Laser writing of longitudinal waveguides in bulk transparent materials degrades with the focusing depth due to wavefront distortions generated at the air-dielectric interface. Using adaptive spatial tailoring of ultrashort laser pulses, we show that spherical aberrations can be dynamically compensated in optical glasses, in synchronization with the writing procedure. Aberration-free structures can thus be induced at different depths, showing higher flexibility for 3D processing. This enables optimal writing of homogeneous longitudinal waveguides over more significant lengths. The corrective process becomes increasingly important when laser energy has to be transported without losses at arbitrary depths, with the purpose of triggering mechanisms of positive refractive index change.
© 2008 Optical Society of America
Ultrafast laser radiation is successfully employed in three dimensional processing of bulk dielectric materials [1–3] due to precise localization of energy. The energy confinement is determined by a highly nonlinear multiphoton absorption mechanism. Consequently, opticallydriven structural material transformations are induced on mesoscopic and macroscopic scales, resulting in unique structural phases  and in new optical properties due to refractive index variations . The morphology characteristics and, therefore, the optical properties of the structures induced by ultrashort laser radiation depend on the efficiency of excitation (intensity effect) and on the rate of energy relaxation in electronic, thermal, and mechanical forms (material effect). As a function of the material response, of the scale of the energy confinement, and of the irradiation dose, the dielectric function changes in a complex way. High or low refractive index phases may be formed, with partial birefringence and low absorption properties [6, 7]. The major outcome is the formation of a quasi-pure phase object showing various levels of refractive index change. Applications in integrated optics have emerged relying on thus-induced optical functionalization of dielectric materials [8–11].
One of the application fields concerns the formation of light-guiding structures embedded in bulk materials [1, 5, 8–11] by replicating the laser structures over large distances. Efficient waveguiding structures were obtained in different optical materials by translating a focused laser beam longitudinally or transversally with respect to the propagation axis and creating regions of positive refractive index contrast. Nevertheless, focusing through an air-dielectric interface causes important wavefront distortions that are detrimental to bulk laser processing of transparent materials. When significant processing depths are required, these artifacts alter dramatically the energy confinement during propagation. In particular, refraction of optical rays at an interface between materials of different refractive indices induces an aperture-dependent longitudinal spreading of focal spots. The spherical aberration is then responsible for an elongation of the focal volume, a longitudinal spread of intensity, and a lower value of the axial energy density. This generates structures longer than desired. A schematic representation of the focusing characteristics and the effect of an interface is given in Fig. 1, showing various points of light concentration and the corresponding energy spread. The axial stretching of the focal volume augments linearly with the focusing depth, causing a drop of the peak intensity  and a modulation in the axial intensity profile [13, 14]. This fact has dramatic consequences on energy propagation in the processed zones, on the formation of the phase objects, and, consequently, on the morphology and homogeneity of the laser-induced structures [15–17]. In particular, distortions forbid longitudinal waveguide writing strategies, in despite of their potential advantages (in terms of symmetry) with respect to the transversal writing techniques. The consequences of aberrated beams for laser photowritten waveguides are manyfold: increased losses, inhomogeneous modulation of the refractive index contrast, or the apparition of non-guiding domains. The effect becomes increasingly severe when high index glasses  are concerned and requires corrective approaches. The employment of dynamic procedures for wavefront aberration corrections enables transporting the laser energy to the point of impact without significant spatial dispersion. This has a dual interest. Firstly, creating similar excitation conditions irrespective of the focusing depth may preserve a constance in the processed material morphology, leading to an upgrade in uniformity. This is limited at the present to the employment of low numerical apertures [19–21] which delivers higher radial extension for the written structures and are prone to filamentation phenomena. On the other hand, as it will be shown below, it is possible to preserve sufficient energy density over long distances in order to trigger specific mechanisms of positive index modifications. Creating optimal conditions for positive index changes allows generating light-guiding structures suitable for symmetric guiding. An increase in homogeneity is expected to have an impact in reducing the optical losses of the guiding trace, and, as well, an increase in the guiding domains of the waveguide. Thus, dynamic correction of optical distortions is of prime interest for emerging photonic applications.
