This paper is devoted to analyzing the principle and applications of the linear electro-optic (EO) effect for the control of the carrier-envelope-phase (CEP). We introduce and detail here an original method, which relies on the use of an EO dispersive prism pair in a compressor-like configuration. We show that, by choosing an adequate geometry, it is possible to shift the CEP without changing the group delay (isochronous carrier-envelope-phase shifter) or change the induced group delay without varying the CEP. According to our calculations, when applying an electric field around 400 V/cm to the rubidium titanyle phosphate (RTP) prisms in a double pass configuration (2 × 40 mm total length), one obtains a CEP shift of π rad at 800 nm without inducing a group delay. In contrast, this CEP shift is obtained for an electric field around 1.4 kV/cm in a RTP rectangular slab of the same total length and, in this case, the group delay is of the order of a few fs.
References
[1]
Goulielmakis, E.; Schultze, M.; Hofstetter, M.; Yakovlev, V.S.; Gagnon, J.; Uiberacker, M.; Aquila, A.L.; Gullikson, E.M.; Attwood, D.T.; Kienberger, R.; et al. Single-cycle nonlinear optics. Science 2008, 320, 1614–1617.
Nisoli, M.; Sansone, S. New frontiers in attosecond science. Prog. Quantum Electron. 2009, 33, 17, doi:10.1016/j.pquantelec.2008.10.004.
[4]
Reichert, J.; Holzwarth, R.; Udem, T.; H？nsch, T.W. Measuring the frequency of light with mode-locked lasers. Opt. Commun. 1999, 172, 59–68, doi:10.1016/S0030-4018(99)00491-5.
[5]
Telle, H.R.; Steinmeyer, G.; Dunlop, A.E.; Stenger, J.; Sutter, D.H.; Keller, U. Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation. Appl. Phys. B 1999, 69, 327–332.
[6]
Jones, D.J.; Diddams, S.A.; Ranka, J.K.; Stentz, A.; Windeler, R.S.; Hall, J.L.; Cundiff, S.T. Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 2000, 288, 635–639.
[7]
Kakehata, M.; Takada, H.; Kobayashi, Y.; Torizuka, K.; Fujihira, Y.; Homma, T.; Takahashi, H. Measurements of carrier-envelope phase changes of 100-Hz amplified laser pulses. Appl. Phys. B 2002, 74, S43–S50, doi:10.1007/s00340-002-0880-1.
[8]
Baltu？ka, A.; Paulus, G.G.; Lindner, F.; Kienberger, R.; Krausz, F. Femtosecond Optical Frequency Comb Technology. Principles, Operation and Application; Ye, J., Cundiff, S., Eds.; Springer Science+Business Media: New York, NY, USA, 2005; Volume Chapter 10, pp. 263–307.
[9]
Apolonski, A.; Poppe, A.; Tempea, G.; Spielmann, C.; Udem, T.; Holzwarth, R.; H？nsch, T.W.; Krausz, F. Controlling the phase evolution of few-cycle light pulses. Phys. Rev. Lett. 2000, 85, 740–743.
[10]
Grebing, C.; G？rbe, M.; Osvay, K.; Steinmeyer, G. Isochronic and isodispersive carrier-envelope phase-shift compensators. Appl. Phys. B 2009, 97, 575–581, doi:10.1007/s00340-009-3739-x.
Chang, Z. Carrier-envelope phase shift caused by grating-based stretchers and compressors. Appl. Opt. 2006, 45, 8350–8353, doi:10.1364/AO.45.008350.
[13]
Tournois, P. Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems. Opt. Commun. 1997, 140, 245–249, doi:10.1016/S0030-4018(97)00153-3.
[14]
Crozatier, V.; Forget, N.; Oksenhendler, T. Toward Single Shot Carrier-Envelope Phase Stabilization for Multi kHz Ultrafast Amplifiers. In Proceedings of the Lasers and Electro-Optics Europe (CLEO EUROPE/EQEC), 2011 Conference on and 12th European Quantum Electronics Conference, Munich, Germany, 22–26 May 2011.
[15]
Canova, L.; Chen, X.; Trisorio, A.; Jullien, A.; Assion, A.; Tempea, G.; Forget, N.; Oksenhendler, T.; Lopez-Martens, R. Carrier-envelope phase stabilization and control using a transmission grating compressor and an AOPDF. Opt. Lett. 2009, 34, 1333–1335.
[16]
Kakehata, M.; Takada, H.; Kobayashi, Y.; Torizuka, K. Generation of optical-field controlled high-intensity laser pulses. J. Photochem. Photobiol. A 2006, 182, 220–224, doi:10.1016/j.jphotochem.2006.05.025.
[17]
Gobert, O.; Paul, P.M.; Hergott, J.F.; Tcherbakoff, O.; Lepetit, F.; D'Oliveira, P.; Viala, F.; Comte, M. Carrier-envelope phase control using linear electro-optic effect. Opt. Express 2011, 19, 5410–5418.
[18]
Gobert, O.; Fedorov, N.; Tcherbakoff, O.; Hergott, J.F.; Perdrix, M.; Lepetit, F.; Guillaumet, D.; Comte, M. Measurement of Carrier-Envelope-Phase shifts using spectral interferometry with a broad frequency laser source. Opt. Commun. 2012, 285, 322–327.
[19]
Hergott, J.-F.; Tcherbakoff, O.; Paul, P.-M.; Demengeot, Ph.; Perdrix, M.; Lepetit, F.; Garzella, D.; Guillaumet, D.; Comte, M.; D’Oliveira, P.; et al. Grating based, chirped-pulse amplified laser, using Electro-Optic effect in a LiNbO3 crystal. Opt. Express 2011, 19, 19935–19941.
[20]
Gobert, O.; Fedorov, N.; Mennerat, G.; Lupinski, D.; Guillaumet, D.; Perdrix, M.; Bourgeade, A.; Comte, M. Wavelength dispersion measurement of electro-optic coefficients in the range of 520 to 930 nm in rubidium titanyl phosphate using spectral interferometry. Appl. Opt. 2012, 51, 594–599.
[21]
Weis, R.S.; Gaylord, T.K. Lithium niobate: Summary of physical properties and crystal structure. Appl. Phys. A 1985, 37, 191–203, doi:10.1007/BF00614817.
[22]
Andrushchak, A.S.; Mytsyk, B.G.; Demyanyshyn, N.M.; Kaidan, M.V.; Yurkevych, O.V.; Solskii, I.M.; Kityk, A.V.; Schranz, W. Spatial anisotropy of linear electro-optic effect in crystal materials: I Experimental determination of electro-optic tensor in LiNbO3 by means of interferometric technique. Opt. Lasers Eng. 2009, 47, 31–38, doi:10.1016/j.optlaseng.2008.08.005.
[23]
Martinez, O.E.; Gordon, J.P.; Fork, R.L. Negative group-velocity dispersion using refraction. JOSA A 1984, 1, 1003–1006, doi:10.1364/JOSAA.1.001003.
[24]
Fork, R.L.; Martinez, O.E.; Gordon, J.P. Negative dispersion using pairs of prisms. Opt. Lett. 1984, 9, 150–152, doi:10.1364/OL.9.000150.
[25]
Arissian, L.; Diels, J.C. Carrier to envelope and dispersion control in a cavity with prism pairs. PRA 2007, 75, 1–10.
[26]
Mikami, T.; Okamoto, T.; Kato, K. Sellmeier and thermo-optic dispersion formulas for RbTiOPO4. Opt. Mater. 2009, 31, 1628–1630, doi:10.1016/j.optmat.2009.03.012.
