Morphing refers to the smooth transition from a specific shape into another one, in which the initial and final shapes can be significantly different. A typical illustration is to turn a cube into a sphere by continuous change of shape curvatures. Here, we demonstrate a process of laser-induced morphing, driven by surface tension and thermally-controlled viscosity. As a proof-of-concept, we turn 3D glass structures fabricated by a femtosecond laser into other shapes by locally heating up the structure with a feedback-controlled CO2 laser. We further show that this laser morphing process can be accurately modelled and predicted.
© 2015 Optical Society of America
1.1 The concept of morphing
The idea of morphing is based on the existence of a smooth transformation between two different shapes of an object. The term is popularized as a visual effect in film production to depict a person’s face magically turning into another one. The transition between the two character’s faces is seamless, keeping the same general facial features throughout the transformation. Here, we use this analogy to depict a fabrication process where a given initial shape is gradually transformed into another, radically different shape, using physical processes to drive the smooth transformation between the two.
As an illustration (see Fig. 1), let us consider a cube that is heated so that its viscosity decreases. Surface tension will gradually turn the object into a sphere, which in this case corresponds to a minimum surface energy. This is just an example. The concept can be generalized to any force field capable of shaping a viscous volume of matter.
In micromanufacturing, the concept of morphing driven by surface tension is attractive for multiple reasons. First, the final shape will absorb shape imperfections that may be present in the original. Parameters such as surface roughness and/or waviness are no longer relevant, since this fine level of detail will disappear. In particular, optical components such as resonators require levels of surface quality that cannot easily be achieved using traditional machining approaches. Second, some shapes are impossible to realize through known direct machining methods. A typical example is a volume enclosing a void with optical surface quality. As we will demonstrate throughout this paper, shape morphing offers a possible route for fabricating these objects.
1.2 A possible route for implementing surface-tension driven shape morphing
To implement surface tension driven shape morphing, we propose to combine femtosecond laser, three-dimensional machining techniques, with feedback-controlled CO2 laser heating.
1.2.1 3D manufacturing using femtosecond lasers and chemical etching
Femtosecond laser exposure combined with chemical etching [1–3] has emerged over the last decade as an efficient manufacturing technique for fabricating a variety of three-dimensional shapes. These include devices combining multiple functionalities, such as optical waveguides [4,5], mechanical functions  and fluidics . The typical fabrication procedure consists of first, exposing the material to femtosecond radiation at an energy level where the material structure is modified but no ablation takes place and second, performing a chemical etching step using HF or KOH etchants. Using this process, arbitrary three-dimensional shapes can be created that form the basis for complex structures such as molds  or three-dimensional flexures .
1.2.2 Controlled viscosity in glass using CO2 lasers
As tool for melting material, CO2 lasers have been used in a variety of applications since the early 80s. Various application examples include optical polishing [10–18], fabrication of toroidal optical resonators , repair of laser-induced damage in optical components , fabrication of micro-lenses [17,18], and glass mold fabrication for micro-lenses arrays . Recently , CO2 laser controlled melting was also used in combination with femtosecond laser fabrication to produce structures similar to those reported in , but in an all-glass substrate.
In this study, we show that CO2 laser melting combined with three-dimensional femtosecond laser micromachining offers an opportunity to implement shape morphing. We demonstrate the potential of this technique for future applications by applying it to a shape with a complex topology, leading to a self-sealed cavity. Unlike previous works, we further demonstrate a full model of the dynamic evolution of a shape during laser exposure. Finally, we show that this model is in good agreement with observations and is applicable to any arbitrary object geometry.
