Design and fabrication of double-chirped mirrors

Group delay dispersion monitoring for computational manufacturing of dispersive mirrors

We present a computational manufacturing program for monitoring group delay dispersion (GDD). Two kinds of dispersive mirrors computational manufactured by GDD, broadband, and time monitoring simulator are compared. The results revealed the particular advantages of GDD monitoring in dispersive mirror deposition simulations. The self-compensation effect of GDD monitoring is discussed. GDD monitoring can improve the precision of layer termination techniques, it may become a possible approach to manufacture other optical coatings.

Complementary dispersive mirror pair produced in one coating run based on desired non-uniformity

We report a novel one-coating-run method for producing an octave-spanning complementary dispersive mirror (DM) pair. The anti-phase group delay dispersion (GDD) oscillations are realized by two mirrors of the DM pair due to the certain thickness difference. Both mirrors are deposited within a single coating run enabled by the non-uniformity of the ion beam sputtering coating plant, which is obtained by tuning the distance between the source target and coating substrates. Since the DM pair is produced in a single deposition run, the GDD performance is more robust against deposition errors than that of the conventional complementary DM pair, in which two separated coating runs are necessary. Moreover, the new DM pair is compatible for both laser polarizations under the same angle of incidence, which could effectively reduce the difficulties of alignment for their implementation in laser systems than the double angle DM pair. The new DM pair is successfully applied to compress pulses from a Ti: Sapphire laser system down to 4.26 fs in pulse duration.

Compact millijoule Yb3+:CaF2 laser with 162 fs pulses

We report on a compact diode-pumped, chirped pulse regenerative amplifier system with a pulse duration of 162 fs and an output pulse energy of 1 mJ before as well as 910 µJ after compression optimized for the probing of ultrafast relativistic laser-plasma processes. A chirped volume Bragg grating (CVBG) acts as a combined pulse stretcher/compressor representing a robust solution for a CPA laser system in the millijoule range. Yb³⁺:CaF₂ is used as gain medium to support a large bandwidth of 16 nm (FWHM) when spectral gain shaping is applied. Chirped mirrors compensate for any additional dispersion introduced to the system.

Broadband negative group velocity dispersion in all-dielectric metamaterial and its role in supercontinuum generation

All-dielectric metamaterials conforming to an optical reflectionless potential (ORP) offer broadband, omni-directional suppression of reflection. Though they are predicted to possess broadband negative group velocity dispersion (GVD), ultrashort pulse propagation through such materials has not been studied so far, to the best of our knowledge. In this work, we demonstrate negative GVD and group delay dispersion over broadband covering visible to near-infrared wavelengths. We investigate the role of ORP in supercontinuum generation (SC), which is observed to be polarization independent. The negative GVD in ORPs is interesting for pulse compression, phase compensation, dispersion engineering, and controlled SC generation.

High efficiency terahertz generation in a multi-stage system

We describe a robust system for laser-driven narrowband terahertz generation with high conversion efficiency in periodically poled Lithium Niobate (PPLN). In the multi-stage terahertz generation system, the pump pulse is recycled after each PPLN stage for further terahertz generation. By out-coupling the terahertz radiation generated in each stage, extra absorption is circumvented and effective interaction length is increased. The separation of the terahertz and optical pulses at each stage is accomplished by an appropriately designed out-coupler. To evaluate the proposed architecture, the governing 2-D coupled wave equations in a cylindrically symmetric geometry are numerically solved using the finite difference method. Compared to the 1-D calculation which cannot capture the self-focusing and diffraction effects, our 2-D numerical method captures the effects of difference frequency generation, self-phase modulation, self-focusing, beam diffraction, dispersion and terahertz absorption. We found that the terahertz generation efficiency can be greatly enhanced by compensating the dispersion of the pump pulse after each stage. With a two-stage system, we predict the generation of a 17.6 mJ terahertz pulse with total conversion efficiency η_total = 1.6% at 0.3 THz using a 1.1 J pump laser with a two-lines spectrum centered at 1 μm. The generation efficiency of each stage is above 0.8% with the out-coupling efficiencies above 93.0%.

