1. Introduction

Polymer-based optics are a subject of great interest in fundamental research and applications alike. They are easy to process and easily tailored in their optical properties [1] which makes them a relatively cheap and lightweight alternative to glasses. There are many different techniques to create in-plane waveguides on polymer substrates, e.g., photolithography [2], hot embossing [3] or the “Mosquito method” [4]. Femtosecond laser writing combines the advantages of maskless fabrication, full 3D-capabilities, and being a one-step process which only requires one material. A change in refractive index is induced below the surface of a dielectric material via nonlinear absorption of tightly focused laser pulses. Complex three-dimensional structures can then be fabricated by moving the focal spot through the sample, which is an advantageous feature for rapid-prototyping applications.

There exists a large geometrical variety of ultrafast laser written waveguide structures [5]. Here, we differentiate two basic writing approaches based on the morphology of the resulting refractive index modification. If an increase in refractive index is induced directly in the focal volume the guiding may take place directly within a single femtosecond laser written track [6]. This type of waveguide typically forms in amorphous glasses. However, femtosecond laser pulses can also cause an expansion of the lattice which is typically accompanied by a decrease in refractive index and material damage [7]. The surrounding areas on the other hand may possess a relatively high increase in refractive index through stress-related effects [7]. With adequate spacing the stress fields of two adjacent tracks can be overlapped to support a well-confined waveguide. This approach holds some advantages when it comes to waveguiding in crystalline materials. Since the core lies between two modification tracks, the bulk characteristics of the material are only slightly affected there. Especially the luminescence and nonlinear properties are conserved [8, 9]. These properties are important for many applications such as frequency doubling [10] or electro-optic modulation [11] along a waveguide. Also the cross-sectional dimensions of the guided mode can be controlled to some degree by the spacing between tracks. Guiding of light may also be polarization dependent for some target materials [12].

While ultrafast laser writing is a widely applied technique to create waveguide devices in glasses and crystals [13], still relatively little work has been done in polymers [14–16]. Their low damage threshold and material specific effects during femtosecond laser irradiation such as chain scission or crosslinking [17] demand for alternative writing schemes in polymers to overcome drawbacks such as reported high propagation losses of 3 dB/cm [16]. In [18] we presented a new possibility to fabricate waveguides in PMMA exploiting a cascaded-focus during the writing process which enabled us to reduce the propagation losses to 0.5 dB/cm. However, to create compact and efficient networks of photonic structures, not just low propagation losses but also reasonable bend losses are required which depend upon a large positive index contrast Δn [19,20].

In this work we fabricate and characterize straight and s-curved waveguides in PMMA utilizing a writing approach which uses multiple parallel tracks to confine the waveguide core and to achieve a large Δn. We demonstrate single-mode guiding of light at 638 nm and 850 nm with propagation losses as low as 0.3 dB/cm and practically no bend-losses for curve radii R ≥ 20 mm. These curved waveguides are the basic building blocks for more complex optical devices or waveguide networks which might be included in future lab-on-a-chip applications.

2. Experimental setup

As laser source we use an experimental Yb:KYW based, two-crystal, positive-dispersion oscillator with cavity dumping which was specially developed for our purposes [21]. The 8 nm spectral bandwidth is centered at 1048 nm and the pulses are compressed to 600 fs with a grating compressor. An external Pockels-cell based pulse picker can tune the output repetition rate of 1 MHz down. Using a 0.55 NA aspheric lens (Newport 5722-H-B) with a transmission of 97 % at the given wavelength the pulses are tightly focused inside a 1.5 mm thick PMMA substrate (PMMA-03, microfluidic ChipShop GmbH). The pulse energy is measured before the focusing lens. The sample is moved perpendicularly to the laser propagation direction by two computer controlled high-precision air bearing translation stages (Aerotech ABL1000). A third stage moves the focusing lens to define the writing depth which is set to 150 μm below the surface. The laser beam is linearly polarized in the writing direction and waveguides are written across the entire sample to a length of up to 50 mm.

After processing, the edges of the sample are polished to expose the cross-sectional structure of the modifications for optical inspection and to minimize coupling losses. For characterization light is butt-coupled into the waveguides from a cleaved single-mode fiber (Thorlabs SM600). Transmitted light is collected by a microscope objective and is either imaged onto a CCD camera to observe the mode-profiles or sent to a power meter. Scattered light which is not part of the guided mode is shielded by an iris diaphragm to the best possible degree.

