Re: measuring the characteristics of photons in confined spaces

Greetings Charles:

References:

1. S. Ramo, J. R. Whinnery, T. Van Duzer,
Fields and Waves in Communication Electronics, John Wiley & Sons, 1967

2. National Science Foundation's (NSF) Particle Adventure Web site:
http://par ticleadventure.org/particleadventure/index.html

3. NASA's Electromagnetic Spectrum we site:
ht tp://imagine.gsfc.nasa.gov/docs/science/know_l2/emspectrum.html

4. Richard P. Feynman, Robert B. Leighton, Matthew Sands,
The Feynman Lectures on Physics Volume 3, Addison- Wesley 1963.

5. Waveguide Modes Applet Select: Electromagnetic Waves in a Waveguide
http://www.falstad.com/mathp hysics.html

Your questions have many complex answers and several books have been written
about various parts of your question. Reference 1 is a classic in the field.
Since there have been a number of questions to the Mad Science web site about
the general subject of photon behavior, this long answer will try to give
you and readers a top level introduction to the subjects that you ask about.

The wave - particle duality exhibited by photons and other fundamental particles
have been described mathematically in the field of Quantum Electrodynamics
(QED). However, we cannot fully comprehend quantum particle behavior because
it is so unlike ordinary experience and it appears mysterious to everyone
including the late Nobel Lauriat, Professor Richard Feynman, who also states
this in Reference 4. When the location of a stopped photon is measured the
Heisenberg Uncertainty Principle, discussed in Reference 2, shows that we
cannot accurately measure photon velocity and momentum. On the other hand
if we measure photon velocity and/or momentum, we cannot accurately measure
the location of the photon. In Reference 4 Professor Feynman uses several
simple examples to discuss the measurement problems encountered in quantum
physics because of the wave/particle duality observed in fundamental particles
including photons.

Photons

A photon is a force carrying particle and is a packet of electromagnetic energy
that has no mass and must travel at the speed of light to exist. Photons exhibit
both wave like behavior and particle like behavior. The NSF Particle Adventure
web site in Reference 2 is a great introduction to fundamental particles and
starts at a high school level of physics. However, it does become very complex
as you proceed into this large web site. Go as far as you can in the Adventure
and skip the rest.

Before discussing complex structures I'll discuss the interaction of photons
with atoms. A photon has both an electric field and a magnetic field that is
normal (90 degrees) to the electric field. We use the Right Hand Rule to
determine the direction of the fields. If you bend the middle finger of your
right hand 90 degrees from the index finger and raise your thumb up 90 degrees
from your index finger, and if you point the index finger in the direction the
photon or electromagnetic wave is traveling, your middle finger points in the
direction of the electric field and your thumb points in the direction of the
magnetic field. We call the direction of the electric field the polarization
of the photon which also determines the polarization of the electromagnetic
(EM) wave.

Photons Interaction with Atoms

Photons do not reflect! Metals (conductors) have loosely bound electrons and
when a photon hits a metal atom in a surface, the photon disappears and the
added energy temporarily raises the energy state of the atom. The atom can
then dissipate the excess electron energy as heat (absorption) or after a very
brief period of time it can emit a new photon at the same frequency as the
incident photon (this is what we call reflection) back out of the surface. For
reasons beyond the scope of this answer, the frequency of the newly emitted
photon has a 180 degree phase shift relative to the frequency of the original
photon. Thus at the quantum mechanical level reflection is a more complex
process than what we use in studying the properties of mirrors etc while
studying conventional optics. Metals such as silver, aluminum and copper have
low absorption and high emission (reflection) characteristics. Metals such as
lead have high absorption and poor emission (reflection) characteristics.
However, these properties often change in different frequency regions of the
spectrum. For example, in the infrared frequency region gold, is a better
reflector (photon emitter) than aluminum, which is preferred for mirror coatings
in the visible light region of the spectrum.

Dielectrics (insulators) such as glass have tightly bound electrons and when a
photon hits a surface atom it can be absorbed as heat (absorption), or the atom
can emit a new photon that can proceed on into the material in a direction
similar to the direction of the original photon until it hits another atom and
the process is repeated (we call this transmission), or the atom can emit a new
photon back out of the material (we call this reflection). We have all seen
visible light absorbed, transmitted and reflected from glass. As the transmitted
photons go from atom to atom through the dielectric material, there is a slight
delay at each atom as the photon excites the atom and the atom emits a new
photon. This delay appears to slow down the speed of light in the material and
we call this the index of refraction of the material. However, the photons still
travel at the speed of light in a vacuum within the material. The apparent
delay is caused by the atoms stopping photons and emitting new photons. The
frequency of each new photon emitted in a dielectric has a phase shift relative
to the phase of the incoming photon and the degree of phase shift is different
for each type of dielectric material. This knowedge is important in developing
glass fiber optic waveguides. More about waveguides in a later section.

