1. Introduction

Several methods have been developed for the characterization of femtosecond laser pulses in the near infrared and the visible spectral region with respect to pulse duration and temporal structure. These include second and third order autocorrelations, but most importantly FROG [1] and SPIDER [2] techniques. Various iterative algorithms to reconstruct the phase from a measured autocorrelation and the pulse spectrum have been developed [3-5]. These methods are well established and routinely used in the laboratory. Many techniques employ second-order nonlinearities which limits the spectral range to wavelengths longer than 410 nm when BBO is used [6], or 340 nm when KBBF is employed, a crystal not yet commercially available [7]. On the other hand many photophysical applications require shorter wavelengths of the femtosecond pulses, particularly in the UV. While the generation of laser light in this spectral region is comparatively easy to achieve by frequency conversion of visible femtosecond pulses in non-linear crystals or by OPA systems, the determination of their duration, being essential for the assessment of the temporal resolution and its optimization, remains a difficult task.

In the ultraviolet the quest for high-power KrF lasers at 248 nm prompted the development of various, even phase-sensitive and single-shot autocorrelation methods. These include two-photon ecxited excitonic fluorescence in BaF₂, CaF₂ or fused silica [8-10]. These methods, however, require pulse energies in the µJ or even mJ range for sub-picosecond pulses. Two-photon absorption in diamond crystals has also successfully been used to characterize ultrashort UV pulses at 310 nm and can potentially be used down to the bandgap of diamond at about 225 nm [11]. However, this method is not capable of recording fringe-resolved autocorrelations and requires the measurement of very small changes in the transmission.

Polarization gating, a third-order process often used in FROG set-ups, needs only low pulse energies of a few nJ and may extend the spectral range into the near UV, but requires very good and thin polarizers with an extinction ratio of at least10⁻⁵, not commonly available in the deep ultraviolet region [12]. At higher pulse energies of several tens of microjoules a similar set-up for single-shot FROG measurements has been demonstrated for sub-picosecond pulses at wavelengths of 310 nm [13] and 248 nm [14]. For ultrashort pulses, however, it suffers from the same limitations of the polarizers, namely thickness and extinction ratio. An alternative in FROG set-ups is the use of a transient grating, which is a third order nonlinear process, where two spatially crossed pulses interact in a Kerr active medium. Here, there interference pattern inside the medium periodically alters the refractive index and therefore the medium acts as a grating for a third pulse that arrives at a variable delay with respect to the first pulses [12].

Surface second harmonic generation and sum frequency mixing overcome phase matching limitations, because the nonlinearity occurs in an extremely thin layer with a thickness well below the wavelength of UV and VUV light. These methods have been demonstrated at GaAs and metal surfaces [15,16]. However, they require pulse energies of several microjoules and long integration times for applications in SPIDER set-ups [16]. Alternatively the transient reflectivity induced by irradiating on a surface can be used for cross-correlations. This surface effect has recently been used for cross-correlation measurements of XUV FEL and optical femtosecond pulses on a GaAs surface [17]. Here, the XUV pulses with photon energies of 39.5 eV excite the gallium 3d state. Equilibration of this excited state leads to a high density of free carriers in the crystal and thus lowers the reflectivity. However, this method is not capable of phase reconstruction and requires knowledge of the temporal structure of the reflected pulse.

Autocorrelations can also be recorded by using a photodiode with a band gap larger than the incident photon energy [18]. In this case, the absorption of two or more photons is required to generate free carriers in the diode, thereby incorporating nonlinearity and detector in a single device. When the absorption length in the material is shorter than the wavelength, which often is the case in solid materials, phase matching is not necessary. Therefore, the acceptance bandwidth which these diodes offer is larger than in nonlinear crystals [18]. Due to the lack of large band gap photodiodes this method has so far been restricted to wavelengths longer than about 380 nm achieved in SiC [20].

Alternatively, photoconductive switches made from fused silica have successfully been used for wavelengths down to 267 nm and can potentially be applied down to about 140 nm. These devices, however, suffer from a high dark current due to the required high bias voltage [21]. In addition, they are also limited to wavelengths below 280 nm, thus leaving a gap of about 100 nm between their region of operation and that of the aforementioned SiC diodes.

