1.8: Photons and Electromagnetic Waves

Most of the time it is not necessary to consider the quantum nature of radio waves. Considering electric and magnetic fields, and Maxwell’s equations, is sufficient to understand radio systems. Still the underlying physics is that currents in circuits derive from the movement of quantum particles, here electrons, and propagating EM signals are transported by photons, also quantum particles.

In a receiver system, information is translated by a metallic antenna from the propagating photons to moving charges in a conductor. This transfer of information is through the interaction of a photon with charge carriers. So the information transfer is based on the quantized energy of a photon and it is possible that quantum effects could be important. The relative level of the photon energy and the random kinetic energy of an electron is important in determining if quantum effects must be considered.

With all EM radiation, information is conveyed by photons and the energy of a photon is conventionally expressed in terms of electron volts (\(\text{eV}\)). An electron volt is the energy gained by an electron when it moves across an electric potential of \(1\text{ V}\) and \(1\text{ eV} = 1.602\times 10^{−19}\text{ J}\) (\(1\text{ J}=6.241509\times 10^{18}\text{ eV}\)). The energy of a photon is \(E = h\nu = hf\), where \(h = 6.6260693\times 10^{−34}\text{ J}\cdot\text{s}\) is the Plank constant and \(\nu\) and \(f\) are frequency, with the symbol \(\nu\) preferred by physicists and \(f\) preferred by engineers. So the energy of a photon is proportional to its frequency. At microwave frequencies the energy of a microwave photon ranges from \(1.24\:\mu\text{eV}\) at \(300\text{ MHz}\) to \(1.24\text{ meV}\) at \(300\text{ GHz}\). This is a very small amount of energy.

Note

Physically \(kT\) is the amount of energy required to increase the entropy (corresponding to movement) of the electrons by a factor of \(e\) [12].

The thermal energy of an electron in joules is \(E|\text{J} = kT\) where \(k = 1.3806505\times 10^{−23}\text{ J/K}\) is the Boltzmann constant and \(T\) is the temperature in kelvin. This applies to an electron that is moving in a group of electrons, say in a plasma, in thermodynamic equilibrium. Freely conducting electrons in a conductor are in a plasma. The thermal energy of such an electron is its random kinetic energy with \(kT =\frac{1}{2}mv^{2}\) where \(m\) is the mass of the electron and \(v\) is its velocity. (The thermal energy of an isolated electron, i.e. in a non-interacting electron gas, is \(\frac{3}{2}kT\), but that is not the situation with microwave circuits.) At room temperature (\(T = 298\text{ K}\)) the thermal energy of a conducting electron in a metal is \(kT = 25.7\text{ meV}\). This is much more than the energy of a microwave photon (\(1.24\:\mu\text{eV}\) to \(1.24\text{ meV}\)). Thus at room temperature discrete quantum effects are not apparent for microwave signals and so microwave radiation (at room temperature) can be treated as a continuum effect.

A photon has a dual nature, as a particle and as an EM wave. The break point as to which nature helps the most in understanding behavior depends on the energy of the photon versus the thermal energy of an electron. When a microwave photon is captured in a metal at room temperature it makes little sense to talk about the photon as increasing the energy state of an individual electron. Instead, it is best to think of the photon as an EM wave with an electric field that accelerates an ensemble of free electrons (in the conduction band). Thus the energy of one photon is transferred to a group of electrons as faster moving electrons but with the energy increase being so small relative to thermal energy that a quantized effect is not apparent. However even a very low power microwave signal has an enormous number of photons (a \(1\text{ pW}\) \(300\text{ GHz}\) signal has \(5\times 10^{9}\) photons per second) and each photon accelerates the free electrons a little bit with the combined effect being that the electric field of the microwave signal results in appreciable current. This is the view that we use with room temperature circuits and antennas at microwave frequencies; the EM signal (instead of discrete photons) interacts with the free electrons in a conductor and produces current. Quantum effects must be considered when temperature is very low (say below \(4\text{ K}\)) or frequency is very high, e.g. the photon energies for red light (\(400\text{ THz}\)) is \(1.7\text{ eV}\).