1. Detection of Electromagnetic Radiation Phil Mauskopf, University of Rome 12/14 January, 2004

2. The Ultimate Radiation Detectors Goals - Particle point of view: Measure for each photon 1) Arrival time 2) Energy and direction (momentum) 3) Polarization Wave point of view: Measure the E (and/or B) field: 1) Amplitude and phase 2) Frequency 3) Polarization

3. The Ultimate Limit: Quantum fluctuations in the signal Particle point of view: - Can’t know both the arrival time and the photon energy simultaneously Wave point of view: - Can’t know both the amplitude and phase simultaneously So: How close are we? Depends on overall instrument design...

4. How to design an instrument: Define requirements - like an engineer: 1. Angular resolution required? 2. Sensitivity required - intensity of source? 3. Dynamic range - minimum vs. maximum signal? 4. Speed of response required - fastest change in signal? 5. Frequency bandwidth of source? 6. Frequency resolution required? 7. Polarisation discrimination required?

5. 1. Angular resolution required  optics design Fundamentally limited by diffraction 2. Sensitivity required  collecting area, number of detectors, detector and optics configuration Fundamentally limited by photon noise from source 3. Dynamic range  detector and readout type 4. Speed of response required  detector and readout type 5. Frequency bandwidth of source  filtering system 6. Frequency resolution required  filtering and detectors 7. Polarisation discrimination required

6. Design tools: Optics: ZeMAX, CODEV, GRASP, etc. - Ray tracing - Fraunhofer diffraction - Physical optics calculations Only limited by complexity of optics and computing power Complex structures - I.e. waveguides, transmission lines: HFSS, ADS, SONNET, etc. - 2-D and 3-D solutions to Maxwell’s equations - Full calculation of electric and magnetic fields Only limited by complexity of structures and computing power Need to know basics in order to make reasonably simple design Normally courses on electromagnetics discuss methods of solving Maxwell’s equations with a variety of boundary conditions Only necessary today if you don’t own a computer...

7. Detector sensitivity: NEP = Noise Equivalent Power (W/  Hz) = Noise/Signal Photon shot noise (BLIP) =  2Ph (W/  Hz) or  N (number of photons) dominates under small photon occupation number Photon ‘wave’ noise = P/  proportional to intensity dominates under large photon occupation number P=radiation power detected in Watts = nh P~ I  A  so if we know the source intensity, throughput and resolution we can calculate the sensitivity limit (and necessary detector sensitivity)

8. Sources of noise: 1) Variation in photons from astronomical source 2) Other stuff emitting - extra photon noise ~ Temperature of surroundings => Cool optics and go to space 3) Noise in detectors ~ Temperature of detector => Cool detectors - cryogenics

9. Bare minimum: The CMB Assume:  /  A  =  P opt =  (h  /  exp  h  T)-1) NEP BLIP = h  exp  h  T)-1)) at 2 mm,  NEP BLIP = 5 x 10 -18 W/  Hz Convert to  T and compare with what we need for CMB B-mode polarisation: At 2 mm, optimum ~ 50  K/  Hz, OK (Note it gets harder as  / gets smaller but) easier as gets bigger)

10. Detector applications/requirements: Ground-based telescopes: Large arrays, multiplexing, photon noise limited sensitivity Space-based telescopes: Same but higher sensitivity Spectrometer-on-chip: Astronomy - high sensitivity; instrumentation - 4 K operating temperature mm-wave interferometry: Single detectors, FAST (tens of kHz)

11. FIR photon counting detector requirements: The customer - balloon, satellites, ground-based telescopes 1. Durability - Detectors should not degrade over time or require special handling 2. Sensitivity - see next slides 3. Speed - depends on signal modulation - 1 ms for scanning, up to 1 MHz for phase chopped 4. Ease of fabrication/arrays - need 1,000’s of devices, high yield 5. Able to multiplex readout - need small number of wires, low DC impedence for SQUIDs, high DC impedence for FETs, HEMTs? 6. Low 1/f noise for slow scanning 7. Ease of integration in receiver - I.e. no B-fields? 8. Ease of coupling power - 50 Ohm RF impedence or separate detector/thermometer and absorber

12. Sensitivity requirements: ExperimentNEP required ------------------------------------------------------------------------ Ground-based continuum surveys10 -17 W/  Hz e.g. BOLOCAM, SCUBA2 Space-based CMB10 -18 W/  Hz e.g. post-PLANCK Ground-based spectrometer10 -19 W/  Hz e.g. z-spec Space-based spectrometer10 -20 W/  Hz e.g. SPECS, SAFIR

13. 1990s: SuZIE, SCUBA, NTD/composite 1998: 300 mK NTD SiN PLANCK: 100 mK NTD SiN

