Download Photon counting FIR detectors

Detection of Electromagnetic
Radiation
Phil Mauskopf, University of Rome
12/14 January, 2004
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
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...
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?
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
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...
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/n
proportional to intensity
dominates under large photon occupation number
P=radiation power detected in Watts = nhn
P~ I(n)AW (n) e
so if we know the source intensity, throughput and resolution we
can calculate the sensitivity limit (and necessary detector
sensitivity)
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
Bare minimum: The CMB
Assume: n/n=0.25, 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 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 n/n gets smaller but)
easier as n gets bigger)
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)
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
Sensitivity requirements:
Experiment
NEPrequired
-----------------------------------------------------------------------Ground-based continuum surveys
10-17 W/ Hz
e.g. BOLOCAM, SCUBA2
Space-based CMB
e.g. post-PLANCK
10-18 W/ Hz
Ground-based spectrometer
e.g. z-spec
10-19 W/ Hz
Space-based spectrometer
e.g. SPECS, SAFIR
10-20 W/ Hz
1990s: SuZIE, SCUBA, NTD/composite
1998: 300 mK NTD SiN
PLANCK: 100 mK NTD SiN
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 + ??
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
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
Propagation of electromagnetic radiation in vacuum I:
From Maxwell’s equation we get the wave equation for
EM waves in a vacuum:
 = 
 = 
 =  +
 = 0
 = 
 = e
In a vacuum with no sources,  =  = 0
Taking  = () - 2 gives the wave equation
2 = e 2 2
Propagation of electromagnetic radiation in vacuum II:
Expressed in terms of the 4-potential, A = (, A)
and current,  = (, J)
Maxwell’s equations are:
n = n
where
n =  An - n A
E = - - A/t
B = A
Propagation of electromagnetic radiation in vacuum III:
If we choose the Lorentz gauge:
A = - e /t
Maxwell’s equations become 2 driven wave equations:
e 2/t2 - 2 = /e and
e 2A/t2 - 2A = j
Summary wave equations:
  e 2/t2 - 2
 = /e = 0 in vacuum, with no sources and
A = j = 0 in vacuum with no sources or
A = 0
E = 0
B = 0
Propagation of electromagnetic radiation in vacuum IV:
  e 2/t2 - 2
e has units of (time/distance)2 = 1/v2 = 1/c2
or c = 1/ e
 is magnetic permeability: free space = 4  10-7 H m-1
e is the dielectric constant: free space = 8.84  10-12 F m-1
/e has units of (H/F) = (Ohms/Hz)/(1/Ohms Hz) = Ohms2
So, Z =  /e = impedance of free space = 377 W
Ratio of electric and magnetic fields in vacuum, Z=E/H
Just as fundamental a constant as the speed of light...
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)
i(kz-t)
Ex = E0e
i(kz-t)
Hy = H0e
From  =  and  =+
0 z =  0   k0 = 0
0 z = e 0   k0 = e0
and 0  0 =  /e
y
z
x
Propagation of electromagnetic radiation in vacuum VI:
Find a conservation law for Electromagnetic waves
Sources follow charge conservation: nn = 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 + e2] - ()
E·J = Power dissipated
(1/2) [2 + e2] = Energy density in EM field
 () = momentum density in EM field, flux = W/m2
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
Units of magnetic flux density:
V
• Magnetic flux density, B
2
[tesla] = (1 V sec)/(1 m )
1V
Meaning:
t
1s
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?
1 m2
+
-
B
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dl
Units of electric flux density:
V
• Magnetic flux density, D
2
2
[coul/m ] = (1 A sec)/(1 m )
1A
t
Meaning:
1s
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?
A=1 m2
I
D
Units of electric flux density:
• Voltage depends on material in which electric field lines
exist (I.e. between plates)
Described by dielectric constant, e, and electric field, E
E = D/e
Definition of electric potential:
V =  Edl
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
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
Propagation of electromagnetic radiation:
General - transmission line approach
I
V
L
C
L = Inductance per unit length
C = Capacitance per unit length
Transmission line wave equation:
V(x) I(x) V(x+dx)
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 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.
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.
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)
w
d
I
h
+
-
4. Definition of inductance:
LI =  Vdt = 1  L = (d  h)/w
Proceedure also works if include field outside…modifies L
How to calculate capacitance:
1. Apply 1 A for 1 sec to plates
w
with area = d  h
 Develops D field, charge
D = 1/(d  w)
2. Calculate E from e, D
h
E = D/e = 1/e(d  w)
3. Calculate current from
Integrate between plates to get V
V =  Edl = h/e(d  w)
4. Definition of capacitance:
CV =  Idt = 1  C = e(d  w)/h = eA/h
Just like we knew...
d
I

Impedance of transmission line:
C = e(d  w)/h  C = e (w/h)
L = (d  h)/w  L =  (h/w)
 Z = L/C = L/C = (h/w) /e
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
Common transmission lines:
1. Microstrip
2. Coplanar waveguide
3. Coplanar striplines/Slotline
Resistive elements in transmission line - loss:
R
L
C
G
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
Dielectric materials, index of refraction, impedence mismatch:
I
e1
R
Transmission line analogy
T
e2
+
-
Z1
Z2
What are optical analogies for:
T = 2Z1Z2/(Z1+Z2)2
+
-
Z1
Short circuit
+
-
Z1
Open circuit
R = (Z1-Z2)2/(Z1+Z2)2
Z1= /e1
Z2= /e2
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?
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