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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5410–5418
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Carrier-envelope phase control using linear electro-optic effect

O. Gobert, P.M Paul, J.F Hergott, O. Tcherbakoff, F. Lepetit, P. D 'Oliveira, F. Viala, and M. Comte  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 5410-5418 (2011)
http://dx.doi.org/10.1364/OE.19.005410


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Abstract

We present a new method to control the Carrier-Envelope Phase of ultra-short laser pulses by using the linear Electro-Optic Effect. Experimental demonstration is carried out on a Chirped Pulse Amplification based laser. Phase shifts greater than π radian can be obtained by applying moderate voltage on a LiNbO3 crystal with practically no changes to all other parameters of the pulse with the exception of its group delay. Time response of the Electro-Optic effect makes possible shaping at a high repetition rate or stabilization of the CEP of ultra short CPA laser systems.

© 2011 OSA

1. Introduction

A laser pulse, corresponding to an electric field, is usually described by the product of a wave envelope and a carrier wave. The envelope propagates at the group velocity, which corresponds to the speed of propagation of the energy, whereas the carrier wave propagates at the phase velocity.

In a dispersive medium, phase and group velocities are different, inducing a slippage of the carrier frequency wave inside the envelope (Fig. 1
Fig. 1 Temporal drift of the carrier wave inside the pulse envelope from shot to shot.
). This slippage is usually of no concern for long pulses (a ns pulse at optical frequency contains of the order of 3 × 105 optical cycles). For ultra-short pulses, which contain few optical cycles, physical phenomena induced in a medium can strongly depend on the electric field and not only on its envelope [1

1. A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003). [CrossRef] [PubMed]

,2

2. M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, and G. Tondello, “Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high-order-harmonic spectra,” Phys. Rev. Lett. 91(21), 213905 (2003). [CrossRef] [PubMed]

]. In this case, it is of prime importance to control the Carrier-Envelope Phase (CEP).

Laser systems emitting ultra-short pulses do not generate a train of pulses with the same CEP value. This is mainly due to environmental effects such as vibrations and thermal drift. One elegant way to get rid of these variations is to use an optical parametric amplifier in a specific configuration [3

3. A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88(13), 133901 (2002). [CrossRef] [PubMed]

]. Different methods [4

4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]

6

6. S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4(7), 462–465 (2010). [CrossRef]

] also exist in order to obtain, through the use of a fast loop, a train of CEP stabilized pulses from mode locked-oscillators.

Laser systems used to generate ultra-short pulses with energy per pulse above ten µJ are based on the Chirped Pulse Amplification technique [7

7. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985). [CrossRef]

] (Fig. 2
Fig. 2 CPA laser system design.
). In these systems, a mode-locked oscillator generates a train of ultra-short pulses (repetition rate of the order of 100 MHz, energy ~1 nJ, spectrum tens of nm wide); these pulses are temporally stretched from fs to ps range. The pulses are then amplified in media such as Ti:Sa which allows a gain well above 106. After amplification, the pulses are compressed back to some tens of fs. Filamentation in a rare gas cell or propagation in a hollow waveguide filled with rare gas, in combination with the use of a chirped mirror or prism compressor can be used to obtain sub-ten fs pulses with energy per pulse above the mJ level [8

8. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997). [CrossRef] [PubMed]

10

10. C. F. Dutin, A. Dubrouil, S. Petit, E. Mével, E. Constant, and D. Descamps, “Post-compression of high-energy femtosecond pulses using gas ionization,” Opt. Lett. 35(2), 253–255 (2010). [CrossRef] [PubMed]

].

Different techniques already exist to stabilize the CEP of the amplified pulses of a CPA laser system seeded by a CEP stabilized mode locked oscillator. They are mainly based on a slow feedback loop containing a f-2f interferometer [11

11. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100-Hz amplified laser pulses,” Appl. Phys. B 74(9Suppl.), S43–S50 (2002). [CrossRef]

], a PID and a specific technique to correct the CEP. These techniques can be split into two categories. In the first one, the correction is made by modifying parameters inside the cavity of the mode-locked oscillator [4

4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]

] which can have the disadvantage of inducing coupling between fast and slow loops, leading to an increase of noise in amplitude and phase. In the second one, the corrections are made outside the mode-locked oscillator, usually before the amplification.

