Derivation and Experimental Verification of the Near-field 2D and 3D Optical Intensities From a Finite-size Light Emitting Diode (LED)

We derive the near-field light intensity distributions of an inorganic LED on its surface and in volumetric space. Our closed-form solution for 3D intensity distribution for a finite-size LED is consistent with Lambert's Cosine Law, which provides the 3D intensity distribution for an infinitesimal, flat light source. We also derive the formula for the 2D intensity distribution on a diode surface showing its similarity to a Gaussian function, which is typically used to approximate the surface light intensity profile for an LED and a laser diode. Our 2D intensity distribution function produces light propagation similar to the Gaussian beam propagation in space. However, unlike the Gaussian approximation, our formula invariably produces this behavior without assuming the refractive index inside the diode follows a quadratic function of the transverse spatial domains. Our 2D and 3D spatial intensity formulas in near-field for LEDs offer a unique way to calculate the peak intensity that occurs at the center of the flat LED source. We demonstrate, as expected, that the peak intensity increases with the size of the LED source as well as the brightness of each radiative electron-hole pair, which is a function of the drive current and quantum efficiency of the LED.