Two-dimensional spectral interferometry in the extreme-ultraviolet enabled by computational phase-stabilization

One of the largest branches of modern optics is laser technology, which offers a wide range of applications in industry, medicine and research. In particular, the generation of subpicosecond laser pulses has greatly expanded the possibilities for the application of laser systems. An important milestone in the development of pulsed laser systems was the chirped pulse amplification (CPA) principle developed by Strickland and Mourou in 1985 [1], which earned them the Nobel Prize in 2018. The high peak powers that can be achieved by lasers employing the CPA schemes are used e.g. for experiments aiming at laser-driven proton acceleration. Such experiments are performed at the high intensity laser system POLARIS (Petawatt Optical Laser Amplifier for Radiation Intensive Experiments) which is operated at the Helmholtz Institute Jena. In order to characterize the plasma conditions during such experiments very precisely, an independent pump-probe setup is currently being developed. With this setup the precise characterization of the formation and temporal evolution of the plasma target becomes possible. For the plasma characterization setup, a CPA system consisting of a pulse stretcher, regenerative amplifier and pulse compressor is being developed. In order to characterize the pre-plasma, knowledge of the temporal shape of the laser pulse is important. One of the main big issues is the measurement of ultra short laser pulses with durations of 50 fs, which is shorter than the response time of any electronic detector. In order to measure such kind of laser pulses, a reference pulse with a comparable duration can be used to sample the pulse to be measured by a suitable detector. Such a sample pulse can be the pulse itself or another well characterized femtosecond laser pulse [2]. It is important to measure both amplitude and phase of the spectrum, although it is usually not possible to measure the latter directly. One of the most effective methods of laser pulse characterization is called spectral interferometry (SI) which was pioneered by Froehly et al. in 1973 [3]. It offers the p ossibility to measure the spectral phase and has attracted the attention of researchers because of its large sensitivity and high spectral resolution.SI has many applications in spectroscopy [4], plasma probing [5], characterization of dispersion, studies of nonlinear processes [6], materials and characterization of crystals [7]. SI is also the basis for new techniques of spectral phase measurement, such as frequency resolved optical gating (FROG) [2] or spectral phase interferometry for direct electric field construction (SPIDER) [8]. In section 2 of this Bachelor thesis, the fundamentals of ultrafast optics based on Maxwell’s equations are presented, Gaussian beams, optical pulses and their propagation in dispersive media are introduced. The method of spectral interferometry (SI) is fundamentally introduced and explained in section 3, different possibilities for characterizing the spectral phase are presented. The experimental setup for the characterization and a referencing measurement to well characterized materials is done in section 4. It is also investigated in section 4 which experimental issues can occur, how large their influences on the measurement are and how they can be resolved. The derived methods of spectral phase characterization are used in section 5 to specify the optical components of an amplifier in a CPA laser system. The components of the laser amplifier are categorized and their effects on the spectral phase are compared and discussed. It is then summarized why dispersion measurements are important and how the method of SI can be utilized to select suitable components for a laser amplifier.

A fast implementation of the Gabor wavelet transform for phase retrieval in spectral interferometry is discussed. This algorithm is experimentally demonstrated for the characterization of a supercontinuum, using spectral phase interferometry for direct electric-field reconstruction (SPIDER). The performance of wavelet based ridge tracking for frequency demodulation is evaluated and compared to traditional Fourier filtering techniques. It is found that the wavelet based strategy is significantly less susceptible toward experimental noise and does not exhibit cycle slip artifacts. Optimum performance of the Gabor transform is observed for a Heisenberg box with unity aspect ratio. As a result, the phase jitter of 60 individual measurements is reduced by about a factor 2 compared to Fourier filtering, and the detection window increases by 20%. With an optimized implementation, retrieval rates of several 10Hz can be reached, which makes the fast Gabor transform a superior one-to-one replacement even in applications that require video-rate update, such as a real-time SPIDER apparatus.

New results in spectral interferometry are presented. The effect of imperfect calibration of the optical spectrometer is demonstrated both theoretically and experimentally. It is shown in particular that slight calibration imperfections can lead to mistakes because of the principle of spectral interferometry itself. Efficient methods are demonstrated to overcome this problem and to provide spectrometer calibration with a precision far superior to the instrument’s optical resolution. Results for spectral phase interferometry for direct electric-field reconstruction are also demonstrated.

Intense mid-infrared pulses tunable between 5 and 14 µm with pulse energies of several microjoules were generated by difference-frequency mixing (DFM) in a GaSe crystal. Longer wavelengths (up to 18 µm) were achieved by DFM in a CdSe crystal. The infrared pulses were then characterized using various techniques: The spectrum was measured using a Fourier-transform spectrometer, which was then modified to determine the interferometric second-order autocorrelation. The electric field spectral phase was measured using the same setup, thus leading to a full characterization of the mid-infrared pulses. The spectral phase was measured using the time-domain homodyne optical technique for spectral phase interferometry for direct electric field reconstruction, where spectral interferometry was replaced with time-domain interferometry. The measured pulse duration was 100 fs, nearly transform limited.

