Einstein’s impact on optics at the frontier

The seminal contributions made by Einstein a century ago have enabled a new frontier area of science, called high-field science. This research involves the physics of the interactions of matter with electromagnetic fields at its highest levels ever achieved in the laboratory. Besides being of fundamental importance to physics research, the discoveries being made in this area are also leading to a new generation of compact and ultrashort-duration particle accelerators and X-ray light sources, with applications ranging from nuclear fusion to cancer therapy. 121 digitalcommons.unl.edu i it l . 122 D. Um s t a D t e r i n Ph y s i c s Le t t e r s A 347 (2005) 1.2. Relativistic optics and high field science In 1905, the most powerful laboratory light source was the X-ray tube, which produced approximately 1 kW of peak power. The electromagnetic field strength produced by such a source was quite minuscule when compared to the field that binds the electron to the nucleus. Thomson had just discovered at this time that light scattered from an electron was emitted at the same frequency as the light that was incident, and that the electron would follow the electric field of the light wave. In 1960, nearly half a century later, the laser was invented, which as based upon Einstein’s quantum theory of light. With the ensuing dramatic increase in power, light could be focused to sufficient intensity to cause nonlinear optical effects in atomic media. In conventional nonlinear optics, where the electric field of a light wave E is much smaller than an atomic field, Eat = 3 × 109 V/cm, various nonlinear phenomena, such as self-focusing, harmonic generation and Raman scattering, arise due to the anharmonic motion of electrons in the combined fields of atom and laser. Approximate analytical solutions can be obtained by means of perturbation expansion methods, using E/Eat as the expansion parameter. At higher light fields, when E approaches Eat, this method breaks down and the medium becomes photo-ionized, creating a plasma, as illustrated by Figure 2. Further increases in light intensity enabled nonlinear optical effects of even these free plasma electrons (see Figure 1).The nonlinearity arises in this case because the electrons oscillate at relativistic velocities in laser fields that exceed 1011 V/cm, resulting in relativistic mass changes that exceed the electron rest mass and the light’s magnetic field becoming important. The work done by the electromagnetic field (E) on an electron (eEλ) over the distance of a laser wavelength (λ) then approaches the electron rest mass energy (mec), where e is the elementary charge of an electron, me is the electron rest mass and c is the speed of light. Effects analogous to those studied with conventional nonlinear optics—self-focusing, self-modulation, harmonic generation, and so on—are all found, but based on this entirely different physical mechanism. Thus, a new field of nonlinear optics, that of relativistic electrons, has been launched, as illustrated by Figure 2. One outcome of accessing this new optical regime is the generation of ultra-short duration frequencyshifted light in a spectral region where there are no other compact sources. Another is the acceleration of other types of particles, such as positrons, ions and neutrons. These novel radiation sources have properties (femtosecond duration, micron source size, MeV energy) that make them suitable for numerous applications in imaging and spectroscopy in basic research, as well as medical diagnostics, cancer therapy, energy production and space propulsion. Rapid advancement is underway and new research tools, subfields and commercial products are on the horizon: e.g., compact and ultrashort pulse duration laser-based electron accelerators and X-ray sources. Another physical regime will be encountered at even higher intensities (Iλ2 ~– 1024 W/cm2), when even protons will quiver relativistically: i.e., the work done on an proton over the distance of a laser wavelength approaches the rest mass energy. This might be called the nuclear regime of laser–plasma interactions, because of the fusion and fission reactions and the generation of pions, muons and neutrinos that should occur as nuclei collide in such energetic plasmas. For more detailed descriptions of recent progress in experiments and theory, several review papers have been published on related topics: (1) relativistic nonlinear optics [25, 31, 33, 34, 35], (2) high-intensity laser development [26], (3) laser accelerators [9], (4) intense laser–plasma interactions [13, 15, 18, 23, 24, 33], (5) relativistic scattering [8, 14, 17], and (6) light ion acceleration [22]. Figure 1. History of light sources over the last century. Each advance in laser power enables a new regime of optics. Reproduced from [33]. ei n s t e i n ’s i m p a c t o n o p t i c s a t t h e f r o n t i e r 123 2. Single-particle motion in high electromagnetic fields An electron that is in the field of an electromagnetic wave propagating in the +z direction has an orbit that is governed by the Lorentz equation,