With the development of methods to dope diamond for p- and n-type conduction it is now possible to fabricate pin photodiodes with a band gap of 5.5 eV corresponding to a wavelength of about 225 nm [22]. In this letter we present first results of fringe-resolved autocorrelation of femtosecond UV pulses employing two-photon induced photoconductivity in such diamond pin diodes and demonstrate the possibility to iteratively reconstruct the phase from the recorded autocorrelation and spectrum of the pulses.

2. Characterization of the diamond diode

The diamond photodiodes are based on a commercial HPHT Type 1b {111} oriented diamond substrate of 5 mm diameter and a thickness of 0.5 mm. On this substrate first a boron doped diamond layer with a thickness of $\text{1 .5 μm}$ for p-type conduction is epitaxially grown by chemical vapor deposition (CVD), followed by a 700 nm thick intrinsic layer, and finally a phosphorus doped layer (300 nm) for n-type conduction. The boron doped layer is contacted by first etching an outer ring off the two layers on top of it and then evaporating thin layers of titanium and aluminum. Another thin layer (< 10 nm) of aluminum is deposited on the P-doped top layer to provide electrical contact and preserve a moderately high transmittance for UV light (typically 20 to 50%). The prototype used in the present experiments has been developed for a space mission of the European Space Agency and therefore the top Al layer is not protected. Due to this it is operated in a hydrocarbon-free vacuum chamber with a 1 mm thick fused silica entrance window to protect the Al from hydrocarbon and dust. The spectral responsivity and other properties of such diamond diodes has previously been characterized by BenMoussa et al. [23] using various lamps. The absolute spectral responsivity has been measured by the Physikalisch-Technische Bundesanstalt (Berlin) using synchrotron radiation at the storage ring BESSY II.

As the photon energy exceeds the band gap, the photoresponsivity increases by several orders of magnitude, as shown in Fig. 1 for one of the diodes from the production series. In the spectral range from about 230 to 450 nm, the single photon response is thus suppressed by four to five orders of magnitude compared to photon energies above the band gap, permitting a use as nonlinear detector.

 

Fig. 1 Spectral responsivity of a diamond pin diode from the production series used in our experiments.

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To successfully use the diamond diode as nonlinear detector for UV pulses it is important to verify that the free-carrier-generation at the wavelength of interest is dominated by the absorption of two photons (TPA) as this is a second-order process. In contrast to this, the absorption of a single photon is a linear process and therefore has to be much less efficient than the TPA to ensure the non-linear characteristics required for autocorrelation measurements.

The experiments are carried out with a Ti:sapphire multipass amplifier system delivering pulses of 1.1 mJ energy and a duration of 28 fs centred around 793 nm at a repetition rate of 6 kHz [24]. For second harmonic generation a 250$\mu \text{m}$ thick BBO crystal is used, resulting in pulse energies of about 100$\mu \text{J}$centered around 401 nm. The third harmonic with about 3$\mu \text{J}$pulse energy is generated by sum frequency generation of the second harmonic and the fundamental laser beam in another BBO crystal of 100$\mu \text{m}$thickness. The corresponding harmonics are separated from the remaining fundamental beam using dichroic mirrors. No attempts have been made to compensate the dispersion introduced by the non-linear crystals by re-compressing the generated harmonics with a prism pair. A concave mirror focuses the corresponding harmonic laser pulses to a spot size of 80$\mu \text{m}$ and the diode is placed in its focal point. The diode is used in photovoltaic mode to avoid any dark current, and the photocurrent is simply measured with a picoammeter (Model 6485, Keithley Instruments Inc.).

For both the violet and the UV radiation the generated photocurrent is measured for various incident pulse energies. In this measurement the beam is attenuated using fused silica wedges and a half-wave plate to adjust the pulse energy by changing the polarization. Figure 2 shows in a double logarithmic plot the photocurrent generated in the diamond diode at various incident pulse energies for the second (blue triangles) and third harmonic (black squares) of the Ti:sapphire laser system. The slope of the fit is determined to ($1.98\pm 0.05$) at 401 nm, measured over the range from 2 to 28 nJ, and to ($1.95\pm 0.09$) for 265 nm at pulse energies between 2 and 13 nJ. This indicates a quadratic response of the diode at both 265 nm and 401 nm within this range of comparatively low pulse energies. As the photoresponse of the diode dramatically increases at wavelengths shorter than about 225 nm, it is therefore applicable as non-linear detector for wavelengths between 450 and 225 nm at pulse energies of a few nJ.

