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Today the generation of frequency combs nearly exclusively relies on passive mode-locking, requiring a phase lock between the longitudinal modes of a laser. In order to overcome the non-equidistance of the cold cavity modes, it is generally considered mandatory to include an effective saturable absorption mechanism in the laser cavity. However, there exist a number of experimental demonstrations of mode-locking or comb formation in which saturable absorption was clearly absent. Here we show that four-wave mixing may equally well lead to a mode-locking effect. However, the resulting pulse trains are only partially coherent, and the comb structures lack perfect equidistance. Operation of lasers in the pseudo mode-locked regime can easily be confused with traditional mode-locking. We discuss indications and characterization approaches for unveiling pseudo mode-locking as well as limitations for application of pseudo combs.

Since the advent of mode-locked laser frequency combs, metrology has experienced a rapid improvement of the precision in frequency measurements. Best reported microwave-based measurements with cesium fountain clocks reached a fractional uncertainty of 10 -15 in 2005 [1] . In 2010 optical frequency measurements took the lead, and more recent experiments with optical lattice clocks reached 10 -18 values. Frequency transfer experiments even demonstrated sub 10 -20 levels [2] . Fractional uncertainities currently decrease at the pace of one order of magnitude every 4 years. If this Moore’s Law of frequency metrology continues at the same rate, one expects to see 10 -22 uncertainties at the end of this decade. Similar to Moore’s Law, however, the question arises for how long this trend can further continue before some fundamental physical mechanism eventually causes stagnation. And one such fundamental barrier arises due to Schawlow-Townes noise in the mode-locked laser, causing a 1/ f -like drift mechanism between two independent frequency combs.

Amplified spontaneous emission (ASE) causes fluctuations of pulse energy, of the optical phase and of the timing of the pulse intensity envelope in a mode-locked laser or frequency comb. Starting from the assumption of one ASE photon per longitudinal laser mode and roundtrip, we rederive analytic equations for the three fundamental types of quantum noise in a laser. To this end, we analyze the interference of the coherent intracavity field and a spectrally localized ASE photon as a function of wavelength and phase of the latter. Performing an integration over all wavelengths and phases and taking stochastic noise into account, we compute ASE-induced jitters for all quantities considered. Continuing this approach, we then derive an expression for the resulting carrier-envelope phase noise of the comb, for which so far only numerical estimates exist. We further compute analytical estimates for ASE induced pulse chirp and duration variations and address the issue of resulting pulse contrast in a mode-locked laser and the resulting coherence properties. Considering three example cases, we finally compute estimates for all quantities analyzed. Taken together, our analysis provides a comprehensive view of ASE effects in a mode-locked laser, which unites numerous scattered reports across the literature.

Microresonator combs have revolutionized the field of frequency metrology, replacing bulky mode-locked laser setups with chip-scale devices. While these novel comb sources have demonstrated their usefulness in numerous applications the exact nature of the mode-locking process in these devices appears to be not fully understood as it is commonly believed that synchronization between laser modes can only be achieved in the presence of an effective saturable absorber inside cavity. In the absence of saturable absorption, one would therefore expect that soliton solutions of the Haus master equation are not unconditionally stable against residual third-order dispersion. Consequently, deviations from a perfect equidistance may arise. Here we show that four-wave mixing processes can, to some extent, take over the role of saturable absorption and lead to a synchronization of modes. Within a certain range of dispersions, stable soliton solutions can be found not only in the anomalous dispersion regime, but also for zero, normal, or third-order dispersion. However, if the soliton conditions are not exactly matched, breather solutions form, and the resulting combs show deviations from equidistance.

We experimentally demonstrate how the optical Doppler effect can be exploited to modulate the carrier-envelope frequency of a mode-locked laser without causing detrimental side-effects and without any intervention into the laser.

Self-mode-locking of semiconductor lasers has been frequently reported, defying all known solutions of the Haus Master Equation approach. Here we show that four-wave mixing all by itself suffices to mode-lock a laser.

Controlling the CEP in mode-locked lasers over long timescales is crucial for real-world applications. We present a hybrid stabilization system in an Er: Yb:glass mode-locked laser with 75 hours of stabilization and IPN below 14 mrad.

Controlling the CEP in mode-locked lasers over long timescales is crucial for real-world applications. We present a hybrid stabilization system in an Er:Yb:glass mode-locked laser with 75 hours of stabilization and IPN below 14 mrad.

