Jesús Garduño-Mejía

Designer femtosecond pulses using adaptive optics

We describe a femtosecond pulse shaper using a deformable membrane mirror. The pulses are measured with a real time second-harmonic-generation frequency-resolved optical gating system. Pulse shapes are modified according to a prescribed spectral phase. Accurate spectral phase design as well as pulse intensity modulation was achieved by using negative feedback mirror-surface control. Convergence to the chosen spectral phase design was typically achieved within several seconds.

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: 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.

Third-order dispersion effects generated by non-ideal achromatic doublets on sub-20 femtosecond pulses

Gaussian temporal envelope pulses with initial durations of 10 fs, 15 fs and 20 fs and a carrier wavelength of 810 nm were analyzed at the paraxial focal plane of non-ideal achromatic doublet lenses for well-collimated incoming pulses parallel to the optical axis. The wave vector is expanded up to third order, to investigate the effect of third-order group velocity dispersion on the pulse and the results are compared to those obtained when the wave number is expanded up to second order. The propagation time difference and the primary spherical aberration were included in the calculations using the thin lens approximation theory. Results are presented for a homogenous illumination beam.

Experimental method to characterize the retardance function of optical variable retarders

In this work, we present an experimental method to characterize variable optical retarders, which can have linear or non-linear behavior of the retardance variation. A theoretical analysis of such is presented using a combination of Stokes vectors and Mueller matrixes for three different optical retarders. A straightforward method for phase unwrapping, or reconstructing the original phase from the measured retardance, is proposed that yields high-accuracy results. This work can be used in an undergraduate optics lab to help students understand the concepts of retardance and its control and also how variable retardance devices work.

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.

Aberration effects on femtosecond pulses generated by nonideal achromatic doublets

There are three main effects that affect the femtosecond pulse focusing process near the focal plane of a refractive lens: the group velocity dispersion (GVD), the propagation time difference (PTD), and the aberrations of the lens. In this paper we study in detail these effects generated by nonideal achromatic doublets based on a Fourier-optical analysis and Seidel aberration theory considering lens material, wavelength range, lens surface design, and temporally and spatially uniform and Gaussian intensity distributions. We show that the residual chromatic aberration in achromatic lenses, which has been neglected so far, has a considerable effect on the focusing of pulses shorter than 20 fs in the spectral range between the UV and IR, 300 to 1100 nm, and is particularly important in the blue and UV spectral range. We present a general fitted function for an estimation of the pulse stretching parameter, which depends only on the numerical aperture and focal length of the doublet as well as the wavelength of the carrier of the pulse.

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.

Analytical method for calculating the electric field envelope of ultrashort pulses by approximating the wavenumber up to third order

For optical pulses shorter than 20 fs duration or highly dispersive materials in the visible range of the spectrum, high-order terms in the Taylor expansion for the wave vector, around the carrier frequency, should be considered. By expanding the wave vector near the center of optical frequency ω0 in a Taylor series up to the third-order approximation, we present an analytical method for calculating the electric field envelope of a pulse after it has propagated through a medium that contributes second- and third-order group velocity dispersion. To verify the method we present some examples for both 20 and 15 fs pulses propagating through pieces of glass made of low and high dispersive material. Limitations of the method are discussed.

Real time femtosecond optical pulse measurement using a video-rate frequency-resolved optical gating system

We describe an improved instrument for measuring at video rate (30 frames per second) the second-harmonic frequency-resolved optical gating trace of femtosecond pulses from a mode-locked laser oscillator. The system comprises separate scanning acquisition and pulse retrieval elements which together enable the exact pulse profile to be viewed in real time with a typical refresh rate of 1 Hz. Details are given of the optical system used, the electronic synchronization circuits and the acquisition and retrieval software employed.