15. New and improved detector and readout technologies c.f. 2002: Zoology 1. Multiplexable bolometers with new types of thermistors Transition Edge Superconductors + SQUIDs Ultra-high R silicon thermometers (Gigaohm) + CMOS Kinetic Inductance thermometers + HEMTs Hot Electron Bolometers + ?? Cold Electron Bolometers + quasiparticle amplifier 2. Semiconductor and superconductor photoconductors and tunnel junction detectors (I.e. everything else) BIB Ge and GaAs photoconductors + JFET CIA Quantum dot photoconductor + quantum dot SETs Long-wavelength QWIP detectors SQPT photoconductor + RF SET KID direct detector (couple radiation directly) SIS/STJ video detector + ??

16. To understand how these detectors work and can be used in an instrument, we have to do some background review Things that you always thought you understood until you had to teach them: Propagation of electromagnetic radiation Transmission lines and waveguides Geometrical, diffraction and physical optics Scattering matrix for linear systems Photon statistics and noise

17. Today: Lightning review of radiation, transmission lines Friday: Lightning review of optics and scattering matrix Monday: Photon statistics and noise + periodic structures and filters? Tuesday?: Instrument configurations - spectrometers, interferometers, imagers Wednesday: Detectors I Friday: Detectors II + readouts

18. Propagation of electromagnetic radiation in vacuum I: From Maxwell’s equation we get the wave equation for EM waves in a vacuum:         +      0     In a vacuum with no sources,  = = 0 Taking  =  (  ) -  2  gives the wave equation  2  =   2    2

19. Propagation of electromagnetic radiation in vacuum II: Expressed in terms of the 4-potential, A  = ( , A) and current,  = ( ,  J) Maxwell’s equations are:      where     A -  A  E = -  -  A/  t B =  A

20. Propagation of electromagnetic radiation in vacuum III: If we choose the Lorentz gauge:  A = -   /  t Maxwell’s equations become 2 driven wave equations:   2  /  t 2 -  2  =  /  and   2 A/  t 2 -  2 A =  j Summary wave equations:     2 /  t 2 -  2   =  /  = 0 in vacuum, with no sources and  A =  j = 0 in vacuum with no sources or  A  = 0  E = 0  B = 0

21. Propagation of electromagnetic radiation in vacuum IV:     2 /  t 2 -  2  has units of (time/distance) 2 = 1/v 2 = 1/c 2 or c = 1/    is magnetic permeability: free space = 4   10 -7 H m -1  is the dielectric constant: free space = 8.84  10 -12 F m -1  /  has units of (H/F) = (Ohms/Hz)/(1/Ohms Hz) = Ohms 2 So, Z =   /  = impedance of free space = 377  Ratio of electric and magnetic fields in vacuum, Z=E/H Just as fundamental a constant as the speed of light...

22. Propagation of electromagnetic radiation in vacuum V: Solutions - plane waves For wave propagating in the z-direction, E = (E x,0,0) and H = (0,H y,0) E x = E 0 e i(kz-  t) H y = H 0 e i(kz-  t) From   and    =+      0  z     0    k  0    0   0  z    0    k  0   0 and  0   0    /  x y z

23. Propagation of electromagnetic radiation in vacuum VI: Find a conservation law for Electromagnetic waves Sources follow charge conservation:   0 Fields follow energy-momentum conservation: Energy dissipated at point x, time t = Change in energy in field at point x + Energy flowing out of point x - Energy flowing into point x Poynting’s theorem: E·J = -(1/2)  /  t[  2 +  2 ] -  (  ) E·J = Power dissipated (1/2) [  2 +  2 ] = Energy density in EM field  (  ) = momentum density in EM field, flux = W/m 2

24. Relation of fields to voltage and current: Electric field - Represented by capacitance - Voltage is result, source is applied A sec = charge Magnetic field - Represented by inductance - Current is result, source is applied V sec

25. Units of magnetic flux density: Magnetic flux density, B [tesla] = (1 V sec)/(1 m 2 ) Meaning: Apply 1 V for 1 sec to a loop with area 1 m (cause) Result is B (flux density) of 1 tesla (ramps up like charging a capacitor) What about current? V t 1 V 1 s +-+- 1 m 2 B 

26. Units of magnetic flux density: Current in loop depends on properties of material in which field lines exist Described by magnetic permeability, , and magnetic field, H H = B/  Ampere’s law: I =  H  d l

27. Units of electric flux density: Magnetic flux density, D [coul/m 2 ] = (1 A sec)/(1 m 2 ) Meaning: Apply 1 A for 1 sec to a capacitor plates with area 1 m 2 (cause) Result is D flux of 1 A sec/m 2 What about voltage? V t 1 A 1 s I  A=1 m 2 D