Carrier envelope phase (CEP) stabilization has proven an indispensable tool in attosecond science [1, 2] and precision frequency metrology [3]. Although fully CEP stabilized mode-locked fiber lasers and Ti:sapphire lasers are commercially available, CEP stabilization and all-optical frequency synthesis are still far away from general applicability to any given mode-locked laser. Stabilizability ultimately relies on the availability of at least 10 photons per pulse in the detection scheme [4]. Astro-combs, e.g., are rather demanding in this regard as they require ultra-high repetition rates. Moreover, despite their high pulse energies, thin-disk lasers have proven notoriously difficult to stabilize. Here we demonstrate that introduction of active optical gain into the infrared arm of an f-to-2f interferometer [5] can boost the signal by up to 20 dB, making stabilization of notoriously unstabilizable mode-locked lasers possible, e.g., high repetition-rate oscillators or thin-disk lasers.

Carrier-envelope phase (CEP) stabilization plays an important role in the field of attosecond pulse generation and high-field physics [1]. Low-jitter CEP stabilization of ultrashort pulses typically relies on active stabilization schemes, either employing feedback or feed-forward control. However, both established methods come with a detrimental side effect. Feedback control directly modulates pump power or intracavity loss, which causes unwanted power fluctuations of the laser output. While feed-forward control does not corrupt the output stability, it nevertheless induces beam pointing variations in the acousto-optic frequency shifter employed. Here we demonstrate a novel method for modulating the CEP of a laser oscillator, which is based on the Doppler effect and displays neither of the above-mentioned side-effects.

Frequency combs have revolutionized frequency metrology, enabling optical clockworks with unprecedended precisions approaching the 10−18 range [1]. Early frequency comb measurements exclusively relied on mode-locked lasers, which provide a periodic waveform as a matter of working principle. In turn, the resulting frequency comb is guaranteed to be absolutely equidistant. While this expectation is ultimately based on theoretical mode-locking models, experimental tests have scrutinized deviations from equidistance of mode-locked laser combs down to the 10−15 level. Experimental tests of equidistance are rather elaborate and typically require beating of different spectral parts of the comb with a reference comb. Such tests have also been performed with microresonator combs [2], which are not a priori guaranteed to be equidistant from theoretical considerations. Finally, there are rather recent reports of quantum cascade laser combs; yet careful investigations of the equidistance of such sources still appear to be outstanding. Here we propose and demonstrate a novel experimental test for the equidistance of frequency combs.

The past 30 years have seen spectacular progress in the development of techniques for measuring the complete temporal field, and even the complete spatiotemporal field, of ultrashort laser pulses. The challenge has been to measure a pulse without the use of a shorter event or an independent known reference pulse, neither of which is typically available. We begin with autocorrelation, the first such “self-referenced” pulse-measurement method ever proposed, which measures only a rough pulse length, and we describe its limitations. One such limitation is the presence of a somewhat unintuitive “coherent artifact,” which occurs for complicated pulses and also when averaging over a train of pulses whose shapes vary from pulse to pulse. We then describe the most important modern techniques capable of measuring the complete temporal intensity and phase of even complicated ultrashort pulses, as well as their ability (or inability) to measure such unstable pulse trains. A pulse reliably measured with such a device can then be used as a reference pulse in conjunction with another technique, such as spectral interferometry or holography, to measure pulses otherwise unmeasurable by a self-referenced technique. Examples include techniques for measuring low-intensity pulse(s) and for measuring the complete spatiotemporal intensity and phase of arbitrary pulse(s). This Tutorial is limited to well-established, proven methods, but other methods whose description proves instructive will be discussed.

Controlling the carrier envelope phase (CEP) in mode-locked lasers over practically long timescales is crucial for real-world applications in ultrafast optics and precision metrology. We present a hybrid solution that combines a feed-forward technique to stabilize the phase offset in fast timescales and a feedback technique that addresses slowly varying sources of interference and locking bandwidth limitations associated with gain media with long upper-state lifetimes. We experimentally realize the hybrid stabilization system in an Er:Yb:glass mode-locked laser and demonstrate 75 hours of stabilization with integrated phase noise of 14 mrad (1 Hz to 3 MHz), corresponding to around 11 as of carrier to envelope jitter. Additionally, we examine the impact of environmental factors, such as humidity and pressure, on the long-term stability and performance of the system., 11 pages, 6 figures, 1 table; to be published in Optics Express; revisions include adjustment of some citations, additions to section 2, and added information in table 1