 

Fig. 2 Generated photocurrent for the second harmonic (blue triangles) and the third harmonic (black squares) at different pulse energies. The lines represent the best fit for each wavelength with slopes of 1.98 for 401 nm and 1.95 for 265 nm.

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To compare the consistency of our measurement with previous experiments we calculate the two photon absorption coefficient β, which is given by

For the measurements at 401 nm ($h\nu$ = 3.1 eV), we record N_e = 5.2 x 10⁵ electrons per pulse at a fluence of 0.4 mJ/cm² (pulse energy of 20 nJ). The interaction length is given by the thickness of the intrinsic layer of the diode, therefore L = 700 nm. The focal area amounts to A = 5x10⁻⁵cm² and the pulse duration to ${\tau }_p=34\text{fs}$as described in the following section, taking into account the dispersion of the entrance window to the vacuum chamber. As the precise thickness of the aluminum layer is unknown, a transmission of 20 to 50% as described by BenMoussa et al. [23] is assumed, which correspondingly reduces the fluence impinging on the active layer of the pin diode. With the corrected fluence the measured values correspond to a two-photon absorption coefficient in the range of β₄₀₁ = 0.26…1.7 cm/GW. At 265 nm ($h\nu$ = 4.7 eV), the generated photocurrent corresponds to N_e = 2.9 x 10⁵ electrons per pulse at a fluence of 0.25 mJ/cm² and a pulse duration of ${\tau }_p=63\text{ fs}$. With the same assumption for the transmission of the aluminum layer as for 401 nm, these values indicate a two-photon absorption coefficient of β₂₆₅ = 1.0 …6.1 cm/GW.

Other experiments at different wavelengths found β to be $1.6\pm 0.3$cm/GW for 248 nm [25], $0.75\pm 0.15$cm /GW for 310 nm [11], 0.3 cm/GW for 354.7 nm and <0.26 cm/GW for 532.1 nm [26]. Assuming the transmission of the aluminum layer of our diode sample to be close to 50%, the two-photon absorption coefficients obtained from our experiment are in very good agreement with those observed in previous experiments.

3. Autocorrelation and pulse reconstruction

In this study the duration and temporal shape of femtosecond UV pulses shall be characterized, which therefore requires also the determination of the spectral phase of the laser pulses. Then the pulse duration at a sample to be investigated by the UV pulses may be estimated by taking into account the dispersion of all optical components between the laser output and the sample. As described in the introduction knowledge about the spectral phase of a laser pulse can be gained from a simple autocorrelation measurement by implementing an iterative algorithm that reconstructs the phase from simultaneous measurements of the spectrum and the autocorrelation. Autocorrelations are recorded using a Michelson-type interferometer with two beam splitters and retroreflectors as proposed by Spielmann et al. [27] (Fig. 3 ). This ensures that both pulses propagate through the same amount of material and experience the same amount of dispersion. It also offers a second output enabling us to simultaneously record the second-order interferometric autocorrelation with the diamond diode at one output and the linear interferogram with a Si-diode (Hamamatsu S1336-BQ) at the second output. The path difference of the two interferometer arms is measured by simultaneously recording the interferences of a He-Ne laser with its beam propagating parallel to the pulsed laser beam with another Si-diode (Hamamatsu S5793) in order to eliminate the influence of drifts of the piezo transducer on the measurement.

 

Fig. 3 Layout of the interferometer. M: Mirrors, BS: Beam splitter, HeNe: Helium-neon laser, 266/400 nm: Pulsed laser

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From these measurements the pulse is reconstructed in the time domain using an iterative algorithm derived from the IRIS formulation [3]. The flowchart of this reconstruction algorithm is shown in Fig. 4 . At first, the spectrum of the pulse is calculated from the linear interferogram using a Fourier transformation. From the square root of the intensity the amplitude of the electric field $\left|E(\omega )\right|$ is obtained. Starting with a random phase${\phi }_{test}(\omega )$ a possible electrical field $E_{try}(\omega )$ is calculated from the amplitude and transformed to the time domain by an inverse Fourier transformation. Convolving the squared electric fields then provides the theoretical second order autocorrelation of$E_{try}(t)$, which is then compared to the measured autocorrelation by means of the relative variance over the whole autocorrelation trace. The initial phase ${\phi }_{test}(\omega )$ is then refined by a genetic and a simplex algorithm until the convergence criteria are met.