Examples of those techniques are the use of a pair of wedges to modify the optical path in the dispersive element composing these wedges [12

12. C. Grebing, M. Görbe, K. Osvay, and G. Steinmeyer, “Isochronic and isodispersive carrier-envelope phase-shift compensators,” Appl. Phys. B 97(3), 575–581 (2009). [CrossRef]

], the modification of one parameter of the compressor or of the stretcher (this parameter can be the distance between the gratings) [13

13. Z. Chang, “Carrier-envelope phase shift caused by grating-based stretchers and compressors,” Appl. Opt. 45(32), 8350–8353 (2006). [CrossRef] [PubMed]

], the use of an Acousto-Optic Programmable Dispersive Filter (AOPDF) [14

14. P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997). [CrossRef]

,15

15. L. Canova, X. Chen, A. Trisorio, A. Jullien, A. Assion, G. Tempea, N. Forget, T. Oksenhendler, and R. Lopez-Martens, “Carrier-envelope phase stabilization and control using a transmission grating compressor and an AOPDF,” Opt. Lett. 34(9), 1333–1335 (2009). [CrossRef] [PubMed]

] or of a 4f system with an adaptive phase modulator device [16

16. H. Wang, M. Chini, Y. Wu, E. Moon, H. Mashiko, and Z. Chang, “Carrier–envelope phase stabilization of 5-fs, 0.5-mJ pulses from adaptive phase modulator,” Appl. Phys. B 98(2-3), 291–294 (2010). [CrossRef]

].

In this paper, we consider a new method to control the CEP by using the linear electro-optic (EO) effect with a specific arrangement for the direction of the applied static electric field and the polarisation of the laser field relative to the crystal axes. We first present the conceptual idea of the method. The mathematical expression of the CEP variation as a function of the applied electric field is derived in the case of a uniaxial crystal like LiNbO3. Experimental demonstration using an f-2f interferometer and comparison with the calculation is presented in the case of LiNbO3. The problem of the practical CEP stabilization will not be considered in great detail in this paper, the aim being to demonstrate the feasibility of the EO CEP control.

2. Phase and group velocity in a dispersive medium

We consider a laser pulse whose carrier angular frequency is ω0, propagating in a homogeneous dispersive medium of length L which is non-centrosymmetric and exhibits a Pockels effect. The phase delay Tφ and the group delay Tg are defined as follows:
Tϕ=n(ω0)cL;Tg=ng(ω0)cL
(1)
n(ω0) and ng0) are the refractive index and the group refractive index, c is the speed of light in vacuum. The delay due to the difference between the group and phase velocities can be written:
TgTϕ=[ng(ω0)n(ω0)]Lc
(2)
To obtain the expression of ng0), one can use the following usual relations where k = nω0/c, is the wave vector modulus and vg0) the group velocity at pulsation ω0:
1vg(ω0)=ng(ω0)c=kω|ω0=n(ω0)c+ω0cnω|ω0
(3)
Using the wavelength λ0 instead of ω0, (3) leads to:
ng(λ0)=n(λ0)λ0nλ|λ0
(4)
The difference between group and phase delay which is directly connected to the CEP, can be written:

TgTϕ=λ0nλ|λ0Lc
(5)

3. Changing the CEP by the linear EO effect

The purpose of this paragraph is to establish the expression of the CEP change of an ultrashort laser pulse at the exit of an EO medium when an electric field is applied in a specific geometry. Calculations will be restricted to the case of a uniaxial crystal and more specifically to the case of LiNbO3 (uniaxial crystal, point group 3m).

3.1 EO effect

A static electric field E applied on the medium generates a variation of the refractive index due to the Pockels effect. In a solid, the relationship between the refractive index and the applied electric field can be written:
Δ(1/n2)ij=krijkEk
(6)
Where Δ(1/n2)ij is the second-rank tensor describing the change in relative permittivity, Ek is the k-th component of the electric field, and i, j, k = x, y, z. The term rijk, the linear EO coefficient tensor, is a third-rank tensor with 27 elements.

