  The design of optical systems capable of processing and manipulating
ultra-short pulses and ultra-focused beams is highly challenging with far
reaching fundamental technological applications. One key obstacle routinely
encountered while implementing sub-wavelength optical schemes is how to
overcome the limitations set by standard Fourier optics. A strategy to overcome
these difficulties is to utilize the concept of generalized uncertainty
principle (G-UP) that has been originally developed to study quantum gravity.
In this paper we propose to use the concept of G-UP within the framework of
optics to show that the generalized Schrodinger equation describing short
pulses and ultra-focused beams predicts the existence of a minimal spatial or
temporal scale which in turn implies the existence of maximally localized
states. Using a Gaussian wavepacket with complex phase, we derive the
corresponding generalized uncertainty relation and its maximally localized
states. We numerically show that the presence of nonlinearity helps the system
to reach its maximal localization. Our results may trigger further theoretical
and experimental tests for practical applications and analogues of fundamental
physical theories.

Exactly Solvable and Integrable Systems;Optics