 

Fig. 4 Flowchart of the iterative algorithm used to recover the spectral phase of the pulses. FT: Fourier transform, IFT: inverse Fourier transform, shaded boxes: measured data

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As the second order autocorrelation is ambiguous in time a single autocorrelation is not sufficient to fully reconstruct the temporal structure of the pulse. Therefore another autocorrelation is recorded directly after the first one, but with a dispersive element of known dispersion in the path of the beam. This measurement is simultaneously processed by the algorithm taking into account the difference in dispersion introduced by the fused silica block. Because the time direction is only determined by the algebraic sign of the phase, this additional measurement removes the ambiguity [28]. Additionally, the influence of all dispersive elements, such as the beam splitters and the entrance window of the vacuum chamber in which the diamond diode is placed, is also subtracted from the result to reconstruct the original pulse before passing through these elements. This part of the reconstruction algorithm also enables us to properly calculate the pulse duration and its temporal structure at the experiment by taking all dispersive elements into account.

3.1 Fundamental pulse

As a test of the accuracy of the algorithm we first recorded an autocorrelation of the fundamental laser beam using the same set-up and a GaAsP diode (Hamamatsu G1115). The results obtained for the reconstructed pulse and spectrum are directly compared with those from a commercial SPIDER system (APE) and a spectrometer (Ocean Optics HR 4000). Figure 5(a) shows the recorded linear interferogram. The calculated spectrum agrees with a measurement using the commercial spectrometer (Fig. 5(b)). The second-order autocorrelation at the fundamental wavelength with a FWHM of 72 fs is shown in Fig. 6(a) , with the reconstructed autocorrelation (blue line) compared to the measurement (dots) shown in Fig. 6(b). As autocorrelations are symmetric, only one half of the reconstruction is shown to facilitate an evaluation of the quality of the retrieval, and the inset shows a detail of the fringes. The FWHM of the autocorrelation corresponds to a pulse duration of $\tau =47\text{\hspace{0.17em}fs}$ assuming a Gaussian pulse shape, and to a duration of $\tau =38\text{\hspace{0.17em}fs}$ assuming a squared secans hyperbolicus pulse shape.

 

Fig. 5 (a) Recorded interferogram at the fundamental wavelength. (b) Spectrum recovered from the interferogram with a central wavelength of 793 nm and a FWHM of 23 nm (blue dots) compared to the measurement of a commercial spectrometer (black line).

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Fig. 6 (a) Measured second-order autocorrelation trace at the fundamental wavelength of 793 nm. (b) Reconstruction (line) compared to the measurement (dots). Inset: Detail of the fit.

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In the spectral regions of high intensity the reconstructed phase shows good agreement with the result of the commercial SPIDER (Fig. 7(a) ). The discrepancy in the wings of the spectrum may be accounted for by either an inaccuracy of the SPIDER measurement due to very low intensity of the SPIDER signal in these regions or by instabilities of the laser, resulting in an incorrect extrapolation of the phase. This conjecture is supported by the on-line view of the SPIDER measurement, where it is observed that the measured phase rapidly flips up and down in the regions of low intensity (λ < 765 nm and λ > 814 nm).

 

Fig. 7 (a) Spectrum (red line) and spectral phase recovered using the iterative algorithm (blue line) compared to spider measurement (black dots). (b) Resulting pulse extracted from the autocorrelation.

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Figure 7(b) shows the temporal shape of the pulse obtained from the spectrum and the iteratively reconstructed phase. The duration of $\tau =44\text{\hspace{0.17em}fs}$ FWHM is in good agreement with the rough estimate from the FWHM of the autocorrelation. As there is no fundamental difference in the way the algorithm works at other wavelengths, the reliability of the reconstruction should only differ slightly when using the second and third harmonic wavelengths, albeit the higher noise level may increase uncertainties.

