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Abstract
We demonstrate, for the first time, the direct writing of curved optical waveguides in monocrystalline silicon with curve radii from 2 mm to 6 cm. The bending loss of the curved waveguides is measured and a good agreement with theoretical values is found. Raman spectroscopy measurements suggest the formation of inhomogeneous amorphous and polycrystalline phases in the laser-modified region. This direct laser-writing method may advance fabrication capabilities for integrated 3D silicon photonic devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser writing of optical waveguides inside dielectrics, especially glass, has been well developed in the past decades [1,2]. Generally, the waveguide is generated by producing a refractive-index contrast between the laser-induced structural modifications and the surrounding unmodified regions [3–5]. Two-photon–induced internal modification of Si was studied by Verburg et al. [6]. Investigations of the elongated structures and internal modifications formed by ns laser pulses were reported in [7–10]. Single-mode waveguides written inside Si with ns, ps and fs laser pulses were also demonstrated in [11–15]. Temporal contrast of the ultrashort pulses is proved to be a critical driving parameter in the process of modification formation [16].
Longitudinal writing and transverse writing are two commonly used methods to write waveguides [1]. The waveguides lengths are often less than several millimeters in the longitudinal writing because of the limitation of the lens focal distance [7,10–15]. On the other hand, the transverse method provides the possibility of writing long waveguides without the restriction of lens working distance. However, the cross-sectional shape of the waveguide is usually asymmetric in the transverse method. Fortunately, this drawback could be overcome by using shaped beams [2,17,18].
An advantage of the transverse writing method is that it provides more flexibility to write waveguide paths with complex shapes, i.e., shapes other than linear paths. Semicircular, or curved, waveguide paths are one example, which we demonstrate here. We study the performance of the curved waveguides, specifically with regard to the bending loss. The theory of bending loss in curved waveguides is established [19–24]. Marcuse [21] developed the first loss formula for optical fibers with a constant radius of curvature.
Our previous work has shown the possibility of transverse writing of waveguides inside silicon by shaped beams [20]. In this paper, we write curved waveguide paths with different radii and measure the bending loss caused by the curvature. We compare our measurements with calculated results based on the theory and find that they are in good agreement. Finally, we conduct Raman spectroscopy of the waveguides and show the formation of amorphous and polycrystalline silicon.
2. Experimental setup
The silicon wafers used in this study are intrinsic, (100)-oriented, and 1-mm thick. The resistivity is greater than 200 Ω·cm. The experimental arrangement used for writing is shown in Fig. 1. The wavelength and the pulse duration of the laser (MWTech, PFL-1550) are 1550 nm and 3.5 ns, respectively. The repetition rate is 20 kHz and the maximum pulse energy is 20 µJ. The diameter of the output beam is 6 mm. A pair of cylindrical lenses, CL1 and CL2, are used to shape the beam. The distance between the two lenses is $|{{f_1}} |- |{{f_2}} |$, where ${f_1}$ (30 cm) and ${f_2}$ (-3 cm) are the focal lengths of the two lenses, respectively. A spherically corrected objective lens (Olympus, LCPLN100XIR, NA = 0.85) is used to focus the beam into the silicon sample. At the focal point in the $x$-$z$ plane, the focal spot size is $2{w_0} = 1.22\lambda /NA = 2.2\; \mathrm{\mu}\textrm{m},$ and the Rayleigh length is ${z_R}$ = 2.6 μm in air and ${z_{R\; }} \approx \; 9.2\; \mathrm{\mu}\textrm{m}\; \; $in Si. Along the y and z directions, the spot radii are both 9.2 μm [20].
Fig. 1. Experimental arrangement used for transverse writing of semicircular, i.e., curved waveguides. The combination of a polarizer (P), half-wave plate (HWP), and polarizing beam splitter (PBS) is used to tune the output power. Other optical elements include mirrors (M), and two cylindrical lenses (CL1) and (CL2). A Si wafer sample is mounted on a rotation stage with the rotation axis parallel to the z-axis as shown.
The silicon samples in our experiment are 40×40 mm2 in size and they are mounted on a motorized rotation stage (Newport, SR50PP), which itself is mounted on an XYZ translation stage (Newport, ILS100PP). The laser light is focused at the depth of 0.5 mm. Curved waveguides are written by rotating the silicon sample. The laser writing speed for all the curved waveguides with different radii is kept at 38.5 mm/s by controlling the angular speed of the rotation stage. The use of the rotation stage ensures that the waveguides are written by the same beam profile [20]. The rotation stage is rotated through 90$^\circ $ for each waveguide and a total of 14 of quarter-circle waveguides are written with radii of curvature ranging from 0.2 cm to 6 cm. Each waveguide is buried in the silicon at a depth of 0.5 mm. Marks are scribed on the sample surface to aid locating the waveguides in later analysis.