The amount of energy (E) in a photon is equal to Planck's Constant (h) times
the frequency (f) of the photon:

E = h * f

Where: E = energy in joules
h = 6.625 * 10 ^ - 34 joule second
f = frequency in Hertz (cycles per second)

Note: one joule for one second = one watt of power. Thus (h) provides a very,
very, very small amount of power for detecting one photon per second or even
1000 photons per second.

The equation shows that the energy of a photon is linear with
increasing frequency so that there are huge energy differences between radio
photons and gamma-ray photons.

Radio photons have enough energy to vibrate the nucleus of water molecules
as used in magnetic resonance imaging (MRI). Microwave photons have enough
energy to rapidly vibrate molecules as used in the heating of water molecules
in microwave ovens. Infrared photons are being used in laser weapons to burn
holes in missiles. Visible light photons interact with electrons causing them
to change orbits generating coherent light as used in lasers. X- rays,
gamma-rays and other ionizing radiation photons have enough energy to pass
through matter while tearing atoms and molecules apart and they also can be
harmful to life.

Limits of Measuring Equipment

Scientific experience has found that when the photon wavelength is much larger
(lower frequencies) than the measuring equipment (equipment such as radio
receivers and antennas), we can best study the wavelike properties of photons.
These radio, and microwave photons have such low energy that we need thousands
of them to study their wave like behavior. When the photon wavelength is small
(higher frequencies) compared to the measuring equipment ( equipment such as
photomultiplier tubes and Geiger Counters) , we can best study the particle
like behavior of photons in the infrared (IR), visible light, ultra violent
(UV) light, x-rays, and Gamma rays (see Reference 3).

Listening to Photons as Particles

We can hear a photon's particle like behavior by listening to the output of a
photomultiplier tube when it detects IR, visible light or UV photons
by connecting the device to an audio amplifier and loud speaker system. If we
have more than about 1000 photons per second incident on the tube, we obtain a
steady rushing sound which can show wave like behavior. However, when we reduce
the light intensity the rushing sound becomes weaker and at a level of a just
few photons per second, the amplifier output sounds like pop corn randomly
popping in a kettle. The photon arrivals are randomly spaced in time and we
can't accurately predict their arrival and so we do not observe wave like
behavior.

Listening to Photons as Waves

If we have more than 1000 radio or microwave photons per second arrive on an
antenna, we can begin to study the wave like properties of radio photons by
listening to the output of a very sensitive radio receiver. Antennas can convert
electron motion (current)in a conductor to photons or convert photons to
electron motion. A beam of 1 Gigahertz photons (1 billion cycles per second),
such as used for cellular telephone
communications, has a wave length of 30 cm (11.8 inches). If this beam is
incident on a metal plate with a round hole in it, we can use a calibrated
receiver to measure the microwave power passing through the hole. If the hole
is greater than a wavelength in diameter all of the power incident on the hole
is transmitted through it. However, as the diameter of the hole decreases the
amount of power passing through the hole rapidly decreases and when the hole
gets to about 1/10 wavelength in diameter very little of the power incident
on the hole gets through. At a diameter of 1/100 of a wavelength, the signal
passing through the hole will be almost undetectable. However, if we close
the hole entirely, quantum mechanics teaches us that some photons will still
pass through the plate by a process called Quantum Tunneling! However, it
takes very special radio/microwave equipment called MASERS cooled to liquid
helium temperatures to detect less than 100 photons per second at these
frequencies. The probability of a photon tunneling through a barrier depends
on the type of material used in the barrier and on its thickness. In our cell
phone example the probability of a photon tunneling through a 2.5 mm (1/10 inch)
thick aluminum plate is practically zero and it may take millions of years to
detect a tunneling photon. However, if we reduce the metal barrier's thickness
to less than 10 nanometers (10 billionths of a meter), as we do in microwave
semiconductor devices, perhaps 10 % of the incident photons will tunnel through
the metal barrier! From this experiment we can conclude that a hole one wavelength in
diameter has little effect on a photon; however, smaller holes less than one
wavelength in diameter reflect some but not all of the photons. This does not
give us the size of the photon but it does tell us that the size of the hole
relative to a photon's wavelength does affect the probability of transmitting
a photon through a hole in a metal barrier.

Since the development of MASERS in the mid 1950s and the subsequent development
of LASERS (first called optical masers) in the 1960s, the wave like
and particle like behavior of both radio and light photons has been demonstrated
to be identical. A photon is a photon regardless of it's frequency and apparent behavior.

Discussion about photon propagation in three dimensional structures.

In the oscillating fields of a traveling electromagnetic (EM) wave, the electric
field of a group of photons will point in one direction during one half of a
cycle and will point 180 degrees in the opposite direction for the second half
of a cycle. Also, the amplitude of the electric and magnetic fields (the number
of photons) will vary in amplitude in a sinusoidal manner for each cycle of the
photon frequency. Because of the right hand rule the magnetic field will also
alternate directions every half cycle. This type of EM wave is called a linear
polarized wave. There can also be EM waves in which have electric fields that
rotate in a circular or an elliptical manner during a cycle. These EM waves
are said to have circular or elliptical polarization. For simplicity I will
stay with simple linear polarization for the remainder of this discussion.