The effect of spherical aberration in ultrafast laser material processing was previously analyzed via depth-dependent material modification thresholds and aspect-ratio measurements, and the importance of preserving excitation conditions was underlined [15–17]. Microscope objective collars delivering adjustable compensation of spherical aberration were employed for controlling the modification size in bulk optical materials . Corrective functions using adaptive optics were applied to minimize depth-dependent aberrations  for data storage and microscopy applications. Consequences for quality waveguide writing were already indicated [14, 17]. With emphasis on applications in waveguiding technologies we propose here a technique able to dynamically correct spherical aberration and to optimize the process of photowriting longitudinal waveguides in a dielectric environment using programmable spatial phase filtering integrated in adaptive closed loops. This is based on spatial phase retardation introduced by programmable optical modulators responding to a feedback derived from the laser action and being driven by a global optimization strategy. Even though the problem of spherical aberration can be addressed analytically using Zernike-polynomial decomposition, this requires a good calibration of the phase retardation induced by the shaping system and, most important, an accurate correspondence between the phase-manipulation plane and the pupils of the optical focusing system. We intend to show that global search algorithms  represent an effective calibration-free technique, able to significantly improve the structuring process. It can be applied in the absence of information related to the nature of the wavefront deformations that may include inherent distortions caused by nonlinear propagation. Advantages for material structuring applications may be derived when the feedback response is obtained directly from a laser processing result. In addition, the proposed method includes pulse spectral frequency dispersion control as a supplementary factor to optimize nonlinear contributions to energy deposition.
The paper is organized as follows. The experimental sections provide the argumentation of the material choice, as well as an overview of the irradiation setup and the adaptive loop. The discussion section concentrates on three major issues. It will firstly describe qualitatively the aspect of laser-induced structures in view of possible nonlinearities and will show that a regime of positive refractive index change exists above a certain energy density, allowing waveguide writing. Secondly, it will describe the impediments posed by spherical aberration in reaching this index increase regime. Thirdly, the results of the adaptive correction procedure will be shown and evaluated with respect to the possibility to induce symmetric channels of high-contrast positive index changes over long distances.
2. Experimental description
For demonstration purposes we have chosen Schott BK7 borosilicate crown glass as a model material due to potential applications in optics and microfluidics. A second reason is related to the fact that this material shows a narrow laser processing window for positive refractive index changes . This requires fine tuning of the energy density which enhances the demands for precise processing and, therefore, for preserving excitation conditions at arbitrary depths. It will be shown below that a dynamic regime of positive index modification is possible for high concentration of energy. An index increase is beneficial for waveguide writing since it provides the conditions of light guiding and the possibility for reducing losses in symmetric guiding. Wavefront distortions have then consequences for writing performant waveguides of increased dimensions, leading to the challenge of preserving energy densities and positive index changes at arbitrary distances.
BK7 parallelepipedic samples (10×20×3mm) are irradiated with 150 fs pulses from an 800nm Ti:Sapphire ultrafast laser system delivering 130 mW of usable power at a repetition rate of 100 kHz. The laser beam is focused inside the target by a long working distance microscope objective (working distance 17 mm, numerical aperture NA=0.45). To preserve a high energy throughput, the size of the beam at 1/e 2 was adjusted to the objective aperture, which results in a lower effective NA. The beam truncation factor is approximately 0.7. The irradiation dose is controlled via an electromechanical shutter and by the use of neutral density filters. The irradiation time is set to 1 s.
To estimate the results of laser exposure, a fast microscopy method is employed. Optical detection of the laser-induced structures is realized online by Zernike-type positive optical phase-contrast microscopy (PCM) which provides a convenient way for studying phase objects determined by the variation of the real part of the dielectric function. The method, which is based on constructive/destructive interference of the direct and object-deflected beams in the image plane, allows one to monitor relative changes in the refractive index, realizing a two-dimensional map of the phase object. A high-resolution Charge-Coupled Device (CCD) camera coupled to the microscopy arrangement delivers a side-image of the spatially-resolved relative changes in the refractive index induced by irradiation. The phase-based microscopy layout allows detection from a sub-µm thick layer located at the center of the structure. Positive or negative optical phase changes relative to the background can be readily detected and evaluated based on the gray-value shift in the image. For small phase variations, the observable gray-level shift corresponds directly to the phase change. Correspondingly, black colors denote positive index changes, while the white color indicates a negative refractive index variation or the presence of light scattering centers. Thus, the axial extent of the damage can be precisely evaluated for different laser focusing depths.
