I. 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)
(Image source: https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:Quadrupol_Wave.gif)

SI Unit: Joule (J)
Mathematical Expression: $$Q_e = \int_{t_1}^{t_2} \Phi_e(t) dt$$ where: $\Phi_e(t)$ is the time-varying radiant flux (unit: Watt, W), representing the radiant energy transferred per unit time; $t_1-t_2$ is the integration time interval.

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.

II. Physical Properties
Radiant energy is carried by electromagnetic radiation and can propagate at the speed of light c in a vacuum, while its propagation speed decreases in a medium.
In the photon model, the energy of a single photon is proportional to its frequency, expressed as:
$$E = h\nu$$ where $h$ is the Planck constant and $\nu$ is the radiation frequency.
Radiant energy can exhibit different spectral distribution characteristics, with its energy distributed across various wavelength or frequency ranges.
When electromagnetic radiation is absorbed by an object, the radiant energy is typically converted into thermal energy; in photoelectric materials, it can also be converted into electrical energy via the photoelectric effect.

III. 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.
• Scattering: Radiant energy is dispersed and propagates in different directions due to inhomogeneous structures within the 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:
$$\alpha + \rho + \tau = 1$$