Development of coherent x-ray lasers*

Abstract

Proposed x-ray laser applications such as interferometry and holography require coherent radiation. The fact that x-ray laser media are short-lived high-temperature plasmas leads to very different coherence properties from those of ordinary lasers. Research aimed at developing theoretical models and experimentally characterizing and improving x-ray laser coherence is discussed. Longitudinal coherence is already sufficient for several applications due to the narrow linewidths. However, transverse coherence is estimated to be poor for most current x-ray lasers. To quantify these estimates and to design better lasers, both wave and geometric optics propagation and coherence theories have been developed. These theories and resulting predictions of the coherence length are presented and compared. Measurements of x-ray laser beam patterns and coherence lengths are presented and compared to detailed theoretical simulations. Designs for more coherent lasers are given.

An atomic inner-shell laser pumped with an x-ray free-electron laser

“…by the geometry of the amplifying plasma column [27] and is given by L T = λL 2πr . For a lasing transition around λ = 1 nm, we therefore find a transverse coherence length of L T = 1 µm, implying that the XRL will basically have full spatial coherence and a single transverse mode.…”

Propagation of mutual coherence in refractive x-ray lasers using a WKB method

“…(3.14) This result is in agreement with the ray optics model of Refs. [3] and [5]. Note that for exp(z) ))1, we have the scaling x =0.30F '6'~2e' c ' r r 0 30F -16 1/2 z -3 /2 =0.30(g FG) '~e xp(gG/F)' (3.15) where the last two lines use the conventional gain length and Fresnel number.…”

“…It is also well established that gain guiding causes mode discrimination which also leads to enhanced coherence over the constant gain case [1 -3]. These results were determined by a variety of means, including modal analysis [1 -3], numerical solution of the paraxial wave equation [4], ray optics estimates [3,5], and Wentzel-Kramers-Brillouin (WKB) approximations [6,7].…”

Pumping a photoionization atomic inner-shell x-ray laser by x-ray free-electron laser radiation

“…Focusing an XFEL pulse of 1 keV photon energy with a Gaussian spatial beam profile to a focal radius of r = 1 µm results in a focal depth of approximately 5 mm, which defines the length L of the amplifying plasma column of extremely low aspect ratio. The spatial coherence properties of the XRL can be characterized by the geometry of the x-ray amplifying plasma column 23 : The transverse coherence length is given by L T = λL 2πr . For a lasing transition around λ = 1 nm, we therefore find a transverse coherence length of L T = 1 µm, implying that the XRL will have nearly full spatial coherence.…”