3. Adaptive feedback loop description
The laser system incorporates as a pulse control unit a programmable, optically-addressed two-dimensional pulse-shaping apparatus which performs spatial pulse tailoring using spatial phase filtering of the incident laser pulse . The external spatial light modulator comprises a non-pixellated optically-addressed liquid-crystal light valve, which is imaged onto the focusing system used for material processing. The optical addressing method using a video projector determines a matrix of 256×256 phase-retardation points. Details on the spatial shaping unit were provided elsewhere . Additionally, prior to the spatial shaping system, a computer controlled one-dimensional liquid-crystal pixellated array was installed in a zero-dispersion unit. This supplementary device has the role to disperse, manipulate, and recollimate the spectral frequency components of the pulse, allowing for spectral phase modulation and subsequent pulse temporal shaping . As a result, the output laser beam can be tailored spatially and temporally in a flexible way to quasi-arbitrary intensity profiles.
A feedback loop is realized between the microscopy detection and the pulse spatial control unit, guided by an adaptive optimization algorithm based on an evolutionary strategy. The pulse tailoring unit performs the variation of the incoming pulse spatial phase and the detection of the material modification delivers the quantitative evaluation of the laser action. The feedback loop involves recording sequence by sequence the 2D map of the photoinscribed phase object and the evaluation of its axial size. The evaluation is made along the axial cross-section of the detected phase map. Structure length is determined by the sum of pixels that have a gray-value different from the average background. The minimization of the trace longitudinal size defines the success of the irradiation sequence (the number of pulses corresponding to the exposure time determining the apparition of the trace). A note (fitness) is assigned to the corresponding phase pattern in accordance to its performance. In our case the fitness is determined by comparison to the unaberrated structure and is related to the inverse of the trace length. In order to avoid trivial solutions which are highly energy dispersive and lead to damage on limited regions (where the threshold was surpassed), an additional condition regarding the contrast of the phase shift in the structure was added. A schematic representation of the optimization strategy is depicted in Fig. 2. A set of arbitrary phase patterns is initially applied on the optical modulator and evolves in a genetic manner towards an optimal solution. Since the spherical aberration has circular symmetry, the spatial phase information was encoded on a narrow circular sector which was then radially replicated to fill the laser pulse aperture. This encoding procedure allows to represent a potential phase solution by a string of real numbers corresponding to a radial section of the mask. The discrete string containing phase retardation values determines the pattern, its performance, and the genetic dowry of the phase mask. We use 64 genes, one gene corresponding to two addressing point values. The mechanism of optimization is the following [27–29]. At each step the irradiation phase masks are tested by evaluating microscopically the resulting trace and ranked according to their success in minimizing the length. The algorithm suggests an improved collection of excitation envelopes. The population evolves from iteration to iteration through genetic propagators, namely crossover and mutation, altering in a self-improving way the gene information or exchanging genes between chosen more performant solutions. The genetic information is exchanged between individual patterns that already indicated a good experimental success. The improved phase mask collection which re-enters the optimization process contains the best masks of a previous generation as well as new masks derived genetically from the prior solutions. The solution space is thus explored iteratively, similarly to biological evolution  until convergence is achieved, and the best solution of the group is chosen. The optimal outcome is a spatial phase distribution that produces index patterns close to the unaberrated structure for various focusing depths.
4. Results and discussion
4.1. Laser excitation
A fundamental issue for quantifying the effect of aberrations in bulk material processing relates to the spatial aspect of the excited region in irradiation conditions corresponding to aberrated and non-aberrated cases. If the focal area elongation can be determined using linear methods , we have additionally estimated in a qualitative manner some of the consequences of the nonlinear propagation. The discussion is considered necessary to support experimental observations of the laser-induced modification presented in the next paragraphs.
Three photon excitation in BK7 (energy gap 4.2eV) triggers the formation of an electron-hole plasma in the focal region. The subsequent relaxation of the absorbed laser energy induces a local variation of the refractive index. The average power threshold corresponding to a visible modification under the present experimental conditions and unaberrated tight focusing is around 7mW. This low value rests approximately 4 times below the critical power for self focusing (for BK7, with a nonlinear refractive index of n 2=3.45×10-16cm2/W, the critical peak power is 1.96MW, corresponding to 30mW of average power). Material transformation takes place before strong nonlinearity develops. A main consequence emerges. Under tight focusing conditions, efficient plasma generation occurs in the early stages of the pulse, well before the activation of the self-focusing mechanisms. The generated plasma introduces a negative phase shift, peaked on the axis, acting as a divergent lens. Most of the incoming pulse energy is then spread around the focal region. In these conditions, self-focusing plays a secondary role. However, once the focusing point advances into the bulk, the input threshold power for visible modification increases significantly. A quasi-linear increase of the modification threshold energy with the working depth was previously observed [15, 17].
