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Letter
Vol. 42, No. 8 / April 15 2017 / Optics Letters
Laser-induced birefringence measurements by quantitative polarized-phase microscopy THOMAS DOUALLE,1 ALEXANDRE OLLÉ,1 PHILIPPE CORMONT,2 SERGE MONNERET,1
AND
LAURENT GALLAIS1,*
1
Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, Marseille 13013, France Commissariat à l’Energie Atomique et aux Energies Alternatives, Centre d’Etudes Scientifiques et Techniques d’Aquitaine (CEA CESTA), CS60001, Le Barp 33116, France *Corresponding author:
[email protected]
2
Received 24 February 2017; revised 22 March 2017; accepted 23 March 2017; posted 23 March 2017 (Doc. ID 287472); published 12 April 2017
A technique that provides quantitative and spatially resolved retardance measurement is studied for application to laser-induced modification in transparent materials. The method is based on the measurement of optical path differences between two wavefronts carrying different polarizations, measured by a wavefront sensor placed in the image plane of a microscope. We have applied the technique to the investigation of stress distribution induced by CO2 laser processing of fused silica samples. By comparing experiments to the results of thermomechanical simulations we demonstrate quantitative agreement between measurements and simulations of optical retardance. The technique provides an efficient and simple way to measure retardance of less than 1 nm with a diffraction-limited spatial resolution in transparent samples, and coupled to thermomechanical simulations it gives access to birefringence distribution in the sample. © 2017 Optical Society of America OCIS codes: (140.3330) Laser damage; (190.3270) Kerr effect; (320.7100) Ultrafast measurements. https://doi.org/10.1364/OL.42.001616
Laser micromachining of optical materials has many applications, such as realization of waveguides, integrated components, diffractive optical elements, microfluidic devices, etc. [1–3]. Such processes can lead to residual birefringence in the material that can be related to stress in the case of thermal processes with a CW laser, but it is also observed in the case of the ultrashort regime [4–6]. The birefringence levels and gradients depend on laser parameters, as the physical effects that lead to stress and anisotropy in the material. More particularly, thermomechanical stresses in glasses are related to the fast cooling down of the material after laser irradiation: thermal expansion of the heated material during irradiation is followed by a strong viscosity increase during the rapid cooling that prevents the release of the stresses [7]. Other mechanisms such as nonuniform densification or asymmetric material structuration can induce birefringence in the material [8,9]. On the one hand this birefringence can be detrimental for some applications, but on the other hand one can benefit from the local stress-induced birefringence to create innovative optical 0146-9592/17/081616-04 Journal © 2017 Optical Society of America
components for polarization control and manipulation [10–13]. In both cases, for the control and optimization of laser processing, and for the fundamental understanding of laser material interactions, fast and accurate methods are needed to measure the retardance level, and hence stress, with high spatial resolution. Among the different techniques that can quantify stress-induced birefringence with high spatial resolution, imaging polarimeters with compensators and phase-shifting methods can be used [14,15]. Digital holographic imaging in a two-polarization configuration has also been reported [16], as noninterferometric quantitative optical-phase microscopy techniques [17] or spectral multiplexing interferometry combined with galvo scanning [18]. In this Letter, we use a technique initially introduced in Ref. [19] for biological applications, based on a high-resolution quadriwave lateral shearing interferometer to perform quantitative linear retardance and birefringence measurements. We demonstrate here interest of this technique to quantitatively characterize birefringence patterns in transparent bulk materials due to residual stress after CO2 laser processing. Such laser processes are indeed particularly relevant for thermal processing of glass with control of optical quality [20]. At last, we simulate birefringence distribution resulting from laser processing with thermomechanical models and obtain quantitative agreement between experiments and simulation. The configuration that we have used in this work is schematically described in Fig. 1. The experimental setup is composed of an inverted microscope (TE2000-U, Nikon, Japan), equipped with a 20 × , 0.5 numerical aperture objective and a Koehler white light illumination system. A linear polarizer, mounted on a motorized rotation stage, has been placed into the illumination light path before the sample. A commercial wavefront sensor (SID4Bio, Phasics, France), based on quadriwave lateral shearing interferometry, was mounted on the video port of the microscope. It allows the measurement of the wavefront shape in the image plane that can be considered as the sum of the incident wavefront (reference) to the optical path distribution (OPD) related to the sample. Differential measurements with and without the sample thus give the requested OPD distribution of the sample [21]. A bandpass filter, centered at 633 nm, has been inserted between the sample and
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Vol. 42, No. 8 / April 15 2017 / Optics Letters
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Fig. 1. Experimental configuration. P, polarizer; Obj., microscope objective; BPF, bandpass filter; TL, tube lens. Inset describes the sample preparation for the case of laser processed site on fused silica.
