The study of light dates back over 1000 years. In that time, the manipulation of light has allowed technological progress across fields. In particular, the advent of the laser ushered in the modern age of scientific research and is perhaps most critically relied upon today as a facilitator of the modern internet.

The figure above shows a cross-section of a Gaussian laser beam, a common geometry, as it focuses and then defocuses once again. Due to the finite size of the beam at the input, the beam can never converge to a single point. Rather, the focal spot must be of finite width.

  • The Physics of Maxwell's Equations
    [Mathematical Physics] Maxwell’s Equations govern the study of electromagnetism, one of the fundamental forces of nature. Here, I attempt to motivate these beautiful equations and present some of their more interesting consequences.