Spectral coherence is an important prerequisite for many applications of femtosecond supercontinua, including precision frequency metrology, attosecond science, and high-field physics. These applications often critically depend on measurement of the carrier-envelope phase via f − 2 f interferometry. As mode-locked laser sources cannot directly provide octave-spanning spectra, one typically resorts to spectral broadening in highly nonlinear optical fibers to generate the necessary spectral coverage. This process comes with a caveat, as coherence can be severely degraded in the broadening process. This degradation can be mitigated by suitable choice of a fiber dispersion profile. Here we numerically investigate prototypical fiber designs and analyze their susceptibility to coherence degradation. It is found that the generally favored soliton fission process provides the best broadening efficiency at the expense of rather scarce coherence conditions. Sufficient pulse energy provided, all-normally dispersive fiber designs fare far better in terms of spectral coherence. Finally, fiber designs with flattened normal dispersion provide the best compromise between efficiency and resulting spectral coherence. Our study indicates that the spectral width of a supercontinuum may be deceiving. Even when compressible into a short pulse, this does not automatically qualify for sufficient spectral coherence to conduct carrier-envelope-phase-sensitive experiments. The numerical simulations in this study provide a guideline for coherent spectral broadening. In turn, these guidelines may help to improve carrier-envelope phase stabilization and, in particular, to enable stabilization of laser oscillators that have previously proven difficult to stabilize.

Mode locking of a 1.34 μm vertical external cavity surface emitting laser is demonstrated using a GaSb-based semiconductor saturable absorber mirror (SESAM). The SESAM includes six AlGaSb quantum wells (QWs) with an absorption edge at ∼1.37 μm. The proposed approach has two key benefits: the QWs can be grown lattice matched, and only a small number of Bragg reflector layers is required to provide high reflectivity. Pump–probe measurements also reveal that the AlGaSb/GaSb structure exhibits an intrinsically fast absorption recovery on a picosecond timescale. The mode-locked laser pulse train had a fundamental repetition rate of 1.03 GHz, a pulse duration of ∼5 ps, and a peak power of ∼1.67 W. The demonstration paves the way for exploiting GaSb-based SESAMs for mode locking in the 1.3–2 μm wavelength range, which is not sufficiently addressed by GaAs and InP material systems.

Even more than 15 years after their first experimental demonstration, supercontinua have remained an extremely active field of research. In particular, photonic crystal fibers enable the broadening a laser source with a few nanometer initial spectral coverage to a supercontinuum that may encompass several octaves. Unfortunately, this extreme broadening does not come without a caveat: the initially coherent laser light loses most of this favorable property, which makes it impossible to compress the white-light pulse train to the bandwidth-limited single-cycle duration that two octaves could theoretically support. More precisely, this problem arises because of a loss of interpulse coherence, i.e., subsequent white-light pulses exhibit dramatically varying amplitude and phase structures. In fact, these variations are so extreme that they do not even follow a Gaussian distribution anymore, which gives rise to the phenomenon of optical rogue waves. Optical rogue waves are often explained by soliton dynamics. In the light of the above considerations, however, this seems quite paradoxical as solitons are coherent waveforms that evolve in a highly deterministic fashion. Moreover, frequency metrology applications of supercontinua exist which do not seem to be corrupted by a loss of interpulse coherence. In order to resolve this apparent conflict, we propose a new intrapulse coherence definition, which is experimentally verified by fringe contrast measurements in an f-to-2f interferometer. Numerical simulations indicate that intrapulse coherence is typically quite robust in the case of Kerr-dominated spectral broadening whereas it also quickly vanishes in plasma-dominated broadening scenarios, e.g., during filamentation. Interpulse coherence, in contrast, becomes more fragile at the low photon numbers of oscillator sources. As these two types of coherence appear rather independent of each other, situations can arise where interpulse coherence is conserved but intrapulse coherence vanishes and vice versa. Moreover, compressibility into a train of short pulses must not be used to conclude on the robustness of intrapulse coherence. We believe that this new coherence criterion has important implications, both for frequency metrology as well as for carrier-envelope phase stabilization of lasers. Specifically, in frequency metrology, limitations may arise for the obtainable maximum precision of optical frequency measurements. These limitations may impact the redefinition of the fundamental time and length units replacing the current microwave cesium standard by an optical one.

The near-ultraviolet photoluminescence of ZnO nanorods induced by multiphoton absorption of unamplified Ti:sapphire pulses is investigated. Power dependence measurements have been conducted with an adaptation of the ultrashort pulse characterization method of interferometric frequency-resolved optical gating. These measurements enable the separation of second harmonic and photoluminescence bands due to their distinct coherence properties. A detailed analysis yields fractional power dependence exponents in the range of 3-4, indicating the presence of multiple nonlinear processes. The range in measured exponents is attributed to differences in local field enhancement, which is supported by independent photoluminescence and structural measurements. Simulations based on Keldysh theory suggest contributions by three- and four-photon absorption as well as avalanche ionization in agreement with experimental findings.

