- Email: [email protected]
Femtosecond pulse duration measurements utilizing an ultrafast nonlinearity of nickel
1 February 1998
Optics Communications 147 Ž1998. 148–152
Femtosecond pulse duration measurements utilizing an ultrafast nonlinearity of nickel P.J. Bennett, A. Malinowski, B.D. Rainford, I.R. Shatwell, Yu.P. Svirko, N.I. Zheludev ) Department of Physics, UniÕersity of Southampton, Southampton SO17 1BJ, UK Received 7 July 1997; accepted 23 September 1997
Abstract A new, broadband, background free autocorrelation technique for measuring pulse durations of visible and infrared femtosecond laser pulses is described. The technique is based on the use of a reflective polarization-sensitive interaction in metallic nickel. q 1998 Elsevier Science B.V. PACS: 42.65.-k; 42.60.Jf; 78.47.q p Keywords: Autocorrelation measurements; Femtosecond optics; Nonlinearity of metals
Optical autocorrelation techniques are commonly used for measurement of the duration of femtosecond laser pulses. A variety of nonlinear interactions have been exploited in autocorrelators. These include, for example, second harmonic generation w1x, two photon fluorescence w2x, multiple order fluorescence w3x, the optical Kerr effect w4x, surface harmonic generation w5x, second harmonic generation on reflection w6x, two photon absorption in semiconductors w7,8x, and many others. Nonlinear interactions are used to determine the intensity and phase of femtosecond optical pulses by interferometric autocorrelation w9,10x or frequency-resolved optical gating ŽFROG. w11–15x. Clearly, ultrafast autocorrelation measurements require fast nonlinearities with broad spectral ranges. Recently, a new type of very fast optical nonlinearity has been reported in metallic gold w16x. In the current paper, we investigate the potential of metallic nonlinearities for use in optical correlators and report on a femtosecond autocorrelator for the visible–near infrared range employing a nonlinearity of metallic nickel. This polarimeter has been designed to minimise the effects of group velocity dispersion. A math-
)
Corresponding author. E-mail: [email protected].
ematical derivation of the output of the polarimeter is shown. We have made the first reported measurement of ImŽ x x x y y y x x y y x . for nickel. Since bulk metallic samples are opaque a reflective type nonlinear interaction must be used to perform the intensity multiplication process necessary for obtaining an autocorrelation function. Incoherent reflective polarization sensitive interactions of two waves w17x have the advantage of being easy to measure over a large dynamic range. Also, they need not impose phase matching requirements and consequently may be used over a very wide spectral range. In the autocorrelator reported here, we used the nonlinear polarization-sensitive wave interaction occurring in the Specular Inverse Faraday Effect ŽSIFE. to generate the intensity cross-correlation function of two optical pulses. The SIFE is the nonlinear optical phenomenon of rotation of the polarization azimuth of a probe wave reflected from a medium which results from stimulation of the medium by a second, circularly polarized pump wave w18–20x. Gold could be used in an autocorrelator as it exhibits a very fast optical nonlinearity, but the rotation observed was rather small, ; 10y5 rad per GWrcm2 of the pump intensity Ž l s 1260 nm. making the use of gold unpracti-
0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 Ž 9 7 . 0 0 5 6 3 - 4
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
cal with most femtosecond lasers. We found that metallic nickel films show much larger SIFE effect than gold in the visible and near infrared spectral bands, and therefore are much more suitable for use in the autocorrelation measurements. We prepared samples by vapour deposition using 99.98% pure nickel onto optically polished glass substrates at 208C in a vacuum of 4 = 10y6 mbar. The films were grown at approximately 1 nm per second to a thickness of 155 nm. This is much thicker than the nickel skin depth d s s c r Ž2 v n 2 . which is 16 nm at 810 nm and 19 nm at 1260 nm. We did not observe any static magnetisation of the samples after preparation. Fig. 1 shows a schematic of the autocorrelator. The beam of the laser for which the pulse duration is to be measured is split by the pellicle beamsplitter BS into two separate beams: A weak probe beam a1, and an intense pump beam a2. The probe is initially linearly polarized by the birefringent polarizing prism BP. The pump is circularly polarized by a first-order mica lr4 plate. Beams a1 and a2 are then focused by a parabolic mirror PM onto the nickel sample to a spot diameter of 40 mm. The polarization azimuth of the reflected beam a1 is modulated at a frequency V 1 f 6 kHz with an amplitude of 7 = 10y3 rad by a Faraday cell FM containing a terbium gallium Garnet crystal. Beam a2 is chopped by chopper CP at frequency V 2 f 2 kHz. The reflected beam a1 passes a Glan prism GP which has its transmission axis perpendicular to the birefringent polarizer BP. The intensity of the probe beam is measured after the Glan prism by a silicon or germanium photodetector and a phase sensitive detector locked at frequency V 1 q V 2 ; 8 kHz. Particular
149
care has been taken to limit the group velocity dispersion effects in the polarimeter: The pump and probe beams are passed through the polarization prism BP close to its apex, minimizing pulse spreading in the prism to ; 3 fs for a transform-limited 30 fs pulse at l s 810 nm, and an even smaller amount at longer wavelengths. It is important to note that the dispersive effects of the TGG crystal in the Faraday modulator FM and of the Glan prism GP are unimportant for time resolution, as the beam does not pass through them until after it has interacted with the sample. Let us consider the SIFE, in a medium where the nonlinear response time is much shorter than the duration of the pulses interacting through the nonlinearity. The pump induces reflected probe polarization rotation a i Ž t . s m IpŽ t ., which is proportional to the instantaneous pump intensity IpŽ t . w19x. The coefficient of proportionality m depends on the cubic nonlinearity x Ž3. of the medium:
ms"
Ž1 y R . 2 n 0
'R
< n < n12
Im x eyi f 4 =
2p c
,
Ž1.
