This paper demonstrates the fabrication and measurements of flexible photonic lightwave circuits in glass substrates. Using temporally and spatially shaped ultrafast laser pulses, highly symmetrical and low-loss optical waveguides were written in flexible glass substrates with thicknesses ranging from 25 µm to 100 µm. The waveguide propagation loss, measured by optical frequency domain reflectometry, was 0.11 dB/cm at 1550 nm telecommunication wavelength. The bend loss of the waveguide is negligible at a radius of curvature of 1.5 cm or greater. Additionally, the waveguides are thermally stable up to 400°C. This paper presents alternatives to fabricating flexible photonics in traditionally used polymeric materials.
© 2015 Optical Society of America
Since the discovery of high-quality organic optical materials in the 1990s, polymer photonics has evolved into a dynamic field of engineering research and industrialization. The distinct advantages of polymer photonic devices, compared to inorganic photonic devices, are their low device/material costs and remarkable mechanical flexibility [1,2]. These unique traits have instigated worldwide R&D efforts on polymer photonics at both device and system levels. The mechanical flexibility and low material cost of polymer photonics opens up a number of tangible possibilities for diverse photonic applications. Some prominent applications include board-level and rack-level optical interconnects [3–8], “the last mile problem” associated with Fiber-To-The-Home (FTTH) applications [9–11], all-optical data processing [12–14], integrated sensor systems [15–17], and other short-haul communication applications.
Over the last decade, a majority of R&D efforts in flexible photonics have been invested in the development of a wide range of optical polymer systems with characteristics that meet requirements in many photonic applications . These material characteristics include refractive index, optical loss, birefringence, mechanical properties, and material stability . While the development of high-quality polymer optical materials has achieved some successes, it still incurs relatively high optical loss especially at telecom wavelength of 1.5 μm. As data rates dramatically increase in short-haul communication systems driven by the digital revolution, the optical power required to support high data bandwidth in optical waveguides also increases significantly. The relatively poor polymer thermal stability coupled with high optical loss of polymer photonic devices pose significant limitations of polymer photonic devices for high data bandwidth applications.
Over the last several years a brand new class of flexible glass materials has been produced by major material companies for commercial electronics. By reducing the thickness of the glass substrate to less than 100 μm, remarkable mechanical flexibilities have been realized [20–25]. The dramatic reduction of glass thickness, resulting lower stiffness, and lower bend stress permit roll-to-roll processes to produce high-quality glass substrates on a manufacturing scale that support pervasive consumer electronics applications. In addition to electronic device applications such as displays and photovoltaics, these flexible glasses enable new opportunities for flexible optical substrates.
These flexible glass substrates possess the same superior optical, mechanical, surface, thermal, and dimensional stability properties as the conventional thicker, rigid glass materials. Thus, these new, glass-based flexible optical substrates are inherently more stable and have better optical properties than the typical polymer optical substrates. The advent of flexible glass substrates provides an alternative to designing flexible lightwave circuits besides polymeric options. This paper explores the opportunity of using flexible glass substrates to enable new flexible photonic applications, device designs, performance levels, and fabrication techniques. It should be noted that all glass substrates can be made flexible when their thickness is reduced since the stiffness is related to (thickness) 3. The glass substrates used in this paper are an alkali-free borosilicate glass that is compatible with both flexible photonic as well as flexible electronic applications. It is known that high-quality waveguides can be produced in this glass family using the ultrafast laser direct writing process .
In this paper, we report on the fabrication of waveguides in flexible glass substrates using the ultrafast laser direct writing technique . Single-mode waveguides at 1550 nm with propagation loss as low as 0.11 dB/cm have been successfully produced in flexible glass with thickness of 25 µm, 35 µm, 50 µm, and 100 µm. Waveguide bend losses and thermal stability of fabricated waveguides and waveguide grating devices were also studied in this paper.
2. Experimental setup
The flexible glass substrates used for the waveguide fabrication were 25 µm, 35 µm, 50 µm, and 100 µm thick. Figure 1 shows the schematic of the experimental setup. A Coherent RegA 9000 laser system produced laser pulses at 800nm at a repetition rate of 250 kHz. The pulse width of the laser system was tuned by adjusting the grating compressor in the RegA 9000 amplifier. During the experiment, the impact of pulse width on the laser processing outcome was thoroughly studied from the transform-limited 190 fs to 1.8 ps. It was found that 300 fs pulses yielded the best results. The laser writing beam was sent through a beam shaping cylindrical telescope to control the shape and size of the focal volume . The combined optimization of spatial pulse shaping and temporal beam shaping was critical to produce symmetrical waveguide profiles especially in thin glass substrates with thickness less than 50 µm. The writing beam was then focused below the sample surface by an 80X aberration-corrected microscope objective (NA = 0.75). During the writing, the flexible glass samples were mounted on a three-axis motion stage (Aerotech ABL2002) and translated in the direction perpendicular to the writing beam and parallel with the laser polarization. A range of pulse energies from 1000 to 1200 nJ and writing velocities from 2 to 50 mm/s were investigated to optimize the writing parameters for waveguide fabrication in the flexible glass substrates.
After the writing process, the waveguides were characterized by (1) observation of index change profile by optical microscopy; (2) observation of guiding mode profile; (3) measurement of insertion loss; and (4) measurement of propagation loss. For the observation of guiding mode profile and measurement of propagation loss, the experimental setup shown in Fig. 2 was used. A CW laser at 1550nm was launched into the waveguide under test by butt-coupling to a single mode fiber (SMF-28). The output from the waveguide was collected and collimated using a microscope objective (NA = 0.55). The collected output was then sent to an integrating sphere to estimate the insertion loss or imaged by a lens on an IR camera to observe its guiding mode profile. An Optical Frequency Domain Reflectometer (Luna OBR4600) was used to measure the Rayleigh backscattering signal from the waveguide to evaluate propagation loss of waveguides at 1550 nm. In these measurements, the tunable laser from the OFDR was coupled into the waveguide using the same optical coupling setup.
3. Results and discussions
3.1. Beam shaping and optimization of writing parameters
Figure 3(a) shows the cross-section of a waveguide written under the condition that the laser beam was focused directly by an 80 × aberration-corrected microscope objective without going through the beam shaping telescope. The focal volume is elongated inside the sample. This produces a laser-induced plasma with highly asymmetric stresses and results in an asymmetric guiding region. The laser-induced damage (dark region in Fig. 3(a) ) is also found in the vicinity of the guide region. This causes significant propagation loss (>1 dB/cm). The laser-modified zone, which is visible under transmission microscope as shown in Fig. 3(a), is highly asymmetric. It extends more than 25 µm along the propagation direction of the writing laser beam (from top to bottom) although the FWHM size of the guided mode is only 9.44 µm along the same direction. Using this laser writing condition, it is not possible to write waveguides inside glass with thickness < 50 µm due to laser-induced surface damages. Poor insertion loss with telecom fibers and high waveguide birefringence could arise from this waveguide asymmetry.
To overcome this problem, a cylindrical beam shaping setup  is used to control the focal volume of the writing beam and fabricate highly symmetrical waveguides in the flexible glass substrates. Figure 3(b) shows the cross-section of a waveguide using a spatially shaped ultrafast laser beam. The telescope laser beam shaping setup leads to a much more symmetrical laser-modified region. The larger focal volume also eliminates the dark laser damage region as shown in Fig. 3(a). The large focal volume produced by the cylindrical telescope only leads to a slightly larger guided mode size as shown in Fig. 3(b) than those without the telescope beam shaping. Under optimized laser writing conditions, highly symmetrical waveguides have been successfully inscribed in 25 µm, 35 µm, 50 µm, and 100 µm thick flexible glass substrates (Fig. 3(c)).
The ultrafast laser pulse width was observed to have significant influence on the laser processing window and laser processing outcome in flexible glass substrates. In this work, the laser processing parameters, including waveguide writing speeds and pulse energy, were explored to optimize the mode-field diameter (MFD) and waveguide insertion loss for pulse widths ranging from 190 fs to 1.8 ps. Two-centimeter waveguides in 100 µm thick flexible glass substrates were used for laser process optimization. At the femtosecond regime around 300 fs pulse width, a wide range of laser writing speeds (5-50 mm/s) and pulse energies (1000 – 1400 nJ) are useful for producing waveguides. The optimized laser processing parameters were the combination of laser writing speed of 10 mm/s and 1.0-1.1 μJ pulse energy. However, when the laser pulse was stretched to picoseconds, the laser processing window decreased drastically. At 1.8 ps pulse width, waveguides were formed at much lower writing speeds between 1 mm/s and 5mm/s with very narrow windows for pulse energy between 820 nJ and 960-nJ. Waveguides produced by 1.8 ps pulses incurs much higher insertion loss than those formed by 300 fs pulses. The MFDs of the waveguides produced by 1.8 ps pulses are also 20% larger than those formed by 300 fs pulse. Waveguides written in the flexible glass with these optimized parameters were further characterized by propagation loss and bend loss.
3.2. Waveguide propagation and bend loss
Measurements of the waveguide propagation loss were based on optical frequency domain reflectometry (OFDR) and performed by an optical backscatter reflectometer (OBR) (LUNA OBR4600). Either a tunable laser output centered at 1550 nm or a broadband source is butt-coupled to the waveguide under test via a single mode fiber (SMF-28) mounted on a 3-axis translation nano-stage. Index matching gel was applied to both ends of the waveguide to reduce the impact of the reflection peaks from the two the substrate facets.
Figure 4(a) shows a measurement trace of an 11.4 cm long waveguide written in a 100 μm thick flexible glass substrate with the optimized writing condition (i.e. 300 fs pulse width, 1000 nJ pulse energy, and 10 mm/s translation speed). The peaks in the trace reveal the front and back facets of the substrate respectively. The propagation loss can be obtained from the slope of a linear fit of the data between the two reflection peaks. The linear fit of the Rayleigh backscattering signal shown in Fig. 4(a) yields a 0.11 dB/cm propagation loss of the waveguide written in 100 µm thick flexible glass. This measurement was repeated on 10 waveguides inscribed in the same sample with the same writing parameters. All the waveguides yielded similar low propagation loss ranging from 0.1 dB/cm to 0.25 dB/cm, as shown in Fig. 4(b). Waveguide cut-back approach were also used to characterize the propagation loss of embedded waveguides. The cut-back method yield propagation loss in the range of 0.1-0.3 dB/cm, which is consistent with the OFDR measurements presented in Fig. 4. Eight out of ten waveguides have propagation loss less than 0.2 dB/cm. We believe these results are among the best loss performances of waveguide structures made by ultrafast laser processing. There is no obvious reason why the propagation loss variation was observed since all of the laser processing conditions were kept constant during the laser waveguide writing. A likely source could come from different glass surface conditions such as dust. As the large size glass sample is mounted on the sample stages using a vacuum chuck, the uneven glass surface created by the suction force might be another reason for the waveguide quality variation.
The bending performance of the flexible waveguides is related to both the glass substrate mechanical flexibility and the refractive index of the waveguides inscribed by the lasers. The mechanical reliability of glass materials and devices depends on the defect size distribution and the applied stress. In general, the mechanical reliability will be dominated by the distribution of defects on the surface and edges of the glass substrates. Laser modified regions that are embedded in the bulk of glass substrates will have minor impacts on the mechanical reliability of glass substrates. Mechanical reliability of creating an optical waveguide at the central stress-free neutral plane would be minimal. Thus, the reliability of glass substrates is more sensitive to the specific handling, processing, and cutting conditions used in the fabrication of the flexible glass devices. As examples of flexible glass substrate mechanical reliability, compatibility of flexible glass with continuous roller handling and roll-to-roll device fabrication has been demonstrated  as well as cyclic bend testing of electronic structures at 25,000 cycles on flexible glass substrate . From the laser processing perspective, it was reported that ultrafast laser is capable to induce large refractive index change up to Δn~0.1. However, these large refractive index changes often accompany with significant optical losses. Therefore, in this work, we used the recommended minimum bending radii of glass substrates as guidelines to fabricate waveguide with “appropriate” refractive index profiles. This ensures the waveguides maintain both negligible bend loss within its allowable bending radii and also possess excellent optical quality.
The bend loss for waveguides in 100 μm, 50 μm, 35 μm, and 25 μm thick glasses were tested by wrapping waveguides around cylinders with various diameters. For 100 μm glass substrates, ¼ turn of wrapping was used to gauge the bend loss. For the other thinner glass, substrates were wrapped around cylinders by half turns. Figure 5 shows optical photographs of bent waveguides in the different flexible glass substrates. Green laser light at 532 nm was butt-coupled into waveguide using optical fibers. The minimum bending radii of curvatures shown in Fig. 5 are 13.5 cm for 100 μm glass in Fig. 5(a), 2.1 cm for 50 μm glass shown in Fig. 5(b), and 1 cm for 25 μm glasses shown in Fig. 5(c).