Wave guiding structures.

During the 1930s, while working at the Bell Telephone Laboratories (BTL),
George Southworth discovered a new form of radio frequency transmission line
called Waveguides. Waveguides are more efficient than coaxial cable transmission
lines for transmitting radio waves and microwaves to and from transmitters,
receivers and antennas. Typical waveguide runs can range from a few feet in
an airplane to several hundred feet in the giant dish antennas used in radio
astronomy or for space communications. Typical waveguides are cylindrical or
rectangular metallic tubes, usually made from copper with a silver coating and
containing air or a vacuum inside of them through which the EM waves pass.
A waveguide run resembles water pipes with straight sections, T joints,
Y joints, bends and twists. More recently, starting in the 1970s and
continuing today, glass fiber optic waveguides have been developed to
efficiently transmit IR and visible light waves hundreds of kilometers (miles) in
telecommunication systems. I will not discuss the more complex fiberoptic
waveguides here but their operation is somewhat similar to EM wave
transmission in metallic microwave waveguides.

A microwave power source can be connected to a small 1/4 wave long wire
antenna inserted into the center of a cylindrical metallic pipe called a waveguide.
The antenna converts the energy of moving electons (current)into photons.
The photons produce EM waves in the waveguide which will travel through
the waveguide in a zig zag manner, reflecting off the metallic surfaces
along the way (Remember each reflection is really a
new photon being emitted by the metal atoms each time another
photon hits the inner surface of the metal cylinders walls). This results in
a moving three dimensional electrical field pattern called a Mode.
The mode travels down the waveguide at a velocity much slower than the speed of light.
The reduced velocity of the mode's wave is caused by the photons zig zagging.
The photons in the mode do travel at the speed of light; however, they are traveling
greater distances as they criss cross the waveguide as they move down the cylinder.
To make a long story short, the optimum dimension for most efficiently transmitting
EM waves in a cylindrical waveguide is about one wavelength in diameter
(Note this is similar to the hole experiment). If the transmitted wavelength
is greater than the waveguide diameter, little or no power will travel down
the waveguide (some what similar to a series of smaller holes in the hole
The frequency were EM transmission stops is called the waveguide's
cut-off frequency. Frequencys below the cut-off frequency will not transmit
through the waveguide. If the source wavelength is smaller than the diameter
of the waveguide, the waves will travel down the waveguide; however, for
reasons too complex to discuss here, the smaller the wavelength relative to
the waveguide diameter, the less efficient will be the transmission line
because of greater absorption in the metal walls (more reflections per unit
length of waveguide). Also when the transmitted wavelength is smaller than
the waveguide diameter more complex three dimensional EM mode patterns are
set up in the waveguide.


In practice rectangular waveguides are used more often than cylindrical
waveguides in microwave systems because they preserve the direction of
polarization of the EM waves as they travel around bends and twists. However,
I will not go into the details of rectangular waveguides. Because
the flat walls of a rectangular pipe can act like mirrors, the optimum width
of a rectangular waveguide is one half wavelength and the optimum height is
one quarter wavelength. Reference 5 is a website where you can observe various
modes moving through rectangular waveguides. There are dozens of mode patterns
that can propagate in both cylindrical and rectangular waveguides. These modes
are identified as on the web site as Transverse Electric field modes (TE modes)
or transverse magnetic field modes (TM modes). The number following the
TM or TE identifier is the number of one half wavelengths that can fit across the
waveguide at the operating frequency . The first number after the identifier
is the width in 1/2 wavelengths and the second number is the height of the
rectangular cross section in one half wavelengths.

The web site starts with a view the basic mode TE 10 which represents the
fundamental, most efficient mode in a rectangular wave guide. Then clear the
screen and select the TE 21 mode on the matrix at the bottom of the display.
The display will then fit twice the number of one half waves across each dimension
of the rectangle. Note how complex the mode pattern becomes as you fit more
½ wavelengths into the waveguide dimentions. This complexity is why these modes
are less efficient. However, for some applications these higher order modes are
used when the reduced transmission efficiency can be tolerated. Don't let the zero
bother you in the TE 10 mode, in a rectangular waveguide for only the width
determines the cutoff frequency, the height is the direction (polarization) of
the electric field and to first order not a frequency limiting factor. This is
fairly complex stuff so enjoy the plots for they do show what occurs in a
waveguide transmission line. Why they occur takes a lot more EM theory.

If you place end plates on a waveguide spaced by an integer number of 1/2
wavelengths you can form a resonant cavity which is tuned to a single
microwave frequency. This is similar to the acoustic modes in a pipe
organ's pipes, where each pipe is tuned to a different audio frequency.
In a communications satellite cavity filters are used to separate the hundreds
of microwave channels being transmitted through the satellite. You can view
cavity modes on the web site just above the wavguide mode applet.

Best regards Your Mad Scientist
Adrian Popa