3. Fabrication procedure

In [18] we demonstrated single-mode waveguiding along a modification track written with a cascaded-focus in PMMA. A refocusing effect occurs at pulse energies above 300 nJ and leads to a smaller secondary modification, thus creating two stacked modifications with a single scan. A proper choice of writing parameters results in a waveguiding zone directly beneath the secondary modification with a guided mode that exhibits almost spherical symmetry. We also showed that a single cylindrical material modification leads to a tubular waveguide surrounding this structure. The increase in refractive index can therefore be attributed to material compression and stress-related effects.

Here, we explore the possibility of overlapping lateral index modifications of ultrafast laser written structures in PMMA. For this approach simultaneous writing of a primary and a secondary modification achieved by a cascaded-focus is advantageous. It extends the vertical dimension of each track which helps to confine a waveguide core. First experiments showed that two consecutively written tracks – one on each side of the desired core – do not yet support waveguiding in between, but only at the outer edges. However, we find that they already have a mutual influence on the morphology of the induced refractive index change, long before the directly irradiated zones overlap. In a second step we created a block of multiple modifications with a constant spacing of Δy = 16 μm schematically depicted in Fig. 1(a). We observe that the interaction of several tracks over a larger distance leads to a joint densification between the modifications which causes an increase in refractive index relative to the unaffected bulk material adequate to support waveguiding. An experimentally obtained intensity distribution of the guided mode is shown in Fig. 1(b).

 

Fig. 1 Femtosecond laser writing scheme. (a) Cross-sectional schematic depiction of stress-induced waveguiding zones between multiple modification tracks written with a cascaded-focus at a constant spacing Δy = 16 μm. (b) Measured intensity distribution of a guided mode at 638 nm which occurs between every two adjacent tracks in this pattern.

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To maximize the densification effect for one waveguide core and to minimize the lateral dimension of the structure, we now move all modification tracks as close together as possible (Δy = 10 μm) except for a single gap of length l in the middle, schematically depicted in Fig. 2(a). If Δy gets decreased further, the laser beam might be distorted by an existing material modification which can lead to defects during processing. A cross-sectional microscope image of the resulting waveguide is shown in Fig. 2(b). One can see that the modification tracks on each side merge together and form a single modification block. At the waveguide core the material gets compressed from two sides which creates the optimal refractive index increase. A tuning parameter to influence the mode-field diameter is given by l. In principle a total of two modifications on each side can be sufficient to support waveguiding in between. In this case we experimentally observe identical intensity distributions of the guided mode, but less transmitted power. The same goes for three modifications per block. In our case, blocks of four modifications on each side proved to be the optimal configuration; increasing the number to five did not show additional benefits.

 

Fig. 2 Waveguide morphology. (a) Two blocks of each four modifications get written with a gap of length l which forms the core of the waveguide. Within each block the modifications are separated by Δy. (b) Cross-sectional dark field microscopy image of a waveguide structure. (c) To create s-curved waveguides each individual track has to vary in radius of curvature. The reference radius R refers to the center of the waveguide.

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We performed several experiments with varying writing parameters and observed optimal waveguides at a repetition rate of f_rep = 100 kHz, pulse energy of E_p = 450 nJ, and writing speed of v = 40 mm/s which will be applied for the fabrication of all further waveguides. Since with the present setup the modifications have to be written consecutively we investigated the influence of various writing sequences for the modifications depicted in Fig. 2(a). We found no difference in the waveguide performance when writing “from-left-to-right” (A,B,C,D,E,F,G,H), “from-outside-to-inside” (A,B,C,D,H,G,E,F) and “from-inside-to-outside” (D,C,B,A,E,F,G,H). We also examined alternating sequences, e.g. (A,H,B,G,C,F,D,E), but experiments showed that this scheme increases the risk of material defects during fabrication which later result in undesirable scattering losses along the waveguide. For simplicity we chose the basic “from-left-to-right” sequence for the rest of the experiments.

