Spatial coherence of short wavelength high-order harmonics

Nonperturbative high-order harmonic conversion of high-intensity, ultrafast laser pulses in gases represents a unique means to generate high-brightness, coherent XUV, and soft X-ray radiation. We review the physics controlling the spatial qualities of harmonic radiation and recent experimental measurements of high-order harmonic spatial profiles. We also examine the factors controlling the spatial coherence of the harmonics. A detailed series of Young’s two-slit experiments that measure the spatial coherence of the harmonics is presented. These measurements indicate that the harmonics exhibit good fringe visibility and high spatial coherence. PACS: 42.65.Ky; 42.25.Kb Since the first observation of nonperturbative high-order harmonic generation of laser light in a gas by McPherson et al. in 1985 [1], high-order harmonics have received considerable attention as a potential high brightness, coherent source of X-rays [2]. High-order harmonics are produced when a high intensity laser is focused into a gas, and the nonlinear oscillations of the atoms in the medium re-emit photons at odd harmonics of the incident laser light. Though low-order harmonics, such as those with harmonic order less then the seventh or ninth, have been studied for many years [3], the experiment of [1] and many others that followed soon after illustrated that at high intensities (> 1013 W/cm2) the exponential drop in yield with increasing harmonic order usually associated with a lowest-order perturbation theory treatment does not continue with higher harmonic orders [4–7]. Instead, above a low order the harmonic spectrum exhibits a plateau of many harmonics with roughly equal yield, which can reach to very high orders. For example, harmonics as high as the 155th order have been observed from the harmonic conversion of 800 nm light in helium [8]. These very high-order harmonics have wavelengths that stretch into the XUV and soft X-ray region. The high-order harmonics may represent a very attractive source of short wavelength radiation. The extensive research of high-order harmonic generation has been motivated by the potential of using these harmonics as a source of highbrightness, coherent, soft X-ray radiation. A number of recent experiments have explored the possibility of using the harmonics in various applications requiring short pulses of XUV or soft X-ray radiation. Haight et al. have used harmonics in time resolved pump probe photoelectron spectroscopy of GaAs [9, 10]. Balcou et al. utilized harmonics in photoionization spectroscopy of noble gases with photon energy as high as 100 eV [11] and Larsson et al. exploited the short pulse nature of the harmonics to measure the lifetime of the 1s2p 1P state in helium [12]. XUV harmonics have also been used to probe the dynamics of laser plasmas [13]. Aside from these applications, the properties of these harmonics have been very carefully studied by a number of groups around the world in recent years [4, 5, 14, 15]. Probing the shortest wavelengths attainable with harmonic generation has been a topic of extensive research. In addition to the 155th harmonic of a Ti:sapphire laser, the 141st harmonic from a 1 ps, 1054 nm laser has been observed [16] and the 37th harmonic of a 248 nm KrF laser has been reported [17]. The harmonic spectra that result in most experiments typically have a number of important features in common. The harmonic yield drops exponentially over the first few orders (up to the 7th or 9th). This drop is followed by a long plateau of roughly constant yield between harmonics, which is in turn followed by an abrupt cutoff. Theoretical and experimental studies of this behavior indicate that the location of the harmonic cutoff, and hence the shortest wavelengths achievable, is usually given by a universal scaling law [18–20]: hωcut ≈ Ip+3.2Up , (1) where Ip is the atom’s ionization potential, Up is the ponderomotive field of the laser, and hωcut is the cutoff harmonic photon energy. This law has been confirmed in many experiments though some deviations from this scaling have been observed [21, 22]. Other properties of the high-order harmonics have been studied as well. The energy yields and conversion efficiency of the harmonics have been measured. Yields as high as 60 nJ in the 200 Å wavelength range have been reported [23]. The