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1. Boosting the efficiency of high harmonic amplification by modulating a plasma-based X-ray laser with the second harmonic of the fundamental frequency laser field

   Khairulin, I.R.; Antonov, I.R.; Kocharovskaya, O. (October 2021, International conference on Ultrafast Optical Science)

   Attosecond pulses formed by high order harmonics (HHs) of an infrared (IR) laser field is a powerful tool for studying and controlling ultrafast dynamics of electrons in atoms, molecules and solids at its intrinsic time-scale. However, in the X-ray range the energy of attosecond pulses is rather limited. Their amplification is an important but very challenging problem since none of the existing amplifiers can support the corresponding PHz bandwidth. In our previous work [1] we proposed a method for the attosecond pulse amplification in hydrogen-like active medium of a recombination plasma-based X-ray laser dressed by a replica of the fundamental frequency IR field used for the HH generation. Due to the IRfield-induced sub-laser-cycle Stark shift and splitting of the lasing energy levels the gain of the active medium is redistributed over the combination frequencies, separated from the resonance by even multiples of the frequency of the IR field. If the incident HHs forming an attosecond pulse train are tuned in resonance with the induced gain lines and the active plasma medium is strongly dispersive for the modulating IR field, then during the amplification the relative phases of harmonics and (under the optimal choice of the IR field strength) the shape of the amplified pulses will be preserved. In the present work we show the possibility of boosting the efficiency of HH amplification by modulating the active medium of an X-ray laser with the second harmonic of the fundamental frequency IR field. We show that under the action of a laser field (with arbitrary frequency) the gain redistribution occurs not only over the even combination frequencies discussed in [1], but also over the odd frequencies separated from the resonance by odd multiples of the laser frequency. Besides, nearly half of the medium gain is contained in the even induced gain lines, and nearly half in the odd. If the modulating field is the second harmonic of the IR field, used for the generation the HHs and attosecond pulses, then the seeding HHs can be tuned in resonance with both even and odd gain lines simultaneously, which will make the overall gain much higher as compared to the previously considered case of the fundamental frequency modulating field (when only the even gain lines play the role). By the example of the C5+ X-ray laser with 3.38 nm wavelength of the inverted transition we show the possibility of increasing the efficiency of 430 as pulse amplification by 8.5 times when the active medium is modulated with the second harmonic of the fundamental frequency IR field with wavelength 2.1 µm. 

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2. Enhanced Amplification of Attosecond Pulses in a Hydrogen-like Plasma-Based X-ray Laser Modulated by an Infrared Field at the Second Harmonic of Fundamental Frequency

   https://doi.org/10.3390/photonics9020051  

   Khairulin, Ilias R.; Antonov, Vladimir A.; Ryabikin, Mikhail Yu.; Kocharovskaya, Olga (February 2022, Photonics)

   In a recent work (Antonov et al., Physical Review Letters 123, 243903 (2019)), it was shown that it is possible to amplify a train of attosecond pulses, which are produced from the radiation of high harmonics of the infrared field of the fundamental frequency, in the active medium of a plasma-based X-ray laser modulated by a replica of the infrared field of the same frequency. In this paper, we show that much higher amplification can be achieved using the second harmonic of the fundamental frequency for modulating of a hydrogen-like active medium. The physical reason for such enhanced amplification is the possibility to use all (even and odd) sidebands induced in the gain spectrum in the case of the modulating field of the doubled fundamental frequency, while only one set of sidebands (either even or odd) could participate in amplification in the case of the modulating field of the fundamental frequency due to the fact that the spectral components of the high-harmonic field are separated by twice the fundamental frequency. Using the plasma of hydrogen-like C5+ ions with an inverted transition wavelength of 3.38 nm in the water window as an example, it is shown that the use of a modulating field at a doubled fundamental frequency makes it possible to increase the intensity of amplified attosecond pulses by an order of magnitude in comparison with the previously studied case of a fundamental frequency modulating field. 

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3. Amplification of a train of attosecond pulses in a plasma-based X-ray laser driven by an IR field

   https://doi.org/10.1088/1742-6596/1412/7/072019  

   Antonov, V A; Han, K C; Khairulin, I R; Kocharovskaya, O (January 2020, Journal of Physics: Conference Series)

   Synopsis We suggest a technique to amplify a train of attosecond pulses, produced via high-harmonic generation of an infrared laser field, in active medium of a plasma-based X-ray laser driven by a replica of the same IR field as used to produce high harmonics forming a train of attosecond pulses. 

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4. Lightwave-electronic harmonic frequency mixing

   https://doi.org/10.1126/sciadv.adq0642  

   Yeung, Matthew; Chou, Lu-Ting; Turchetti, Marco; Ritzkowsky, Felix; Berggren, Karl K; Keathley, Philip D (August 2024, Science Advances)

   Electronic frequency mixers are fundamental building blocks of electronic systems. Harmonic frequency mixing in particular enables broadband electromagnetic signal analysis across octaves of spectrum using a single local oscillator. However, conventional harmonic frequency mixers do not operate beyond hundreds of gigahertz to a few terahertz. If extended to the petahertz scale in a compact and scalable form, harmonic mixers would enable field-resolved optical signal analysis spanning octaves of spectra in a monolithic device without the need for frequency conversion using nonlinear crystals. Here, we demonstrate lightwave-electronic harmonic frequency mixing beyond 0.350 PHz using plasmonic nanoantennas. We demonstrate that the mixing process enables complete, field-resolved detection of spectral content far outside that of the local oscillator, greatly extending the range of detectable frequencies compared to conventional heterodyning techniques. Our work has important implications for applications where optical signals of interest exhibit coherent femtosecond-scale dynamics spanning multiple harmonics. 

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5. Electro-optic frequency comb generation via cascaded modulators driven at lower frequency harmonics

   https://doi.org/10.1364/OE.537836  

   Eliason, Todd; Parker, Payton_A; Reber, Melanie_A_R (September 2024, Optics Express)

   Electro-optical modulation of a continuous wave laser is a highly stable way to generate frequency combs, gaining popularity in telecommunication and spectroscopic applications. These combs are generated by modulating non-linear electro-optic crystals with radio frequencies, creating equally spaced side-bands centered around the single-frequency seed laser. Electro-optic frequency comb architectures often choose between optical bandwidth (cascaded GHz combs) or higher mode density (chirped RF generation). This work demonstrates an electro-optic frequency comb with > 120 GHz of bandwidth and an 80 MHz repetition rate. The comb has three cascaded electro-optic modulators driven at sequentially lower harmonics, the last megahertz modulation dictating the repetition rate. This architecture can modulate at any individual harmonic and repetition rate without changes to the components. This comb can be used in any applications where a stable and tunable repetition rate is needed. 

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