We demonstrate frequency-doubling of an amplified femtosecond laser with electric-field induced second-harmonic generation in air. The method promises application with unattenuated terawatt lasers and offers wavelength conversion beyond the ultraviolet limit of nonlinear crystals.

Frequency doubling of an amplified laser is experimentally demonstrated with electric-field induced second-harmonic generation in air. The method promises application with unattenuated terawatt laser and offers wavelength conversion beyond the ultraviolet limit of nonlinear crystals.

The intrapulse coherence is introduced as a measure for judging a fixed phase relation between different spectral components within a laser pulse. This new criterion plays an important role for passive CEP stabilization of OPA systems.

The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulse-to-pulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage. Notwithstanding the apparent loss of interpulse coherence, however, supercontinua enable applications in precision frequency metrology that rely on coherence between different spectral components within a laser pulse. To judge the suitability of a light source for the latter application, we define an alternative criterion, which we term intrapulse coherence. This definition plays a limiting role in the carrier-envelope phase measurement and stabilization of ultrashort pulses. It is shown by numerical simulation and further corroborated by experimental data that filamentation-based supercontinuum generation may lead to a loss of intrapulse coherence despite near-perfect compressibility of the pulse train. This loss of coherence may severely limit active and passive carrier-envelope phase stabilization schemes and applications in optical high-field physics.

A precise control of the electric field nodes relative to the maximum of the intensity envelope is a prerequisite for attosecond pulse generation and experiments in high-field physics [1]. Many carrier-envelope phase (CEP) stabilization schemes start with stabilization of an oscillator, which is nevertheless often difficult to obtain as the CEP has proven highly sensitive to environmental parameters, including temperature, air pressure, and humidity. This very high susceptibility to environmental changes is considered more of a nuisance than anywhere useful. Here, we show that the extreme sensitivity of the CEP can be exploited for quantitative measurements of the electro-optic Kerr effect in atmospheric air, i.e., an extremely weak effect that has previously only been measurable by combining effective path lengths of 100m with tens of kilovolt voltages. In contrast, we can obtain a measurable effect by placing an 8 cm long high voltage capacitor into the intracavity beam path of a mode-locked few-cycle Ti: sapphire oscillator, and we only require rather moderate driver voltages of less than 5 kV.

Stabilizing the carrier-envelope phase (CEP) of mode-locked laser sources has made tremendous progress in recent years, enabling the generation of isolated attosecond pulses and precision frequency metrology at the 10−18 uncertainty level. While some laser types can be very well stabilized, other interesting laser materials have proven notoriously difficult or even impossible to be CEP stabilized. The exact mechanisms behind these problems are poorly understood. Here, we present a novel diagnostic method that provides unprecedented insight into the inner workings of noise generating mechanisms in laser oscillators.

A novel pulse characterization method is presented, favorably combining interferometric frequency-resolved optical gating (FROG) and time-domain ptychography. This new variant is named ptychographic-interferometric frequency-resolved optical gating (πFROG). The measurement device is simple, bearing similarity to standard second-harmonic FROG, yet with a collinear beam geometry and an added bandpass filter in one of the correlator arms. The collinear beam geometry allows tight focusing and circumvents possible geometrical distortion effects of noncollinear methods, making πFROG especially suitable for the characterization of unamplified few-cycle pulses. Moreover, the direction-of-time ambiguity afflicting most second-order FROG variants is eliminated. Possible group delay dispersion of pulses leads to a characteristic tilt in the πFROG traces, allowing the detection of uncompensated dispersion without a retrieval. Using nanojoule, three-cycle pulses at 800 nm, the πFROG method is tested, and the results are compared with spectral phase interferometry for direct electric field reconstruction measurements. Measured pulse durations agree within a fraction of a femtosecond. As a further test, the πFROG measurements are repeated with added group delay dispersion, and found to accurately reproduce the dispersion computed with Sellmeier equations.

Attosecond spectroscopy and precision frequency metrology depend on the stabilization of the carrier-envelope phase (CEP) of mode-locked lasers. Unfortunately, the phase of only a few types of lasers can be stabilized to jitters in the few-hundred millirad range. In a comparative experimental study, we analyze a femtosecond Ti:sapphire laser and three mode-locked fiber lasers. We numerically demodulate recorded time series of the free-running carrier-envelope beat note. Our analysis indicates a correlation between amplitude and frequency fluctuations at low Fourier frequencies for essentially all lasers investigated. While this correlation typically rolls off at frequencies beyond 100 kHz, we see clear indications for a broadband coupling mechanism in one of the fiber lasers. We suspect that the observed coupling mechanism acts to transfer intracavity power fluctuations into excess phase noise. This coupling mechanism is related to the mode-locking mechanism employed and not to the gain medium itself. We further verify this hypothesis by numerical simulations, which identify resonances of the saturable absorber mirror as a possible explanation for the coupling mechanism. Finally, we discuss how to avoid a detrimental influence of such resonances.