2. Experiments: feedback controlled CO2 laser heating
A key requirement for achieving repeatable and accurate results is to implement a feedback loop in order to maintain a constant temperature in the system. A schematic of the optical and mechanical assembly is shown in Fig. 2. A CO2 laser (SYNRAD Firestar ti80) irradiates the sample through a ZnSe focusing lens (f = 50 mm). The laser profile was measured at the sample plane using a knife-edge technique and was found to be Gaussian with radius of 300 μm (1/e2 diameter). To compensate for fluctuations in the laser output power (about ± 7%), a PID controller was implemented, using an IR temperature measurement from the specimen for feedback. The performance of the controller exhibited zero overshoot and a rise time of about 200 ms. Mean error from the constant reference was typically less than 0.1%. The feedback signal was provided by an InGaAs photodiode (Thorlabs, DET410) with a spectral sensitivity window spanning from 800 to 1700 nm. Although the temperature was not measured directly, the closed-loop guarantees a perfect temperature stability and very good repeatability of the experiments. An indirect estimate based on the numerical model (to be outlined later) is that the temperature stability achieved during experiments was about ± 1%. The laser power ranged from 8 to 14 W with an exposure time of 0.5 to 60 s.
A CMOS camera (acquisition rate of 25 frames per second) equipped with a 20x telecentric objective (Moritex-Schott SOD-10X + 2X) was used to observe a side-view of the evolution of the microstructure shape during CO2 laser exposure, providing an accurate profile measurement during the morphing process.
The sample holder was made of aluminum with relatively large dimensions compared to the sample, resulting in a very good heat sink at the bottom of the specimen, giving a constant temperature reference. OH-rich (>1000 ppm) synthetic fused silica was used as substrate for the experiments. The sample patterns were fabricated in a 250 μm-thick substrate using the process described in . Laser exposure was performed using an Ytterbium-fiber based femtosecond laser (Amplitude Systèmes), emitting 270 fs pulses at a rate of 400 kHz and pulse energy of 220 nJ.
3. Numerical modelling
To model and predict the final shape during CO2 exposure, a numerical model was developed, putting emphasis on applicability to arbitrary object geometry. A three-dimensional finite element analysis model was chosen; covering both the surface tension driven flow and heat transfer in the material. This model was implemented using a commercially available software (COMSOL Multiphysics). Two predefined segregated solvers, optimized for the fluid flow and heat transfer, were used on a common deformable mesh following the object shape. The heat transfer solver uses quadratic elements by default while the fluid flow solver employs linear elements for both pressure and velocity. These two solvers are iterated at each time step until the criteria for all dependent variables tolerance is satisfied.
The coupled problem is defined by the following set of partial differential equations:
One of the difficulties here is that most of these material properties are strongly temperature dependent. Even though fused silica is one of the most investigated materials, the temperature dependent properties are not always consistent in the literature. For example, the thermal conductivity exhibits a significant discrepancy above 1000 °K. Kingery  claims that the thermal conductivity of fused silica rises rapidly above this limit, while other authors [22, 23] have reported that the conductivity approaches a constant value above 2000 °K. Finally, Combis et al.  observed a significant conductivity drop between 1500 and 2000 °K. A similar variability could be found for the viscosity, as stated in .
In this study, we decided to use the data provided by the manufacturer (Heraeus ) for synthetic fused silica, in particular to fit an Arrhenius model to capture the thermal dependence of viscosity, as follows:27]. The parameters used in this simulation are further described in the appendix (see Table 1).
The next step in this modeling is the definition of the boundary conditions. For the heat transfer equation, there are four main contributors: The first is a heat source that depends on the beam profile, laser power, and the shape of the object to be heated. The beam profile was Gaussian and, together with the laser power, was measured experimentally. The absorption of the laser light was modeled as a surface phenomenon, due to the high absorption of fused silica at 10.6 μm. In this case, the penetration depth is negligible compared to the area covered by the beam. The absorption is modeled using Fresnel’s equations, as follows:
The reflectivity coefficient is mainly dependent on the incidence angle of the laser light and refractive index of fused silica. The other three contributors to the heat transfer boundary conditions are related to the system cooling: cooling due to the ambient air, radiation losses, and thermal contact with the sample holder. Of these three, the most significant factor is the thermal contact, which was modeled as 5-μm air gap between the specimen and a perfect heat sink at 300 K (the heat sink used in the experiment was coarse-polished, black-anodized aluminum).
For modeling the glass flow (as a viscous fluid), only one boundary condition is related to the external force Q(x,t), which in our case is the surface tension.
To accurately compare the numerical model with the experiments, the CO2 laser was kept under closed-loop control (PID) using an IR diode as feedback so that the average temperature of the specimen was constant, though a temperature gradient was still present. To best match the model with experimental conditions, a fixed temperature boundary was not used, but rather the feedback loop was simulated in the numerical model. The irradiance was then modeled in a very similar way as it was in the experiment, i.e. the irradiance level is adjusted according to the mean temperature in the system until a referenced value is reached. This method enables virtual, stable regulation of the average temperature in the system (as it is during the experiment) while not disturbing the temperature distribution by enforcing a constant temperature boundary condition.
The agreement with the experimental dynamics shows the efficiency of this approach, since it effectively compensates small nuances between the model and reality, and makes the simulation particularly robust to small variations of the starting conditions.
4. Results and discussions
For the experiments, we consider two test shapes, illustrated in Fig. 3, which were micromachined in fused silica using femtosecond laser machining combined with chemical etching according the process described in . The first shape is a cube sitting on a pillar. The objective is to demonstrate the ability to fabricate a small supported sphere that can act as a micro-lens or whispering-gallery-mode optical resonator. The second shape is a cylinder with a conical cavity in the middle. Here the objective is to demonstrate that this morphing technique can be used to change the surface topology, creating a sealed cavity. One could imagine using this concept for trapping a gas for applications such as a gas reference cell for a miniaturized atomic clock.
4.1 Case 1. From a cube to a sphere
In addition of demonstrating the concept of morphing, we also seek to show agreement between experimental observation and the derived model, and in particular, the ability of the model to capture the dynamic evolution of the shape morphology during heating. For this purpose, recorded video plays a major role since it captures the dynamics of the morphing process in real-time. For fitting the numerical model with the experiment, we have chosen to use the mean temperature as the unique tuning parameter (see previous discussion).
Assuming the average temperature is stable throughout the morphing process, we have found an excellent agreement between the actual shapes and the modeled ones at various time steps as shown in Figs. 4 and 5, demonstrating that the model effectively captures the dynamics of the morphing process.
In practice, there are many influencing factors affecting the process dynamics, such as fluctuations in the emitted laser power, small specimen misalignment, nonhomogeneous thermal conductivity , as well as the temperature dependence of extinction coefficient for fused silica . These inherent process fluctuations are not easily predictable, however their influence can be effectively compensated using feedback-controlled laser heating, as illustrated in Fig. 6, which shows still images for four different specimens, taken after the same exposure time (+/− 0.2 s).
In the model, two indirect links with the real temperature can be inferred. The first is the morphing dynamics that are driven by surface tension, which is directly related to the temperature-dependent viscosity of the glass. The second link refers to the laser irradiance, which is related to the heat transfer in the system. The first link, i.e. the dynamic evolution of the shape morphology, has been used to fit the model to experimental observation, while the second was confronted with the experimental data. After calibrating the model at different temperatures, the simulated and measured value of laser irradiance was found to stay within a 15% tolerance, suggesting a good fidelity between the model and experiments. This is due to the fact that the implemented PID control loop maintains a constant temperature during heating with the CO2 laser.
With a good fit of the numerical, we can test the importance of certain parameters on the morphing technique. Figure 7 shows the irradiance level evolution in time during laser exposure, as well as the shape obtained after 2 s for a given maximum temperature set point. The time-dependent irradiance exhibits two noticeable regimes. In the first regime, the initial heating of the material takes place, which is dependent on the specific heat. This transient regime is typically very fast for the volume considered (about 100 microns cube), with a time constant of about 100 ms. The second regime is driven by the glass viscosity, and accounts for the morphing process itself. This process is much slower, typically lasting for several seconds depending on the set temperature in the PID loop. In this regime, the laser irradiance decreases gradually. This variation is due to the larger laser exposed area of a sphere in contrast to the original cube. This change is compensated by the controller which leads to the lower laser irradiance to maintain a constant temperature.
