Abstract
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.
Highlights
LEDs and lasers are widely used and considered for display and lighting applications
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
The most effective way to analyze the characteristics of LED and laser optics would be to analytically derive their 2D and 3D near field intensity distributions, in closed-form solutions if possible, which would provide a method to calculate both near and far field light intensity distributions by propagating the near field intensity pattern along the optic axis as a function of distance from the light source
Summary
LEDs and lasers are widely used and considered for display and lighting applications. The most effective way to analyze the characteristics of LED and laser optics would be to analytically derive their 2D and 3D near field intensity distributions, in closed-form solutions if possible, which would provide a method to calculate both near and far field light intensity distributions by propagating the near field intensity pattern along the optic axis as a function of distance from the light source. Speaking, such analysis for a finite-size, flat light source cannot be found in prior literature; approximate formulations only exist in literature for a. Our formula for the 2D surface intensity profile proves that the light propagation behavior from an LED and that expected for a laser diode is similar to Gaussian beam propagation, which has been previously demonstrated experimentally and via numeric simulation [10], [11]
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