This paper represents a systematic investigation of detection shot noise in carrier-envelope phase (CEP) stabilization. Numerical simulations are conducted to calculate the influence of shot noise in laser oscillators. These results are compared with experimental results for Ti:sapphire lasers. It is found that shot noise imposes a limitation for obtaining sub-100 mrad CEP jitters. Careful interferometer design is necessary to push this limit toward 10 mrad. In contrast to oscillator stabilization, shot noise appears to play a much more restrictive role in amplifier stabilization. Using spectral interferometry together with spectral broadening in sapphire, it already appears practically challenging to reach sub-100 mrad jitters. Adaption of the optical nonlinearity in the broadening step appears key to further improvements of the CEP jitter of amplified systems. We believe that these improvements open a perspective for currently unfeasible applications of CEP stabilized pulses. Moreover, our considerations can be easily adapted to CEP stabilization of other laser types beyond Ti:sapphire.

We investigate the influence of the optical Doppler effect on the carrier-envelope frequency (CEF) of a mode-locked pulse train. The laser pulses are Doppler-shifted in frequency during reflection off a periodically moving mirror that is driven by an electro-dynamical exciter inside an 𝑓-2𝑓 interferometer. Depending on the relative movement of the mirror at the instant of reflection, we experimentally demonstrate a CEF shift of the laser pulses up to ±69 kHz, which is sufficient for the carrier-envelope phase control of laser amplifiers with repetition rates of 10 kHz and beyond. Using piezoelectric thick films, we show that the scheme also appears to be adaptable to the megahertz repetition rates of typical oscillators. As the phase control is exerted extra-cavity, Doppler-induced CEF modulation is virtually free of any side effects of traditional stabilization schemes that typically act on the pump power. Finally, the Doppler scheme may overcome servo loop bandwidth limitations associated with pump power control.

A novel fiber technology is presented that enables the transmission of 200 nm wide spectra over meter-long distances with minimal temporal reshaping and acceptable losses down to about 3 dB/m. Delivery of a 10 fs pulse over nearly meter distance is experimentally demonstrated, which sets a new standard for the fiber-based delivery of few-cycle pulses. Numerical simulations provide insight into the unique guiding mechanism in the novel hollow-core fiber technology, enabling dispersion parameters that are within an order of magnitude of those available in free space propagation.

A method for analyzing the statistical nature of laser noise is demonstrated. By application to CEP noise characteristics, the method is shown to enable discriminating between deterministic technical and stochastic quantum noise contributions.

Universal use of single-walled carbon-nanotube based saturable absorber devices for mode-locking of bulk solid-state lasers between 0.8 and 2 μm is discussed. The advantages in comparison to semiconductor saturable absorbers are emphasised. We briefly describe the manufacturing process and the essential optical properties, and review experimental results obtained with various types of femtosecond and picosecond solid-state lasers in the steady-state regime. We also demonstrate that a single hybrid saturable absorber used in transmission can be used to mode-lock four different types of lasers operating between 1 and 2 μm.

The application of single-walled carbon nanotubes (SWCNTs) as saturable absorbers (SA) in a Nd:glass femtosecond laser is verified as a promising alternative to traditional semiconductor saturable-absorber mirrors (SESAMs). The shortest laser pulses achieved with a SWCNT-SA fabricated by the slow-evaporation method are reported herein. Nearly Fourier-limited 288 fs pulses are obtained with negative-dispersion soliton mode-locking. The importance of the properties of the starting material, such as the degree of purity and the chirality, and the successive slow-evaporation deposition method is proven by using a multitechnique approach based on X-ray diffractometry, scanning electron microscopy, and μ-Raman spectroscopy. The high degree of nanotube alignment on the glass substrate and also the slight metallic character due to electron transfer between the glass matrix and the nanotubes themselves are identified as the main features responsible for the good laser response.