3.2 Noise sensitivity of the algorithm

In order to estimate the accuracy and reliability of the algorithm we simulated autocorrelation measurements with noise added, using real spectra measured within this work and applying a known spectral phase. The simulations have been carried with multiplicative white noise added to the artificial autocorrelation trace. Noise levels of up to 40% of the local amplitude have been added. In the 10 to 30% noise range, thereby far exceeding the noise in the real measurements, these simulations show very good agreement of the retrieved phase with the input target phase, regardless of the starting value for ${\mathrm{\phi }}_{\text{test}}$. As an example, Fig. 8(a) shows the target phase (black dashes), the retrieved phase (blue line) and the spectral intensity of the pulse at 401 nm (red line) for a noise level of 30%. The retrieved phase shows an rms error of 0.8% at 30% noise level. Most of the small deviations from the target phase are in areas of very low spectral intensity (412 to 420 nm). Figure 8(b) shows in a logarithmic plot the influence of the error of the phase retrieval on the retrieved pulse (black line) compared to the target pulse (red dashes), with a linear plot of the reconstructed pulse shown in the inset.

 

Fig. 8 (a) Spectrum (red line), target spectral phase (black dashes) and spectral phase retrieved at 30% white noise level by the iterative algorithm (blue line). (b) Resulting target pulse (red dashes) and reconstructed pulse (black line) in a logarithmic plot. Inset: reconstructed pulse in a linear plot.

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The algorithm applied should therefore be reliable for the noise levels of this experiment. At noise levels of 40% the retrieved phase becomes more sensitive to starting values for ${\mathrm{\phi }}_{\text{test}}$, and slightly more inaccurate and unreliable with rms errors of up to 10%. Simulations for artificial 265 nm pulses yielded the same results regarding the phase retrieval errors as those for 401 nm.

In all experiments conducted with our set-up the retrieval of the spectrum from the linear interferogram was found to be very insensitive to noise levels and slight asymmetries between the minimum and maximum values and always agreed well with measurements carried out with the commercial CCD spectrometer. Therefore the retrieval is limited by the noise in the second-order autocorrelation rather than by that in the linear interferogram.

3.3 Second harmonic pulse

The second-order autocorrelation at the second harmonic Ti:sapphire wavelength recorded with the diamond pin diode is shown in Fig. 9(a) . The best fit (blue line) to the measurement (black dots) is shown in Fig. 9(b) with a display of individual fringes in the inset. In a simple estimate the FWHM of the autocorrelation of 64 fs corresponds to pulse durations of $\tau =42\text{\hspace{0.17em}fs}$ assuming a Gaussian pulse shape and $\tau =34\text{\hspace{0.17em}fs}$assuming a sech²-shaped pulse. As expected, the fringe separation is now reduced to 1.34 fs. Measurements are taken in steps of about 72 as, thus each fringe is obtained from about 19 data points. The contrast ratio of the measured autocorrelation is 8:1 as expected for second-order interferometric autocorrelations. Fluctuations of the laser pulse energy during the measurement are the reason for the noise in the measurement, which is evident especially in the wings of the autocorrelation trace. This experiment was carried out at pulse energies of about 20 nJ with a focal diameter of 80$\mu \text{m}$, corresponding to a fluence on the diamond pin diode of $0.4\text{\hspace{0.17em}mJ}/{\text{cm}}^2$.

 

Fig. 9 (a) recorded autocorrelation of the Ti:sapphire second harmonic. The FWHM of 64 fs indicates a pulse width of 42 fs or 34 fs when assuming a Gaussian or a sech² pulse shape, respectively. (b) Fit of the data (blue line) compared to the measurement (dots). Inset: detail of the fit.

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The spectrum at this wavelength is calculated from the linear interferogram recorded at the second output of the interferometer, as described in the previous section. The central wavelength is ${\lambda }_0=401\text{\hspace{0.17em}nm}$with a spectral width of $\mathrm{\Delta }\lambda =10.4\text{\hspace{0.17em}nm}$FWHM (blue line, Fig. 10(a) ). Assuming no phase modulation, this corresponds to a transform-limited pulse with a duration of about $\tau =22\text{\hspace{0.17em}fs}$. The spectral phase reconstructed from the spectrum and the autocorrelation is mostly determined by even-order phase terms with a small odd-order contribution (red dashed line, Fig. 10(a)). This leads to a longer and slightly asymmetric pulse with a duration of $\tau =29\text{\hspace{0.17em}fs}$ FWHM as shown in Fig. 10(b). The seeming discrepancy between the actual pulse duration and the rough estimation from the width of the autocorrelation arises from the fact that in the pulse reconstruction the dispersion of the beam splitters in the autocorrelator and the window to the vacuum chamber has been taken into account, as described above.

