Nonlinear focal shift due to the Kerr effect for a Gaussian beam focused by a lens.

When a low-power, monochromatic Gaussian beam is focused by a thin lens in air and the waist of the beam is in the plane of the lens, there is a shift of the focus position if the waist of the beam is much smaller than the size of the lens. The point of maximum intensity relative to the geometrical focal point shifts closer to the lens. We show that for ultra-intense light beams, when the Kerr effect is unavoidable, there is a nonlinear focal shift. The nonlinear focus position shifts closer to the lens for laser powers below the critical power. To avoid the nonlinear focal shift below the critical power, the correct combination of Gaussian beam waist and focal system has to be used in the experimental setup. It will be shown that as the Fresnel number N w associated with the Gaussian beam radius increases, the nonlinear focal shift first increases and then begins to decrease.

Polarimetric measurement of non-depolarizing optical systems.

The use of polarization measurements has become more common in recent years, as it gives more information than pure intensity measurements. Polarimetric components such as fixed or variable retarders and polarizers must be included in optical systems to obtain the polarization parameters required, and in many cases the optical system also includes other components such as relay and/or imaging optical systems. In this work we present a simple and robust method for the polarimetric characterization of non-depolarizing polarization components and other optical elements in the system, which does not require a full polarimeter. Since there is no depolarization, we represent the components as pure retarders with diattenuation and find their parameters (transmittance for the polarization components, angle of orientation of the fast axis, and retardance), from which we can retrieve their Mueller matrix. Our results show that the proposed method is accurate when compared with results obtained with a Mueller matrix dual-rotating retarder polarimeter calibrated using the eigenvalue calibration method, considered in this work as the gold standard, and is comparatively easier than the latter to implement, particularly for imaging polarimeters.

Rough surface scattering using a source able to produce an incident beam with controlled polarization and coherence.

We present a comparison of the first numerical and experimental results for the scattering of light from rough surfaces using a recently developed variable coherence polarimetry source that permits obtaining information on the object without having to scan over incidence or scatter angle. We present, for the first time, we believe, the application of this source to a 1D rough surface and show how to analyze the scattered field to retrieve useful information about the surface. This source uses a liquid-crystal phase modulator to control the polarization as well as the coherence of the beam illuminating the rough surface. Changing the polarization state distribution at the source plane, by controlling the phase distribution on a spatial light modulator, gives a scan of two source spots over the rough surface. The scattered beam is analyzed with a Stokes polarimeter. The Kirchhoff approximation is used to calculate the scattered Stokes vector using the experimental incident Stokes vector and intensity distribution as a source. Good agreement is obtained between the numerical and experimental results, for a simple calculation of the number of intensity maxima obtained as the two first-order source spots are scanned across the sample.

Characterization of retardance spatial variations over the aperture of liquid-crystal variable retarders.

We present a comparison of two experimental methods to measure retardance as a function of applied voltage and as a function of position over the aperture of liquid-crystal variable retarders. These measurements are required for many applications, particularly in polarimetry. One method involves the scan of an unexpanded laser beam over the aperture, and the other uses an expanded beam from a LED and a CCD camera to measure the full aperture with a single measurement. The first method is time consuming, is limited in the measured spatial resolution, and requires more expensive equipment to perform the scan, whereas the second method is low cost, with the spatial resolution of the CCD, and fast, but in principle has variations of the incident beam over the aperture that affect the measured retardance values. The results obtained show good agreement for the average values of retardance for the two methods, but the expanded-beam method shows more noise, particularly close to the voltage values at which the variable-retarder retardance versus voltage curves are unwrapped. These retardance variations can be reduced by smoothing the retardance image, which makes the expanded-beam method an attractive method for polarimetry applications since it gives the complete information in the full aperture of the device with the additional advantages of low cost, simplicity, and being less time consuming.

Simultaneous measurement of DC two-photon absorption signal offset and amplitude of the intensity autocorrelation in the focusing of femtosecond pulses.

In this work, the DC two-photon absorption signal offset (${{\rm DC}_{\rm TPA}}$DCTPA) and the amplitude of the autocorrelation (${{\rm A}_{\rm AC}}$AAC) are measured simultaneously around the focal point of an apochromatic microscope objective using the z-scan autocorrelation technique. The ${{\rm A}_{\rm AC}}$AAC is obtained from the nonlinear sensor response given by the two-photon-absorption, generated in a GaAsP photodiode, for femtosecond laser pulses. We verify that the change in the ${{\rm DC}_{\rm TPA}}$DCTPA signal along $z$z is coincident with the amplitude of the intensity autocorrelation, and that the highest amplitude of the AC is reached at the same position as the highest amplitude of the ${{\rm DC}_{\rm TPA}}$DCTPA signal. The ${{\rm DC}_{\rm TPA}}$DCTPA signal is typically used as a reference for the alignment in a collinear intensity autocorrelator, and we show that it can also be used as a practical procedure to estimate the depth of focus. The ${{\rm DC}_{\rm TPA}}$DCTPA signal measurement allows us to locate the optimum spatial-temporal coupling given by the highest amplitude of the intensity autocorrelation. Additionally, we find a variation in the pulse duration within the same region due to the radially varying group delay dispersion.