A novel variant of spectral phase interferometry for direct electric-field reconstruction (SPIDER) is introduced and experimentally demonstrated. Unlike most previously demonstrated variants of SPIDER, our method is based on a third-order nonlinear optical effect, namely self-diffraction (SD), rather than the second-order effect of sum-frequency generation. On the one hand, SD substantially simplifies phase-matching capabilities for multioctave spectra that cannot be hosted by second-order processes given manufacturing limitations of crystal lengths in the few-micrometer range. However, on the other hand, SD SPIDER imposes an additional constraint as it effectively measures the spectral phase of a self-convolved spectrum rather than immediately measuring the fundamental phase. Reconstruction of the latter from the measured phase and the spectral amplitude of the fundamental turns out to be an ill-posed problem, which we address by a regularization approach. We discuss the numerical implementation in detail and apply it to measured data from a Ti:sapphire amplifier system. Our experimental demonstration used 54 fs pulses and a 500 μm thick BaF2 crystal to show that the SD SPIDER signal is sufficiently strong to be separable from stray light. Extrapolating these measurements to the thinnest conceivable nonlinear media, we predict that bandwidths well above two optical octaves can be measured by a suitably adapted SD SPIDER apparatus, enabling the direct characterization of pulses down to single-femtosecond pulse durations. Such characteristics appear out of range for any currently established pulse measurement technique.

In this work, we study the effects of noise present on spectral interferometry signals, for femtosecond pulse retrieval such as in the SPIDER technique (spectral phase interferometry for direct e-field reconstruction). Although previous works report SPIDER robustness, we have found that noisy signals with low signal-to-noise ratio (SNR), in the acquired spectral interferogram, could cause variations in the temporal pulse intensity retrieval. We demonstrate that even in a filtered SPIDER signal, following standard procedures, at some point the noise on the spectral interferogram could affect the spectral phase retrieval. As a novel alternative for spectral interferograms filtering, we have applied the wavelet transform and propose a target criterion to automatize the optimization algorithm. We apply this method on SPIDER signals and analyze its effectiveness on the spectral phase retrieval. We present numerical and experimental results to show the improvement in the phase retrieval and the temporal pulse reconstruction after applying this filtering method and compare the results with a standard method.

Mid-infrared ultrashort pulses of 9.2-microm center wavelength are characterized in both amplitude and phase. This is achieved by use of a variant of spectral phase interferometry for direct electric field reconstruction in which spectral interferometry has been replaced with time-domain interferometry, a technique that is well suited for infrared pulses. The setup permits simultaneous recording of the second-order interferometric autocorrelation, thus providing an independent check on the retrieved spectral phase.

The frequency dependence of the group delay of both a pulse stretcher and a stretcher–compressor system of a chirped pulse amplification laser is determined with a two-dimensional extension of a spectral interferometric method called the stationary phase point method. The 800-nm, 15-fs probe pulse from a Ti:S oscillator propagates through the stretcher or the stretcher–compressor system. The reference pulse is one of the subsequent oscillator pulses but passes the system and interferes with the probe pulse; hence, a Mach–Zehnder-type interferometer is formed. The shape of the spectrally resolved interference fringes is peculiar to the amount and sign of the relative dispersion properties of the pulses. Group-delay dispersion is obtained from the observation of the position of the stationary phase point in spectrally resolved interferograms at different time delays. This simple method allows for an almost complete and fast alignment of the stretcher–compressor system from scratch until the final adjustments.

Nonlinear propagation through optically transparent media is characterized using two-dimensional spectral interferometry. Spatio-temporal coupling and differences in nonlinear effect versus the polarization state are quantified.

Two-dimensional spectral interferometry is a linear, real-time method for spatio-temporal beam characterization. It is used here to measure the spatio-temporal structures induced by a 2D pulse shaper and to enhance a time-resolved spatial phase measurement.

We report on coherent synthesis of two ultra-broadband optical parametric amplifiers, each compressed by chirped mirror pairs, resulting in almost-octave-spanning (520-1000 nm) spectra supporting nearly single-cycle sub-4 fs pulse duration. Synthesized pulse timing is locked to less than 30 as by a balanced optical cross-correlator. The synthesized pulse is characterized by two-dimensional spectral interferometry and has a 3.8 fs duration.

