Definition
Radiant Energy is the energy carried by electromagnetic radiation during its emission, propagation, or absorption. It is a fundamental energy quantity in radiometry, used to characterize the total energy transferred by radiation, and is denoted by the symbol: $Q_e$.

Electromagnetic radiation produced by the Sun

(Image source: https://en.wikipedia.org/wiki/Solar_energy#/media/File:Sunset_over_the_gulf_of_Mexico_-_iss042e034066.jpg)

SI Unit: Joule (J)

Mathematical Expression: $$Q_e = \int_{t_1}^{t_2} \Phi_e(t) dt$$

where $\Phi_\mathrm{e}(t)$ is the radiant flux in watts (W) and $[t_1,t_2]$ is the time interval of integration.

For pulsed radiation, the radiant energy corresponds to the total energy contained in a single pulse; for continuous radiation, the radiant energy is typically obtained by integrating the radiant flux over a given time interval.

Physical Properties
Radiant energy is carried by electromagnetic radiation; it propagates at the speed of light $c$ in vacuum and more slowly in a material medium. It may have various spectral distributions, with its energy spread over different wavelength or frequency ranges.

At the microscopic level, radiant energy is quantized, consisting of photons whose individual energy is given by the Planck relation $$E = h\nu$$ where $h$ is the Planck constant and $\nu$ is the frequency.

When electromagnetic radiation is absorbed by an object, the radiant energy is typically converted into thermal energy; in photovoltaic materials, it can also be converted into electrical energy via the photoelectric effect.

Interaction with Matter
When electromagnetic radiation interacts with matter, the radiant energy can be redistributed according to the optical properties of the material. The main forms include:

• Absorption: After being absorbed by an object, radiant energy is typically converted into thermal energy; in certain photoelectric materials, it can also be converted into electrical energy.
• Reflection: Radiant energy changes direction at the material surface and returns to the original medium.
• Transmission: A portion of the radiant energy passes through the object and continues to propagate.

For opaque objects, the incident radiant energy typically satisfies the conservation of energy relation:
$$\alpha + \rho = 1$$ where: $\alpha$ is the absorptance; $\rho$ is the reflectance.
For translucent media, the transmittance $\tau$ must also be considered, yielding the relation:
$$\alpha + \rho + \tau = 1$$