The final irradiance rise, which is visible at higher temperatures, is related to the melting of the supporting pillar, lowering of the thermal resistance of heat to flow toward the cooled, bottom region of the substrate.
The simulation also shows that the differences between reachable object shapes at different temperatures are nearly negligible. This means that a same object shape can be produced at various temperatures by adjusting the exposure time properly. However, it is still important to optimize the temperature. Due to the fast cooling rate of the system (typical time constant of 100 ms), different fictive temperatures, and therefore different properties for the final object , such as refractive index , can be obtained, depending on the maximum temperature from which the object melt started.
Figure 8 shows that nearly perfect circular profile can be obtained after a few seconds of heating. Since gravity plays virtually no role at this scale, perfect spherical profiles corresponding to the lowest surface energy can be achieved. A dramatic illustration is further shown in the SEM images presented in Fig. 9. The first image is a cube after femtosecond laser exposure and chemical etching. The second image shows a similar cube turned into a perfect sphere with sub-nanometer roughness after laser morphing.
4.2 Case 2. From a cylinder with a cone toward a sealed cavity
As an illustration of a more complex shape morphing, we now consider a cylinder with a conical cavity. In this case, the morphing process is much less intuitive than in the case we considered in the previous section.
The shape evolution of the conical cavity is depicted in Fig. 10. The cavity self-seals during laser exposure, capturing the surrounding gas inside. The corresponding result of our simulation is in shown in Fig. 11. Unfortunately, we are not able to simulate the coalescence of the top of the cylinder, because the surface is modeled with a moving mesh, which cannot change topology during simulation. However, our model properly simulates the evolution of the shape up to the point where the cavity nearly seals itself.
The simulation results were also compared with actual profilometry data obtained from experiments before closing of the cavity (Fig. 12). The simulation was aligned the same way as in case of the cube and we again observed a good conformity with the experiment. The profilometry covers only part of the surface where the slope is sufficiently small to be visible on a confocal profilometer.
In this paper, we have introduced the concept of laser morphing. This concept was tested in the case of surface-tension driven morphing by first machining an arbitrary three-dimensional shape using femtosecond laser exposure and chemical etching, and second, by heating the microstructures with a CO2 laser until they converge toward the desired final shape. This morphing technique brings practical benefits, such as an ultra-smooth surface, effective forming of spherical shapes, as well as the ability to change the surface topology in order to create ‘impossible’ objects like self-sealed cavities.
The proposed feedback-controlled laser heating system, combined with a temperature-calibrated 3D numerical model, shows that this technique can be accurately controlled and predicted. This model further allows for effective optimization of the process on arbitrary geometry.
As a proof of concept, we have demonstrated the morphing of a cube into a well-defined glass microsphere, supported by a small pillar. Additionally, we have also shown an example of morphing with higher complexity shape that resulted in a self-sealing cavity, illustrating a dynamic change of surface topology. In these examples perfect spheres can be used as optical resonators [32,33] while self-sealed cavities offer an efficient means for capturing small volumes of gas.
The stay of Jakub Drs at EPFL was partially supported by Czech Technical University (CTU) under a MSc student exchange program. The project is supported by the European Research Council (ERC Stg Galatea - 307442). The Galatea Lab further acknowledges the sponsoring of Richemont International. The authors express their gratitude to Ben McMillen for the final proof-reading. In this work, JD performed the experiments as well as the simulations, TK participated in discussions and brainstorming about spherical resonators, YB designed and supervised the research and suggested the concept of laser shape morphing presented in this paper. YB and JD wrote the manuscript. All authors participated to the manuscript revisions and improvements.
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