Programmable micro-optics for ultrashort pulses

We first managed to combine the advantages of low-dispersion layer optics with the near-paraxial design of ultraflat micro-optical elements—and exploit them for high-precision shaping and as diagnostics of femtosecond-laser pulses with durations of a few optical cycles—with thin-film structures fabricated by mask-supported vapor deposition.¹ With refractive, reflective, and hybrid micro-axicons (conical lenses) consisting of dielectric, metallic, or compound layers, we demonstrated that ultrashort-pulsed Bessel-like nondiffracting beams (known as ‘X pulses’ or ‘light bullets,’ described by Bessel functions) can be generated easily in linear optical setups.^2–4 The unique propagation properties of such beams, including extended depth of focus, high tilt tolerance, axial-field components, and self-reconstruction,⁵ make them very attractive for applications such as highly robust Shack-Hartmann wavefront sensors,⁶ multichannel materials processing,⁷ or 2D autocorrelation.^1,8

However, adaptive functionality is urgently required to improve the dynamic measurement range (for instance, by encoding the sub-beams of a wavefront sensor), address individual channels for more flexible processing, or significantly enhance the resolution of interferometric or holographic metrology through the use of additional phase-step procedures. Unfortunately, digital-mirror displays with large numbers of small subapertures are typically limited to amplitude switching and suffer from heat-transfer problems. Liquid-crystal spatial light modulators (LC-SLMs), on the other hand, enable phase and amplitude programming. They were first applied to temporal pulse shaping using Fourier-plane optical processors⁹ (where pulse duration is not important). However, transmitting LC-SLMs exhibit crucial pulse distortions that become apparent as dispersion in the substrate and liquid-crystal layer. We recently achieved important improvements by introducing new types of liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs). Their substrate dispersion is eliminated by working in reflection (liquid-crystal layer on a mirror).

We systematically analyzed the key problem of pulse transfer as a function of spectral phase and temporal pulse information using a titanium:sapphire laser oscillator with pulse durations of <20fs.¹⁰ We showed that (for selected types of LCoS-SLMs) excellent temporal-transfer characteristics can be obtained. We detected small residual phase distortions, which can be explained by Gires-Tournois interference.¹¹ This could be verified by diffraction experiments and spectral-phase interferometry for direct electric-field reconstruction with an extended nonlinear crystal (e.g., LX-SPIDER). Our results agree with theoretical estimates.¹⁰ The linear dependence of the LCoS-SLM phase on gray level (voltage signals) allows programming of micro-optical components using calibrated gray-scale maps.

If the maximum phase difference is divided into sufficient steps (say, 256), the resulting resolution allows approximation of phase profiles comparable to dielectric nanolayer structures. Therefore, even fringe-free nondiffracting beams (needle beams¹ or—in the pulsed regime—needle pulses) can be shaped that exhibit extraordinarily large aspect ratios. With arrays of addressable, separated femtosecond needle pulses, we demonstrated¹² the concept of diffractionless ‘flying images.’¹³ Figure 1 shows the setup of a programmable (needle) beam-array generator. In Figure 2, we show the radial intensity variation of a femtosecond Bessel beam (part of an array containing 20 illuminated elements) with conical angle θ_n(n=1, 2, 3) of a micro-axicon (programmed into the phase map) at a distance of z=28mm. The corresponding spatial frequencies vary between 0.009 and 0.0156/μm.

Figure 1. Experimental setup for programming micro-optical functionality into gray-value maps of a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). The image shows generation of an array of needle beams for multichannel processing.

Figure 2. Variable, ultrashort-pulse Bessel beam generated with a phase-only LCoS-SLM. The spatial frequency depends on the conical angle θ_n (n = 1, 2, 3) of the micro-axicon programmed in the phase map (titanium:sapphire oscillator, pulse duration 13fs, measuring distance z = 28mm). The spatial frequencies for the angular interval vary between 0.009 and 0.016/μm.

We recently tested the performance of adaptive systems, including LCoS-SLMs, for shaping complex optical fields. Figure 3 shows an example of a propagating femtosecond-wave field. In addition, we explored generating and detecting wave packets carrying a nonzero extrinsic orbital angular momentum.¹⁴ We are currently investigating 2D pulse diagnostics with wavefront-dividing Shack-Hartmann-type architectures, in particular novel schemes of spatio-temporal autocorrelators (e.g., nonlinear phase-step Bessel autocorrelators, which extract temporal information from the wobbled fringe envelopes of frequency-converted Bessel pulses¹⁵). In summary, LCoS-SLMs are promising high-resolution beam shapers for ultrafast micro-optics.¹⁶ They enable 2D spatial shaping and diagnostics of laser pulses. Under optimized conditions, wave packets with pulse durations in the sub-20fs range are transferred with acceptably low distortion. We are also investigating adaptive, nondiffracting wave phenomena like tubular beams, light slices, and phased arrays for high-resolution metrology, multichannel materials processing, and advanced methods of autocorrelation.

Figure 3. Nondiffracting propagation of a pulsed complex pattern (Max Born Institute logo) programmed into the gray-scale map of the SLM (far left). Red: Axial distance. Field of view: 2.5×2.5mm². The sub-beam diameters (at a distance of z = 3mm) were 90μm (2× Gaussian-waist radius).