Synchronous multi-color laser network with daily sub-femtosecond timing drift

Filming atoms in motion with sub-atomic spatiotemporal resolution is one of the distinguished scientific endeavors of our time. Newly emerging X-ray laser facilities are the most likely candidates to enable such a detailed gazing of atoms due to their angstrom-level radiation wavelength. To provide the necessary temporal resolution, numerous mode-locked lasers must be synchronized with ultra-high precision across kilometer-distances. Here, we demonstrate a metronome synchronizing a network of pulsed-lasers operating at different center wavelengths and different repetition rates over 4.7-km distance. The network achieves a record-low timing drift of 0.6 fs RMS measured with 2-Hz sampling over 40 h. Short-term stability measurements show an out-of-loop timing jitter of only 1.3 fs RMS integrated from 1 Hz to 1 MHz. To validate the network performance, we present a comprehensive noise analysis based on the feedback flow between the setup elements. Our analysis identifies nine uncorrelated noise sources, out of which the slave laser's inherent jitter dominates with 1.26 fs RMS. This suggests that the timing precision of the network is not limited by the synchronization technique, and so could be much further improved by developing lasers with lower inherent noise.

Enhancement of the damage resistance of ultra-fast optics by novel design approaches

Dielectric components are essential for laser applications. Chirped mirrors are applied to compress the temporal pulse broadening crucial in the femtosecond regime. However, the design sensitivity and the electric field distribution of chirped mirrors is complex often resulting in low laser induced damage resistances. An approach is presented to increase the damage resistance of pulse compressing mirrors up to 190% in the NIR spectral range. Layers with critical high field intensity of a binary mirror design are substituted by ternary composites and quantized nanolaminates, respectively. The deposition process is improved by an in situ technique monitoring the phase of reflectance.

Enhancement of laser-induced damage threshold in chirped mirrors by electric field reallocation

In this paper, the relation between the laser-induced damage threshold (LIDT) and the electric field intensity (EFI) distribution inside a CM is investigated experimentally. We show that it is possible to increase the LIDT values by slightly modifying the electric field of a standing wave distribution without loss of spectral and dispersion performance. Suggested CM design improvement could increase reliability and LIDT performance of both CM elements and high-power systems they are used in.

100-nm tunable femtosecond Cr:LiSAF laser mode locked with a broadband saturable Bragg reflector

We report broad tunability of a femtosecond (fs) diode-pumped Cr:LiSAF laser mode-locked with a broadband saturable Bragg reflector (SBR). The SBR had seven pairs of Al_xO_y(n∼1.5) and Al_0.17Ga_0.83As(n∼3.5) layers in its Bragg stack, enabling a 250 nm reflectivity bandwidth around 850 nm. A 6-nm-thick strained In_0.15Ga_0.85As quantum well placed between Al_0.17Ga_0.83As cladding layers was used as a broadband saturable absorber in the 800-920 nm wavelength range. The laser was pumped by 6 single mode diodes-four at 640 nn and two at 660 nm. Mode locking was self-starting and fs pulses could be continuously tuned from 800 nm to 905 nm by an intracavity birefringent filter with an out-of-plane optic axis. The pulse widths varied from 70 fs to 255 fs as the laser was tuned. The laser had an 85.5 MHz repetition rate and the output power varied from 80 mW to 180 mW with tuning.

Dispersive mirror for the mid-infrared spectral range of 9-11.5 μm

A dispersive multilayer interference mirror with a group delay dispersion (GDD) of +1500  fs² for the spectral range of 9-11.5 μm is presented. It is designed to compensate the GDD of an ultrashort light pulse gained when transmitting 1 mm of a zinc selenide substrate. The coating process for the mirror manufacturing is described. The optical properties of the mirror are fully characterized by measuring the group delay, the GDD, the reflectance, and the transmittance.