3. Results and discussion
Figure 2 shows three of the 14 curved waveguides written with this method. The radii are 0.5 cm, 2.5 cm, and 5 cm. To obtain this figure, we couple a continuous wave (CW) laser beam by an objective (NA = 0.2) at λ = 1550 nm into each waveguide at the locations indicated by the red arrows at the bottom of Fig. 2. A portion of the light scatters out of the waveguide during propagation due to material defects in the waveguide. We image this scattered light with an IR camera and objective lens (NA=0.3) across the portions of the wafer surface where the illuminated waveguide resides, i.e., portions of the x-y plane. Because the field of view of the objective lens is not sufficient to cover the (90$^\circ $) arc length of an entire waveguide, multiple images are taken and then stitched together manually to form a mosaic revealing the entire waveguide. Figure 2 clearly shows that light is confined and propagates along these curved waveguides, exhibiting a gradual decay in intensity along the arc. We use the method described in [14] to obtain “shadowgraphs” of the modification and confirm a positive index change (see Supplement 1). It should be noted that the diverging light exceeding the acceptance angle of the waveguide diffracts out of the waveguide and thus does not contribute to the decay of the guided light. Notice that the light decays faster in waveguides with a smaller radius of curvature. As far as we know, this is the first time that multiple curved waveguides of different radii inside silicon are written by a shaped laser beam.
Fig. 2. Curved waveguides with different radii written in Si by the method in Fig. 1. Three waveguides in a single Si sample are shown with radii, R1 = 0.5 cm, R2 = 2.5 cm, and R3 = 5.0 cm as labeled. Infrared light is coupled into each guide from the bottom of the figure shown by the red vertical arrows. The light scatters as it travels along a waveguide arc and this scattered light is imaged with an IR camera over a limited field of view. By stitching together multiple images, a mosaic is formed revealing the entire waveguide arc length. Examples of single constituent images of a mosaic are shown via the remaining red arrows displayed. Note the decay of scattered light along a given waveguide as the light propagates up from its coupling point at the bottom of the figure. The top left image is the far-field (2.5 cm to the end facet of the waveguide) light intensity distribution from the curved waveguide with R = 2.5 cm.
Next, we measure the bending loss of the curved waveguides of different radii [20]. The total loss $\mathrm{\alpha}$ of a curved waveguide is expected to be the sum of the damping loss of a straight waveguide ${\mathrm{\alpha}_\textrm{s}}$ with the same length as the curved waveguide plus the bending loss ${\mathrm{\alpha}_\textrm{b}}$ caused by the curvature, i.e., $\mathrm{\alpha} = {\alpha _\textrm{s}} + {\alpha _\textrm{b}}$. To determine ${\mathrm{\alpha}_\textrm{s}}$, we write a group of straight waveguides in Si with lengths equal to the arc length of the curved waveguides. Then, the power of the laser light through each of the straight and curved waveguide is measured. The damping loss is calculated by the equation $\mathrm{\alpha} = 10\textrm{ log}({{P_1}/{P_2}} )$/d, where d, ${P_1}$ and ${P_2}$ are the waveguide length, input power and output power, respectively. We measure the input power P1 at the entrance side of each waveguide and the output power P2 at the exit side using a power meter. In this calculation, the loss due to the Fresnel reflection at both the front and back face (3.2 dB) and the coupling loss due to the NA mismatch between the objective lens and the waveguide (14.4 dB) are subtracted from the total loss. Note that scattering loss is included in the damping loss. By subtracting the measured damping loss of a straight waveguide ${\mathrm{\alpha}_\textrm{s}}$ with length d from the α measured for a curved waveguide with arc length d, the bending loss ${\mathrm{\alpha}_\textrm{b}}$ is determined. The dependence of ${\alpha _\textrm{b}}$ for curved waveguides on the radius of curvature R is shown in semi-log scale in Fig. 3 where the dots in the plot are the measurement results. For improved accuracy, we repeated these measurements five times for each of the 14 waveguides.
Fig. 3. Dependence of the bending loss ${\alpha _\textrm{b}}$ with curvature radius, R for the curved waveguides. The red curve is Eq. (1) while the blue line shows the scattering loss ${\alpha _\textrm{s}}$ (not bending loss) of a straight waveguide written with the same conditions as the curved waveguides.
To give context to our loss measurements, we compare to the theoretical treatment of bending loss in a curved waveguide given by [19]. The theory relates to a curved waveguide with a circular core cross-section of radius a and waveguide curvature radius R, where the bending loss is given by (simplified version of Eq. 3.6-7 in [19]) as:
Equation (1) includes waveguide and mode parameters $q = \; \sqrt {{\beta ^2} - \; n_2^2k_0^2} $, $h = \; \sqrt {n_1^2k_0^2 - \; {\beta ^2}} $, and $V = \; \sqrt {{{({ha} )}^2} + \; {{({qa} )}^2}} $, where ${k_0} = \; {\raise0.7ex\hbox{$\omega $} \!\mathord{\left/ {\vphantom {\omega c}} \right.}\!\lower0.7ex\hbox{$c$}}$ and $\omega $ is the laser angular frequency, and c is the speed of light in vacuum. Here, ${n_{1\; }}$and ${n_{2\; }}$ are the refractive index of core and cladding, respectively. Using the values $\mathrm{\lambda } = 1.55{\; }\mathrm{\mu}\textrm{m}$ $a = 5.0\; \mathrm{\mu}\textrm{m}$, ${n_{1\; }} = 3.502$, ${n_{2\; }} = 3.500$ appropriate for our sample, we obtain the propagation constant $\beta = \; 1.419 \times {10^7}$ based on Eq. 3.3-26 in [19], i.e.