In this work, we present a two-dimensional extension of the stationary phase point (SPP) method which is suitable for measuring the group-delay dispersion (GDD) of a stretcher or a compressor. The light path in the chirped-pulse amplification (CPA) laser is completed to form a Mach-Zehnder type interferometer, and only the stretcher is placed in the sample arm. The recombined pulses from the interferometer are sent to the entrance slit of an imaging spectrograph. The group delay as a function of wavelength can be determined from the position of the center of the spectrally resolved interference (SRI) fringes.

Pulse train instabilities have been a plaguing problem in the era of dye lasers, when coherent artifacts have frequently been misinterpreted as a repetitive train of coherent and short pulses. While the coherent artifact has often been considered an obsolete problem after dye lasers had been replaced with solid-state lasers, recent debates about self-mode-locked semiconductor lasers clearly indicate the opposite. Moreover, numerical investigations of several instability scenarios indicated that autocorrelation based pulse characterization techniques including FROG have a clear edge over those that are based on spectral interferometry [1]. In fact, it has been claimed that spectral phase interferometry for direct electric-field reconstruction (SPIDER), as the prototypical example of a spectral-interferometry based technique, measures only the coherent artifact. In the following, we show that SPIDER measurements hold some hidden information on pulse train instability, which is normally discarded in the interpretation of measured SPIDER traces. In particular, we address the case of an instability of the chirp of the pulse, i.e., fluctuations of the group delay dispersion (GDD). For this case, SPIDER shows a remarkable sensitivity whereas autocorrelation-based techniques do not appear overly susceptible to this instability.

We develop a method capable of characterizing both the amplitude and phase of ultrafast optical pulses with the aid of a synchronized incoherently-related clock pulse based on a novel variation of SPIDER. It exploits degenerate four-wave-mixing and its design is amenable for full ?on chip? signal characterization. By implementing our method in a CMOS compatible waveguide, we measure pulses with 1THz, and up to 100ps pulsewidths. Our novel reconstruction algorithm that we call Fresnel-Limited Extraction Procedure (FLEA), yields a time-bandwidth product (TBP)>100. Full Text: PDF References R. Trebino, "Frequency Resolved Optical Gating: the Measurement of Ultrashort Optical Pulses", (Kluwer Academic, 2002) [CrossRef] I. A. Walmsley and C. Dorrer, "Characterization of ultrashort electromagnetic pulses", Adv. Opt. Photon. 1, 308-437 (2009) [CrossRef] Nature Photonics Workshop on the future of optical communication,Tokyo, Oct. 2007. M. A. Foster et al.,"Silicon-chip-based ultrafast optical oscilloscope", Nature 456, 81-84 (2008) [CrossRef] E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz., "Ultrafast pulse characterization using cross phase modulation in silicon", Appl. Phys. Lett. 95, 051101 (2009) [CrossRef] A. Pasquazi et al.,"Sub-picosecond phase-sensitive optical pulse characterization on a chip", [CrossRef] C. Iaconis and I.A. Walmsley,"Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses", Opt. Lett., 23, 792-794 (1998) [CrossRef] L. Gallmann et al.,"Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction", Opt. Lett., 24, 1314-1316 (1999) [CrossRef] C. Dorrer et al.,"Single-shot real-time characterization of chirped-pulse amplification systems by spectral phase interferometry for direct electric-field reconstruction", Opt. Lett., 24, 1644-1646 (1999) [CrossRef] D. Keusters et al.,"Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components", J. Opt. Soc. Am. B, 20, 2226-2237 (2003) [CrossRef] M. Hirasawa et al.,"Sensitivity improvement of spectral phase interferometry for direct electric-field reconstruction for the characterization of low-intensity femtosecond pulses", Appl. Phys. B, 74, S225-S229 (2002) [CrossRef] J. Wemans, G. Figueira, N. Lopes and L. Cardoso,"Self-referencing spectral phase interferometry for direct electric-field reconstruction with chirped pulses", Opt. Lett., 31, 2217-2219 (2006)Self-referencing spectral phase interferometry for direct electric-field reconstruction with chirped pulses [CrossRef] M. Peccianti et al.,"Subpicosecond optical pulse compression via an integrated nonlinear chirper", Opt. Express, 18, 7625-7633 (2010) [CrossRef] A. Pasquazi et al.,"All-optical wavelength conversion in an integrated ring resonator", Opt. Express 18, 3858-3863 (2010) [CrossRef]

We present a new method for measuring the spectral phase of ultrashort pulses that utilizes spectral shearing interferometry with zero delay. Unlike conventional spectral phase interferometry for direct electric-field reconstruction, which encodes phase as a sensitively calibrated fringe in the spectral domain, two-dimensional spectral shearing interferometry robustly encodes phase along a second dimension. This greatly reduces demands on the spectrometer and allows for complex phase spectra to be measured over extremely large bandwidths, potentially exceeding 1.5 octaves.