Ultrafast laser-scanning time-stretch imaging at visible wavelengths

Optical time-stretch imaging enables the continuous capture of non-repetitive events in real time at a line-scan rate of tens of MHz-a distinct advantage for the ultrafast dynamics monitoring and high-throughput screening that are widely needed in biological microscopy. However, its potential is limited by the technical challenge of achieving significant pulse stretching (that is, high temporal dispersion) and low optical loss, which are the critical factors influencing imaging quality, in the visible spectrum demanded in many of these applications. We present a new pulse-stretching technique, termed free-space angular-chirp-enhanced delay (FACED), with three distinguishing features absent in the prevailing dispersive-fiber-based implementations: (1) it generates substantial, reconfigurable temporal dispersion in free space (>1 ns nm-1) with low intrinsic loss (<6 dB) at visible wavelengths; (2) its wavelength-invariant pulse-stretching operation introduces a new paradigm in time-stretch imaging, which can now be implemented both with and without spectral encoding; and (3) pulse stretching in FACED inherently provides an ultrafast all-optical laser-beam scanning mechanism at a line-scan rate of tens of MHz. Using FACED, we demonstrate not only ultrafast laser-scanning time-stretch imaging with superior bright-field image quality compared with previous work but also, for the first time, MHz fluorescence and colorized time-stretch microscopy. Our results show that this technique could enable a wider scope of applications in high-speed and high-throughput biological microscopy that were once out of reach.

High dispersive mirrors for erbium-doped fiber chirped pulse amplification system

We report on the development of near-infrared high dispersive mirrors (HDM) with a group delay dispersion (GDD) of -2000 fs². A HDM pair based on one optimized result at two reference wavelengths (1550 nm and 1560 nm) can reduce the total oscillation of the GDD effectively in the wavelength range of 1530-1575 nm. This HDM pair is designed and fabricated in a single coating run by means of the nonuniformity in film deposition. For the first time, near-infrared HDMs with two different reference wavelengths have been successfully applied in an erbium-doped fiber chirped pulse amplification system for the compression of 4.73 ps laser pulses to 380 fs.

Group delay dispersion measurements in the mid-infrared spectral range of 2-20 µm

We present two measurement devices which both allow the direct measurement of the group delay (GD) and group delay dispersion (GDD) of laser optics, covering the near- and mid-infrared (MIR) spectral range from 2 to 20 µm (500-5,000 cm^-1). Two different kinds of devices were developed to measure the GDD of multilayer interference coatings. One is a resonant scanning interferometer (RSI) and the other is a white light interferometer (WLI). The WLI is also capable of measuring the GDD in transmission, for instance of bulk material. GDD measurements of a high dispersive mirror for wavelengths from 2.0 to 2.15 µm and one of a multilayer mirror from 8.5 to 12.0 µm are presented. A measurement of a zinc selenide (ZnSe) substrate in transmission was made with the WLI demonstrating the full bandwidth of the device from 1.9 to 20 µm. The comparison of all measurements with their related theoretical values shows a remarkable correspondence.

Continuous-wave phase-matched molecular optical modulator

In optical modulation, the highest available modulation rate is basically limited to the GHz frequency range at best. This is because optical modulation is often performed using electro-optic or acousto-optic effects that require application of an external signal to solid-state nonlinear optical materials. Here we describe optical modulation of continuous-wave radiation at frequencies exceeding 10 THz based on ultrafast variation of molecule polarizability arising from coherent molecular motion. The optical modulation efficiency is extensively enhanced by fulfilling phase-matching conditions with the help of dispersion control of the optical cavity, generating sidebands with a highest ratio of 7.3 × 10(-3). These results will pave the way for development of versatile optical modulation-based techniques in a wide range of research fields in optical sciences, such as mode-locked lasers operating in the THz range.