where c is the velocity of light and n s n1 q i n 2 is the complex refractive index of the material, n 0 is the refractive index of the matter interfacing with the metal Ž n 0 s 1 in the case of vacuum–metal interface. and R is the intensity reflectivity coefficient from the interface. The sign of the coefficient depends on the handedness of circular polarization of the pump. We will see below, that the polarimeter response is proportional to the convolution of the pump and probe intensity envelopes in the time domain and therefore may be used for measuring intensity autocorrelation functions.
Fig. 1. Schematic of femtosecond autocorrelator using reflective polarization-sensitive interaction in metallic nickel.
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
150
The output signal of the correlator may be derived as follows. Let us set a Cartesian coordinate frame in which the nickel sample is in the xy-plane and the incident probe beam propagates along the z-direction being initially polarized along the x-direction. If the probe beam a1 is reflected from the nickel sample the power of the light transmitted by analyser GP will be: Pout Ž t , t . s
Ps Ž t y t . 2 Ž1 q h .
reflected probe polarization rotation a i . Since at higher frequencies the laser noise is normally lower, the detection of the signal proportional to the induced rotation would be more suitable at the sum frequency V 1 q V 2 . This current is measured by a phase-sensitive detector. Recalling that a i Ž t . s m Ip Ž t ., we therefore find that the lock-in sensitive detector output voltage returns the pump-probe time domain convolution function:
w1 q h V Ž t , V 1 q V 2 . A A Is Ž t y t . a i Ž t . d t
H
q Ž h y 1 . Ž cos 2 f Ž t . cos 2 a Ž t . cos 2h Ž t . qsin 2 f Ž t . sin 2 a Ž t . cos 2h Ž t . . x .
Ž2.
Here, PsŽ t y t . is the reflected probe light pulse intensity which is delayed with respect to the pump by t , a Ž t . and h Ž t . are the azimuth rotation and induced elipticity which occur on reflection from the sample, respectively, f Ž t . s A cosŽ V 1 t q f 1 . is the polarization azimuth rotation in the Faraday modulator FM, and h is the extinction ratio of the polarizer BP, analyser GP pair. For f Ž t ., a Ž t ., h Ž t . < p : Pout Ž t , t . s
Ps Ž t y t . 2 Ž1 q h .
y4 Ž 1 y h . A a Ž t . cos Ž V 1 t q f 1 .
qA2 cos Ž 2 V 1 t q 2 f 1 . q A2 q 2 h .
Ž3.
The polarization azimuth rotation at the nickel sample a Ž t . may be presented as the sum of the pump independent component a 0 and the pump-induced component which is modulated at a relatively low frequency V 2 in comparison with the repetition rate of the laser:
a Ž t . s a 0 q 12 a i Ž t . w 1 q cos Ž V 2 t q f 2 . x .
Ž4.
Substituting Eq. Ž4. into Eq. Ž3. we derive the following formula for the correlator output signal: Pout Ž t , t . s
Ps Ž t y t . 2 Ž1 q h .
y Ž1 y h . A a i Ž t .
=cos Ž Ž V 1 q V 2 . t q f 1 q f 2 . y Ž1 y h . A a i Ž t . =cos Ž Ž V 1 y V 2 . t q f 1 y f 2 . qA2 cos Ž 2 V 1 t q 2 f 1 . qA2 q 2 h y 2 A Ž 1 y h . Ž a i Ž t . q 2 a 0 . =cos Ž V 1 t q f 1 . .
Ž5.
The integration time T of the photodetector is chosen such that 1rV 1,2 4 T, but it is significantly longer than the optical pulse duration. Therefore, the integrated photodetector current will oscillate at V 1 q V 2 , V 1 y V 2 , 2 V 1 and V 1 and will also have a DC component. The DC component and the component at 2 V 1 of the photodetector current are not sensitive to the induced rotation. However the current spectral components at V 1 q V 2 and V 1 y V 2 are directly proportional to the pump induced
A m A Ip Ž t . Is Ž t y t . d t.
H
Ž6.
The intensity of the probe can be approximated to a constant. Indeed our measurements have shown that the reflectivity of the nickel sample changes not more than 0.2%. Since the pump and the probe pulses come from the same source, the polarimeter output V Žt . is directly proportional to the value of the pulse intensity auto-correlation function. This technique has the potential to be combined with spectral analysis of the signal from the polarimeter, as with FROG w11–15x. The autocorrelator has been tested with two laser sources, operating in the visible and near-infrared, respectively: A Kerr-lens mode-locked Ti:sapphire laser Ž l s 810 nm. w21x, and a Kerr-lens mode-locked Cr:forsterite laser Ž l s 1260 nm. w22x. With nickel samples evaporated onto glass substrates, illuminating the nickel surface directly we were able to detect the auto-correction functions with a 70:1 signal-to-noise ratio the for a 100 mW Ti:sapphire laser and a 60:1 signal-to-noise ratio the for a 100 mW Cr:forsterite laser both operating at 82 MHz repetition rate Žsee Fig. 2.. The solid lines are best fits to the data, returning pulse durations of 76 fs for the Cr:forsterite laser and 32 fs for the Ti:sapphire assuming a sech2 pulse shape. Induced polarization azimuth rotations were seen which were accurately proportional to the pump intensity with m , 8 mrad GWy1 cm2 at 810 nm and m , 200 mrad GWy1 cm2 at 1260 nm Žsee Fig. 2.. For a signal to noise ratio of 10:1 a cw equivalent power of 2 mW at 1260 nm or 40 mW at 810 nm is required Žfor 100 fs pulses with a repetition rate of 82 MHz., which means this technique is suitable for use with commercial Kerr-lens mode-locked lasers. The autocorrelation functions for the Cr:forsterite laser were symmetric. The autocorrelation functions from the Ti:sapphire laser are slightly asymmetric. This indicates that at these shorter pulse lengths we are close to the response time of the material. Using Eq. Ž1. we calculated the effective nonlinearity to be mainly imaginary with ImŽ x x x y y y x x y y x . to be 2 = 10y10 esu at 810 nm and 1 = 10y9 esu at 1260 nm. Using the refractive indices of nickel films n s 2.50 q i3.91 at 810 nm and n s 3.50 q i5.18 at 1260 nm w23x. Although a theory has been developed for the ultrafast metallic nonlinearity observed in the noble metal gold
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
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ferent surface states and creation of a transitional layer at the glass interface. This interesting phenomenon deserves a comprehensive study. In conclusion, we have demonstrated a new background-free femtosecond autocorrelation technique based on the Specular Inverse Faraday effect in nickel which is suitable for infrared, visible and UV measurements, potentially up to the plasma frequency of nickel. An obvious advantage of the technique reported above is its suitability for femtosecond pulse duration measurements over a very broad spectral range, in particular in the infrared, where use of other autocorrelation techniques may be unsuitable. Changing wavelength does not require major retuning. This technique uses standard or inexpensive optical and electronic components, is easy to set up and simple to use.
References
Fig. 2. Normalised autocorrelation traces for Cr:forsterite Žv . Ž l s1260 nm. and Ti:sapphire Ž`. Ž l s810 nm. Kerr lens mode-locked femtosecond lasers. The inset below shows the linearity of the correlator: The magnitude of the autocorrelation function as measured at zero pump-probe delay is plotted against the pump intensity: 100% pump is equivalent to a peak intensity of 0.6 GW cmy2 for 1260 nm and 20 GW cmy2 for 810 nm.
w16,24,25x, a theory has not yet been developed for the ultrafast nonlinearity in nickel. We believe both free electron and interband spin related mechanisms are important in nickel, with possible enhancement due to collective correlation effects in this ferromagnetic material. With the Ti:sapphire laser we also studied nickel samples illuminated through the substrate glass. Unexpectedly, with the same handedness of the polarization state of the pump, the rotation of the probe polarization azimuth observed from the glass side was stronger than, and in the opposite direction to, the rotation observed directly from the nickel. The effective nonlinearity calculated for illumination through the glass substrate was also calculated to be ImŽ x x x y y y x x y y x . s 2 = 10y10 esu, using a refractive index for the nickel film at a glass surface of n s 2.50 q i3.91 w23x Ža bigger rotation at the same pump intensity gives the same nonlinearity because of the factor 'R < n < n12 in Eq. Ž1... The change of the sign of the nonlinearity indicates that different mechanisms dominate the nonlinearity in nickel interfacing with glass in comparison with the nickel–air interface. Such difference may be due to oxidization of the nickel surface, the transitions through dif-
w1x M. Maier, W. Kaiser, J.A. Giordmaine, Phys. Rev. Lett. 17 Ž1966. 1275. w2x J.A. Giodmaine, P.M. Rentzepis, S.L. Shapiro, K.W. Wecht, Appl. Phys. Lett. 11 Ž1967. 216. w3x N. Sarukura, M. Watanabe, A. Endoh, S. Watanabe, Optics Lett. 13 Ž1988. 996. w4x D.J. Kane, R. Trebino, J. Opt. Soc. Am. A 10 Ž1993. 1101. w5x A. Gierulski, G. Marowsky, B. Nikolaus, N. Vorob’ev, Appl. Phys. B 36 Ž1985. 133. w6x V.M. Gordienko, M.S. Dzhidzhoev, S.V. Krayushkin, S.A. Magnitskii, V.T. Platonenko, Y.A. Repeev, Kvantovaya Elektron. 15 Ž1988. 875. w7x Y. Takagi, T. Kobayashi, K. Yoshihara, S. Imamura, Optics Lett. 17 Ž1992. 658. w8x D.T. Reid, M. Padgett, C. McGowan, W.E. Sleat, W. Sibbett, Optics Lett. 22 Ž1997. 233. w9x T. Kurobori, Y. Cho, Y. Matsuo, Optics Comm. 40 Ž1981. 156. w10x A. Watanabe, H. Saito, Y. Ishida, Optics Comm. 69 Ž1989. 405. w11x D.J. Kane, R. Trebino, IEEE J. Quantum Electron. 29 Ž1993. 571. w12x D.J. Kane, R. Trebino, Optics Lett. 18 Ž1993. 823. w13x K.W. Delong, R. Trebino, D.J. Kane, J. Opt. Soc. Am. B 11 Ž1994. 1595. w14x K.W. Delong, R. Trebino, J. Hunter, W.E. White, J. Opt. Soc. Am. B 11 Ž1994. 2206. w15x T. Tsang, M.A. Krumbugel, K.W. Delong, D.N. Fittinghoff, R. Trebino, Optics Lett. 21 Ž1996. 1381. w16x N.I. Zheludev, P.J. Bennett, H. Loh, S.V. Popov, I.R. Shatwell, Yu.P. Svirko, V.E. Gusev, V.F. Kamalov, E.V. Slobodchikov, Optics Lett. 20 Ž1995. 1368. w17x S.V. Popov, N.I. Zheludev, Yu.P. Svirko, J. Opt. Soc. Am. B 13 Ž1996. 2729. w18x M. Kuwata, J. Luminesc. 38 Ž1987. 247. w19x Yu.P. Svirko, N.I. Zheludev, J. Opt. Soc. Am. B 11 Ž1994. 1388. w20x S.V. Popov, N.I. Zheludev, Yu.P. Svirko, Optics Lett. 19 Ž1994. 13.
152
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
w21x M.M. Murnane, H.C. Kapteyn, Mode-locked Ti:sapphire Laser, Rev. 1.6, Washington State University 1993. w22x A.A. Ivanov, V.F. Kamalov, A.P. Lifanov, J. Lucassen, B.I. Minkov, E.V. Slobodchikov, Kvantovaya Elektron. 20 Ž1993. 1039. w23x K.H. Clemens, J. Jaumann, Z. Phys. 173 Ž1963. 135.
w24x N.I. Zheludev, S.V. Popov, I.R. Shatwell, V.E. Gusev, in: P.F. Barbara, J.G. Fujimoto, W.H. Knox, W. Zinth ŽEds.., Ultrafast Phenomena X, Springer, Berlin, 1996, p. 461. w25x R.W. Schoenlein, W.Z. Lin, J.G. Fujimoto, G.L. Eesley, Phys. Rev. Lett. 58 Ž1987. 1680.