To produce an s-curve waveguide each modification track has to follow an individual path with varying radii of curvature at constant angle δ which defines the length of the curve as depicted in Fig. 2(c). The reference radius R always refers to the center of the waveguide core and is constant for both curve segments. The total covered angle of an s-curve is 2δ.

4. Waveguide characterization

Typical mode profiles for different lateral spacings are depicted in Fig. 3. The smallest possible lateral distance between the two modification blocks that still support well-confined waveguiding is observed for l = 16 μm. In this case the mode profile is quite elliptical as can be seen in Fig. 3(a). With increasing distance l the guided mode becomes more and more circular as shown in Figs. 3(b) and 3(c). The mode field diameter for l ≤ 20 μm varies between 5 μm and 10 μm on the horizontal axis. On the vertical axis it does not show a systematic dependence on l and the values remain fairly constant at approximately 10 μm. We do not observe higher modes when scanning the coupling edge with the tip of a single-mode fiber. In vertical direction, sometimes additional waveguiding zones may be coupled which usually show less transmission efficiency and poor confinement compared to the central waveguide. For l ≥ 24 μm the confinement gets less clear and guiding becomes multimode as can be seen in Fig. 3(d).

 

Fig. 3 Mode profiles in false color representation for different lateral spacings l between the modification blocks and its influence on the ellipticity. The white dots represent three more modifications on each side with a respective distance of 10 μm.

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By measuring the mode-field diameter in the far field for different distances from the end-facet of the waveguide the NA was obtained. Applying the relation $\text{NA}=\sqrt{2n\mathrm{\Delta }n}$ allows for an estimation of the refractive index increase. The measured refractive index change Δn lies between 1 · 10⁻³ and 2 · 10⁻³, with higher values achieved at smaller l. This observation is explainable by the fact that a smaller l yields a more dense compression of the material at the waveguide core, resulting in a larger Δn. These values are higher than our reported Δn = 6.2·10⁻⁴ for single-track waveguides [18] and are in the range of numbers reported in the literature for waveguides in PMMA [14, 15]. We calculate the normalized frequency $V=\frac{2\pi a}{\lambda }\text{NA}$ by estimating the core radius a from the mode-field diameter of the measured intensity profiles. For small l the results for 638 nm and 850 nm satisfy the condition V < 2.405 for single-mode operation.

Propagation losses are investigated by preparing samples at different lengths between 10 mm and 50 mm. Each sample contains multiple waveguides written with the same set of parameters. The insertion losses IL = −10 log(P_out/P_in) were measured and averaged over identical waveguides. We varied l between 16 μm and 22 μm to restrict our investigation to well confined modes. We did not observe a systematic dependence of waveguide performance with respect to the writing direction when coupling light successively from both edges. Measured variations in transmitted power – which manifest as error bars shown in Fig. 4 – can mainly be attributed to fluctuations in coupling efficiency and scattering losses due to individual defects which can occur during processing. The results for guided light at 638 nm and 850 nm are depicted in Fig. 4(a) and (b) respectively. The propagation losses α are calculated as the slope of a linear fit.

 

Fig. 4 Insertion losses for waveguides at different lengths with l = 16, 18, 20, and 22 μm for two test-wavelengths: (a) λ = 638 nm and (b) λ = 850 nm. Propagation losses α are determined from a linear fit.

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For l = 18, 20, and 22 μm the propagation losses are identical, the value for l = 16 μm is slightly higher which is an indication that l is approaching its lower limit for an optimal waveguide core. The measured propagation losses go down to 0.3 dB/cm at 638 nm, and even 0.26 dB/cm at 850 nm with an error of the linear regression in the order of ±0.05 dB/cm. We conservatively estimate the total error to be ±0.1 dB/cm, taking systematic errors into account, such as, the detection of scattered light not belonging to the guided mode. The obtained values are an order of magnitude smaller than losses for other ultrafast laser written waveguides in polymers consisting of just a single-track modification [15,16]. The intrinsic material attenuation is given by the data sheet of the manufacturer as around 0.1 dB/cm for the visible region.

