Light waveguiding appears as a key mechanism in all modern technologies spanning from telecommunications to applications in medicine, as well as in fundamental research. Femtosecond lasers have proven to be a powerful tool for creating complex three-dimensional waveguides in transparent materials during the past decades [1]. A femtosecond laser pulse focused inside a transparent medium induces a material modification via nonlinear absorption in and around the focal volume with a locally altered refractive index. First demonstrated in glass [2], ultrafast waveguide writing was quickly established as a standard micromachining process for dielectric materials such as crystals and different types of glasses with or without doping [3–6]. The transfer of this technique to polymers would have certain advantages. Among other things, polymers are flexible, lightweight, and can easily be tailored in their optical properties to meet specific demands [7]. Also, low production costs and easy processing of the material make polymers good candidates for disposable implementations, e.g., in medical applications or large scale foils with integrated sensory elements. Especially, the biocompatible poly (methyl methacrylate) (PMMA) is—due to its high transmission in the visible and near-infrared—a popular material for the fabrication of optical components, optical fibers, and planar waveguide devices [8,9]. While there are many other techniques to fabricate polymer waveguides, e.g., photolithography [10] or direct laser patterning [11,12], ultrafast waveguide writing combines the advantages of maskless fabrication and the ability to create virtually arbitrary three-dimensional structures. In addition, the formation of the waveguide is a one-step process, and writing below the surface of the material makes the method environmentally insensitive. Despite some early promising results [13,14] and the first demonstration of simple coupler structures [15,16], the performance of femtosecond laser written waveguides in polymers has not yet reached the level as that in glass. One major drawback is evidenced by reported high propagation losses between $3–6\mathrm{dB}/\mathrm{cm}$ [17]. Here, we present a new possibility for writing waveguides in bulk PMMA using a femtosecond laser. We demonstrate guiding of an almost symmetric fundamental mode and propagation losses down to $0.5\mathrm{dB}/\mathrm{cm}$. We attribute the guiding area to a refocusing effect, which leads to a secondary modification followed by a zone of increased refractive index.

For the waveguide fabrication, we use a home-built two-crystal Yb:KYW chirped-pulse oscillator with cavity dumping [18]. The laser has an output repetition rate of 1 MHz and an 8 nm spectral bandwidth centered at 1048 nm. The laser pulses are compressed to a pulse duration of 600 fs. With a Pockels-cell-based pulse picker the repetition rate can be further decreased. To provide a focal volume with close to spherical symmetry, the pulses are tightly focused 150 μm below the surface of the PMMA substrate by a 0.55 NA aspheric lens (Newport 5722-H-B) with a transmission of 97% for the given wavelength. Two computer controlled high-precision air bearing translation stages (Aerotech ABL1000) move the sample in a plane perpendicular to the laser beam direction, while a third stage moves the focusing lens. The laser beam is linearly polarized in the writing direction. We used 1.0–1.5 mm thick samples of commercially available Vistacryl CQ UV medical grade PMMA (Vista Optics Ltd) and PMMA-03 (microfluidic ChipShop GmbH). Both materials provided similar results.

Waveguides are written across the entire sample with a spacing of 100 μm between them to avoid cross talk. The pulse energy is measured before the focusing lens. After writing, the side surfaces are polished to an optical quality to minimize coupling losses. The final waveguides have a length of up to 46 mm. To analyze the waveguiding behavior, light with a wavelength of 660 nm or 850 nm is butt-coupled from a single-mode fiber. The transmitted power is measured, and the mode profile at the end facet is carefully imaged onto a CCD camera by a microscope objective.