Plasma-ion-assisted coatings for 15 femtosecond laser systems

Large-aperture deposition of high-laser-damage-threshold, low-dispersion optical coatings for 15 femtosecond pulses have been developed using plasma-ion-assisted electron-beam evaporation. Coatings are demonstrated over 10 in. aperture substrates.

Pulse compression to 14 fs by third-order dispersion control in a hybrid grating-prism compressor

A pulse compressor consisting of a fiber and a compact hybrid grating-prism dispersive delay line (DDL) is used to compress readily-available 140-fs pulses from a Ti:sapphire laser. We generate broadband pulses of up to 75 THz FWHM bandwidth in normally-dispersive single-mode conventional and photonic crystal fibers, with a potential of compression to 6 fs. Pulse dechirping in our hybrid DDL through second- and third-order dispersion (TOD) compensation results in 10× compression to 14 fs, limited by the bandwidth of the DDL transfer function and higher-order dispersion. The large tunability of the TOD of the hybrid DDL is shown.

Reflection spectra of etched FBGs under the influence of axial contraction and stress-induced index change

We present a new theoretical model for the broadband reflection spectra of etched FBGs which includes the effects of axial contraction and stress-induced index change. The reflection spectra of the etched FBGs with several different taper profiles are simulated based on the proposed model. In our observation, decaying exponential profile produces a broadband reflection spectrum with good uniformity over the range of 1540-1560 nm. An etched FBG with similar taper profile is fabricated and the experimental result shows good agreement with the theoretical model.

High-dispersive mirrors for high power applications

We report on the development and manufacturing of two different types of high-dispersive mirrors (HDM). One of them provides a record value for the group delay dispersion (GDD) of -4000 fs2 and covers the wavelength range of 1027-1033 nm, whereas the other one provides -3000 fs2 over the wavelength range of 1020-1040 nm. Both of the fabricated mirrors exhibit a reflectance of >99.9% and are well suited for intracavity applications. Mirrors of the second type have been successfully employed in a Kerr-lens mode-locked Yb:YAG thin-disk oscillator for the generation of 200-fs pulses with multi-10-W average power.

Creating circularly polarized light with a phase-shifting mirror

We report on the performance of a system employing a multi-layer coated mirror creating circularly polarized light in a fully reflective setup. With one specially designed mirror we are able to create laser pulses with an ellipticity of more than ε = 98% over the entire spectral bandwidth from initially linearly polarized Titanium:Sapphire femtosecond laser pulses. We tested the homogeneity of the polarization with beam sizes of the order of approximately 10 cm. The damage threshold was determined to be nearly 400 times higher than for a transmissive quartz-wave plate which suggests applications in high intensity laser experiments. Another advantage of the reflective scheme is the absence of nonlinear effects changing the spectrum or the pulse-form and the scalability of coating fabrication to large aperture mirrors.

Direct generation of 81 nJ pulses and external compression to a subpicosecond regime with a 4.9 MHz chirped-pulse multipass-cavity Cr⁴⁺:forsterite oscillator

We report direct generation of 81 nJ chirped pulses from a room-temperature, Kerr lens mode-locked Cr⁴⁺:forsterite oscillator operating at 1258 nm. To increase the pulse energy, the pulse repetition rate of the short x-type resonator was lowered from 143 to 4.9 MHz by the addition of a q-preserving multipass cavity, which provided an additional effective optical path length of 59.4 m. The duration of the chirped pulses was around 5.5 ps with a spectral width of 21 nm. The pulses were externally compressed to 607 fs by using a diffraction grating pair. To our knowledge, this is the highest reported pulse energy directly generated from a room-temperature mode-locked Cr⁴⁺:forsterite laser.