GaAs- and InP-based Semiconductor saturable absorber mirrors (SESAMs) operating at around 1 μm and 1.55 μm wavelength domains are well understood reliable components used in a large variety of ultrafast lasers. Recently, we demonstrated the first 2 µm GaSb based saturable absorber mirrors used for pico- and femtosecond pulse generation in a mode-locked semiconductor disk laser. Here we report on the fabrication and characterization of similar type of GaSb-based SESAMs with an in-depth focus on the growth parameters and their impact on the dynamic properties of the SESAMs. In particular the effects of quantum well growth temperature and strain on absorption recovery time were investigated by pump probe measurements. The results reveal fast absorption recovery times for SESAMs grown under typical growth conditions used to fabricate high quality quantum-well laser structures. The absorption recovery exhibited a double exponential decay characteristic with a fast component having a characteristic time of about 0.5 ps and a slow component of about 10 ps. (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Broadband characterization of the carrier-envelope phase (CEP) noise spectral density of free-running mode-locked lasers is essential for advanced low-noise optical frequency comb designs. Here we present a direct method that utilizes an optical heterodyne beat between a pair of repetition-rate-locked mode-locked lasers for CEP noise characterization, without requiring an f-2f interferometer or nonlinear optical conversion steps. A proof-of-principle experiment in a femtosecond Yb-fiber laser achieves CEP noise spectral density characterization with >270 dB dynamic range over a Fourier frequency range from 5 mHz to 8 MHz. The measurement noise floor is well below 1 μrad/√Hz, enabling dependable detection down to a quantum-limited noise floor. The method can resolve various noise mechanisms that cause specific CEP noise spectral shapes. The underlying mechanisms are further analyzed in terms of spurious temporal correlation to distinguish between technical and stochastic noise signatures. Moreover, a Hadamard deviation analysis reveals a varying degree of frequency stability in the measured CEP time series.

Single-walled carbon-nanotube absorbers are experimentally demonstrated for laser mode-locking. A saturable absorber device is used to mode-lock three different bulk solid-state lasers in a 500 nm-wide wavelength interval. The devices exhibit a low saturation fluence of

A plasma induced temporal break-up in filamentary propagation has recently been identified as one of the key events in the temporal self-compression of femtosecond laser pulses. An analysis of the Nonlinear Schrodinger Equation coupled to a noninstantaneous plasma response yields a set of stationary states. This analysis clearly indicates that the emergence of double-hump, characteristically asymmetric temporal on-axis intensity profiles in regimes where plasma defocusing saturates the optical collapse caused by Kerr self-focusing is an inherent property of the underlying dynamical model.

The design of mixed wedge pairs for control of the carrier-envelope phase of femtosecond laser pulses is discussed. The wedge pairs can be designed in such a way that they practically only compensate for the difference between group and phase delay, but leave either the group delay or the dispersion of the wedge assembly constant. Such isochronous or isodispersive compensators can be used for intracavity as well as for extracavity applications. Other side effects, such as the residual angular dispersion of the wedge pair are considered, and it is shown, both theoretically and experimentally, that material combinations exist that even enable a good compromise in reducing practically all disturbing side effects. Based on the two commonly available Schott glasses N-BK10 and N-PK51, a compensator assembly is experimentally tested inside a 10-fs Ti:sapphire oscillator. It is found that undesired variations of the laser repetition rate are reduced by a factor 50 compared to a set of identical silica wedges.

In this paper, the properties of chirped photonic crystal fibers for guiding sub-100-fs pulses are discussed by numerical simulations and approximate analytical considerations. The nearly distortion-free guiding properties are explained by a spectral distribution of detrimental dispersive resonances. Deeper analysis reveals the geometrical properties of the innermost layer of the photonic cladding structure as a key parameter for the dispersive properties of this fiber. It is further investigated how systematic manipulation of the geometry can be exploited for influencing the guiding parameters.

Photonic crystals have widely increased the facility to guide and confine light at wavelengths close to the optical wavelength1,2,3. Because they can include extremely sharp bends, photonic-crystal waveguides are a key element in future integrated optical devices4. Moreover, they enable the manipulation of the spontaneous emission properties of luminescent devices5, the localization of light in microcavities6, and they may serve to generate negative refraction7,8. A special class of these devices are the hollow-core photonic-crystal fibres9,10,11, which confine the light by means of a periodic cladding, consisting of several layers of identical cells. This design resonantly decreases the transmission losses of such fibres to values of a few dB km−1 in a narrow wavelength range. However, the rather narrowband transmission bands and the detrimental third-order dispersion characteristics of this single-cell design generally render application of such hollow-core fibres difficult in the femtosecond range12. Therefore, no fibre-based concept can currently provide guiding of sub-100 fs pulses over extended distances. By introducing a radial chirp into the photonic crystal, we here demonstrate a novel concept for photonic-crystal fibres that breaks with the paradigm of lattice homogeneity and enables a new degree of freedom in photonic-crystal-fibre design, eliminating much of the pulse duration restriction of earlier approaches. Hollow-core photonic-crystal fibres enable confinement of light on a much tighter scale than is possible with conventional fibre. But dispersion makes it difficult to transmit very short, sub 100 fs, pulses over long distances. A chirped structure could offer a solution.

