2015
International Year of Light and Light-Based Technologies
Photonics
tk3078 (Yahoo!
2010-12-29)
Studying the quanta of light.
What's the difference between
photonics and optics?
Optics deal with light in a classical way
(i.e, without quantum concepts) using one of two viewpoints:
Geometrical optics
is based on the concept of light rays
propagating in a straight line according to the classical laws of reflection
(angle of reflexion = angle of incidence) and refraction
(Snell's law).
Both of these where unified as consequences of the principle of least time
postulated by Pierre de Fermat iaround 1635 and confirmed experimentally in 1851
(when it was finally established that the celerity of light is indeed inversely proportional
to the index of refraction of the medium).
The wave theory of light, on the other hand,
explains diffraction
(as well as the laws of reflexion and refraction of geometrical optics, incidentally).
It was first championned by Christiaan Huygens and
received experimental support from Thomas Young in 1803.
The idea that light is a form of electromagnetic wave is due to
Michael Faraday,
who was later vindicated mathematically by James Clerk Maxwell
(Maxwell's equations, 1864).
By contrast,
quantum optics (fundamental research)
and
photonics (applied science)
are based on the explicit idea that light consists of
packets of energy proportional to its frequency
(the coefficient of proportionality being
Planck's constant).
This idea was formally put forth in 1905 by
Albert Einstein to explain the
photoelectric effect
(in 1900, Max Planck
had paved the way by showing that the blackbody spectrum
could be explained by postulating that
all energy exchanges between radiation and matter
could only occur in quanta of energy proportional to the frequency).
So, the key difference between optics and photonics is that the latter deals primarily
with the
quantization of light which is ignored by the former.
Also, in optics we consider light to consist either
of particles (explaining the
light rays and sharp shadows
on which geometrical optics is based)
or waves (which explain diffraction using Huygens principle).
In photonics, we integrate the quantum notion that the light quanta
(photons) have properties characteristic of both waves and particles.
(2011-01-03) The Photoelectric Effect (Einstein, 1905)
What is the work function of a metal?
The photoelectric effect was first observed in 1887, by
Heinrich Hertz (1857-1894).
He found that an illuminated metallic surface produced an electric current
proportional to the intensity of the light (as could be reasonably expected)
but only if the light frequency exceeded a certain threshold
which depended on the metallic surface involved.
That was a surprise begging for an explanation which
Einstein would only provide in 1905
(he was awarded the 1921 Nobel prize mostly for that reason).
When the surface is highly polished the experimental value
of the aforementioned threshold depends on the metal involved and
its crystalline structure.
Einstein conjectured that every electron was bound to the metallic structure
by some binding energy W,
dubbed work function.
Einstein further assumed that energy was carried by light carried in disrete packets
proportional to the frequency n
(for which Lewis
coined the word photon, in 1926).
Using the constant of proportionality h introduced by
Planck in 1900.
the kinetic energy of each released electron would then be:
½ m v2 =
h n - W
That conjecture was verified experimentally in 1915 by
Robert A. Millikan
(1868-1953; Nobel 1923) who gave h to about 1% in the process...
(2015-05-08) Minimal signal-to-noise ratio of a light sensor :
The ultimate limit depends only on the number of photons received.
This imposes a lower limit on the noise of the image sensors used on modern digital cameras.
Those are composed of a digital array consisting of millions of individual sensors
of the type analyzed below: One per pixel for a black-and-white sensor,
up to four per pixel
for color photography.
The arrival of photons in a monochromatic light beam is essentially a
Poisson process whose activity
a is equal to the radiant power
of the beam (in watts, W) divided into the
energy of each photon (in joules, J).
For standard yellow-green light (540 THz)
the luminous power in lumens (lm) is, by definition,
683 times the radiant power in watts (W).
A surface area of S square meters receiving an illumination of L
(expressed in lx, a lux being defined as a lumen per square meter)
thus receives an average number of photons per second equal to the activity
in becquerels (Bq) of the aforementioned Poisson process, namely:
a =
S (L / 683) / (h 5.4 1014 Hz)
= L S 4.092 1015
If we express
a in Bq,
L in lx and S in square microns, we have:
a = 4092 L S
In a Poisson process
with an activity of a becquerels,
the probability of observing exactly n arrivals in t seconds is given by:
Pn =
exp(-lt) (at) n / n!
The average number of arrivals is
at. Let N be the RMS of the noise:
N 2 + (at) 2
=
S n
Pn n 2
For the right-hand-side summation, we use the following remarks:
S n x n/ n!
= exp (x)
S n n x n/ n!
= x d/dx exp (x) = x exp (x)
S n n 2 x n/ n!
= x d/dx [ x exp (x) ]
= x exp (x) + x 2 exp(x)
Applying this to the above with x = at yields:
N2 + (at) 2
=
(at) + (at) 2 So, the RMS value of the noise is
N = Ö(at).
and the signal to noise ratio is:
(2020-04-07) Dual Noise (Einstein. 1909)
Shot noise of photons is added to the
speckle of lightwaves.
Gibbs (1902) and
Einstein (1904) independently found the following expression
for the mean-square energy fluctuations per unit of a constant volume V
in thermal equilibrium with a bath at temperature T:
< e2 > = k T2
(
¶ <E> ¶T
)
V
For blackbody radiation,
the mean energy density [energy per unit volume] of the photons whose frequencies are between
n and n+dn
is given by Planck's radiation formula :
Introducing the spectral density of photons r we have
r hn = un .
Therefore, < e2 > =
(
hn r +
c3 8p n2
r2
)
dn
Einstein noticed that the first term of that bracket corresponds to
the shot noise discussed in the previous section,
which would be the sole noise observed if light was purely corpuscular,
while the second can be attributed to the wavelike nature also
possessed by Plankian light radiation.
He interpreted that as a direct clue to the dual nature
of light. Both a wave and a flow of particles...
(2019-02-15) Quantum Optics
Describing quantum states of light without classical analogs.
The semi-classical model of interactions between light and matter is
fairly adequate to descrive the photoelectric effect
and the stimulated emission of radiation
on which lasers are based,
but it can't explain spontaneous emission or purely quantum effects like:
