Detection of Electromagnetic Radiation

1
Detection of Electromagnetic Radiation

• Phil Mauskopf, University of Rome
• 12/14 January, 2004

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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 - Cant know both
the arrival time and the photon energy
simultaneously Wave point of view - Cant 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?
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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
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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 Maxwells 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
Maxwells equations with a variety of boundary
conditions Only necessary today if you dont own
a computer...
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Detector sensitivity NEP Noise Equivalent
Power (W/?Hz) Noise/Signal Photon shot noise
(BLIP) ?2Phn (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 Pradiation
power detected in Watts nh? P I(n)AW (Dn)
e so if we know the source intensity, throughput
and resolution we can calculate the sensitivity
limit (and necessary detector sensitivity)
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Sources of noise 1) Variation in photons from
astronomical source 2) Other stuff emitting
- extra photon noise Temperature of
surroundings gt Cool optics and go to space 3)
Noise in detectors Temperature of
detector gt Cool detectors - cryogenics
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Bare minimum The CMB Assume Dn/n0.25, AW
l2 Popt e(hn2 /2)/(exp(hn/kT)-1) NEPBLIP
hn?(ne/(exp(hn/kT)-1)) at 2 mm, e 0.3, NEPBLIP
5 x 10-18 W/?Hz Convert to DT and compare
with what we need for CMB B-mode
polarisation At 2 mm, optimum 50 ?K/?Hz,
OK (Note it gets harder as Dn/n gets smaller
but) easier as n gets bigger)
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Detector applications/requirements Ground-based
telescopes Large arrays, multiplexing, photon
noise limited sensitivity Space-based
telescopes Same but higher sensitivity Spectrome
ter-on-chip Astronomy - high sensitivity instrum
entation - 4 K operating temperature mm-wave
interferometry Single detectors, FAST (tens of
kHz)
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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 1,000s 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
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Sensitivity requirements Experiment NEPrequi
red ----------------------------------------------
-------------------------- Ground-based continuum
surveys 10-17 W/ ?Hz e.g. BOLOCAM,
SCUBA2 Space-based CMB 10-18 W/ ?Hz e.g.
post-PLANCK Ground-based spectrometer 10-19 W/
?Hz e.g. z-spec Space-based spectrometer 10-20
W/ ?Hz e.g. SPECS, SAFIR
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1990s SuZIE, SCUBA, NTD/composite
1998 300 mK NTD SiN
PLANCK 100 mK NTD SiN
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• 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 ??

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• 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

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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
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Propagation of electromagnetic radiation in
vacuum I From Maxwells 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
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Propagation of electromagnetic radiation in
vacuum II Expressed in terms of the
4-potential, A? (?, A) and current, ?? (?,
?J) Maxwells equations are ?????????? where
???????? A? - ?? A? E -?? - ?A/?t B ??A
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Propagation of electromagnetic radiation in
vacuum III If we choose the Lorentz gauge ??A
- ?? ??/?t Maxwells equations become 2 driven
wave equations ?? ?2?/?t2 - ?2? ?/? and ??
?2A/?t2 - ?2A ?j Summary wave equations
??? ?? ?2/?t2 - ?2 ?? ?/? 0 in vacuum, with
no sources and ?A ?j 0 in vacuum with no
sources or ?A? 0 ?E 0 ?B 0
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Propagation of electromagnetic radiation in
vacuum IV ??? ?? ?2/?t2 - ?2 ?? has units of
(time/distance)2 1/v2 1/c2 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) Ohms2 So, Z ? ?/?
impedance of free space 377 ? Ratio of
electric and magnetic fields in vacuum,
ZE/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 (Ex,0,0) and
H (0,Hy,0) Ex E0ei(kz-?t) Hy
H0ei(kz-?t) From ???????????? and
????????? ??0 ??z ? ?? ??0 ??? ? k?0 ? ????0
??0 ??z ? ?? ??0 ??? ? k?0 ? ????0 and ?0
? ?0 ? ? ?/?
y
z
x
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 Poyntings theorem EJ
-(1/2) ?/?t??2 ??2 - ??(???) EJ Power
dissipated (1/2) ??2 ??2 Energy density in
EM field ? (???) momentum density in EM field,
flux W/m2
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• 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

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• Units of magnetic flux density
• Magnetic flux density, B
• tesla (1 V sec)/(1 m2)
• 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
1 V
t
1 s
1 m2
-
B ?
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• 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/?
• Amperes law
• I ? H?dl

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• Units of electric flux density
• Magnetic flux density, D
• coul/m2 (1 A sec)/(1 m2)
• Meaning
• Apply 1 A for 1 sec to a capacitor
• plates with area 1 m2 (cause)
• Result is D flux of 1 A sec/m2
• What about voltage?

V
1 A
t
1 s
A1 m2
I ?
D
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• 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?dl

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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
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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
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Propagation of electromagnetic radiation General
- transmission line approach
I
L
V
C
L Inductance per unit length C Capacitance
per unit length
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Transmission line wave equation
I(x)
V(x)
L
V(xdx)
C
L dx dI(x)/dt V(xdx) - V(x) ? L dI/dt dV/dx
C dx dV(x)/dt I(x) - I(x-dx) ? C dV/dt
dI/dx L d2I/dxdt d2V/dx2 C d2V/dt2 d2I/dxdt
(1/L) d2V/dx2 LC d2V/dt2 d2V/dx2 Same
equation for current Wave solutions have
property V/I ?L/C Z of line v2
1/?LC speed of prop.
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Inductance and Capacitance in microstrip line
w
d
H
h
E
Approximation Fields are contained completely
between plates - negligable outside Note - this
is good from point of view of radiation
losses, etc.
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How to calculate inductance
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?dl 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
outsidemodifies L
w
d
I
h
-
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How to calculate capacitance
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?dl h/?(d ? w) 4. Definition
of capacitance CV ? Idt 1 ? C ?(d ? w)/h
?A/h Just like we knew...
w
d
I
h
?
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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
L
Z

C
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Common transmission lines 1. Microstrip 2.
Coplanar waveguide 3. Coplanar striplines/Slotline
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Resistive elements in transmission line - loss
R
L
G
C
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
?(Ri?L)/(Gi?C) Z has real part and imaginary
part. Imaginary part gives loss
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Dielectric materials, index of refraction,
impedence mismatch
Transmission line analogy
I
T
?1
?2
Z1
Z2
R
-
What are optical analogies for
Z1
T 2Z1Z2/(Z1Z2)2 R (Z1-Z2)2/(Z1Z2)2 Z1
??/?1 Z2 ??/?2
Short circuit
-
Z1
Open circuit
-
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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 GHz1 THz?
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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