Optics Communications 147 Ž1998. 148–152
Femtosecond pulse duration measurements utilizing an ultrafast nonlinearity of nickel P.J. Bennett, A. Malinowski, B.D. Rainford, I.R. Shatwell, Yu.P. Svirko, N.I. Zheludev ) Department of Physics, UniÕersity of Southampton, Southampton SO17 1BJ, UK Received 7 July 1997; accepted 23 September 1997
Abstract A new, broadband, background free autocorrelation technique for measuring pulse durations of visible and infrared femtosecond laser pulses is described. The technique is based on the use of a reflective polarization-sensitive interaction in metallic nickel. q 1998 Elsevier Science B.V. PACS: 42.65.-k; 42.60.Jf; 78.47.q p Keywords: Autocorrelation measurements; Femtosecond optics; Nonlinearity of metals
Optical autocorrelation techniques are commonly used for measurement of the duration of femtosecond laser pulses. A variety of nonlinear interactions have been exploited in autocorrelators. These include, for example, second harmonic generation w1x, two photon fluorescence w2x, multiple order fluorescence w3x, the optical Kerr effect w4x, surface harmonic generation w5x, second harmonic generation on reflection w6x, two photon absorption in semiconductors w7,8x, and many others. Nonlinear interactions are used to determine the intensity and phase of femtosecond optical pulses by interferometric autocorrelation w9,10x or frequency-resolved optical gating ŽFROG. w11–15x. Clearly, ultrafast autocorrelation measurements require fast nonlinearities with broad spectral ranges. Recently, a new type of very fast optical nonlinearity has been reported in metallic gold w16x. In the current paper, we investigate the potential of metallic nonlinearities for use in optical correlators and report on a femtosecond autocorrelator for the visible–near infrared range employing a nonlinearity of metallic nickel. This polarimeter has been designed to minimise the effects of group velocity dispersion. A math-
)
Corresponding author. E-mail: [email protected].
ematical derivation of the output of the polarimeter is shown. We have made the first reported measurement of ImŽ x x x y y y x x y y x . for nickel. Since bulk metallic samples are opaque a reflective type nonlinear interaction must be used to perform the intensity multiplication process necessary for obtaining an autocorrelation function. Incoherent reflective polarization sensitive interactions of two waves w17x have the advantage of being easy to measure over a large dynamic range. Also, they need not impose phase matching requirements and consequently may be used over a very wide spectral range. In the autocorrelator reported here, we used the nonlinear polarization-sensitive wave interaction occurring in the Specular Inverse Faraday Effect ŽSIFE. to generate the intensity cross-correlation function of two optical pulses. The SIFE is the nonlinear optical phenomenon of rotation of the polarization azimuth of a probe wave reflected from a medium which results from stimulation of the medium by a second, circularly polarized pump wave w18–20x. Gold could be used in an autocorrelator as it exhibits a very fast optical nonlinearity, but the rotation observed was rather small, ; 10y5 rad per GWrcm2 of the pump intensity Ž l s 1260 nm. making the use of gold unpracti-
0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 Ž 9 7 . 0 0 5 6 3 - 4
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
cal with most femtosecond lasers. We found that metallic nickel films show much larger SIFE effect than gold in the visible and near infrared spectral bands, and therefore are much more suitable for use in the autocorrelation measurements. We prepared samples by vapour deposition using 99.98% pure nickel onto optically polished glass substrates at 208C in a vacuum of 4 = 10y6 mbar. The films were grown at approximately 1 nm per second to a thickness of 155 nm. This is much thicker than the nickel skin depth d s s c r Ž2 v n 2 . which is 16 nm at 810 nm and 19 nm at 1260 nm. We did not observe any static magnetisation of the samples after preparation. Fig. 1 shows a schematic of the autocorrelator. The beam of the laser for which the pulse duration is to be measured is split by the pellicle beamsplitter BS into two separate beams: A weak probe beam a1, and an intense pump beam a2. The probe is initially linearly polarized by the birefringent polarizing prism BP. The pump is circularly polarized by a first-order mica lr4 plate. Beams a1 and a2 are then focused by a parabolic mirror PM onto the nickel sample to a spot diameter of 40 mm. The polarization azimuth of the reflected beam a1 is modulated at a frequency V 1 f 6 kHz with an amplitude of 7 = 10y3 rad by a Faraday cell FM containing a terbium gallium Garnet crystal. Beam a2 is chopped by chopper CP at frequency V 2 f 2 kHz. The reflected beam a1 passes a Glan prism GP which has its transmission axis perpendicular to the birefringent polarizer BP. The intensity of the probe beam is measured after the Glan prism by a silicon or germanium photodetector and a phase sensitive detector locked at frequency V 1 q V 2 ; 8 kHz. Particular
149
care has been taken to limit the group velocity dispersion effects in the polarimeter: The pump and probe beams are passed through the polarization prism BP close to its apex, minimizing pulse spreading in the prism to ; 3 fs for a transform-limited 30 fs pulse at l s 810 nm, and an even smaller amount at longer wavelengths. It is important to note that the dispersive effects of the TGG crystal in the Faraday modulator FM and of the Glan prism GP are unimportant for time resolution, as the beam does not pass through them until after it has interacted with the sample. Let us consider the SIFE, in a medium where the nonlinear response time is much shorter than the duration of the pulses interacting through the nonlinearity. The pump induces reflected probe polarization rotation a i Ž t . s m IpŽ t ., which is proportional to the instantaneous pump intensity IpŽ t . w19x. The coefficient of proportionality m depends on the cubic nonlinearity x Ž3. of the medium:
ms"
Ž1 y R . 2 n 0
'R
< n < n12
Im x eyi f 4 =
2p c
,
Ž1.
where c is the velocity of light and n s n1 q i n 2 is the complex refractive index of the material, n 0 is the refractive index of the matter interfacing with the metal Ž n 0 s 1 in the case of vacuum–metal interface. and R is the intensity reflectivity coefficient from the interface. The sign of the coefficient depends on the handedness of circular polarization of the pump. We will see below, that the polarimeter response is proportional to the convolution of the pump and probe intensity envelopes in the time domain and therefore may be used for measuring intensity autocorrelation functions.
Fig. 1. Schematic of femtosecond autocorrelator using reflective polarization-sensitive interaction in metallic nickel.
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
150
The output signal of the correlator may be derived as follows. Let us set a Cartesian coordinate frame in which the nickel sample is in the xy-plane and the incident probe beam propagates along the z-direction being initially polarized along the x-direction. If the probe beam a1 is reflected from the nickel sample the power of the light transmitted by analyser GP will be: Pout Ž t , t . s
Ps Ž t y t . 2 Ž1 q h .
reflected probe polarization rotation a i . Since at higher frequencies the laser noise is normally lower, the detection of the signal proportional to the induced rotation would be more suitable at the sum frequency V 1 q V 2 . This current is measured by a phase-sensitive detector. Recalling that a i Ž t . s m Ip Ž t ., we therefore find that the lock-in sensitive detector output voltage returns the pump-probe time domain convolution function:
w1 q h V Ž t , V 1 q V 2 . A A Is Ž t y t . a i Ž t . d t
H
q Ž h y 1 . Ž cos 2 f Ž t . cos 2 a Ž t . cos 2h Ž t . qsin 2 f Ž t . sin 2 a Ž t . cos 2h Ž t . . x .
Ž2.
Here, PsŽ t y t . is the reflected probe light pulse intensity which is delayed with respect to the pump by t , a Ž t . and h Ž t . are the azimuth rotation and induced elipticity which occur on reflection from the sample, respectively, f Ž t . s A cosŽ V 1 t q f 1 . is the polarization azimuth rotation in the Faraday modulator FM, and h is the extinction ratio of the polarizer BP, analyser GP pair. For f Ž t ., a Ž t ., h Ž t . < p : Pout Ž t , t . s
Ps Ž t y t . 2 Ž1 q h .
y4 Ž 1 y h . A a Ž t . cos Ž V 1 t q f 1 .
qA2 cos Ž 2 V 1 t q 2 f 1 . q A2 q 2 h .
Ž3.
The polarization azimuth rotation at the nickel sample a Ž t . may be presented as the sum of the pump independent component a 0 and the pump-induced component which is modulated at a relatively low frequency V 2 in comparison with the repetition rate of the laser:
a Ž t . s a 0 q 12 a i Ž t . w 1 q cos Ž V 2 t q f 2 . x .
Ž4.
Substituting Eq. Ž4. into Eq. Ž3. we derive the following formula for the correlator output signal: Pout Ž t , t . s
Ps Ž t y t . 2 Ž1 q h .
y Ž1 y h . A a i Ž t .
=cos Ž Ž V 1 q V 2 . t q f 1 q f 2 . y Ž1 y h . A a i Ž t . =cos Ž Ž V 1 y V 2 . t q f 1 y f 2 . qA2 cos Ž 2 V 1 t q 2 f 1 . qA2 q 2 h y 2 A Ž 1 y h . Ž a i Ž t . q 2 a 0 . =cos Ž V 1 t q f 1 . .
