Nonlinear confocal positioner for micron-scale target alignment.

This paper presents a novel target positioner system that exhibits high sensitivity and accuracy. Specifically, the system is capable of precisely locating rough target surfaces within a micron-scale in the focal plane. The high sensitivity comes from the nonlinear detection scheme which uses the two-photon-absorption process in a Si-photodiode and a CMOS sensor at 1550 [nm]. The setup employs a confocal configuration that is easy to align and does not require a conjugated focal plane selective aperture (pinhole), thus demonstrating its feasibility and tilt tolerance of the target. Moreover, the system offers high accuracy up to 5 [µm], which corresponds to the step size of the focus scanning. The presented positioner system has potential applications in microfabrication with lasers and laser-driven plasma accelerators even at high repetition rates, limited by the detection bandwidth of the photodiode. Additionally, the principle can be extended to cameras if spatial information is needed and the system design can be extended to other spectral ranges with minimal changes.

High accuracy astigmatic-focusing system for laser targets.

An accurate location of the focal position with respect to a solid target is a key task for different applications, for instance, in laser driven plasma acceleration for x-ray generation where minimum required intensities are above 1014W/cm2. For such practical applications, new approaches for focus location and target delivery techniques are needed to achieve the required intensity, repeatability, and stability. There are different techniques to accomplish the focusing and target positioning task such as interferometry-, microscopy-, astigmatism-, and nonlinear-optics-based techniques, with their respective advantages and limitations. We present improvements of a focusing technique based on an astigmatic method with potential applications where maximum intensity at the target position is necessary. The presented technique demonstrates high accuracy up to 5 µm, below the Rayleigh range, and also its capability to work in rough surfaces targets and tilt tolerance of the target, with respect to the normal of the target surface.

Wavelet-based method for spectral interferometry filtering.

In this work, we study the effects of noise present on spectral interferometry signals, for femtosecond pulse retrieval such as in the SPIDER technique (spectral phase interferometry for direct e-field reconstruction). Although previous works report SPIDER robustness, we have found that noisy signals with low signal-to-noise ratio (SNR), in the acquired spectral interferogram, could cause variations in the temporal pulse intensity retrieval. We demonstrate that even in a filtered SPIDER signal, following standard procedures, at some point the noise on the spectral interferogram could affect the spectral phase retrieval. As a novel alternative for spectral interferograms filtering, we have applied the wavelet transform and propose a target criterion to automatize the optimization algorithm. We apply this method on SPIDER signals and analyze its effectiveness on the spectral phase retrieval. We present numerical and experimental results to show the improvement in the phase retrieval and the temporal pulse reconstruction after applying this filtering method and compare the results with a standard method.

Efficiency signal conversion parameter to evaluate astigmatic femtosecond-optical parametric oscillator cavities.

In this work, we define the efficiency signal conversion numerical parameter, Veff, useful to evaluate the operation efficiency of femtosecond-Optical Parametric Oscillator (fs-OPO) cavities considering the astigmatism effect. For the validation of the Veff, we have performed experimental measurements. We present different high efficiency home-made singly resonant fs-OPO cavities, with signal tuneability from 1.1 µm to 1.6 µm based on a 0.5 mm Periodically Poled Lithium Niobate doped with MgO (MgO:PPLN) crystal. We have also defined the pump energy threshold per crystal unit length, ζp,th. Pump threshold, achieved by following the Veff, was 142 mW at 810 nm, and ζp,th = 2.10 nJ/mm, the lowest value, in comparison with other studies. The Veff is based on an ABCD matrix Gaussian beam propagation method, which calculates the mode coupling between the pump and signal beams along the crystal under different cavity configurations taking into account the astigmatism. The model was compared and tested with 3 different experimental singly resonant fs-OPO ring cavity configurations that we have defined as single-folded, two-folded, and direct-pump cavity.

Time-domain measurements reveal spatial aberrations in a sub-surface two-photon microscope.

We show that in a nonlinear microscopy system the effects of chromatic and spherical aberrations are revealed by a difference in the focal positions corresponding to the shortest pulse duration and the minimum lateral resolution. By interpreting experimental results from a high-numerical-aperture two-photon microscope using a previously reported spatio-temporal model, we conclude that the two-photon autocorrelation of the pulses at the focal plane can be used to minimize both the chromatic and spherical aberrations of the system. Based on these results, a possible optimization strategy is proposed whereby the objective lens is first adjusted for minimum autocorrelation duration, and then the wavefront before the objective is modified to maximize the autocorrelation intensity.