For the sake of simplicity, we will consider here the case of LiNbO3 which is uniaxial but analogous results can be obtained in biaxial crystals. Due to the symmetry and using the reduced-subscript notation, the EO effect in lithium niobate can be described by only four independent coefficients (r51, r22, r13 and r33). The measured values of these coefficients depend on the mechanical constraints imposed on the crystal. In the free condition (unclamped crystal), the r coefficient value includes a contribution from the secondary EO effect which is the result of the applied electric field causing a strain in the crystal through the inverse piezoelectric effect. This electrically induced strain then causes a change in the crystal's refractive index through the photoelastic effect [17

17. R. S. Weis and T. K. Gaylord, “Lithium niobate: Summary of physical properties and crystal structure,” Appl. Phys., A Mater. Sci. Process. 37(4), 191–203 (1985). [CrossRef]

]. This secondary contribution is inseparable from the primary linear EO component. The relationship between the clamped coefficient rS and the unclamped coefficient rT can be written:
rijT=rijS+k=16pikdkj
(7)
As a consequence, the phase of the light passing through the crystal is modified by both the change in the refractive index due to the EO effect and the change in the crystal length ΔL due to the inverse piezoelectric effect.

3.2 Geometry of the interaction

We consider an optical pulse propagating in the crystal along the Oz direction (Fig. 3
Fig. 3 The EO configuration chosen for the interaction
). The optical electric field is supposed to be linearly polarized along the Ox direction as well as the applied static electric field. We assume that the crystal is oriented so that X-axis corresponds to the optical axis.

Expressions of the ordinary no(E,λ0) and extraordinary ne(E,λ0) refractive indices when applying an electric field E are, to first order, given by:
no(E,λ0)=no(λ0)12no3(λ0)r13T(λ0)E
(8.1)
ne(E,λ0)=ne(λ0)12ne3(λ0)r33T(λ0)E
(8.2)
In these equations, r13 T0) and r33 T0) are the unclamped EO coefficients of LiNbO3 at wavelength λ0.

3.3 Calculating the variation of CEP when the electric field is applied

The variation of the difference between phase and group delay ΔT when applying the electric field has the following form:
ΔT=(TgTϕ)[E](TgTϕ)[0]=(L+ΔLc)[ng(E,λ0)n(E,λ0)]Lc[ng(0,λ0)n(0,λ0)]
(9)
As n(0,λ0) = ne and using Eq. (5), one obtains:
ΔT=λ0(L+ΔL)c[ne(E,λ)λ|λ0]+λ0Lc[neλ|λ0]
(10)
Using 8.2 gives:
ΔT=λ0(L+ΔL)c[neλ|λ032ne2r33Eneλ|λ012ne3Er33λ|λ0]+λ0Lc[neλ|λ0]
(11)
Which leads to:
(TgTϕ)[E](TgTϕ)[0]=λ0Ec[(32ne2r33Tneλ|λ0+ne32r33Tλ|λ0)(L+ΔL)d32neλ0L]
(12)
Where we used the following relation between the change in the crystal length ΔL due to the inverse piezoelectric effect:
ΔL=d32EL
(13)
d32 is the piezoelectric constant. In the case of LiNbO3, d32 is more than 50 times lower [18

18. A. S. Andrushchak, B. G. Mytsyk, N. M. Demyanyshyn, M. V. Kaidan, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and W. Schranz, “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. 47(1), 31–38 (2009). [CrossRef]

] than the EO coefficient r33 which justifies neglecting all the terms involving ΔL in Eq. (12). Finally, one obtains the variation Δφ CEP of the CEP, after applying the electric field E:

ΔϕCEP2π[32ne2(λ0)r33T(λ0)neλ|λ0+ne3(λ0)2r33Tλ|λ0]LE
(14)

This phase change is proportional to the length of the crystal and to the electric field applied. It can be easily plotted taking into account the wavelength dispersion of the extraordinary index [19

19. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008). [CrossRef]

] and the wavelength dispersion of the EO coefficient [20

20. K. Yonekura, L. Jin, and K. Takizawa, “Measurement of Dispersion of Effective Electro-Optic Coefficients r13E and r33E of Non-Doped Congruent LiNbO3 Crystal,” Jpn. J. Appl. Phys. 47(7), 5503–5508 (2008). [CrossRef]

] for LiNbO3.

4. Practical realization

4.1 Experimental results

The experimental demonstration was made within the IMPULSE laboratory which is a common R&D laboratory associating CEA Saclay and Amplitude Technologies. The laser source was developed in collaboration with Amplitude Technologies and is a classical CEP stabilised Ti:S CPA system which delivers up to 2.5 mJ 35 fs pulses with a shot-to-shot CEP RMS noise after amplification of 320 mrad (over a period of one hour). The EO system (LiNbO3) was inserted between the stretcher and the regenerative amplifier. A train of pulses of 0.6 nJ energy, at a repetition rate of 75 MHz, was sent into the crystal (mean power 45 mW). We used a 5% MgO doped LiNbO3 crystal (provided by CASTECH Inc.) in the configuration described above. The length of the crystal in the z direction was 40mm and the width was 4mm in the X direction where the field is applied (see Fig. 3). Gold was deposited on each side of the crystal normal to the X direction. Using MgO doped crystal limits the photorefractive effects and permits higher incident laser power without beam degradation [21

21. D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44(9), 847–849 (1984). [CrossRef]

]. The simplified experimental set-up is given on Fig. 4
Fig. 4 Experimental set-up (see text for the CEP characteristics of the laser beam).
. A sine wave signal from a low voltage pulse generator is amplified in a high speed, High Voltage (HV) amplifier and applied on the crystal. The CEP variation as a function of the HV voltage is directly measured through the use of an in-house developed fast f-2f interferometer allowing multi-kHz shot to shot measurements.

The results obtained are given on Fig. 5
Fig. 5 CEP shift as a function of applied voltage
which plots the measured change of the CEP as a function of the applied voltage. It clearly shows a linear dependency as predicted by the model. The measured slope of ~3.5 rad/kV for the crystal used is in good agreement with the theoretical value of 3.1 rad/kV given by Eq. (14).

As refractive indices, EO coefficients and their wavelength dispersion for LiNbO3 are known with a good accuracy, the difference (about 10%) is probably due to the precision of the f-2f measurements. The oscillator of the laser source we used is CEP stabilized but this is not the case of the amplifier. The f-2f measurements being made after amplification (see Fig. 1), the accuracy of the phase determination is limited by the CEP noise on the laser. A CEP RMS noise of 320 mrad as mentioned before is quite compatible with the 10% difference observed between calculated and measured values in the studied range.

Finally, Fig. 6
Fig. 6 CEP sweep on f-2f interferometer fringes for different periodic modulated applied high voltage.
shows periodic CEP phase sweep visible on f-2f interferometer fringes when a modulated high voltage is applied on the EO device respectively with a sine (a), a sawtooth (b) and a square function (c).

4.2 Evaluation of the second derivative of the spectral phase

Applying a high voltage to the crystal in the above configuration changes the group velocity dispersion, and can be used to modify the CEP of a laser pulse. It is essential, however, to verify that the other main parameters of the laser pulse are unchanged. In particular, we have to evaluate the possible effects on the temporal laser pulse shape. The spectral phase ϕ(ω) induced by the crystal on the laser pulse is defined by the following relation:
ϕ(ω)=ωTϕ=ne(E)cωL
(15)
Where ne(E) is given by Eq. (8.2). As the wavelength dispersion of ne and r33 are known, the second derivative of ϕ(ω) can be numerically calculated and its square root compared to the pulse duration τ.

Figure 7
Fig. 7 Calculated parameter η (see text) as a function of the wavelength λ, for a laser pulse duration of 5 fs and a calculated CEP shift of 2π radians
plots the parameter η = ([d2ϕ/dω2]1/2)/τ as a function of the laser wavelength λ, for a pulse duration τ = 5 fs and a calculated CEP shift of Δφ CEP = 2π radians (which corresponds to an applied voltage of about 1985 V in our configuration). For wavelengths between 0.6 and 1-µm, the parameter η being lower than 1, no significant change of the temporal laser pulse shape or duration is expected even for sub-ten fs short pulses.

Conclusion

Acknowledgements

The authors acknowledge the financial support from the Conseil Général de l'Essonne (ASTRE program), the ANR-09-BLAN-0031-01 ATTO-WAVE and from the European Community (grant agreement PIAPP-GA-2008-218053).