28. Units of electric flux density: Voltage depends on material in which electric field lines exist (I.e. between plates) Described by dielectric constant, , and electric field, E E = D/  Definition of electric potential: V =  E  d l

29. Interesting point number 1: Dual quantites: B - magnetic flux density  - Electric charge density Important for later devices, quantum mechanics and noise: E.g. Dual devices: SQUID - Measures magnetic flux in flux quanta Noise is tiny fraction of magnetic flux quantum SET - Measures electric charge in charge quanta Noise is tiny fraction of electric charge quantum

30. Propagation of electromagnetic radiation with lossless boundary conditions 1. Conducting walls - waveguide 2. Parallel plates - microstrip 3. Coaxial cable General idea is all the same - E -fields are perpendicular to the conductors and H-fields are parallel Draw field lines - separate into modes which have impedances that depend on frequency

31. Propagation of electromagnetic radiation: General - transmission line approach V I L C L = Inductance per unit length C = Capacitance per unit length

32. Transmission line wave equation: V(x) I(x) L C L dx dI(x)/dt = V(x+dx) - V(x)  L dI/dt = dV/dx C dx dV(x)/dt = I(x) - I(x-dx)  C dV/dt = dI/dx L d 2 I/dxdt = d 2 V/dx 2 C d 2 V/dt 2 = d 2 I/dxdt = (1/ L ) d 2 V/dx 2 LC d 2 V/dt 2 = d 2 V/dx 2 Same equation for current Wave solutions have property: V/I =  L / C = Z of line v 2 = 1/  LC = speed of prop. V(x+dx)

33. Inductance and Capacitance in microstrip line: w h d H E Approximation: Fields are contained completely between plates - negligable outside Note - this is good from point of view of radiation losses, etc.

34. How to calculate inductance: w h I +-+- 1. Apply 1 V for 1 sec to loop with area = d  h  B = 1/ (d  h) 2. Calculate H from , B H = B/  = 1/  (d  h) 3. Calculate current from path integral around loop I =  H  d l No field outside, so integral is just: I = Hw = w /  (d  h) 4. Definition of inductance: LI =  Vdt = 1  L =  (d  h)/w Proceedure also works if include field outside…modifies L d

35. How to calculate capacitance: w h  1. Apply 1 A for 1 sec to plates with area = d  h  Develops D field, charge D = 1/(d  w) 2. Calculate E from , D E = D/  = 1/  (d  w) 3. Calculate current from Integrate between plates to get V V =  E  d l = h/  (d  w) 4. Definition of capacitance: CV =  Idt = 1  C =  (d  w)/h =  A/h Just like we knew... d I

36. Impedance of transmission line: C =  (d  w)/h  C =  (w/h) L =  (d  h)/w  L =  (h/w)  Z =  L/C =  L / C = (h/w)   /  First part depends on geometry, second on materials Therefore, we can choose the impedance of a transmission line by changing the geometry and material Z = L C

37. Common transmission lines: 1. Microstrip 2. Coplanar waveguide 3. Coplanar striplines/Slotline

38. Resistive elements in transmission line - loss: C R G L R represents loss along the propagation path can be surface conductivity of waveguide or microstrip lines G represents loss due to finite conductivity between boundaries = 1/ R in a uniform medium like a dielectric Z =  ( R +i  L )/( G +i  C ) Z has real part and imaginary part. Imaginary part gives loss

39. Dielectric materials, index of refraction, impedence mismatch: 11 22 I T R T = 2Z 1 Z 2 /(Z 1 +Z 2 ) 2 R = (Z 1 -Z 2 ) 2 /(Z 1 +Z 2 ) 2 Z 1 =  /  1 Z 2 =  /  2 Z1Z1 Z2Z2 Transmission line analogy Z1Z1 What are optical analogies for: Short circuit Z1Z1 Open circuit +-+- +-+- +-+-

40. Circuit design in the GHz age: Lumped elements vs. transmission line Used to designing circuits with capacitors and inductors with wire leads? When the size of the component approaches the wavelength of the EM signal propagating in the component, transmission line analysis becomes important… c.f. New computers with clock speeds of 100 GHz…1 THz?

41. Propagation of electromagnetic radiation in vacuum V: Solutions - with boundary conditions Parallel conducting plates Enclose in conducting walls - waveguide Coaxial cable Micro-strip line Coplanar waveguide Coplanar striplines Slotline etc. Given that the solution for the propagation of EM waves is different for each of the above types of boundary conditions, how do we transform a giant plane wave coming from a distant source into a wave travelling down a tiny transmission line without losing information? - Answer: optics