Autocorrelation z-scan technique for measuring the spatial and temporal distribution of femtosecond pulses in the focal region of lenses.

In this work we present an Autocorrelation z-scan technique to measure, simultaneously, the spatial and temporal distribution of femtosecond pulses near the focal region of lenses. A second-order collinear autocorrelator is implemented before the lens under test to estimate the pulse width. Signals are obtained by translating a Two Photon Absorption (TPA) sensor along the optical axis and by measuring the second-order autocorrelation trace at each position z. The DC signal, which is typically not considered important, is taken into account since we have found that this signal provides relevant information. Experimental results are presented for different lenses and input wavefronts.

Temporal widening of a short polarized pulse focused with a high numerical aperture aplanatic lens.

We present a theoretical analysis of the field distribution in the focal plane of a dispersionless, high numerical aperture (NA) aplanatic lens for an x-polarized short pulse. We compare the focused pulse spatial distribution with that of a focused continuous wave (CW) field and its temporal distribution with the profile of the incident pulse. Regardless of the aberration free nature of the focusing aplanatic lens, the temporal width of the focused pulse widens considerably for incident pulses with durations on the order of a few cycles due to the frequency-dependent nature of diffraction phenomena, which imposes a temporal diffraction limit for focused short pulses. The spatial distribution of the focused pulse is also affected by this dependence and is altered with respect to the diffraction limited distribution of the CW incident field. We have analyzed pulses with flat top and Gaussian spatial irradiance profiles and found that the focused pulse temporal widening is less for the Gaussian spatial irradiance pulse, whereas the spatial distribution variation is similar in both cases. We present results of the focused pulsewidth as a function of the NA for the two spatial irradiance distributions, which show that the Gaussian irradiance pulse outperforms the flat top pulse at preserving the incident pulse duration.

Temporal spreading generated by diffraction in the focusing of ultrashort light pulses with perfectly conducting spherical mirrors.

We study femtosecond pulses at the focal plane of a perfectly conducting spherical mirror which is a dispersionless system, that is, it introduces no group velocity dispersion and no propagation time difference to the pulses after reflection. By using the scalar diffraction theory we will show that the neglected terms in the diffraction integral, when using the approximation of the bandwidth being smaller than the frequency of the carrier, have a significant influence on imaging if a laser pulse of a few femtoseconds is used in time-resolved imaging. The neglected terms introduce temporal spreading to extremely short pulses of a few optical cycles incident on the mirror, which avoids a fully compensated pulse, i.e., a one optical cycle pulse, at the focus of the mirror. The study in this paper also applies to refracting optical systems such as microscope objectives or lenses.

Gauss-Legendre quadrature method used to evaluate the spatio-temporal intensity of ultrashort pulses in the focal region of lenses.

We analyze the spatio-temporal intensity of sub-20 femtosecond pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. The numerical errors in this method are negligible by taking 96 nodes and the computational time is reduced by 95% compared to the integration method by rectangles. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). This last effect, however, is also significant. For sub-20 femtosecond pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect. The design of an apochromatic doublet is presented in this paper and the spatio-temporal intensity of the pulse at the focal region of this doublet is compared to that given by the achromatic doublet.

Effects of primary spherical aberration, coma, astigmatism and field curvature on the focusing of ultrashort pulses: homogenous illumination.

We analyze the spatiotemporal intensity of pulses with durations of 20 fs and shorter and a carrier wavelength of 810 nm at the paraxial focal plane of an achromatic doublet lens. The incident pulse is well-collimated, and we use the Seidel aberration theory for thin lenses to evaluate the phase change due to the aberrations of the lens. In a set of cemented thin lenses with the stop at the lens, there is only spherical aberration, coma, astigmatism and field curvature, whereas the distortion aberration in the phase front is zero. We analyze the effect of these aberrations in the focusing of ultrashort pulses for homogenous illumination. We will show that the temporal spreading introduced by these aberrations in pulses shorter than 20 fs at 810 nm is very small but the spatial spreading is not, which reduces the intensity of the pulse considerably.

Effects of primary spherical aberration, coma, astigmatism, and field curvature on the focusing of ultrashort pulses: Gaussian illumination and experiment.