Recent development and new ideas in the field of dispersive multilayer optics

A dispersive-mirror-based laser permits a dramatic simplification of high-power femtosecond and attosecond systems and affords promise for their further development toward shorter pulse durations, higher peak powers, and higher average powers with user-friendly systems. The result of the continuous development of dispersive mirrors permits pulse compression down to almost single cycle pulses of 3 fs duration. These design approaches together with the existing modern deposition technology pave the way for the manufacture of dielectric multilayer coatings able to compress pulses of tens of picoseconds duration down to a few femtoseconds.

Fast numerical methods for the design of layered photonic structures with rough interfaces

A multilayer approach (MA) and modified boundary conditions (MBC) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with an arbitrary permittivity tensor. MA and MBC are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

Robust synthesis of dispersive mirrors

A synthesis technique allowing to obtain a set of robust designs is reported. The robust synthesis is based on simultaneous optimization of spectral characteristics of multiple designs located in a small neighborhood of a so-called pivotal design. Efficiency of this technique is demonstrated by the synthesis and successful experimental realization of a high dispersive mirror. The fabricated dispersive mirror covers 690-890 nm wavelength range and provides the dispersion of -300 fs2 at 800 nm.

Phase distortion ratio: alternative to group delay dispersion for analysis and optimization of dispersion compensating optics

We present a new approach for designing dispersion-engineered optics based on a simple unitless spectral quantity we call the phase distortion ratio (PDR). In contrast to minimizing the group delay dispersion (GDD) deviation from the ideal, minimizing the PDR is optimal in the sense that it minimizes the fraction of pulse energy lost to phase distortions. As an example, a mirror system optimized via PDR is empirically found to result in significantly better compression of single-cycle pulses than a system designed in terms of GDD. In the context of coupling pulse trains to cavities, minimizing the PDR of the cavity is shown to maximize throughput.

Dispersion management in femtosecond laser oscillators with highly dispersive mirrors

Recently the manufacture of highly dispersive mirrors with -1300 fs(2) group delay dispersion per reflection was reported. Here we demonstrate the intracavity applicability of these novel mirrors in Ti:sapphire oscillators for the first time, as well as their capability of compensating a substantial amount of material dispersion in the cavity (40 mm fused silica). We also studied the influence of net negative cavity dispersion, realized with these mirrors, on the achievable maximum pulse energy in long-cavity femtosecond oscillators before the onset of anomalous behavior (e.g. multi-pulsing). In addition, we demonstrate a 0.5 GHz Ti:sapphire oscillator the dispersion compensation of which is realized with a single highly dispersive mirror.

Chirped-pulse amplification of laser pulses with dispersive mirrors

We report a novel implementation of chirped-pulse amplification (CPA) by dominantly using dispersive multilayer mirrors for chirp control. Our prototyp dispersive-mirror (DMC) compressor has been designed for a kHz Ti:sapphire amplifier and yielded--in a proof-of-concept study--millijoule-energy, sub-20-fs, 790-nm laser pulses with an overall throughput of approximately 90% and unprecedented spatio-temporal quality. Dispersive-mirror-based CPA permits a dramatic simplification of high-power lasers and affords promise for their advancement to shorter pulse durations, higher peak powers, and higher average powers with user-friendly systems.

Double-angle multilayer mirrors with smooth dispersion characteristics

We report the feasibility of precision broadband dispersion control with multilayer mirrors produced in a single coating run. Inherent fluctuations of the group-delay dispersion (GDD) are suppressed by using the mirrors at two different angles of incidence. With a specialized version of the needle optimization algorithm, we have designed the multilayer structure to yield a complementary pair with a resultant GDD substantially free from spectral oscillations characteristic of broadband chirped multilayers. Since the mirrors employed at two different incidence angles are produced in a single deposition run, their overall dispersion is more robust to errors in layer thicknesses than that of previous complementary mirror pairs manufactured in two different steps. This offers the potential for improving production yield and quality of femtosecond dispersion control. We have successfully used the first "double-angle" mirrors for compressing pulses to a duration of 4.3 fs.