Algorithm to filter the noise in the spectral intensity of ultrashort laser pulses.

We have developed an algorithm to filter the noise in the spectral intensity of ultrashort laser pulses. The filtering procedure consists of smoothing the noise by using the Savitzky-Golay filter, removing the offset, and using a super-Gaussian window to truncate the frequencies of the spectrum. We have modeled bandwidth-limited ultrashort pulses with Gaussian modulated frequencies to show the estimation of the carrier wavelength, reconstruction of the intensity pulse profile, and pulse duration after applying the algorithm. Theoretical results are presented for pulse durations between 5 fs and 100 fs with a carrier wavelength of 825 nm and three different amounts of signal-to-noise ratio (SNR): 30 dB, 20 dB, and 15 dB, normally found in experiments. The algorithm is also applied to an experimental spectral intensity from a homemade Ti:sapphire laser that produces pulses of about 20 fs at 825 nm at 100 MHz. We will show that using only a low-pass Fourier filter and removing offset is not enough to recover the spectral intensity when a large SNR is present, which may be the case when the ultrashort laser beam has been manipulated to compensate for the group velocity dispersion of an external optical system. In cases like this, the use of the Savitzky-Golay filter prior to the super-Gaussian filter improves the recovery of the carrier wavelength and the spectral intensity. We will also show that the algorithm presented in this paper is suitable for experimental analysis and requires limited user intervention.

Impact of frequency-dependent spherical aberration in the focusing of ultrashort pulses.

In this paper, the temporal and spatial intensity pulse distributions are calculated around the focal region of an optical system using a combination of ray tracing and a wave propagation method. We analyze how to measure the width of the intensity pulse distributions to estimate pulse duration and spot size in order to study the impact of the variation of spherical aberration with frequency in a pulse on the intensity distributions. Two experimental techniques used in the laboratory are also modeled: the knife-edge test to measure spatial distribution and the intensity autocorrelation technique to measure the temporal distribution. We use two measuring criteria, the full-width half-maximum (FWHM) and standard deviation (σ), to compare the spatial and temporal intensity distributions of the calculated diffraction patterns and those obtained from the simulated experimental techniques. We show that the FWHM is not a good criterion, since it gives different results in the measured intensity distributions in time and space when they are measured directly from the theoretical modeling and when they are measured from the modeled experimental techniques used in the laboratory. The standard deviation, however, is a consistent criterion, giving the same results for the calculated intensity distributions and the modeled experiments.

Liquid refractive index measured through a refractometer based on diffraction gratings.

We developed two versions of refractometers to measure the refractive index of liquids. One refractometer comprises a glass cell with a surface relief grating on the inner face of one of its walls, while the other one is a microfluidic channel in the form of serpentine that behaves as a grating. Measurements of the liquid refractive index were performed by sensing the first order intensity. Several liquids have been used including an organic one. Calibration plots are shown.

Liquid Temperature Measurements Using Two Different Tunable Hollow Prisms.

This paper describes the design, fabrication, and testing of two hollow prisms. One is a prism with a grating glued to its hypotenuse. This ensemble, prism + grating, is called a grism. It can be applied as an on-axis tunable spectrometer. The other hollow prism is a constant deviation one called a Pellin-Broca. It can be used as a tunable dispersive element in a spectrometer with no moving parts. The application of prisms as temperature sensors is shown.

Diffraction grating-based sensing optofluidic device for measuring the refractive index of liquids.

We describe a simple and versatile optical sensing device for measuring refractive index of liquids. The sensor consists of a sinusoidal relief grating in a glass cell. Device calibration is done by pouring in the cell different liquids of known refractive indices. Each time a liquid is poured first order intensity is measured. The fabrication process and testing of the prototype device is described. An application in the measurement of temperature is also presented.

Reflection formulae for ray tracing in uniaxial anisotropic media using Huygens's principle.

Ray tracing in uniaxial anisotropic materials is important because they are widely used for instrumentation, liquid-crystal displays, laser cavities, and quantum experiments. There are previous works regarding ray tracing refraction and reflection formulae using the common electromagnetic theory approach, but only the refraction formulae have been deduced using Huygens's principle. In this paper we obtain the reflection expressions using this unconventional approach with a specific coordinate system in which both refraction and reflection formulae are simplified as well as their deduction. We compute some numerical examples to compare them with the common expressions obtained using electromagnetic theory.

Deviation from orthogonal polarization for ordinary and extraordinary rays in uniaxial crystals.

