Theory of electromagnetic wave frequency upconversion in dynamic media

Abstract

Frequency upconversion of an electromagnetic wave can occur in ionized plasma with decreasing electric permittivity and in split-ring resonator-structure metamaterials with decreasing magnetic permeability. We develop a general theory to describe the evolution of the wave frequency, amplitude, and energy density in homogeneous media with a temporally decreasing refractive index. We find that upconversion of the wave frequency is necessarily accompanied by partitioning of the wave energy into low-frequency modes, which sets an upper limit on the energy conversion efficiency. The efficiency limits are obtained for both varying permittivity and varying permeability.

Laser frequency upconversion in plasmas with finite ionization rates

“…At a certain time t, the solution of Eqs. (6) and (7) describes a pair of counter-propagating waves at the same frequency and a static magnetic field (9) whereê is the direction of polarization, ω and k are the wave frequency and wavevector, respectively, obeying the dispersion relation ω 2 =ω 2 p +c 2 k 2 . E ± and B ± are the amplitude of the forward-/backward-propagating electric and magnetic fields, respectively, and they are related to the electric field amplitude by B ± = ±(ck/ω)E ± .…”

“…"Proof-of-principle" numerical simulations predicted [8] that this method may create "tabletop" sources of coherent x rays out of near-infrared lasers at high efficiency and low cost. However, the existing theories only describe either "flash ionization" [3,9], with which the plasma is fully ionized instantaneously, or "adiabatically gradual ionization" [9][10][11][12], with which the plasma is ionized at an infinitely slow rate. These two extremes predict different output amplitudes.…”

“…To provide the background for analyzing the effects of finite ionization rates, we first briefly review the process of "flash ionization" [3,9]. All the electrons are suddenly ionized and begin to oscillate in the laser field.…”

“…All the electrons are suddenly ionized and begin to oscillate in the laser field. The electron oscillations constitute the polarization current [9], which reduces the index of refraction and causes frequency upconversion. The electron oscillation also radiates waves in both forward and backward directions, thereby splitting the input pulse into a pair of counter-propagating pulses.…”

Overcoming the efficiency-bandwidth tradeoff for optical harmonics generation using nonlinear time-variant resonators

“…TVRs have recently attracted considerable attention because of their potential for efficient frequency conversion [12][13][14][15], non-reciprocal devices [16][17][18], topological photonics [19] and time-variant metamaterials [16,20,21]. Using a simple theoretical framework based on the coupled mode theory (CMT) [22,23], a variety of exotic phenomena have been successfully predicted, such as perfect frequency conversion into a sideband with light reversal [24], continuous adiabatic frequency conversion [12], and many others.…”