4.2. Static and dynamic regimes of laser processing
In order to quantify the effect of laser irradiation under optimal focusing conditions we evaluate the results of laser structuring in the vicinity of the surface, where the influence of spherical aberrations is minimal. Fig. 3 shows the result of irradiation of 150 fs pulses (measured before the focusing objective) at a working depth (the physical position of the paraxial focus in the material) of 200µm for two different input average powers, 125mW and 80mW. Parts (a) and (b) show the static refractive index modifications produced by 105 pulses at 200µm depth. The fs irradiation induces a dominant refractive index decrease denoted by the white color. In case of the high energy static structures, a shallow region of positive index change (black color) surrounds the low index core, terminating with an elongated trace of high index material at the structure tip. The low energy preserves somehow the topology with the region of surrounding compression being drastically reduced. An axial cross-section through the index contrast of the structures is depicted as well (Fig. 3(e)).
This specific topology can presumably be connected to a strong expansion of the irradiated volume. In glasses characterized by high thermal expansion such as BK7 energy density plays a paramount role in establishing a positive index change. Under regular irradiation conditions, the refractive index change in BK7 is dominantly negative  and explained by strong radial thermal expansion. Similar transitions to low density phases or voids were observed in various materials under strong laser excitation [4,30]. After the initial laser heating the material expands while cooling, which, in turn, inhibits the backward relaxation and quenches the material in a low density phase. However, high energy densities generate compressive shock waves  and determine the formation of a strongly compacted regions around the low density core. These provide the prerequisites for axial positive change in the refractive index at the structure tip. Upon photoinscription, if the energy concentration stays sufficient, the high density positive index phase can be replicated during the scan, leading to the formation of a waveguide.
In order to observe the consequence for a dynamic regime of photoinscription and to create guiding elements, the focal point was rastered along the irradiation axis. Same irradiation conditions were used to scan the beam longitudinally in a spatial region located around the working depth of 200µm. The scan direction was towards the laser beam, with the starting point into the bulk. The Fig. 3 parts (c) and (d) indicate structures written longitudinally at a scanning speed of 1µm/s, corresponding to the situations (a) and (b). For the high power longitudinal line, a contrasted region of positive index change is visible at high energies, denoted by the intense black color, bordered by narrow lines of decreased index. This structure shows a high and homogeneous index contrast. The low energies correspond mainly to a negative refractive index change represented by the dominant white color. The index variation is not uniform and positive and negative changes alternate. Important for guiding applications, it appears from the figure that a uniform region of positive refractive index change occurs during translation only when a critical density of energy was transported at the interaction place. This indicates the achievement of a high temperature in the interaction region, followed by the onset of the surrounding compressed region. The longitudinal translation at high repetition rates will lead to a high density trace upon scanning in the direction of the laser pulse. To reach this regime of dynamic positive index change, a transition power threshold of approximative 90mW was found necessary in our experimental conditions. The transition power depends as well on the scan velocity. Below this value moderate thermal expansion and subsequent rarefaction upon cooling determine to a large extent the material response, inducing a dominant low density low index phase. Waveguiding becomes impossible. Inevitably upon irradiation at different depths, the energy density decreases due to spherical aberration and limits the possibility to trigger the positive index regime far from the air-glass interface. Consequently, we have attempted to correct the spatial phase distortion using the above-mentioned optimization loop in order to preserve a high energy density.
4.3. Adaptive correction and processing solutions
We noted above that high energy, low density structure replication via scanning delivers a positive refractive index change. This may be connected to the presence of the surrounding high index, compressed region. It indicates as well that dynamic regimes of photoinscription should take into account the effects of a moving heat source. Pointing to this behavior we will focus below on the possibility to restrict the energy spread by spatial phase adjustments. In order to reach the compressive regime at arbitrary depths, it is imperative that the energy delivery remains concentrated to the narrowest region. This was achieved by adaptively determining the corrective phase masks in the microscopy-based feedback loop presented before. We recall that the success of the operation was related to the minimization of the damaged region. An example of the iterative improvement during the optimization run is given in Fig. 4.