The Fresnel losses can be assumed constant since the quality of the polish is homogeneous over the entire edge surface. Light is coupled into the waveguide from a fiber aligned perpendicular to the entrance facet, therefore the Fresnel losses are estimated to be 0.17 dB for each air-PMMA-interface (n_PMMA ≈ 1.49). Subtracting this value two times from the y-intercept gives an experimental value for the average coupling efficiency which lies between 45–60 % depending on l as can be seen in Fig. 4. These values are in good agreement with results calculated from the overlap integral of the waveguide mode and the fiber mode.

We slightly adjusted the characterization setup to check also if guiding depends on the polarization of the coupled light. Light from the fiber gets collimated and a linearly p-polarized beam (parallel to the plane of the modification tracks) is extracted by a Polarizing Beam Splitter. With a λ/2 plate the polarization axis is rotated before the light gets focused into the waveguide by a low-NA lens. We confirme guiding for p-polarization and s-polarization alike. We only find the transmitted power to be approximately 15% higher for s-polarized light which can be explained by micro roughness along the modification tracks which has a larger effect on p-polarized light.

To investigate bend losses, s-curve waveguides have been fabricated according to the schematic depiction in Fig. 2(b). For minimum propagation losses and maximum Δn we chose l = 18 μm. For each radius of curvature R multiple waveguides covering different angles 2δ were created. The resulting different curve lengths allow for calculating the pure bend losses without the transition losses through mode mismatch between a straight segment and a bent one which strongly depends on R as well [22]. To evaluate if the measured bend losses are in agreement with the estimated refractive index increase, we adopt a formula for pure bend losses of single-mode step-index fibers from [22] as first approximation:

 

Fig. 5 Bend losses per unit length of s-curve waveguides with l = 18 μm in dependency of the bend radius R measured at λ = 638 nm. The theoretical curve was calculated according to equation (1) with a = 3 μm, Δn = 1.5 · 10⁻³, and n_eff = 1.49062.

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We find very good agreement between the data and the theoretical curve, even though the waveguides are most likely based on a graded-index structure due to the fabrication mechanism. This agreement also confirms the magnitude of Δn. The bend losses are negligible for bend radii down to R = 20 mm. Additionally, one has to keep in mind that the bend losses depicted in Fig. 5 are per unit length and that the curve length will get shorter as the radius decreases. Therefore, depending on the application, the bend losses for R < 20 mm might be tolerable as well. Transition losses between a straight and a bent segment – which quickly go up with decreasing R – still have to be considered of course. In our case, they were insignificant for R > 20 mm, but already in the order of 50% for R = 10 mm.

In a similar study on bends in ultrafast laser written waveguides in glass an almost one order of magnitude larger Δn was reported which enabled even tighter bends at 1550 nm [19]. These results were achieved by utilizing an annealing technique for a single-track waveguide. Also using the approach of encasing a waveguide core with multiple lateral modifications, bend losses similar to our values were reported in Yb:YAG with Δn ≈ 3.2 · 10⁻⁴ [20].

5. Conclusion

Highly efficient femtosecond laser written single-mode waveguides have been fabricated in PMMA. Propagation losses have been measured to be in the order of 0.3 dB/cm for light at 638 nm and 850 nm. An average refractive index increase of Δn = 1.5 · 10⁻³ at the waveguide core – due to combined material densification by multiple modification tracks – allows for curve radii R ≥ 20 mm at virtually zero bend losses which makes the creation of waveguide networks feasible for compact footprint lab-on-a-chip applications. While the presented data was obtained from 1.5 mm thick samples the technique has also been successfully applied to a 175 μm thin PMMA foil which opens the way to a completely new field of applications utilizing flexibly substrates.

In the future, the fabrication process can be optimized further by writing multiple modification tracks at the same time utilizing a Spatial Light Modulator (SLM), as demonstrated in [23]. This technique reduces the processing time on one side, and on the other side simultaneous formation of the tracks may increase the refractive index modification at the core further, directly resulting in even smaller possible bend radii. Also the inclusion of an active beam stabilization in the experimental setup might enhance the quality of the waveguides through reduced micro roughness of the modification tracks. We believe with these additional measures it will be possible to reduce the propagation losses further to a value close to the intrinsic material attenuation. While the presented work focuses on writing geometry and guiding characteristics, the structural changes of the material are highly interesting as well and require further investigation. As we believe, they could prove to be also a good candidate to create depressed cladding waveguides in polymers by writing a series of modifications completely surrounding a waveguide core.