the wavefront sensor to measure the birefringence at 633 nm. Indeed, even if the sensor is achromatic [21], working at a welldefined wavelength avoids sample refractive index dispersion issues. Additionally, there are many data available at this wavelength in the literature allowing comparison of results with previously published ones. The samples of interest were fused silica of type III (Corning 7980) with 25 mm diameter and 5 mm thickness. They were polished using a super-polishing technology (THALES-SESO, France). We have used a CO2 laser that operates at 10.6 μm to irradiate different sites on the samples with different conditions and study the stress-induced birefringence. The beam diameter on the sample was 400 μm (beam diameter at 1∕e 2 ). The beam was Gaussian with an ellipticity better than 0.9 and linearly polarized. For the following experiments, parametric studies were done by varying the pulse length from 1 to 10 s and the laser power from 1 to 10 W (power was constant during the applied time). In such conditions a stress gradient is generated in the sample with typical lateral extension and depth of few hundred μm that can be clearly observed in conventional polariscope experiments (see for instance Ref. [22]). However, a crater is created at the surface with a depth that can reach 100 μm. This crater will therefore modify the wavefront significantly compared to the 10 nm expected magnitude of the retardance that has been determined from thermomechanical simulations [23]. To highlight retardance contribution, we therefore balanced crater effect by filling it with a fused silica refractive index matching liquid (Cargille 50350), as described in Fig. 1. In the described configuration it is possible to measure the wavefront on the image plane for different directions of linear polarization states. However, issues with possible residual birefringence due to the standard optical elements of the microscope and to an insufficient uniformity of the rotating polarizer have been encountered. We thus implemented the following protocol to obtain a quantitative retardance map on the sample (corresponding measurements reported in Fig. 2):
Fig. 2. (1), (2), (3), and (4) Optical path difference maps obtained with the wavefront sensor at two different polarization orientations. The scale units are nanometers. (1) is a reference measurement taken in an area that has not been irradiated by the laser. The 1 nm noise is intrinsic to the sensor. (2) is the same area measured in the cross-polarization state. The wavefront modulations compared to (1) are related to inhomogeneities of the polarizer and possible birefringence in the microscope. (3) and (4) are similar measurements done on a CO2 laser crater. (5) corresponds to the retardance measurements obtained with the protocol described in the text. Observation of the corresponding site illuminated with white light between cross-polarizers is also given (6) for qualitative comparison.
1. A first wavefront measurement is done on a clean area on the sample (pristine silica as a reference state) for a given polarization direction. 2. A second wavefront measurement is done at the same place after a 90° rotation of the polarization direction. 3. A new wavefront measurement is now done on the area of interest (crater) with the first polarization direction. 4. A last wavefront measurement is done with the crossed polarization direction, without moving the sample. 5. By substracting measurement (3) from (1), the OPD between the laser-irradiated site and pristine silica is obtained for one polarization direction. Similar OPD for the second polarization direction is obtained by subtracting measurement (4) from (2). By substracting these two OPD distributions, the requested optical retardance map is obtained (5). With this protocol any retardance due only to optical components is eliminated thanks to the reference wavefront captured in both crossed polarization directions. Note that in the described experiments a motorized rotation stage has been used for the rotating polarizer that limits the speed of the measurement, but a liquid crystal modulator could be used to speed up the process.