We have derived a closed-form expression for the angle between polarizations of ordinary and extraordinary rays in uniaxial crystals for, first, any two rays propagating in the material, and, second, for rays coming from refraction. We show the cases in which orthogonality holds and that, in general, the deviation from orthogonality is rather small, for it depends on the difference of the optical indices. Specific examples for calcite and quartz are given.

Mode-coupling enhancement by pump astigmatism correction in a Ti:Sapphire femtosecond laser.

To pump a solid-state femtosecond laser cavity, a beam from a CW laser is focused by a single lens into the laser crystal. To increase the output power of the laser, the overlap of the laser mode with the pump mode should be maximized. This is particularly important in the so-called mode coupling and the Kerr-lens mode locking (KLM) operation, where the change in beam waist at the position of the gain medium is exploited to enhance the mode overlap with the pump laser in the crystal. In this paper, the astigmatism in the pump beam is reduced by tilting the pump lens. A Gaussian beam is propagated through the complete focusing system-pump lens, tilted spherical mirror, and crystal cut at Brewster's angle-to show the astigmatism inside the crystal as a function of the tilt of the pump lens. A genetic algorithm is presented to optimize the mode coupling between the pump and laser beam inside the crystal by tilting the pump lens. Experimental results are presented to verify the design, showing an increase in the output power of the laser cavity of about 20%.

Spectrometer and scanner with optofluidic configuration.

We present a spectrometer and scanner based on optofluidic configurations. The main optical component of the spectrometer is a compound optical element consisting of an optofluidic lens and standard blazed diffraction grating. The spectrum size can be changed by filling the lens cavity with different liquids. The scanner comprises two hollow 45° angle prisms oriented at 90° to each other. By changing the liquid inside the prisms, two-dimensional light beam scanning can be performed.

Two-photon absorption spectrometers for near infrared.

We present a Silicon-based Charge-Coupled Device (Si-CCD) sensor applied as a cost-effective spectrometer for femtosecond pulse characterization in the Near Infrared region in two different configurations: two-Fourier and Czerny-Turner setups. To test the spectrometer's performance, a femtosecond Optical Parametric Oscillator with a tuning range between 1100 and 1700 nm and a femtosecond Erbium-Doped Fiber Amplifier at 1582 nm were employed. The nonlinear spectrometer operation is based on the Two-Photon Absorption effect generated in the Si-CCD sensor. The achieved spectrometer resolution was 0.6 ± 0.1 nm with a threshold peak intensity of 2×106Wcm2. An analysis of the nonlinear response as a function of the wavelength, the response saturation, and the criteria to prevent it are also presented.

Refractive index measurement through image analysis with an optofluidic device.

We present a novel optical method, to our knowledge, to measure the refractive index of liquids by means of the images produced by an optofluidic lens. In addition we propose a new method to make optofluidic lenses.

Optofluidic compound microlenses made by emulsion techniques.

Here we present a new method to make liquid lenses. It is based on the microfluidics method and involves the preparation of emulsions one drop at a time. Tests of lenses by image formation are presented. Experimental results are compared with results of an optical design program. We also present a new type of lens that we call a Compound Lens which consists of two spherical lenses, one inside the other.

Optofluidic variable focus lenses.

Here we propose optofluidic spherical microlenses that can change their focal distance by varying the refractive index of the liquid that composes them. These lenses are fabricated in the bulk of a polymeric mixture. Results of a characterization study of the profile of the lenses, the image forming capability, and the behavior of the focal distance as a function of the refractive index are presented. Ionic liquids are suggested as a source of liquids useful for fabricating this type of lens.

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.

Low-energy/pulse response and high-resolution-CMOS camera for spatiotemporal femtosecond laser pulses characterization @ 1.55 µm.

In this work, we present a commercial CMOS (Complementary Metal Oxide Semiconductor) Raspberry Pi camera implemented as a Near-Infrared detector for both spatial and temporal characterization of femtosecond pulses delivered from a femtosecond Erbium Doped Fiber laser (fs-EDFL) @ 1.55 µm, based on the Two Photon Absorption (TPA) process. The capacity of the device was assessed by measuring the spatial beam profile of the fs-EDFL and comparing the experimental results with the theoretical Fresnel diffraction pattern. We also demonstrate the potential of the CMOS Raspberry Pi camera as a wavefront sensor through its a nonlinear response in a Shack-Hartmann array and for the temporal characterization of the femtosecond pulses delivered from the fs-EDFL through TPA Intensity autocorrelation measurements. The direct pulse detection and measurement, through the nonlinear response with a CMOS, is proposed as a novel and affordable high-resolution and high-sensitivity alternative to costly detectors such as CCDs, wavefront sensors and beam profilers @ 1.55 µm. The measured fluence threshold, down to 17.5 µJ/cm2, and pJ/pulse energy response represents the lowest reported values applied as a beam profiler and a TPA Shack-Hartmann wavefront sensor, to our knowledge.