In conclusion, the CFWM process was theoretically analyzed and experimentally studied in bulk transparent media. Theoretical analysis and calculations based on the phase-matching condition taking into account the broadband spectra of the two incident pulses explained the process semi-quantitatively and cleared up the at first glance puzzling phenomena taking place in this process that explaining why the frequency difference between two adjacent sidebands decreased with increasing order number. As many as fifteen spectral up-shifted pulses and two spectral down-shifted pulses were obtained with spectral bandwidth broader than 1.8 octaves. The wavelengths of the sidebands are continuously tunable from near ultraviolet to near infrared by changing the crossing angle between the two input beams or replacing the nonlinear bulk medium. The obtained sidebands have good beam quality, with a M2 factor better than 1.1 and a nice Gaussian spatial profile. The pulse energy of the sideband can reach 1 μJ with power stability smaller than 1% RMS. As short as 15-fs compressed pulses, which were nearly transform-limited, were obtained when one of the two input beams was appropriately negatively chirped and the other was positively chirped. Moreover, broadband 2-D multicolored arrays with more than ten periodic columns and more than ten rows were generated when a sapphire plate was used as a nonlinear medium. By using XPM in conjunction with FOPA in another bulk medium, the obtained sideband was succeeded in smooth broadening of the weak pulse spectrum by a factor of about three and simultaneously amplifying the pulse energy by more than three times. Several weak beams with different wavelengths can be spectral broadened simultaneously at the same time in this way.
Several upshifted and downshifted multicolored femtosecond pulses can be simultaneously obtained and spatially separated from the input beams in the CFWM process. They are thus self-synchronized and convenient for multicolor pump-probe experiments [8], femtosecond CARS spectroscopy [9], and two-dimensional spectroscopy [10]. These wavelength tunable sidebands with good beam quality also suit for ultrafast nonlinear microscopy system [11-13].
In the future, CFWM sidebands could be obtained at much lower pulse energy incidence and higher repetition rate by using a medium with high third-order nonlinearity (for example nano-particle doped
glass). This process can also be extended to the UV and Mid-IR spectral regions by using suitable input parameters. With the development of femtosecond fiber laser [67,68], this method can also be performed by using fiber laser system to make a compact system and even operate at a MHz repetition rate. Furthermore, these broadband sidebands can be used to obtain near single cycle pulse chain through Fourier synthesis of the sidebands. If the input beams are carrier-envelope phase (CEP) stabilized, all the generated sidebands would be CEP stabilized. As a result, CEP stabilized near single cycle pulse chain can be obtained in this way [28].
Acknowledgements
The authors thank Jun Zhang, Zhuan Wang, Yuichiro Kida, Takahiro Teramoto, and Kotaro Okamura for their technical assistance in the experiments. They also thank Eiichi Hanamura, G.I.
Stegeman, and Miaochan Zhi for their helpful discussions and Zhiguang Wang for his help to take the beautiful pictures. This work was partly supported by the 21st Century COE program on “Coherent Optical Science” and partly supported by the grant from the Ministry of Education (MOE) in Taiwan under the ATU Program at National Chiao Tung University. A part of this work was performed under the joint research project of the Laser Engineering, Osaka University, under contract subject B1-27.
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