Ž5.
The integration time T of the photodetector is chosen such that 1rV 1,2 4 T, but it is significantly longer than the optical pulse duration. Therefore, the integrated photodetector current will oscillate at V 1 q V 2 , V 1 y V 2 , 2 V 1 and V 1 and will also have a DC component. The DC component and the component at 2 V 1 of the photodetector current are not sensitive to the induced rotation. However the current spectral components at V 1 q V 2 and V 1 y V 2 are directly proportional to the pump induced
A m A Ip Ž t . Is Ž t y t . d t.
H
Ž6.
The intensity of the probe can be approximated to a constant. Indeed our measurements have shown that the reflectivity of the nickel sample changes not more than 0.2%. Since the pump and the probe pulses come from the same source, the polarimeter output V Žt . is directly proportional to the value of the pulse intensity auto-correlation function. This technique has the potential to be combined with spectral analysis of the signal from the polarimeter, as with FROG w11–15x. The autocorrelator has been tested with two laser sources, operating in the visible and near-infrared, respectively: A Kerr-lens mode-locked Ti:sapphire laser Ž l s 810 nm. w21x, and a Kerr-lens mode-locked Cr:forsterite laser Ž l s 1260 nm. w22x. With nickel samples evaporated onto glass substrates, illuminating the nickel surface directly we were able to detect the auto-correction functions with a 70:1 signal-to-noise ratio the for a 100 mW Ti:sapphire laser and a 60:1 signal-to-noise ratio the for a 100 mW Cr:forsterite laser both operating at 82 MHz repetition rate Žsee Fig. 2.. The solid lines are best fits to the data, returning pulse durations of 76 fs for the Cr:forsterite laser and 32 fs for the Ti:sapphire assuming a sech2 pulse shape. Induced polarization azimuth rotations were seen which were accurately proportional to the pump intensity with m , 8 mrad GWy1 cm2 at 810 nm and m , 200 mrad GWy1 cm2 at 1260 nm Žsee Fig. 2.. For a signal to noise ratio of 10:1 a cw equivalent power of 2 mW at 1260 nm or 40 mW at 810 nm is required Žfor 100 fs pulses with a repetition rate of 82 MHz., which means this technique is suitable for use with commercial Kerr-lens mode-locked lasers. The autocorrelation functions for the Cr:forsterite laser were symmetric. The autocorrelation functions from the Ti:sapphire laser are slightly asymmetric. This indicates that at these shorter pulse lengths we are close to the response time of the material. Using Eq. Ž1. we calculated the effective nonlinearity to be mainly imaginary with ImŽ x x x y y y x x y y x . to be 2 = 10y10 esu at 810 nm and 1 = 10y9 esu at 1260 nm. Using the refractive indices of nickel films n s 2.50 q i3.91 at 810 nm and n s 3.50 q i5.18 at 1260 nm w23x. Although a theory has been developed for the ultrafast metallic nonlinearity observed in the noble metal gold
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ferent surface states and creation of a transitional layer at the glass interface. This interesting phenomenon deserves a comprehensive study. In conclusion, we have demonstrated a new background-free femtosecond autocorrelation technique based on the Specular Inverse Faraday effect in nickel which is suitable for infrared, visible and UV measurements, potentially up to the plasma frequency of nickel. An obvious advantage of the technique reported above is its suitability for femtosecond pulse duration measurements over a very broad spectral range, in particular in the infrared, where use of other autocorrelation techniques may be unsuitable. Changing wavelength does not require major retuning. This technique uses standard or inexpensive optical and electronic components, is easy to set up and simple to use.
References
Fig. 2. Normalised autocorrelation traces for Cr:forsterite Žv . Ž l s1260 nm. and Ti:sapphire Ž`. Ž l s810 nm. Kerr lens mode-locked femtosecond lasers. The inset below shows the linearity of the correlator: The magnitude of the autocorrelation function as measured at zero pump-probe delay is plotted against the pump intensity: 100% pump is equivalent to a peak intensity of 0.6 GW cmy2 for 1260 nm and 20 GW cmy2 for 810 nm.
