Modal study of the role of excess noise in x-ray lasers

Abstract

Current x-ray laser designs rely on amplifying spontaneous emission in a high-temperature plasma. A central problem in the study of x-ray lasers is determining and optimizing the degree of transverse spatial coherence for holographic applications. The inherent non-power-orthogonal character of the normal modes in a general amplifying medium necessarily results in excess noise and cross-correlation e6'ects that can significantly afT'ect the predicted coherence and intensity profiles of an x-ray laser. In particular, loosely bound discrete transverse eigenstates of the paraxial wave equation have previously been found to dominate the intensity and coherence in the low-amplification regime if the continuum eigenstates are omitted from the spectrum [London, Strauss, and Rosen, Phys. Rev. Lett. 65, 563 (1990)]. A detailed analysis of the role of excess noise on steady-state laser intensity and coherence is presented for the simple case of a transverse square gain and density profile in a finite geometry. The inclusion of the continuum portion of the spectrum is found to substantially reduce the level of excess noise and to alter the coherence predictions for low and intermediate gain-length products.PACS number(s): 42.50. Ar, 42.55.Vc, 42.60.Da, 52.25.Nr

Mode structure and the noise performance of a gain-guided amplifier

“…The value of the correlation (&"' (z)&z(z)) is obtained by modeling the amplifier as a completely inverted two-level system. This model, though simple, has been used to describe a wide range of amplifiers from the Raman amplifier to a single-pass xray laser [4]. The details of these calculations can be found in previous work [6].…”

“…[Vr 2ikB, -+ikg(z, rT)]4'"(z,rr) 4'"(z,r ), (4) "k co (z} where A, '" is the eigenvalue associated with the mode 4'"(z,rT). The indices n and l correspond to the radial and angular degrees of freedom, respectively.…”

“…(4), it is convenient to write the nonorthogonal modes as linear combinations of the freespace, or Gauss-Laguerre, modes, which are denoted by U"'(z, rT) [or simply U(z, rT) when n=l=O] [6,7]. The [U"'(z,rz )] are solutions to Eq.…”

Angular divergence and spatial coherence of X-ray laser radiation

“…±ÓË ÎËÐÇÌÐÑÏ ÖÔËÎÇÐËË ÍÑÎÑÍÑÎÑÑÃÓÂÊÐÂâ ÐÇÑAEÐÑ-ÓÑAEÐÑÔÕß ÖÔËÎÇÐËâ ÒÓËÄÑAEËÕ Í AEÑÒÑÎÐËÕÇÎßÐÑÌ ÒÓÑ-ÔÕÓÂÐÔÕÄÇÐÐÑÌ ÔÇÎÇÍÙËË µ³ª, "ÊÂÕâÅËÄÂÐËá" ÇÅÑ Ä ÑÍÓÇÔÕÐÑÔÕß ÏÂÍÔËÏÖÏ a 0 , ÚÕÑ ÖÏÇÐßÛÂÇÕ ÓÂÔØÑAEË-ÏÑÔÕß Ë ÒÑÄÞÛÂÇÕ ÔÕÇÒÇÐß ÍÑÅÇÓÇÐÕÐÑÔÕË [89].¯ÂÒÓË-ÏÇÓ, ÒÓË ÍÄÂAEÓÂÕËÚÐÑÏ ÒÓÑ×ËÎÇ a 0 РÄÞØÑAEÇ ² [80,81] L c z % a 0 0z 3 [96].¯ÂÔÞÜÇÐËÇ ÖÔËÎÇÐËâ AEÇÎÂÇÕ ÒÓÑ×ËÎß ÖÔËÎÇÐËâ ÃÑÎÇÇ ÍÓÖÕÞÏ, ÚÕÑ ÄÇAEÇÕ Í ÖØÖAEÛÇÐËá ÍÑÅÇÓÇÐÕ-ÐÞØ ÔÄÑÌÔÕÄ Ë ÒÓËÃÎËÉÇÐËá Í ÔÎÖÚÂá (77), (78 £Ñ-ÒÇÓÄÞØ, ÓÂÔÜÇÒÎÇÐËÇ ÒÖÚÍ ÏÑÉÐÑ ÃÞÎÑ ÃÞ ÑÃÝâÔÐËÕß ÐÇÑAEÐÑÓÑAEÐÞÏ ÓÂÔÒÓÇAEÇÎÇÐËÇÏ ÍÑà××Ë-ÙËÇÐÕ ÖÔËÎÇÐËâ ÒÑ x, ËÏÇáÜËÏ ÒÓËÑÔÇÄÑÌ ÒÓÑÄÂÎ [12,45]. ±ÓË àÕÑÏ µ³ª ×ÑÓÏËÓÖÇÕÔâ Ä ÑÔÐÑÄÐÑÏ ÄÑ ÄÐÇÑÔÇ-ÄÞØ ÑÃÎÂÔÕâØ Ô ÒÑÄÞÛÇÐÐÞÏ a 0 , ÅAEÇ ÅÓÂAEËÇÐÕ " e ÑÕÍÎÑÐâÇÕ ÎÖÚË ÑÕ ÑÔË.…”

Optimization of single-stage x-ray laser coherence

“…More recently, we have reexamined the modal approach by appending the continuum or free modes to the bound-mode portion of the transverse spectrum for the particular example of transverse square gain and density profiles [5]. The primary motivation for including the continuum is that by virtue of the nonorthogonality and assumed completeness of the eigenmodes, sufficient cancellation from cross terms in the expression for the modal intensity may occur and possibly eliminate to a large extent the excess-noise phenomenon.…”