Digital holographic shape measurements using femtosecond laser pulses are reported. For contouring of very fast moving objects, the simultaneous generation of at least two spectrally separated ultrashort pulses is required. To deliver this particular spectral signature at high pulse energies, a chirped-pulse Ti:sapphire laser amplifier was modified to emit two spectrally separated pulses with energies above 1 μJ each. The wavelength separation of these pulses was adjustable within the 50 nm gain bandwidth, cutting out two distinct wavelength peaks by a variable double-slit assembly in a prism sequence. A Michelson-type interferometer was employed to perform the two-wavelength contouring. The phases of the holograms and the phase differences are calculated numerically, which allow us to deduce the contour lines of the topology of the object. The suitability of the light source for digital holography is demonstrated with contouring of stationary objects and the potential for high-speed applications is indicated.

We discuss a concept for incorporating dispersion compensation into a saturable absorber mirror. This integrated device relies on an absorber layer embedded in a resonator structure and can provide negative dispersion of several 1000 fs2, similar to the spectral phase characteristics of a Gires-Tournois interferometer. A similar integration is possible also for semiconductor gain structures, as they are employed in semiconductor disk lasers. We will provide a detailed analysis of the dispersion compensation capacities of our approach, linking dispersion scaling and nonlinear properties of the device. The theoretical part will be illustrated by dispersion measurements on prototypical devices. We believe that our concept paves the way for fully integrated vertical semiconductor femtosecond lasers but may also find numerous applications in solid state lasers and femtosecond fiber lasers

Tunable and mode-locked laser operation near 2 ?m based on different Tm-doped YAG ceramics, 4 at.% and 10 at.%, is demonstrated. Several designs of GaSb-based surface-quantum-well SESAMs are characterized and studied as saturable absorbers for mode-locking. Best mode-locking performance was achieved using an antireflection-coated near-surface quantum-well SESAM, resulting in a pulse duration of ~3 ps and ~150 mW average output power at 89 MHz. All mode-locked Tm:YAG ceramic lasers operated at 2012 nm, with over 133 nm demonstrated tuning for continuous-wave operation.

Using experimental data from three different rogue wave supporting systems, determinism, and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than 2. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.

We report on a novel method for the characterization of complex ultrashort pulses, in both amplitude and phase. This method is the straightforward extension of interferometric autocorrelation (IAC) toward frequency-resolved optical gating (FROG) and therefore displays all advantages of a collinear method for measuring few-cycle pulses. The interferometric FROG (IFROG) trace contains two independent time-frequency distributions, namely the standard second-harmonic (SH)-FROG trace and a novel non-semidefinite FROG trace, which requires new retrieval algorithms. We discuss one suitable retrieval concept that is based on an adaption of generalized projections and demonstrate it with different types of short laser pulses. The IFROG trace contains additional information that can be used for intrinsic calibration of the FROG traces. The strong redundancy of data increases the robustness of the method. IFROG is a pulse characterization method that is particularly suited for the complex sub-10-fs pulse shapes as they can arise during supercontinuum compression and gives detailed insight into the satellite structures of partly compressed continua.

Using noble gases as a nonlinear medium, it has become possible to compress energetic laser pulses into the sub-10-fs regime. Hollow fiber capillaries can serve to increase the effective interaction length of the pulses, and impressive white-light continua have been reported as a result. With demonstrated bandwidths exceeding the optical octave, this method holds the potential for generating single-cycle optical pulses. On the practical side, however, it becomes very difficult to compensate for dispersive effects and to fully exploit the enormous bandwidth. We will discuss chirped mirrors as one means for pulse compression. A further challenge lies on the characterization side. Utilizing advanced characterization schemes, we were able to demonstrate compression of a white-light continuum down to a pulse duration of 3.8 fs, which corresponds to only about 1.6 cycles at the carrier wavelength. These are the shortest pulses in the visible/near-infrared wavelength range that have ever been produced with a non-adaptive approach to dispersion compensation. Moreover, these are the shortest pulses generated using chirped mirrors, which compares favorably to previous results that were achieved with much more elaborate and lossier adaptive compression schemes.