w16,24,25x, a theory has not yet been developed for the ultrafast nonlinearity in nickel. We believe both free electron and interband spin related mechanisms are important in nickel, with possible enhancement due to collective correlation effects in this ferromagnetic material. With the Ti:sapphire laser we also studied nickel samples illuminated through the substrate glass. Unexpectedly, with the same handedness of the polarization state of the pump, the rotation of the probe polarization azimuth observed from the glass side was stronger than, and in the opposite direction to, the rotation observed directly from the nickel. The effective nonlinearity calculated for illumination through the glass substrate was also calculated to be ImŽ x x x y y y x x y y x . s 2 = 10y10 esu, using a refractive index for the nickel film at a glass surface of n s 2.50 q i3.91 w23x Ža bigger rotation at the same pump intensity gives the same nonlinearity because of the factor 'R < n < n12 in Eq. Ž1... The change of the sign of the nonlinearity indicates that different mechanisms dominate the nonlinearity in nickel interfacing with glass in comparison with the nickel–air interface. Such difference may be due to oxidization of the nickel surface, the transitions through dif-
w1x M. Maier, W. Kaiser, J.A. Giordmaine, Phys. Rev. Lett. 17 Ž1966. 1275. w2x J.A. Giodmaine, P.M. Rentzepis, S.L. Shapiro, K.W. Wecht, Appl. Phys. Lett. 11 Ž1967. 216. w3x N. Sarukura, M. Watanabe, A. Endoh, S. Watanabe, Optics Lett. 13 Ž1988. 996. w4x D.J. Kane, R. Trebino, J. Opt. Soc. Am. A 10 Ž1993. 1101. w5x A. Gierulski, G. Marowsky, B. Nikolaus, N. Vorob’ev, Appl. Phys. B 36 Ž1985. 133. w6x V.M. Gordienko, M.S. Dzhidzhoev, S.V. Krayushkin, S.A. Magnitskii, V.T. Platonenko, Y.A. Repeev, Kvantovaya Elektron. 15 Ž1988. 875. w7x Y. Takagi, T. Kobayashi, K. Yoshihara, S. Imamura, Optics Lett. 17 Ž1992. 658. w8x D.T. Reid, M. Padgett, C. McGowan, W.E. Sleat, W. Sibbett, Optics Lett. 22 Ž1997. 233. w9x T. Kurobori, Y. Cho, Y. Matsuo, Optics Comm. 40 Ž1981. 156. w10x A. Watanabe, H. Saito, Y. Ishida, Optics Comm. 69 Ž1989. 405. w11x D.J. Kane, R. Trebino, IEEE J. Quantum Electron. 29 Ž1993. 571. w12x D.J. Kane, R. Trebino, Optics Lett. 18 Ž1993. 823. w13x K.W. Delong, R. Trebino, D.J. Kane, J. Opt. Soc. Am. B 11 Ž1994. 1595. w14x K.W. Delong, R. Trebino, J. Hunter, W.E. White, J. Opt. Soc. Am. B 11 Ž1994. 2206. w15x T. Tsang, M.A. Krumbugel, K.W. Delong, D.N. Fittinghoff, R. Trebino, Optics Lett. 21 Ž1996. 1381. w16x N.I. Zheludev, P.J. Bennett, H. Loh, S.V. Popov, I.R. Shatwell, Yu.P. Svirko, V.E. Gusev, V.F. Kamalov, E.V. Slobodchikov, Optics Lett. 20 Ž1995. 1368. w17x S.V. Popov, N.I. Zheludev, Yu.P. Svirko, J. Opt. Soc. Am. B 13 Ž1996. 2729. w18x M. Kuwata, J. Luminesc. 38 Ž1987. 247. w19x Yu.P. Svirko, N.I. Zheludev, J. Opt. Soc. Am. B 11 Ž1994. 1388. w20x S.V. Popov, N.I. Zheludev, Yu.P. Svirko, Optics Lett. 19 Ž1994. 13.
152
P.J. Bennett et al.r Optics Communications 147 (1998) 148–152
w21x M.M. Murnane, H.C. Kapteyn, Mode-locked Ti:sapphire Laser, Rev. 1.6, Washington State University 1993. w22x A.A. Ivanov, V.F. Kamalov, A.P. Lifanov, J. Lucassen, B.I. Minkov, E.V. Slobodchikov, Kvantovaya Elektron. 20 Ž1993. 1039. w23x K.H. Clemens, J. Jaumann, Z. Phys. 173 Ž1963. 135.
w24x N.I. Zheludev, S.V. Popov, I.R. Shatwell, V.E. Gusev, in: P.F. Barbara, J.G. Fujimoto, W.H. Knox, W. Zinth ŽEds.., Ultrafast Phenomena X, Springer, Berlin, 1996, p. 461. w25x R.W. Schoenlein, W.Z. Lin, J.G. Fujimoto, G.L. Eesley, Phys. Rev. Lett. 58 Ž1987. 1680.