 

Fig. 10 (a) Spectrum (solid line) and spectral phase (dashed line) of the second harmonic output. (b) resulting temporal shape of the pulse.

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3.4 Third harmonic pulse

The autocorrelation of the third harmonic at ${\lambda }_0=265\text{\hspace{0.17em}nm}$recorded with the diamond diode is shown in Fig. 11(a) . It suffers from a slight asymmetry due to a drift of the fundamental beam within the pulse compressor. At this wavelength a long integration time is needed as the fluctuations of the pulse energy become more prominent due to the two nonlinear processes involved. Nevertheless, an 8:1 ratio between background and the extrema around zero delay of the autocorrelation trace can clearly be noticed. Assuming a Gaussian pulse shape the width of the autocorrelation of 105 fs FWHM corresponds to a pulse duration of $\tau =69\text{\hspace{0.17em}fs}$ and to a duration of $\tau =56\text{\hspace{0.17em}fs}$assuming a squared secans hyperbolicus pulse shape. The best fit (blue line) to the measured autocorrelation (black dots) is shown in Fig. 11(b), with a display of individual fringes in the inset.

 

Fig. 11 (a) Autocorrelation of the third harmonic at ${\lambda }_0=265\text{\hspace{0.17em}nm}$, the FWHM of 105 fs indicates a pulse duration of 69 fs for gaussian shaped pulses and 56 fs for sech²-shaped pulses. (b) Calculated trace (line) compared to the measurement (dots). Inset: Detail of the fit.

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The fringe separation is now reduced to 884 as, while in this measurement the step size is only slightly reduced to about 65 as. This still allows for a good resolution due to more than 13 data points per fringe and yields enough total delay to record the whole autocorrelation trace with the 12 bit ADC used to record the delay steps. For this measurement average pulse energies of about 16 nJ have been used with the same focal diameter as before, resulting in a fluence of $0.3\text{\hspace{0.17em}mJ}/{\text{cm}}^2$.

As second-order autocorrelation traces are symmetric the algorithm is not able to properly reconstruct the whole measurement and therefore only the right half is used to recover the phase. Owing to the symmetry of ideal traces no information is lost when clipping the measurement at zero delay.

The spectrum obtained from the linear interferogram is shown in Fig. 12(a) . It shows a FWHM of $\mathrm{\Delta }\lambda =2.2\text{\hspace{0.17em}nm}$and is centered around ${\lambda }_0=265\text{\hspace{0.17em}nm}$. The width and the structure of the spectrum allow for pulses as short as $\tau =24.6\text{\hspace{0.17em}fs}$assuming transform limited pulses. Odd-order terms now dominate the spectral phase (red dashed line, Fig. 12(a)), leading to several small post-pulses and a longer pulse duration of $\tau =41\text{\hspace{0.17em}fs}$FWHM as shown in Fig. 12(b). As the dispersion of fused silica is stronger at this wavelength and the pulse propagates through more material than at 401 nm due to thicker beam splitters, the reconstructed duration of the UV pulse differs more significantly from the rough estimate. This demonstrates the advantage of the pulse reconstruction over simple autocorrelation measurements, as the material dispersion of the autocorrelation set-up becomes very strong in the UV and is therefore no longer negligible.

 

Fig. 12 (a) Spectrum of the third harmonic centred around 265 nm with a width of 2.2 nm (solid line) and reconstructed spectral phase (dashed line). (b) Resulting pulse with a duration of 41 fs.

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4. Conclusion

We have successfully employed a diamond pin photodiode as non-linear detector for autocorrelations at both the second and third harmonic of Ti:sapphire laser radiation with incident pulse energies down to a few nJ. From the recorded interferometric autocorrelations it is possible to reconstruct the laser pulses for a complete temporal characterization. The large band gap of these diodes allows to employ them in the wavelength range between 450 and 225 nm. Recent advances in non-collinear optical parametric amplifier (NOPA) techniques make this wavelength range readily available for femtosecond pulses.