The red line in Fig. 3 represents Eq. (1) and one can see that the measurements for ${\alpha _\textrm{b}}$ are in a good agreement with the R dependence of the theory.
In particular, notice in Fig. 3 that the measured bending loss ${\alpha _\textrm{b}}$ for the curved waveguides exhibit two clear trends that are also exhibited in Eq. (1). For R approximately larger than one cm, the plot shows a negative linear trend for ${\alpha _\textrm{b}}$, which given the semi-log scale of the plot implies that ${\alpha _\textrm{b}}$ decays exponentially with increasing R. This is logical because as the radius of curvature approaches infinity, the bending loss should vanish as the waveguide becomes straight in that limit. Conversely, for R approximately less than one cm, we see a non-linear trend in Fig. 3. Again, due to the semi-log scale, this implies a hybrid exponential and power-law dependence, the detail of which is revealed by reference to Eq. (1), i.e., the exponential $R$-dependence in the last term in Eq. (1) combined with the inverse $\sqrt R $ dependence in the first term. In other words, as the radius of curvature of the waveguide decreases, the bending loss grows precipitously, which in practical terms may limit the miniaturization of devices with such waveguides. The blue dashed line in Fig. 3 shows the scattering loss of a straight waveguide written under the same conditions as for the curved waveguides. Notice that this line crosses that of Eq. (1) at $R = 1.4$ cm, which means that when $R > 1.4$ cm, the primary loss mechanism is the scattering loss inherit to straight waveguides, while when $R < 1.4$ cm bending loss dominates.
To better characterize the curved waveguides written with this method, Fig. 4 shows Raman measurements of the Si material in the vicinity of the $R = 2.5$ cm waveguide cross section (y-z plane).The sample is cleaved perpendicular to the waveguide. The cross-section of the waveguides was examined under the Raman microscope directly without further processing to avoid any modification of the modified zone. The sample is characterized with a Raman microscope (Renishaw, inVia) at three positions indicated on the inset optical image. The position termed reference signal in Fig. 4 is an unmodified region of the Si sample. This measurement shows the typical Raman features of crystalline Si (c-Si) peaked at 520 cm-1. Two additional measurements were taken within the waveguide cross section, i.e., where the writing laser has modified the material, and are called position 1 and position 2. Here, features representing amorphous Si (a-Si) at 400–500 $\textrm{c}{\textrm{m}^{ - 1}}$ are seen along with decreased crystallinity due to the formation of polycrystalline Si (poly-Si) at 510 cm-1. Specifically, the spectrum corresponding to position 1 in Fig. 4 has a slightly asymmetrical shape about 520 cm-1, which could be due to poly-Si (peak at 510 cm-1, slightly below c-Si at 520 cm-1). The spectrum for position 2 shows the signature of a-Si (wide broadening from 400 to 500 cm-1). In principle, one could extract information about the ratio of laser-induced a-Si and poly-Si with respect to c-Si from these measurements [25]. We estimate that a-Si and poly-Si is no more than a few percent of c-Si based on the theory in [25], although a more precise estimate is not obtained here. Nevertheless, these results mean that the inner region of the waveguide consists mostly of c-Si with a small percentage of disturbed crystalline structures and is consistent with previous studies [26,27].
Fig. 4. Raman microscope spectra in the vicinity of a curved waveguide cross section. The different spectra correspond to the positions indicated in the microscope image. The profiles are normalized based on the assumption that the profiles should overlap beyond 1100 cm-1.
4. Conclusion
We have shown a new method to write semicircular curved waveguides of different radii in silicon with a shaped nanosecond laser beam. The bending losses of the waveguides are measured, showing good agreement with the theoretical prediction. For the fabrication conditions used here, the dependence of the bending loss on curvature radius exhibits an approximate exponential decay for radii greater than one cm and a hybrid exponential/power-law increase for radii less than one cm. Raman spectra of the waveguides demonstrate that a small percentage of amorphous and polycrystalline silicon is generated during the writing process. Our work is a step forward towards the goal of a single-step fabrication process of complicated waveguide structures in silicon for telecommunications applications as one example. Yet, our results show that future work is needed to fully develop this new method and write waveguides with more complicated shapes and better performance. In particular, we envision that a better understanding of the physical mechanism of the waveguides formation process will inform future improvements.
Funding
Air Force Office of Scientific Research (FA9550-19-1-0078); National Science Foundation (1665456, 1903740).
Acknowledgments
The authors thank the James R. Macdonald Laboratory of Kansas State University for their assistance.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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