Comparison of dispersive mirrors based on the time-domain and conventional approaches, for sub-5-fs pulses

Dispersive mirrors based on time-domain approach are compared with mirrors resulting from conventional phase target designs. Phase targets have been applied to complementary-pair dispersive mirrors, used for sub-5-fs pulse compression. While the phase approach has hither to afforded the best performance for the shortest pulses, our new approach, based on time-domain targets and tailored for a specific input spectrum, appears to provide comparable performance for pulse compression for a pulse duration 4.6 fs. Experimental studies using dispersive mirrors made to both designs are described.

Robust chirped mirrors

Optimized chirped mirrors may perform suboptimally, or completely fail to satisfy specifications, when manufacturing errors are encountered. We present a robust optimization method for designing these dispersion-compensating mirror systems that are used in ultrashort pulse lasers. Possible implementation errors in layer thickness are taken into account within an uncertainty set. The algorithm identifies worst-case scenarios with respect to reflectivity as well as group delay. An iterative update improves the robustness and warrants a high manufacturing yield, even when the encountered errors are larger than anticipated.

Efficient optimization of multilayer coatings for ultrafast optics using analytic gradients of dispersion

A fully analytic method for computing gradients of dispersion (to any order) for a dielectric multilayer coating is developed, and it is demonstrated how group delay gradients can be used to optimize the dispersion of such a filter. The algorithm complexity is linear with the number of layers and quadratic in dispersion order. To our knowledge, this is the first published algorithm for computing exact analytic gradients of dispersion. We show an approximation that speeds up the computation significantly, making it linear in dispersion order. MATLAB and C code implementing the algorithms are made available.

Dispersion control over the ultraviolet-visible-near-infrared spectral range with HfO2/SiO2-chirped dielectric multilayers

We report the first realization, to the best of our knowledge, of a chirped multilayer dielectric mirror providing dispersion control over the spectral range of 300-900 nm and the first use of hafnium oxide in a chirped mirror. The technology opens the door to the reliable and reproducible generation of monocycle laser pulses in the blue-violet spectral range, will benefit the development of optical waveform and frequency-comb synthesizers over the ultraviolet-visible-near-infrared spectral range, and permits the development of ultrabroadband-chirped multilayers for high-power applications.

Design, fabrication, and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses

Chirped Mo/Si multilayer coatings have been designed, fabricated, and characterized for use in extreme-ultraviolet attosecond experiments. By numerically simulating the reflection of the attosecond pulse from a multilayer mirror during the optimization procedure based on a genetic algorithm, we obtain optimized layer designs. We show that normal incidence chirped multilayer mirrors capable of reflecting pulses of approximately 100 attoseconds (as) duration can be designed by enhancing the reflectivity bandwidth and optimizing the phase-shift behavior. The chirped multilayer coatings have been fabricated by electron-beam evaporation in an ultrahigh vacuum in combination with ion-beam polishing of the interfaces and in situ reflectivity measurement for layer thickness control. To analyze the aperiodic layer structure by hard-x-ray reflectometry, we have developed an automatic fitting procedure that allows us to determine the individual layer thicknesses with an error of less than 0.05 nm. The fabricated chirped mirror may be used for production of 150-160 as pulses.

Femtosecond dispersion compensation with multilayer coatings: toward the optical octave

Dispersive multilayer coatings have found widespread use, particularly in the compensation of material dispersion in femtosecond oscillators and amplifiers. Other than prism or grating sequences, only chirped mirrors allow for the compensation of a much more general spectral dependence of the dispersion. The current state of the art in ultrabroadband mirror design for dispersion compensation is reviewed. Approaches to expand the utility of chirped-mirror coatings toward the coverage of an even-wider bandwidth beyond the optical octave are discussed.

