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© 2000-2023 Gérard P. Michon, Ph.D.

Photons
Quanta of Electromagnetic Radiation

Let there be light !
Genesis 1:3
Michon

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Efficiency of nanoscale confinement in solar cells by Shanhui Fan et al.

Wikipedia : Photon | Photonics | Nanophotonics


Videos: What is a photon? Where do photons come from? by Steve Johnson.
How do we see light? (Nobel 2012; Serge Haroche, David Wineland) in MinutePhysics.
Lumière et matière (1:53:35) by Jean Dalibard (Espace des siences, 2015年04月07日).
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Photonics


tk3078 (Yahoo! 2010年12月29日) 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.

Wikipedia : Photonics vs. Geometrical optics.

Heinrich Hertz (1743-1794)
(2011年01月03日) 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...

Wikipedia : Photoelectric effect | Work function

The photoelectric effect (22:54) by Barton Zwiebach (MIT 8.04, L3.1, Spring 2016).


(2015年05月08日) 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:

SNR = at / N = (at)½

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Wikipedia : Image noise | Shot noise


(2020年04月07日) 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>
Vinculum
¶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 :


<E> = un dn =
8p hn3 dn
vinculum
c3 ( exp( hn / kT ) - 1 )
(Max Planck, 1900年12月14日)

Introducing the spectral density of photons r we have r hn = un .

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Therefore, < e2 > = ( hn r + c3
Vinculum
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...

On the present status of the radiation problem A. Einstein, Phys. Z. 10, 185-193 (1909).

On the development of our views concerning the nature and constitution of radiation
by Albert Einstein, Physikalische Zeitschrift, 10, 817-826 (1909).

Reappraising Einstein's 1909 application of fluctuation theory to Planckian radiation
by F.E. Irons American Journal of Physics, 72, 8, 1059-1067 (August 2004).


(2015年08月23日) Counting photons without destroying them:
The work for which Serge Haroche was awarded a Nobel Prize (2012).

All ordinary light sensors are receptors of photons, which is to say that they absorb every photon they detect, thereby destroying it.

What Haroche discovered at the

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Serge Haroche (b. 1944)


(2019年02月15日) 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:

  • Single photon.
  • Entangled pairs of photons.
  • Squeezed light (quantum metrology used in LiGO).

Canonical Quantization of Single-Mode Free Radiation :

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56 videos by Alain Aspect and Michel Brune (2017).
One-photon interference experiment (14:21) by Alain Aspect (2017年11月07日).


(2023年07月20日) Soft Photons
With (almost) no energy., they still carry one whole unit of spin.

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Soft particles by Andy Strominger (Lex Fridman 2023年02月15日).

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