We analyze the spatiotemporal intensity of Gaussian temporal envelope pulses with initial durations of 200 fs and a carrier wavelength of 810 nm at the paraxial focal plane of an achromatic doublet lens for a well-collimated incoming pulse beam by using the Seidel aberration theory for thin lenses with the stop at the lens. We analyze the effect of these aberrations in the focusing of ultrashort pulses for Gaussian illumination and present experimental results for 200 fs pulses focused by a near-IR achromatic doublet.

Selection of glasses for achromatic doublets with reduced secondary spectrum. I. Tolerance conditions for secondary spectrum, spherochromatism, and fifth-order spherical aberration.

We describe a way of selecting pairs of glasses for both thin cemented achromatic doublets and thin aplanatic achromatic doublets with a reduced secondary spectrum. By taking one pair of glasses at a time, we can compute and display the secondary spectrum in increasing value. The number of solutions based on the magnitude of the secondary spectrum alone is huge: 40,804 pairs. Some tests are applied at different stages of the design procedure to reduce the number of acceptable solutions. Aberrations that cannot be corrected, namely, spherochromatism and fifth-order spherical aberration, are further calculated to reduce drastically the number of acceptable solutions. To do this, we establish tolerance conditions based on the relationship between the Strehl intensity ratio and the rms wave-aberration error so that the rms wave error is minimized in the presence of the secondary spectrum, spherochromatism, and the fifth-order spherical aberration.

Selection of Glasses for Achromatic Doublets with Reduced Secondary Spectrum. II. Application of the Method for Selecting Pairs of Glasses with Reduced Secondary Spectrum.

The method for selecting pairs of glasses for thin aplanatic achromatic doublets and cemented achromatic doublets with a reduced secondary spectrum, presented in Part I, is applied to the design of two optical systems. The first is a Lister-type 10x microscope objective with a numerical aperture of 0.25 working in the visible band. The second is a camera f/7.5 working in the near-IR spectral band, 0.8521 mum < lambda < 2.3254 mum, of a spectrograph for the San Pedro Martir Observatory in Ensenada, México. Improvement in the performance of both optical systems is shown.

Differential equation for normal glass dispersion and evaluation of the secondary spectrum.

Some of the questions concerning secondary chromatic aberration at both sides of the visible band of the spectrum are the following: (1) What is the bandwidth at different wavelengths, given the permissible chromatic aberration circle and the lens aperture? (2) What is the size of the chromatic aberration circle, given the wavelength, the bandwidth, and the lens aperture? The answers to these and other questions may be found with the new definitions of V-number and relative partial dispersion P based on infinitesimal bandwidths that we propose. In addition, an alignment chart for the secondary color of a normal glass doublet is presented, so fast answers to the questions posed above and to other questions concerned with secondary color can be found. In addition, a continual challenge in computer-aided lens design is the use of optical glasses as design parameters in simultaneous optimization of lens systems over various regions of the spectrum. This problem could be solved if we could find an ideal glass family, not too different from real glasses, such that, given the refractive index n and the V-number at any wavelength, the indices at all wavelengths could be determined. Therefore we derive a differential equation for normal glass dispersion and present a recursive solution.

Application of the see-saw method to all refracting optical systems.

The optical see-saw diagram is a method that describes image correction to third-order approximation over a finite field of view in rotationally symmetric systems that employ aspheric surfaces. The aim of this paper is to describe the correction of aberrations caused by plane surfaces in all refracting optical systems in terms of the see-saw diagram. A lens correction algorithm based on the see-saw method is described to correct analytically the Seidel aberrations, primary spherical aberration, coma, astigmatism, and distortion, in such systems. We then apply this lens correction algorithm to the design of equivalent configurations by aspherizing different surfaces of the system, and the high-order aberrations of the equivalent configurations are evaluated by means of transverse-ray-aberration plots. Results indicate that this method gives information on what the contribution must be to the third-order aberrations that each component should provide to the system to give a better balance of high-order aberrations. Examples of the lens correction algorithm applied to lenses with six refracting surfaces and working for both finite and infinite object conjugates are given.

Profile testing of spherical surfaces by laser deflectometry.

A method for testing the profiles of spherical surfaces is presented. It consists of measuring the transversal deflection of a reflected He-Ne laser beam when the surface is rotated around an axis located near its center of curvature. A set of formulas that enables us to calculate the shape of the profile as well as the decentering of the rotation axis is obtained. By using a simple experimental setup, we found the differences between the experimental profile with respect to the ideal one; the accuracy that was obtained is ~3 µm. The method may be improved and is useful for convex as well as for concave surfaces. With minor modifications it is possible to test large surfaces and weak aspherics.