Chinese Optics Letters

Ultrashort ultra-intense lasers (within duration in femtosecond scale) serve for not only the exploration of scientific unknowns related to extreme states of matter, but also the establishment of scientific facilities to support strategic high-tech such as inertial confinement fusion. However, the wavelength range of ultrashort ultra-intense lasers is restricted to the near-infrared (typically 800 nm and 1053 nm) by the available laser media. Nonlinear frequency conversion based on nonlinear optical crystals has been widely used in order to generate laser frequencies that are not available by direct laser action. The efficiency of nonlinear frequency conversion depends on the fulfillment of phase-matching condition.


Nonlinear frequency conversion —— Nature's color palette


In linear optics, the spectrum of colors contained in a laser beam remains unchanged during propagation. In the regime of nonlinear optics, it becomes possible to transform the frequency of laser beams -- their color -- and even to mix colors to create new ones, much like a painter combines colors on a palette. Such processes are termed as nonlinear frequency conversion, which has been widely used to fill the color gaps of conventional lasers.


Challenges in ultra-broadband nonlinear frequency conversion


The efficiency of nonlinear frequency conversion depends on the fulfillment of a phase-matching condition. To explain phase-matching, we shall take the nonlinear frequency conversion processes of second-harmonic-generation (SHG) as an example, but the conclusions can also be applied to other frequency conversion processes.


Owing to chromatic dispersion of the nonlinear crystal, the newly generated wave at frequency ω2 propagate with a different phase velocity with respect to the incident wave at frequency ω1 2 = 2ω1). As a result, the second harmonic waves that generated in different regions in the crystal will be out of phase, hence destructively interfere. The difference between the incoming and outgoing wave vectors is termed as phase mismatch, denoted Δk.


Conventional methods for phase-matching are normally only efficient for narrow spectra. In order to convert broadband lasers and in particular ultrashort (femtosecond) pulsed lasers, it is necessary to overcome the effects of chromatic dispersion as well as phase mismatch. Dispersion also causes the interacting waves to travel at different group velocities, thereby shortening the effective nonlinear interaction length.


Recently, the research group led by Prof. Lie-Jia Qian at Shanghai Jiao Tong University (SJTU) proposed a ultrabroadband second-harmonic-generation (SHG) scheme based on spatially-chirped phase-matching. A fan-out quasi-phase-matching (QPM) crystal characterized by a varying poling-period along transverse direction is used to frequency convert a spatially-chirped fundamental wave. This scheme cancels the destructive effect of chromatic dispersion inherent to ultrashort lasers as well as high-order phase mismatch via the strategy of frequency conversion arranged in "local narrowband, global broadband". This work was published in Chinese Optics Letters 2024, Vol. 21 No. 1 (Yudong Tao, Wentao Zhu, Yanfang Zhang, Jingui Ma, Jing Wang, Peng Yuan, Hao Zhang, Heyuan Zhu, Liejia Qian. Ultrabroadband second-harmonic generation via spatiotemporal-coupled phase matching[J]. Chinese Optics Letters, 2024, 22(1): 011901) and was selected as the Cover of the issue.


Principle: Ultra-broadband SHG based on spatially-chirped phase-matching is enabled by a spatially-chirped broadband laser beam and a QPM crystal in fan-out design. Based on the spatiotemporally-coupled manipulation of broadband laser, each spectral content of the fundamental laser is mapped onto different spatial coordinate, so that the fundamental laser becomes a spatially-chirped beam which is quasi-monochromatic locally in picosecond duration, fundamentally canceling high-order phase mismatch. A fan-out QPM grating characterized by a linear variation of the poling period along transverse direction exactly supports the QPM of spatially-chirped beam. Such a strategy of "local narrowband, global broadband" leads to ultrabroadband phase-matching.


Figure 1 (a)(b) Exaggerated view of a fan-out QPM crystal and the Schematic setup of broadband SHG system based on spatially-chirped phase-matching. (c) The theoretically optimum space-dependent poling period in comparison with the practical local poling period (red line) of the fan-out QPM crystal; (d)(e) The spectral intensity and the corresponding Fourier-transform-limited temporal profile of the newly generated 2ω pulse.


The SJTU researchers said that this work proposed a spatially-chirped phase-matching scheme that enables ultrabroadband frequency conversion. Being different from conventional phase-matching techniques (angular phase-matching based on birefringent crystals, quasi-phase-matching based on periodically-poled crystals), this scheme chooses to optimize the phase-matching condition as well as eliminate the destructive impacts of chromatic dispersion by manipulating the spatiotemporal coupling property of ultra-broadband laser field. The current focus of the group is to explore the rich phenomenon of spatiotemporal coupling inherent to ultrashort lasers for their applications in optimizing ultrafast optical processes.