We observe the best well-defined and reproducible waveguides as a result of a refocusing effect, which appears at a repetition rate of $f_{\mathrm{rep}}=100\mathrm{kHz}$ with pulse energies $E_p$ between 400–650 nJ and writing speeds $v$ between $20–45\mathrm{mm}/\mathrm{s}$. Figure 1(a) shows a bright-field microscope image of the end facet around the focal spot, and Fig. 1(b) shows the measured intensity distribution of an almost symmetric guided fundamental mode at 660 nm (false color representation). The upper primary material modification, as displayed in Fig. 1(a), is located at the preset writing depth for the focal volume. The circular symmetry of the modified region indicates that heat diffusion from a small laser absorbing a focal volume of about 2 μm diameter is the dominant effect here. It puts the process in the heat accumulation regime [19], where the time interval between subsequent laser pulses is too short to let the absorbed energy diffuse out of the focal volume, and heat gets accumulated. Scattered light from the center region indicates damage related perturbations and corresponds in size to the focal spot. An outer ring area shows homogeneous modification of the material. Due to induced refractive index changes during writing, it acts as a lens on unabsorbed light, and a smaller secondary modification is formed directly beneath. The white dotted lines in Fig. 1(b) mark the outside margins of both zones. It has to be pointed out that the waveguiding here neither occurs inside one of the apparent material modifications, as indicated in [16,20], nor in between the two modifications, as reported in [17], but directly below the secondary modification. This observation implies that the waveguiding takes place in a zone of increased refractive index rather than in between two zones of reduced index. The process with cascaded focus is reproducible, and the waveguide always appears at the same position. We performed a number of experiments for different repetition rates up to 1 MHz. For comparison, Fig. 1(c) shows the bright-field microscope image of a modification that is exemplary for repetition rates above 200 kHz. The experiments show that no secondary modification is formed in this regime. Obviously, the damage in the core of the primary modification is too large for a second focus to form. Note that light is guided here. It partially encloses the modification, as seen in Fig. 1(d). Even though this observation looks similar to the intensity distribution of tubular waveguides reported in [13], in our case, the waveguiding zone is significantly smaller than the reported 20 μm. Overall, the process with just a single focus is much more unreliable, and the guided intensity distribution varies in shape and size.

 

Fig. 1. (a) Bright-field microscope image of a polished end facet of a material modification fabricated at 100 kHz repetition rate, 550 nJ pulse energy, and $35\mathrm{mm}/\mathrm{s}$ writing speed. (b) Mode profile of the corresponding waveguide at 660 nm wavelength. The white dotted line marks the outside margin of the apparent structural changes. (c) Single modification fabricated at 330 kHz and the same energy and writing speed, and (d) corresponding mode profile. The writing laser incidence was from the top.

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In a study on the formation of phase gratings in PMMA by femtosecond laser irradiation, a positive refractive index modification was observed and attributed to a combination of depolymerization and cross-linking [21]. While this process might still be present, it cannot be the main mechanism for waveguide formation in our case, since the directly irradiated zones do not display waveguiding, as clearly seen in Figs. 1(b) and 1(d). We attribute the waveguide-forming mechanism to material densification around a quickly expanding focal volume. As shown in Fig. 1(d), the refractive index is rather uniformly distributed around the core modification. However, in the refocusing case, the radial symmetry is broken. Since the primary modification already created a ring of material densification, the effects of the secondary focus are partially channeled downward, and an almost symmetric fundamental mode waveguide is formed. In the following discussion, we only address these waveguides achieved by double modification, as seen in Figs. 1(a) and 1(b).

The insertion losses (IL) can be considered as the sum of all terms contributing to the total losses occurring in the waveguide, such as coupling, Fresnel, and propagation losses. We follow the definition of $\mathrm{IL}=-10·\log (P_{\text{out}}/P_{\text{in}})$ [5], where $P_{\text{in}}$ is the power coupled into the waveguide, and $P_{\text{out}}$ is the measured output of the waveguide. To quantitatively obtain the propagation losses, several PMMA substrates with different lengths $l$ between 10 mm and 46 mm have been prepared, and multiple identical waveguides have been written in each. In each sample, the measured insertion losses are averaged for identical writing parameters. As a function of $l$, these measured insertion losses now allow for calculating the propagation losses. Exemplary results for waveguides written at 550 nJ with four selected writing speeds are shown in Table 1; similar results are observed at other pulse energies as well. The losses are well below $1\mathrm{dB}/\mathrm{cm}$, which—to the best of our knowledge—are the smallest values reported for embedded femtosecond laser written waveguides in a polymer material so far. We observed no degradation of the waveguides over the course of this investigation, which yields a long-term stability exceeding 8 weeks. In [17], the lowest value is given as $3\mathrm{dB}/\mathrm{cm}$, and [15,16] report $4.2\mathrm{dB}/\mathrm{cm}$. In ultrafast laser processing, a dependence of the material modification on the writing direction has been observed in glass [22], as well as for pattern formation in PMMA [23]. Here, consecutively coupling light into the waveguides from both ends shows no dependence of the propagation losses on the writing direction.

Table 1. Propagation Losses of Waveguides Fabricated at 100 kHz with a Pulse Energy of 550 nJ and Different Writing Velocities^a

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To estimate the change in refractive index $\mathrm{\Delta }n$, the approximation for the numerical aperture (NA) of a step-index waveguide $\mathrm{NA}=\sqrt{2n\mathrm{\Delta }n}$ is used, which is valid for small $\mathrm{\Delta }n$. The NAs of the waveguides have been measured based on the method proposed in [24]. Unguided light from the fiber interferes with light exiting the waveguide and results in a pattern of concentric rings. Measuring the radius at which the fringes decay at different positions in the far field allows for calculating the acceptance angle of the waveguide and deducing the NA. Within the investigated parameter range, no apparent dependence of $\mathrm{\Delta }n$ on either the pulse energy or writing speed occurred, in contrast to the reported dependence of $\mathrm{\Delta }n$ on $E_p$ in [15], which supports the assumption that the waveguide-forming mechanism is a different one in our case. In addition, this result is consistent with the low variation in propagation losses. The most important writing parameters can be combined into a single parameter called energy dosage, which is defined as $D=E_p{f}_{\mathrm{rep}}/(Av)$, where $A$ is the area of the focused laser spot [25]. As can be seen in Fig. 2, $\mathrm{\Delta }n$ shows no dependence on $D$ as well. The average refractive index change lies at $\mathrm{\Delta }n=6.2·{10}^{-4}$, which is agreement with numbers reported in the literature [15,26].

 

Fig. 2. Change in refractive index $\mathrm{\Delta }n$ depending on the energy dosage $D$. The red line marks the mean, with the highlighted background being the standard deviation.

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From an experimental point of view, we do not observe higher modes when horizontally and vertically scanning the entrance facet with the output of a single-mode fiber. Only the coupling efficiency and thereby the transmitted power vary. The $V$ parameter $V=2\pi \mathrm{NA}a/{\lambda }_0$ defines a threshold for the single-mode regime of step-index waveguides. Here, the radius of the waveguide $a$ is approximated from the full width at half-maximum of the measured mode profile. The calculated values for 660 nm and 850 nm both fulfill the condition $V<2.405$ for single-mode operation [27].

So far, it has been shown that low-loss waveguides can be written in a large parameter range with our setup. Nevertheless, the writing process can be disturbed by numerous factors, e.g., surface scratches on the sample, material inhomogeneities, or pulse-to-pulse instabilities of the writing laser. At nonoptimal writing parameters, the process becomes more prone to these disturbances, and they become visible in material modifications. Figure 3(a) shows homogeneous material modification without disturbances in the processing. In Fig. 3(b), a structure with fringed edges, which cause significant scattering losses, is displayed. These deficiencies occur when writing at decreased speeds. If the laser beam is disturbed upon entering the sample by a rough edge or during writing by material imperfections, periodic modulations, as shown in Fig. 3(c), can form at any parameter combination. Nonperiodic disruptions in the material, as displayed in Fig. 3(d), are an indication of overly large pulse energy. The formation of periodic and nonperiodic structures is a common phenomenon in ultrafast material modification [23,28] but proves to be an undesirable effect in this approach on waveguide writing.

 

Fig. 3. (a) Optimal homogeneous material modification. (b) Frayed edges distortion caused by too slow writing speeds. (c) Periodic disruptions. (d) Nonperiodic disruptions caused by too large pulse energies. Writing direction was from left to right.

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To identify the optimal writing regimes, a statistical analysis (a total of 650 waveguides were examined) of several samples, each containing numerous waveguides, was performed for different combinations of pulse energy and writing speed (see Fig. 4). Mostly interested in finding the best low pulse energy writing range, we started at optimal conditions and moved toward the lower threshold. It can be seen that the parameter ranges of $v=35–45\mathrm{mm}/\mathrm{s}$ and $E_p=550–650\mathrm{nJ}$ yield a success probability for the fabrication process of almost 100%, indicated by the dark red area. Only shortcomings of the sample like deep surface scratches, craters, or enclaves in the material can potentially lead to processing failure and malfunction of the waveguide. Moving toward lower writing speeds and pulse energies, this value quickly drops below 50%.

 

Fig. 4. Success probability of the fabrication process and its dependence on writing speed and pulse energy. The dark red area yields a success probability of almost 100%.

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In conclusion, a new scheme for femtosecond laser waveguide writing in polymers has been demonstrated. We exploit a cascaded focus of the writing laser to achieve nearly symmetric fundamental mode waveguides in PMMA. Unlike earlier studies, waveguiding outside the apparent material modification has been observed and attributed to material densification. The mechanism proves to be highly reliable over a fairly large set of different writing parameters, producing identical single-mode waveguides. Propagation losses were measured to go down to $0.5\mathrm{dB}/\mathrm{cm}$. Low losses make these waveguides feasible for lab-on-a-chip applications, as well as implementations on a larger scale, e.g., for a polymer foil with an integrated network of sensoric devices that could be applied on any surface.