Similar optimization runs were effectuated at different depths from 500µm to 3000µm in steps of 500µm. Whereas the objective working distance is usually the limiting factor, the maximum reachable depth was also restricted by the condition that the excitation beam is not clipped by the front surface. Fig. 5(a) shows the results of the optimization procedure for photoinscription as compared to the effect of the uncorrected pulse for different depths into the glass material. For completeness, part (b) shows axial cross-sections through the index change in relative units, corresponding to a range of approximately 50µm for traces at two selected locations, 200µm and 3000µm. If the structures induced by the uncorrected pulse show a threefold increase down to a depth of 3000µm (Fig. 5 left), the correction procedure has stabilized the structure length at almost the initial size (Fig. 5 right). We mention that the optimal results show a slightly more effective size reduction as compared to theoretically calculated masks using Zernike-polynomial decomposition (Fig. 6). This demonstrates the efficiency of the loop, the relatively low non-linear effect contribution for this specific material, and the fact that the adaptive strategy is suitable for more complex aberration correction problems, including wavefront distortions due to nonlinear effects. The reason for the slightly lower effectiveness of the theoretical corrections may also be connected to a slight mismatch between the effective entrance pupil diameter of the microscope objective and the radial extension of the phase map displayed on the spatial phase modulator.
Nevertheless, if the structure size is kept at a constant level, the energy density is slightly decreased as compared to the unaberrated structures, as indicated by the level of the white color (Fig. 5 right (a),(b)). Consequently, the excitation density in the bulk will still be below the threshold for inducing a positive refractive index change during the longitudinal writing in the profound regions. Since the laser source has limited energy output which is just above the transition threshold, only 10% size variation with respect to the unaberrated trace will decrease the energy density below the critical value. To compensate for this slight deviation with respect to the unaberrated structure and due to the limitations in the input laser power in our case, additional corrective solutions are required. A complementary technique for increasing the energy density deposited within the material is represented by pulse linear temporal chirping for the following reason. We have discussed above that ultrafast irradiation focused with moderate to high NAs results in structures where self-focusing is dominated by light defocusing on self-induced electron-hole plasmas. To minimize the effect of light spreading due to defocusing, the moment of reaching the maximum plasma density has to be delayed with respect to the beginning of the laser pulse. A longer temporal intensity envelope and a retarded plasma formation will produce a less effective defocusing, allowing the energy to be concentrated efficiently in the irradiated region.
The success of the operation is verified by effectively writing longitudinal guiding structures. Combining the spatial correction with a gradual increase in pulse duration with depth (up to 2.7 ps at 3mm by programmable second order dispersion) allows writing waveguiding structures as long as 3 mm. To avoid catastrophic damage during the longitudinal scan towards the front surface, the pulse was continuously compressed, reaching the shortest value at a depth of just below 1 mm. A positive quadratic dispersion coefficient was found to be slightly more effective in obtaining the positive index change regime. The spatial phase correction masks were as well applied in synchronization with the advance of the structure inside the glass material. The optimization run offered spatial solutions for depths located at: 500µm, 1000µm, 1500µm, 2000µm, 2500µm, and 3000µm. The maximum optimization depth was restricted due to technical limitations of the microscopy system. Linear interpolation was used to generate patterns for intermediary depths by dividing 500µm domains in 30 steps. The newly generated pattern were applied in five seconds tact at the scan speed of 1µm/s. We mention that, in the hypothesis that spherical aberration is the main distortion factor, the number of optimization solutions could be decreased. The photoinscription outcome is depicted in the top part of Fig. 7 which synthesizes the result of the dual corrective procedure. Both ends of the longitudinal structure are shown. A uniform dark structure is becoming visible indicating a positive index change all along the guide length. Microscope inspection showed good homogeneity for the corrected trace. This indicates that the spatio-temporal correction enables the generation of a uniform cylindrical waveguide with a high positive index contrast for a length superior to standard irradiation and which allows symmetric guiding. By evaluating the numerical aperture of the generated guide at 632 nm, an index increase of approximately 5×10-3 was estimated. For comparison, the uncorrected trace is shown as well in the bottom part of Fig. 7. In this former case, the guiding region is restricted to 1 mm, the rest of the trace showing a negative index change.
We have shown that adaptive optics in the spatio-temporal domain in connection to feedback loops are effective means to fulfill corrective functions during ultrafast laser photoinscription of waveguiding structures in optical glasses. Additionally, the technique is prone to deliver various spatial intensity designs of bulk excitation, offering possibilities for nonlinearities control. We concentrated here on a procedure of wavefront correction, namely spherical aberration, which can be correlated with the photoinscription process, requires no calibration, and allows extended versatility. The spatial correction method was accompanied by pulse temporal stretching to allow efficient energy confinement. Increased precision for 3D processing or long waveguide writing lengths are obtained, leading to a visible improvement of the structuring process. This enables the generation of homogeneouswaveguides over long distances even in tighter focusing conditions. Preserving the energy density irrespective of the processing depth allows triggering mechanisms necessary to induce highly-contrasted positive refractive index change, mandatory for low-loss guiding objects.
Support of ANR and PICS programs is gratefully acknowledged.
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