Field Boundary Element Methods Method of Moments Finite Difference Techniques Diffraction Integrals Modal Analysis Geometrical Optics (ray tracing) Physical Optics Kirchhoff Rayleigh Rayleigh Sommerfeld Sommerfeld 1 2 Debye (Plane Waves) Gaussian Modes Gabor Modes Geometrical Theory of Diffraction Physical Theory Diffraction Aperture Field Method Projected Aperture Method Boundary Wave Analysis Equivalence Theorem Hermite Functions Laguerre Functions S. Withington 13 Stationary Phase Gabor Modes (ZEMAX) Plane Waves (GLAD) Gaussian Beam Modes (MODAL) Physical Optics (MODAL, GRASP)

14 secondary mirror primary mirror HDPE lenses cryostat window 14 focal plane

15 15 Gaussian intensity distribution remains Gaussian at every point along its path of propagation through an optical system Only the width of the Gaussian and its phase radius of curvature change R(z) W(z) W o Z Gaussian Beam Modes + = 2 o 2 o 2 1 ) ( W z W z W π λ + = z W z z R λ π 2 o 1 ) (

16 R. May 1 Standing wave effect between two conical horns -limited mode description coupling between horns with no standing waves included Dr. N. Trappe 16 Power coupling between TE11 modes in single-moded corrugated horns as a function of distance

17 Far-Field Beam Patterns on-axis Care must be taken with fast beams off-axis 17

18 MBI Beam Combiner D=200mm 2A=50mm ν = 90 GHz λ/d 1 for a baseline D 200mm 2a = 25mm λ / D 2 samples per fringe on the focal plane equivalent focal length of 3000mm 4a = 50mm 18

19 19

20 200mm mm

21 Diffraction Analysis The beams from corrugated horns of diameter 2a = 50mm and axial length 130 mm have waist w o a = 1 π + λr a distance Δz = 1+ π ( a) λr ( a) behind the horn aperture. R = = 102.3mm 7.67mm L=130mm R = 132.4mm w o Δz 2a aperture w = 16.1mm 2a 21

22 Diffraction Analysis A phase-flattening lens can be used to move the beam waist to the mouth of the horn The equivalent focal length of the system is f = 3000mm therefore the beam width at the output (focal) plane is: w λf out = π ( d = f ) = mm w o. (First fringe is at 50mm) 22

23 But truncation is a problem in this system 23

24 beam radius concave convex distance from secondary 2a = 10mm detectors 24

25 sky corrugated horns secondary mirror cassegrain beam combiner primary mirror detector plane P. Timbie, G. Tucker, A. Khorotkov & the MBI collaboration 25

26 26

27 MODAL 27 M. Gradziel & G. Curran

28 28

29 physical optics Gaussian beam modes 29

30 30 Summary Corrugated horns Gaussian approximation may not always reproduce the main beam A Bessel function is an excellent description of a scalar horn (phase centre) Electromagnetic mode-matching techniques are used especially for shaped & multimoded horns. Propagation through optics GBM for beam sizes Zemax extremely useful, lenses, optimisation etc. but must take care with certain steps GRASP as benchmark but no lenses, slow for optimisation etc.

31 31