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The example reported in Fig. 2 corresponds to a site that was irradiated during 1 s with a 3 W CO2 laser power. The depth of the crater in this case is 14.2 μm. Because it is filled with a refractive index matching liquid, the crater should not induce any OPD in the measurements (3) and (4) of Fig. 2, whereas a value of approximately 100 nm is evidenced. This indicates that the refractive index of silica is not perfectly matched by the liquid. Because there is no dependence with the polarization of these two effects, their contributions are discarded when retardance maps are determined with the described protocol. In this way, as reported in Fig. 2, a maximum retardance of 10 nm is evidenced around the laser-irradiated site. Retardance distribution can be interpreted, considering that the stress distribution has an azimuthal symmetry: in polar coordinates with the origin at the center of the laser beam, the directions of principal stresses are parallel or orthogonal to the radius. Therefore when the polarization is oriented along, for example, a radial stress direction it experiences a given optical delay, opposite to the case of polarization orthogonally oriented. There is therefore a maximum/minimum measured retardance when the polarization directions are oriented along the principal stress directions. For comparison, an image of the same site taken with white light illumination between cross polarizers is given in Fig. 2(6), with the polarization directions for polarizer and analyzer oriented as in Fig. 2 measurements (1) and (3), and (2) and (4). This image evidences the same birefringence pattern; however, in this case there is no signal when the incident polarization is oriented along a principal stress direction. To quantitatively interpret these results, we have used a 2D axisymmetric finite-element model presented in Ref. [23] to calculate the birefringence distribution resulting from the CO2 laser processing. Heat transfer by conduction associated with structural mechanics under viscoelasticity considerations are used to calculate the temperature rise and distribution of silica heated by CO2 laser irradiation and the residual stress after cooling of the samples. In such a model, the input parameters are critical to describe as accurately as possible the laser material interactions, particularly the temperature dependencies of optical and thermal properties. The main critical parameter to calculate the temperature rise and its distribution in the fused silica sample during the irradiation is the thermal conductivity, and its choice is justified in Ref. [23] based on comparison of simulation with infrared thermography measurements. In the case of residual stress calculations, the temperature dependency of the coefficient of thermal expansion is the critical parameter as pointed out by Vignes et al. [7]. For our simulation, the thermal expansion coefficient is set to 0.6 × 10−6 ∕K at ambient temperature and increases up to 1.5 × 10−6 ∕K at 1900 K. During the CO2 laser irradiation, a temperature gradient is formed in the fused silica with a subsequent material expansion due to the positive thermal expansion coefficient. After the laser is turned off, the thermal expansion of the irradiated region vanishes and the material upon rapid cooling can accumulate a significant amount of residual stress. As an illustration, we have simulated the irradiation presented in Fig. 2, i. e., with an irradiation time of 1 s with a beam diameter of 400 μm and a laser power of 3 W: birefringence distribution at the end of the laser pulse and retardance distribution after cooling down to ambient temperature are shown in Fig. 3. Typical temperature distributions can be found in Ref. [23].
Letter
Fig. 3. (a) Calculated birefringence distribution after irradiation corresponding to the experimental case presented in Fig. 2 (3 W, 400 μm diameter, 1 s irradiation time); (b) Simulated retardance cartography.
Simulation indicates that after cooling of the sample, a birefringence level of a few 10−5 is permanently set into the glass around the irradiated area. A maximum of retardance is evidenced around the crater at the boundary of the heataffected zone by the laser irradiation. Figure 3(b) represents the simulated retardance cartography obtained by integrating the birefringence along the sample thickness e, and it is directly comparable to the experimental retardance results obtained and presented in Fig. 2(5). The comparison between calculated and experimental retardance distributions of the irradiated site along one radial direction is shown in Fig. 4. It reveals that the experimental maximum of the phase retardance (black and red lines) appears at a 180 μm distance from the beam center, and the retardance 15
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Fig. 4. Experimental (black and red lines) and numerical (blue lines) spatial retardance profiles, along the radial direction, extracted respectively from Figs. 2(5) and 3(b).
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spatial resolution. In our configuration the retardance measurements can reach the nanometer level, this level being limited by the wavefront sensor sensitivity given by the manufacturer of 0.5 nm. Such a method can be the basis for optimization of laser processing techniques or the basis of improvement of numerical models of laser material interaction by providing valuable experimental inputs. Additionally, an interesting perspective for the field of laser processing would be to obtain time-resolved measurements of retardance during/after the irradiation by using simultaneous measurements with two wavefront sensors, one for each polarization.
Irradiation time (s)
Fig. 5. Measured (black dots) and calculated (blue dots) maximum retardance as a function of the irradiation time for a laser power of 3 W. In red, maximum temperature reached at the end of the laser irradiation.
decreases rapidly inward and slowly outward. The measured maximum retardance is about 10 1 nm. The numerical simulation result in this case (blue lines) is in very good agreement for the maximum retardance position, consistent with our previous works presented in Ref. [23] and the simulated retardance value. To go further, we have conducted a parametric study on the irradiation parameters and measured the maximum retardance position and value of the corresponding sites. The experimental maximum retardance value depends strongly on the irradiation parameters, and a quasi-linear relation links the quantitative value of the maximum retardance and the position of this maximum with the irradiation time. Results are presented in Fig. 5 for one case (laser power of 3 W and different irradiation times). As shown on this figure, the simulated maximum retardance values correspond to the measured one considering the measurement error bars. Even if not shown on the figure, experiment and simulations correlate for the whole retardance distribution and quantitative values. This was the case for all of the parametric range that was explored (power between 2 and 3 W, and irradiation time between 1 and 10 s). However, at this point the measurement was not sensitive enough to present retardance measurements in the case of low power irradiation with no material removal, but this could be explored for the case of laser wavelengths with longer penetration depths and hence longer optical paths for integration of birefringence, allowing integrating birefringence to reach our required 1 nm sensitivity in the measured optical retardance. As a conclusion, these experiments supported by numerical simulations demonstrate the capability of phase microscopy based on high-resolution quadriwave lateral shearing interferometry, to quantify a low retardance level with a microscope
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