Multiphoton microscopy (MPM) has found a niche in the world of biological imaging as the best noninvasive means of fluorescence microscopy in tissue explants and living animals. Coupled with transgenic mouse models of disease and 'smart' genetically encoded fluorescent indicators, its use is now increasing exponentially. Properly applied, it is capable of measuring calcium transients 500 microm deep in a mouse brain, or quantifying blood flow by imaging shadows of blood cells as they race through capillaries. With the multitude of possibilities afforded by variations of nonlinear optics and localized photochemistry, it is possible to image collagen fibrils directly within tissue through nonlinear scattering, or release caged compounds in sub-femtoliter volumes.

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Nonlinear magic: multiphoton microscopy in the biosciences

Microwave photonics, which brings together the worlds of radiofrequency engineering and optoelectronics, has attracted great interest from both the research community and the commercial sector over the past 30 years and is set to have a bright future. The technology makes it possible to have functions in microwave systems that are complex or even not directly possible in the radiofrequency domain and also creates new opportunities for telecommunication networks. Here we introduce the technology to the photonics community and summarize recent research and important applications.

Microwave photonics combines two worlds

A multiphoton microscopy based on coherent anti-Stokes Raman scattering is accomplished with near-infrared ultrashort laser pulses. We demonstrate vibrational imaging of chemical and biological samples with high sensitivity, high spatial resolution, noninvasiveness, and three-dimensional sectioning capability. {copyright} {ital 1999} {ital The American Physical Society}

Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering

Confocal [1] and multiphoton [2] fluorescence microscopy have become powerful techniques for threedimensional imaging of chemical and biological samples, especially for live cells. This coincides with developments of various natural and artificial fluorescent probes for cellular constituents [3]. For chemical species or cellular components that either do not fluoresce or cannot tolerate labeling, infrared microscopy and spontaneous Raman microscopy can be used as contrast mechanisms based on vibrational properties. Conventional infrared microscopy is limited to low spatial resolution because of the long wavelength of light used. High resolution Raman microscopy of biological samples has been demonstrated with a confocal microscope [4]. However, the intrinsically weak Raman signal necessitates high laser powers (typically .10 mW) and is often overwhelmed by the fluorescence background of the sample. A multiphoton microscopy based on coherent anti-Stokes Raman scattering (CARS) [5] was put forward as an alternative way of providing vibrational contrast [6]. However, the sensitivity of CARS microscopy was limited by the nonresonant background signal, and high resolution three-dimensional sectioning was not achieved. In the study reported here, we demonstrate CARS microscopy in the chemically interesting vibrational spectral region around 3000 cm21 with high spatial resolution and three-dimensional sectioning capability. Most importantly, the use of near-infrared laser pulses generated by a Ti:sapphire laser s,855 nmd and an optical parametric oscillator/amplifier s,1.2 mmd allows a significant improvement in signal to background ratio in CARS detection. Unlike spontaneous Raman microscopy, the highly sensitive CARS microscopy requires only a moderate average power for excitation s,0.1 mWd, tolerable by most biological samples. CARS spectroscopy has been extensively used as a spectroscopic tool for chemical analyses in the condensed and gas phases [7]. In doing CARS spectroscopy, a pump laser and a Stokes laser beam, with center frequencies of np and nS , respectively, are spatially overlapped. The CARS signal at 2np 2 nS is generated in a direction determined by the phase-matching conditions. When the frequency difference np 2 nS coincides with the frequency of a molecular vibration of the sample, the CARS

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Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.

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From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Third harmonic generation near the focal point of a tightly focused beam is used to probe microscopical structures of transparent samples. It is shown that this method can resolve interfaces and inhomogeneities with axial resolution comparable to the confocal length of the beam. Using 120 fs pulses at 1.5 μm, we were able to resolve interfaces with a resolution of 1.2 μm. Two-dimensional cross-sectional images have also been produced.

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Nonlinear scanning laser microscopy by third harmonic generation

We demonstrate an innovative method for a real-time interrogation of fiber Bragg gratings based on low-coherence spectral interferometry of noiselike pulses. By analyzing the spectral interference at the output of a Michelson interferometer we obtained the impulse response of the grating with a time resolution of ∼350 fs. Using the Gabor transformation, we could directly detect nonuniform regions inside the grating and could measure the spatial dependence of the resonance wavelength along the grating.

http://webee.technion.ac.il/people/horowitz/articles/interog.pdf

Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses.

We have demonstrated, for the first time to our knowledge, second‐harmonic generation for a broad input wavelength range of 750–1064 nm in SrxBa1−xNb2O6 crystals, with a controllable spread spectrum of quasiphase matching. Second‐harmonic conversion efficiencies of up to ∼1% were observed. This was done without any temperature or angular tuning of the crystal. The phase matching was obtained by inducing alternating ferroelectric domains in the crystal in real time, using a novel fixing process which is based on screening. The broadband capability of the conversion is allowed by a spread in the range of the domain widths.

http://webee.technion.ac.il/people/fischer/Papers/1993%20APL%2062,%202619%20Broadband%20SHG%20in%20SBN%20by%20phase%20matching%20with%20domain%20gratings.pdf

Broadband second‐harmonic generation in SrxBa1−xNb2O6 by spread spectrum phase matching with controllable domain gratings

We demonstrate a new inverse scattering algorithm for reconstructing the structure of highly reflecting fiber Bragg gratings. The method, called integral layer-peeling (ILP), is based on solving the Gel'fand-Levitan-Marchenko (GLM) integral equation in a layer-peeling procedure. Unlike in previously published layer-peeling algorithms, the structure of each layer in the ILP algorithm can have a nonuniform profile. Moreover, errors due to the limited bandwidth used to sample the reflection coefficient do not rapidly accumulate along the grating. Therefore, the error in the new algorithm is smaller than in previous layer peeling algorithms. The ILP algorithm is compared to two discrete layer-peeling algorithms and to an iterative solution to the GLM equation. The comparison shows that the ILP algorithm enables one to solve numerically difficult inverse scattering problems, where previous algorithms failed to give an accurate result. The complexity of the ILP algorithm is of the same order as in previous layer peeling algorithms. When a small error is acceptable, the complexity of the ILP algorithm can be significantly reduced below the complexity of previously published layer-peeling algorithms.

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Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings

We demonstrate a new method to generate broad spectrum chirped microwave pulses using an electrooptical system. Two fiber Bragg gratings and a mode-locked fiber laser were used to generate pulses with a linear frequency chirp. The bandwidth of the microwave pulses can be significantly broader than the bandwidth that can be obtained using electronic systems. The parameters of the chirp can be easily controlled by adjusting the parameters of the optical system. The same method can be used to generate microwave pulses with a complex frequency modulation.

Moshe Horowitz

Papers

Nonlinear scanning laser microscopy by third harmonic generation

Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses.

Broadband second‐harmonic generation in SrxBa1−xNb2O6 by spread spectrum phase matching with controllable domain gratings

Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings

Optical generation of linearly chirped microwave pulses using fiber Bragg gratings