Efficient analytic computation of dispersion from multilayer structures

We demonstrate an inductive method for computing exact derivatives of reflection phase for layered media by using the transfer-matrix formalism. The algorithm scales linearly with the number of layers. We show a physically realistic approximation that leads to an efficient procedure for accurately computing dispersion significantly faster than with standard finite-difference methods. We discuss the theory behind the approximation and show results for a dispersion-compensating chirped mirror from a Ti: sapphire laser.

Chirped-cavity dispersion-compensation filter design

A new basic structure of a dispersive-compensation filter, called a chirped-cavity dispersion-compensator (CCDC) filter, was designed to offer the advantages of small ripples in both reflectance and group-delay dispersion (GDD). This filter provides a high dispersion compensation, like the Gires-Tournois interferometer (GTI) filter, and a wide working bandwidth, like the chirped mirror (CM). The structure of the CCDC is a cavity-type Fabry-Perot filter with a spacer layer (2 mH or 2 mL) and a chirped high reflector. The CCDC filter can provide a negative GDD of -50 fs2 over a bandwidth of 56 THz with half the optical thickness of the CM or the GTI.

Brewster-angled chirped mirrors for high-fidelity dispersion compensation and bandwidths exceeding one optical octave

A novel design approach for dispersion-compensating chirped mirrors with greater-than-octave bandwidth is proposed. The commonly encountered problem of dispersion ripple is overcome by impedance matching via Brewster incidence in respect to the top-layer coating material. This approach totally suppresses undesired reflections off the interface to the ambient medium without any need for complicated matching sections. It is shown that Brewster-angled chirped mirrors can deliver ultrabroadband dispersion compensation over a much wider bandwidth than conventional doublechirped mirrors and without the mechanical complexity of back-deposition approaches. Due to their relatively simple structure, the sensitivity of the dispersion of the Brewster-angled designs towards growth errors is greatly reduced. Therefore, this new generation of chirped mirrors appears ideal for compression of continuum pulses with a potential of pulse durations in the single-cycle regime.

Diode-pumped passively mode-locked multiwatt Nd:GdVO4 laser with a saturable Bragg reflector

We report a first demonstration, to our knowledge, of a cw passively mode-locked Nd:GdVO4 laser (k = 1063 nm). A relaxed saturable Bragg reflector was used. The laser generates pulses of 9.2 ps at a repetition rate of 119 MHz. As much as 5.4 W of average power was realized with a slope efficiency of 25.7%.

Diode-pumped 10-fs Cr3+:LiCAF laser

We demonstrate 10-fs pulses from a diode-pumped, soft-aperture Kerr lens mode-locked Cr3+:LiCAF laser with a spectral bandwidth of 150 nm and 40 mW of output power at a repetition rate of 110 MHz. For dispersion compensation, double-chirped mirrors and prisms are used. The pulses are characterized by use of spectral shearing interferometry.

High-performance, compact, prismless, low-threshold 30-MHz Ti:Al2O3 laser

We describe the design and operation of a compact femtosecond Ti:Al2O3 laser based on a novel multipass cavity (MPC) design. The laser is all solid state, has prismless dispersion compensation with double-chirped mirrors, and uses a tight-focusing geometry to facilitate efficient low-threshold operation. We increase output pulse energies by extending the resonator length with a compact, scalable MPC, which preserves the characteristics of the Gaussian beam for the short cavity. Although the effective cavity length is approximately 5 m, an extremely compact laser that measures only 30 cm x 45 cm is achieved. With only 1.5 W of pump power, the laser generates 23-fs pulses at a repetition rate of 31.25 MHz and with 88 mW of average output power, corresponding to 2.8 nJ of pulse energy.

Recent developments in compact ultrafast lasers

Ultrafast lasers, which generate optical pulses in the picosecond and femtosecond range, have progressed over the past decade from complicated and specialized laboratory systems to compact, reliable instruments. Semiconductor lasers for optical pumping and fast optical saturable absorbers, based on either semiconductor devices or the optical nonlinear Kerr effect, have dramatically improved these lasers and opened up new frontiers for applications with extremely short temporal resolution (much smaller than 10 fs), extremely high peak optical intensities (greater than 10 TW/cm2) and extremely fast pulse repetition rates (greater than 100 GHz).

