electric dipole radiation
The simplest antenna in the universe is a pair of charges sloshing back and forth — an oscillating electric dipole. Electric dipole radiation is the light such a wiggling dipole throws off, and it is the leading, dominant term for almost every everyday radiator, from a radio mast to a glowing atom.
Take a dipole moment oscillating as p(t) = p_0 cos(omega t). In the radiation zone the fields fall as 1/r, oscillate at frequency omega, and point transverse to the outgoing direction, with amplitude proportional to sin(theta), theta measured from the dipole axis. The time-averaged total radiated power is <P> = mu_0 p_0^2 omega^4 / (12 pi c), equivalently p_0^2 omega^4 / (12 pi epsilon_0 c^3). The screaming feature is the omega^4: double the frequency and the radiated power jumps sixteenfold.
That omega^4 law is why the sky is blue — air molecules act as tiny driven dipoles and scatter short-wavelength (high-omega) blue light far more strongly than red, which is Rayleigh scattering. The sin^2(theta) power pattern means a dipole radiates most broadside and nothing at all along its own axis. This is the E1 (electric dipole) term of the multipole expansion; when it happens to vanish, the weaker magnetic dipole and electric quadrupole terms take over.
Double the driving frequency of an oscillating dipole and, because power scales as omega^4, the radiated power jumps by 2^4 = 16 times. This steep frequency dependence is exactly why the daytime sky is blue rather than uniformly white.
Dipole power ~ p_0^2 omega^4 sin^2(theta); the omega^4 law paints the sky blue.
The neat omega^4 result assumes the source is much smaller than the wavelength (the dipole approximation). Radiation is maximal perpendicular to the dipole and exactly zero along its axis — a dipole never beams along the line it oscillates on.