References and links

1.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003). [CrossRef] [PubMed]

2.

M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, and G. Tondello, “Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high-order-harmonic spectra,” Phys. Rev. Lett. 91(21), 213905 (2003). [CrossRef] [PubMed]

3.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88(13), 133901 (2002). [CrossRef] [PubMed]

4.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]

5.

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004). [CrossRef]

6.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4(7), 462–465 (2010). [CrossRef]

7.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985). [CrossRef]

8.

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997). [CrossRef] [PubMed]

9.

S. Bohman, A. Suda, T. Kanai, S. Yamaguchi, and K. Midorikawa, “Generation of 5.0 fs, 5.0 mJ pulses at 1kHz using hollow-fiber pulse compression,” Opt. Lett. 35(11), 1887–1889 (2010). [CrossRef] [PubMed]

10.

C. F. Dutin, A. Dubrouil, S. Petit, E. Mével, E. Constant, and D. Descamps, “Post-compression of high-energy femtosecond pulses using gas ionization,” Opt. Lett. 35(2), 253–255 (2010). [CrossRef] [PubMed]

11.

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100-Hz amplified laser pulses,” Appl. Phys. B 74(9Suppl.), S43–S50 (2002). [CrossRef]

12.

C. Grebing, M. Görbe, K. Osvay, and G. Steinmeyer, “Isochronic and isodispersive carrier-envelope phase-shift compensators,” Appl. Phys. B 97(3), 575–581 (2009). [CrossRef]

13.

Z. Chang, “Carrier-envelope phase shift caused by grating-based stretchers and compressors,” Appl. Opt. 45(32), 8350–8353 (2006). [CrossRef] [PubMed]

14.

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997). [CrossRef]

15.

L. Canova, X. Chen, A. Trisorio, A. Jullien, A. Assion, G. Tempea, N. Forget, T. Oksenhendler, and R. Lopez-Martens, “Carrier-envelope phase stabilization and control using a transmission grating compressor and an AOPDF,” Opt. Lett. 34(9), 1333–1335 (2009). [CrossRef] [PubMed]

16.

H. Wang, M. Chini, Y. Wu, E. Moon, H. Mashiko, and Z. Chang, “Carrier–envelope phase stabilization of 5-fs, 0.5-mJ pulses from adaptive phase modulator,” Appl. Phys. B 98(2-3), 291–294 (2010). [CrossRef]

17.

R. S. Weis and T. K. Gaylord, “Lithium niobate: Summary of physical properties and crystal structure,” Appl. Phys., A Mater. Sci. Process. 37(4), 191–203 (1985). [CrossRef]

18.

A. S. Andrushchak, B. G. Mytsyk, N. M. Demyanyshyn, M. V. Kaidan, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and W. Schranz, “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. 47(1), 31–38 (2009). [CrossRef]

19.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008). [CrossRef]

20.

K. Yonekura, L. Jin, and K. Takizawa, “Measurement of Dispersion of Effective Electro-Optic Coefficients r13E and r33E of Non-Doped Congruent LiNbO3 Crystal,” Jpn. J. Appl. Phys. 47(7), 5503–5508 (2008). [CrossRef]

21.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44(9), 847–849 (1984). [CrossRef]

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(320.7090) Ultrafast optics : Ultrafast lasers
(320.7160) Ultrafast optics : Ultrafast technology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: January 27, 2011
Revised Manuscript: March 3, 2011
Manuscript Accepted: March 3, 2011
Published: March 8, 2011

Citation
O. Gobert, P.M Paul, J.F Hergott, O. Tcherbakoff, F. Lepetit, P. D 'Oliveira, F. Viala, and M. Comte, "Carrier-envelope phase control using linear electro-optic effect," Opt. Express 19, 5410-5418 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-5410


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References

  1. A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003). [CrossRef] [PubMed]
  2. M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, and G. Tondello, “Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high-order-harmonic spectra,” Phys. Rev. Lett. 91(21), 213905 (2003). [CrossRef] [PubMed]
  3. A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88(13), 133901 (2002). [CrossRef] [PubMed]
  4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]
  5. S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004). [CrossRef]
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