Optimization of chirped mirrors

We demonstrate that a highly efficient global optimization of chirped mirrors can be performed with the memetic algorithm. The inherently high sensitivity of chirped-mirror characteristics to manufacturing errors can be reduced significantly by means of the stochastic quasi-gradient algorithm. The applicability of these algorithms is not limited to chirped mirrors.

Generation of sub-10-fs pulses from a Kerr-lens mode-locked Cr(3+):LiCAF laser oscillator by use of third-order dispersion-compensating double-chirped mirrors

Pulses as short as 9 fs at 220-mW average power and a 97-MHz repetition rate are generated from a cw Ti:sapphire-pumped Kerr-lens mode-locked Cr(3+)LiCAF laser oscillator employing broadband double-chirped mirrors for second- and third-order dispersion compensation. Fine adjustment of dispersion is accomplished with a fused-silica prism pair. The result demonstrates that Raman-induced self-frequency shifting of the pulse does not limit sub-10-fs pulse generation from colquiriite crystals.

Generation of 20-fs pulses by a prismless Cr(4+):YAG laser

Ultrafast optical pulses shorter than 20 fs with 400-mW average power at a 110-MHz repetition rate have been generated by a Cr(4+):YAG laser with only double-chirped mirrors for dispersion compensation. The corresponding pulse spectrum has a peak intensity at 1450 nm and extends from 1310 to 1500 nm full width at half-maximum (FWHM). These pulses, which are believed to be the shortest generated to date from a Cr(4+):YAG laser, are only four optical cycles within the FWHM intensity width.

Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors

We report on double-chirped mirrors with custom-tailored dispersion characteristics over a bandwidth of 170 THz in the visible. The mirrors are used in a prismless compressor for a noncollinear optical parametric amplifier in the visible. The compressed pulses, characterized for the what is believed to be first time by use of the spectral phase interferometry for direct electric field reconstruction technique, display a nearly flat phase from 510 to 710 nm and have a duration of 5.7 fs.

Forbidden gaps in periodic anisotropic layered media

The general case of obliquely incident plane-wave propagation in periodic anisotropic layered media is presented. Arbitrary permittivity tensors of the two alternating anisotropic layers are considered. An immersion model is used with the assumption that each layer is embedded between two isotropic regions that have the same index of refraction as the isotropic medium of incidence and a thickness that is set equal to zero. Then explicit relations are presented for normally incident plane waves in periodic structures that consist of alternating biaxial layers of arbitrary principal-axis orientation. Specific cases of alternating isotropic and biaxial layers are also considered. Unit cell translation matrices are presented for both traveling directions, from the left to the right and vice versa. Dispersion relations that contain information regarding the propagation bands and the forbidden gaps in periodic anisotropic structures are presented.

Relation between coupled-mode theory and equivalent layers for multilayer interference coatings

The method of equivalent layers is a commonly used technique for designing optical multilayer interference coatings. Herpin's theorem [C. R. Acad. Sci. 225, 182 (1947)] states that every symmetrical multilayer structure is equivalent, at one arbitrary wavelength, to a single homogeneous layer. The Herpin equivalent layer is described by two design parameters, the equivalent index and the equivalent thickness. Alternatively, we recently developed an exact coupled-mode analysis for the description of multilayer interference coatings composed of a symmetrical combination of layers. The design parameters of the coupled-mode theory are the exact coupling coefficient and the exact detuning coefficient. Recently we used this method in the design of chirped mirrors for dispersion compensation. We prove that the two methods are equivalent and derive relations that link the design parameters of both formalisms. By use of these relations it is possible to translate between the coupled-mode formalism and the method of equivalent layers. The simultaneous availability of both design methods gives a new perspective on the analytical design of optical interference coatings with challenging spectral response characteristics.