We review the field of femtosecond pulse shaping, in which Fourier synthesis methods are used to generate nearly arbitrarily shaped ultrafast optical wave forms according to user specification. An emphasis is placed on programmable pulse shaping methods based on the use of spatial light modulators. After outlining the fundamental principles of pulse shaping, we then present a detailed discussion of pulse shaping using several different types of spatial light modulators. Finally, new research directions in pulse shaping, and applications of pulse shaping to optical communications, biomedical optical imaging, high power laser amplifiers, quantum control, and laser-electron beam interactions are reviewed.

Femtosecond pulse shaping using spatial light modulators

Advanced Mathematical Methods for Scientists and Engineers

We review progress in quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3. Using the electric-field poling process, we can reliably fabricate 0.5-mm-thick crystals with uniform domain structures over a 15-mm length. Periodically poled material retains the low-loss and bulk power handling properties of single-domain LiNbO3, and quasi phase matching permits noncritical phase matching with d33, the highest-valued nonlinear coefficient. Optical parametric oscillators pumped by 1.064-μm pulsed Nd:YAG lasers have been operated over the wavelength range 1.4–4 μm with tuning by temperature or by quasi-phase-matched period. We have shown an oscillation threshold as low as 0.012 mJ with a Q-switched pump laser and pumping at greater than ten times threshold without damage. We have also demonstrated a cw doubly resonant oscillator near 1.96 μm pumped directly with a commercial cw diode laser at 978 nm.

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Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO 3

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

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Domain wall nanoelectronics

Over the last decade there have been spectacular developments in ultrafast laser technology, due to the introduction of solid state active materials and of new mode-locking and amplification techniques. These advances, together with the discovery of new nonlinear optical crystals, have fostered the introduction of ultrafast optical parametric amplifiers as a practical source of femtosecond pulses tunable across the visible and infrared spectral ranges. This article summarizes the recent progress in the development of ultrafast optical parametric amplifiers, giving the basic design principles for different frequency ranges and in addition presenting some advanced designs for the generation of ultrabroadband, few-optical-cycle pulses. Finally, we also briefly discuss the possibility of applying parametric amplification schemes to large-scale, petawatt-level systems.

Ultrafast optical parametric amplifiers

We report wavelength conversion within the 1.5?µm telecommunications band based on difference-frequency generation in periodically poled lithium niobate waveguides with integrated coupling structures. A conversion efficiency of -7 dB and a normalized efficiency of 260%/W are demonstrated. Static tests show that the conversion bandwidth is 72 nm and the conversion efficiency is constant over the 20-dB range of input powers tested.

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1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures.

We demonstrate the use of an aperiodic quasi-phase-matching (QPM) grating to generate second-harmonic pulses that are stretched or compressed relative to input pulses at the fundamental frequency. We frequency doubled an externally chirped erbium-doped fiber laser generating 17-ps (FWHM) pulses at 1560 nm to produce near-transform-limited 110-fs (FWHM) pulses at 780 nm by use of a 5-cm-long lithium niobate crystal poled with a QPM grating chirped from an 18.2- to a 19.8-µm period.

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Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate.

We present a theory of ultrashort-pulse second-harmonic generation (SHG) in materials with longitudinally nonuniform quasi-phase-matching (QPM) gratings. We derive an expression for the output second-harmonic field generated in an arbitrary QPM grating from an arbitrary fundamental field, valid for arbitrary material dispersion in the undepleted-pump approximation. In the case when group-velocity dispersion can be neglected, a simple transfer-function relationship describes the SHG process. This SHG transfer function depends only on material properties and on the QPM grating design. We use this SHG transfer function to show that nonuniform QPM gratings can be designed to generate nearly arbitrarily shaped second-harmonic output pulses. We analyze in detail a technologically important example of pulse shaping: the generation of compressed second-harmonic pulses from linearly chirped fundamental input pulses. The efficiency of these interactions as well as the limits imposed by higher-order material dispersion are discussed.

Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping

We propose a simple means for compressing optical pulses with second-harmonic generation. Aperiodic quasi-phase-matching gratings impart a frequency-dependent phase shift on the second-harmonic pulse relative to the fundamental pulse and can be engineered to correct for arbitrary phase distortions. The mechanism is discussed, and a detailed analysis of the compression of quadratic phase (linear frequency) chirped pulses is presented.

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Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings

An apparatus and a method for separating a light of a first wavelength μ1 from a second wavelength μ2, where μ1<μ2, in a waveguide such as an optical fiber is described. The apparatus includes a core (12) surrounded by a depressed cladding (16), which itself is surrounded by a secondary cladding (18). The core cross-section, the depressed cladding cross-section, the secondary cladding cross-section, and the refractive indices of the core, the depressed cladding and the secondary cladding are selected to produce a fundamental mode cutoff wavelength μc such that μ1<μc<μ2, and produce a high loss at the secondary wavelength μ2. The apparatus can be used as a filter, and amplifier, a laser, or in a nonlinear optical switch.

Mark A. Arbore

Papers

1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures.

Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate.

Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping

Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings

Optical wavelength filtering apparatus with depressed-index claddings