Polarization-controlled quasi-phase matching for linearly and circularly polarized high harmonic generation

Summary form only given. High harmonic generation (HHG) is a nonlinear process in which odd multiples of a fundamental driving field are produced when an intense laser pulse is focused into a low density gas. HHG is an attractive source of coherent, tuneable light with wavelengths in the XUV and soft X-ray range and has found a broad range of applications in ultrafast physics and imaging. However, due to the phase mismatch between the driving and generated fields, the intensity of the generated harmonics oscillates as a function of propagation distance, z, between 0 and some maximum value. The period of oscillation is 2L_c where L_c is the coherence length. One way of overcoming the problem of phase-mismatching is quasi-phase matching (QPM), in which harmonic generation is suppressed or modified in out-of phase regions. Here we propose a new class of QPM techniques by controlling the polarization in an optical waveguide by either: (i) rotating the polarization of the driving field in a circularly birefringent system [1]; or (ii) modulating the ellipticity of the driver polarization in a linearly birefringent system [2]. The key advantage of this new class of polarization-controlled QPM is its simplicity compared to other QPM techniques.Optical rotation QPM (ORQPM) utilizes a waveguide with circular birefringence, which causes the plane of polarization of linearly polarized light to rotate with propagation distance at a constant rate, with period 2Lr. By matching Lr = Lc, the generated harmonics will grow monotonically. Because the polarization of the driving field remains linear, harmonics are generated locally with the same amplitude at each point. Further, if Lr = Lc at points were - in the absence of QPM - destructive interference would occur, such as at z = Lc, the phase of the driving field is flipped by π, and hence the locally-generated harmonics remain in phase with those generated earlier. As a result, ORQPM is approximately 5 t- mes more efficient than ideal square-wave QPM modulation and only a factor of two less efficient than pure phase matching. Moreover, ORQPM is the first QPM scheme to generate circularly polarized high harmonics, where the harmonics will have the same handedness as the rotation of the driving field. For the linear birefringent system, polarization beating QPM (PBQPM), it is well known that the single-atom efficiency of HHG depends sensitively on the polarization of the driving laser field which arises from the fact that the ionized electron must return to the parent ion in order to emit a harmonic photon. A birefringent waveguide is used to generate beating of the polarization state of a driving linearlypolarized driving laser pulse, where the polarization beats from linear to elliptical to linear and so forth, thereby modulating the harmonic generation process. QPM will occur if the period of polarization beating is suitably matched to the coherence length of the harmonics. Figs 1a and 2 show numerical calculations of the harmonic growth for ORQPM and PBQPM respectively as a function of propagation distance z while Fig 1b indicates circular polarization for ORQPM. In conclusion we have proposed a novel class for QPM HHG, and have undertaken calculations aimed at understanding the optimal experimental conditions for ORQPM and PBQPM.