We demonstrate the generation of ultrabroad spectra in a photonic crystal fiber with a kagome-lattice transverse structure. This two-dimensional periodic photonic lattice allows for strong confinement of light without employing defect states nor using photonic bandgap guiding. Light guiding is mediated by total internal reflection in the intersections of the lattice structure, similar to tapered or micro-structured fibers. The kagome lattice structure is manufactured from a soft glass with a high nonlinearity. Using a Ti:sapphire oscillator as a pump source, we observe for the first time impressive supercontinuum generation in the guided modes of a 2D photonic lattice. Supercontinuum generation is caused by fission and radiation of higher-order solitons in the anomalous dispersion range. Our spectrum encompasses the spectral range from 200 to 1750 nm. The dependence of the continuum on coupling spot location, fiber length, and pump wavelength and power as well as on pulse duration and polarization state is investigated. Using a numerical simulation for the lattice structure, pulse propagation through this structure is theoretically studied. Our model reveals the mechanism of supercontinuuum generation in the 2D photonic structure and explains the essential experimental findings.

Ultrabroadband chirped mirrors with a bandwidth of 270 THz have been manufactured using the BASIC design approach. These mirrors were used to compress the supercontinuum of cascaded hollow fibers down to 4.6 fs. The pulse duration was measured with spectral phase interferometry for direct electric-field reconstruction (SPIDER).

Inside a femtosecond laser oscillator, no coupling mechanism between the propagation speeds of the carrier and the pulse envelope exists. Therefore, the relative delay between carrier and envelope of a femtosecond oscillator will exhibit irregular fluctuations unless this jitter is actively suppressed. Both intensity and beam pointing fluctuations in the laser can introduce carrier-envelope phase changes. Based on our analysis, we are capable of reducing or avoiding certain mechanisms by proper design of the laser cavity. We use such an optimized cavity to stabilize the carrier envelope-phase to an external reference oscillator with a long-term residual jitter corresponding to only 10 attoseconds in a (100 kHz-0.01 Hz) bandwidth. This is the smallest long-term timing jitter of a femtosecond laser oscillator demonstrated to date. However, it is important to note that this stabilization was obtained with an f-to-2f heterodyne technique using additional external spectral broadening in a microstructure fiber which introduces additional carrier-envelope phase noise. We present a direct heterodyne measurement of this additional carrier-envelope phase noise due to the continuum generation process.

The speed of optoelectronic devices is normally limited by the components used on the electronic side of the device. The direct generation of short light pulses from short current pulses, for example, is limited by the speed of an electronic pulse generator or the response time of a laser diode. These electronic bandwidth limitations can be overcome by switching to indirect schemes. These schemes use optical means, whenever bandwidth is an issue. This is combined with much slower optoelectronic technology, bringing together the inherent speed of all-optical approaches and the virtues of standard optoelectronics. Apart from the generation of short pulses, we will also address their detection and characterization, their modulation, and transmission effects. These methods carry the functionality of optoelectronics from a temporal resolution of a few picoseconds well into the femtosecond range.

The ability to generate third-harmonic light with a broad phase-matching bandwidth at any dielectric interface offers a promising tool for the characterization of ultrafast laser pulses. Third-harmonic, interferometric frequency-resolved optical gating (TH-iFROG) exploits this nonlinearity. The TH-iFROG traces contain an abundance of information, but their complicated analytical form poses a problem for standard FROG algorithms. Here we solve the pulse retrieval problem with an evolutionary algorithm known as differential evolution. The algorithm processes a TH-iFROG trace, extracting three novel types of FROG traces that are subsequently used for pulse retrieval. The analytical forms of these FROG traces are also presented. Built-in error correction mechanisms and the large amount of redundant data make the pulse retrieval robust against measurement noise and systematic errors. The technique is demonstrated via the characterization of unamplified few-cycle pulses using a simple fused silica window as the nonlinear medium. Comparison to a reference measurement made with a commercial pulse characterization device shows excellent agreement between the measured complex electric fields.

[Portion of Introduction] In this chapter PL emission and THG by both CBD-grown and VPT-grown ZnO nanorod samples are reported. These studies clearly show that the low temperature PL emission from CBD-grown samples is both weaker in intensity and broader in terms of key feature linewidths than that from VPT-grown samples. By contrast the THG efficiency of samples grown by both the high temperature and low temperature methods are comparable to one another, and both are much larger than THG generated at a bare quartz surface. Intensity dependence measurement and interferometric frequency resolved optical gating (iFROG) measurements are used to study the THG from both sample types.[20,21] The laser pulse parameters are extracted when the pulses are subjected to both high and low chirp and our studies indicate that ZnO nanostructures grown by low temperature methods allow excellent characterization of ultrafast pulses (originally < 10 fs) and can efficiently generate THG. Consequently ZnO nanostructures grown by low temperature methods are excellent candidate materials for the technology applications discussed above.