The waveguide insertion loss as a function of bending radii are presented in Fig. 6 for waveguides inscribed in 25, 35, 50, and 100 μm thick glass. This bend loss is measured against the insertion loss of flat waveguides. All waveguides were fabricated using spatially shaped 300 fs laser pulses with pulse energy of 1000 nJ. Therefore, it was expected that all waveguides would have similar refractive index profiles and that their bending performance will be determined by the mechanical properties of the glass. This is indeed the case as depicted in Fig. 6 when the bending radius is greater than ~1.5 cm where the bend loss is negligible. When the bending radius is smaller than ~1.5 cm, waveguides incur a significant increase in insertion losses. Given that standard telecommunication fibers (Corning SMF-28) have similar bending performance, this suggests that the refractive index change induced by the ultrafast laser at this writing condition is ~5 × 10−3. For 100 μm thick glass substrates, the minimum bending radius tested was 13.5 cm. At this bending radius of curvature or greater, the waveguide incurred negligible insertion loss changes as presented in the inset of Fig. 6 with an insertion loss fluctuation less than 0.04 dB probably due to measurement errors. The bend loss measured from the mechanically bent tests may be different from the bend loss of pure geometrically bent waveguides due to bending-induced mechanical stress effect. The effect of mechanical stress due to mechanical bending will increase the bend loss by about 28% at 15 mm bending radius . Therefore the bend loss for a geometrically bent waveguide will be lower than the mechanically bend loss.
3.3. Waveguide thermal stability and birefringence
To characterize the thermal stability of the waveguide devices, waveguides and waveguide Bragg gratings were characterized in several heating cycles at 250°C, 300°C, 350°C, 400°C, and 500°C. The duration of all of these tests was 1 hour. It should be noted that the annealing point for this glass is approximately slightly over 700°C. These waveguide devices were written with 1000 nJ and 1160 nJ pulses with 300 fs duration. After writing the waveguides and cycling to elevated temperatures, the samples were cooled down to room temperature after each thermal cycle and observed by optical microscope, characterized for mode profile, insertion loss, and Bragg wavelength shift.
The guided mode profiles and microscope images of waveguide tracks subjected to various thermal cycles are shown in Fig. 7. The thermal treatments for waveguides written by the pulse energy of 1000 nJ and its insertion loss changes are shown in Fig. 7(a) and 7(c). The thermal cycling at 300°C shows no change in waveguide characteristics. However, the MFD increases significantly at 500°C from 12.8 µm to 15.6 µm, this is coincident with the increase of waveguide insertion by 1.5 dB. Similar results were observed for waveguides written by the pulse energy of 1160 nJ as shown in Fig. 7(b) and 7(d), while thermal cycling at 350°C shows no significant changes of waveguide performance. Compared with flexible polymer waveguides which start to have weight loss and optical property changes starting at 100°C, the flexible glass has a much better long term thermal stability up to 350°C. This could be a significant advantage to surviving high optical power requirements for high bandwidth data transmission.
3.4. Bragg grating waveguides (BWGs) in flexible glass
Similar to the uniform waveguide writing, Bragg grating waveguides were also fabricated in flexible glass using a single-step laser writing technique . A function generator that produces square waveform with various duty cycles was used to drive the acousto-optic modulator in the regenerative laser amplifier (Coherent RegA 9000). The external modulation signal turns off the output of the amplifier periodically. By translating the substrate in relation to a fixed focal position using the three-axis motion stage, Bragg grating waveguide structures can be formed in desired locations and sections of waveguides. All Bragg grating waveguides were written by 300 fs pulses using a pulse energy of 1160 nJ, which yielded waveguide with low propagation loss. The writing speed used to write the Bragg grating waveguides was 1 mm/s. The period of Bragg grating waveguides Λ, is determined by the modulation frequency 𝑓 and the sample translation speed 𝑣, as Λ = 𝑣/𝑓 . The Bragg resonance wavelength 𝜆𝑩 is given by 𝜆𝑩 = 2𝑛𝑒𝑓𝑓Λ/𝑚 = 2𝑛𝑒𝑓𝑓𝑣/(𝑚𝑓), where 𝑛𝑒𝑓𝑓 is effective refractive index of the guided mode, and 𝑚 is the grating order. Bragg grating waveguides in this work were designed for a central wavelength of 𝜆𝑩 ~1550 nm and 𝑛𝑒𝑓𝑓 = 1.496. It is found that 25% duty cycle (25% laser on) at grating order 𝑚 = 3 provides the best fringe visibility and leads to the strongest resonant wavelength peaks .
For spectral measurements, broadband emission (MPB EBS-7210 Er3+ broadband source) centered around 1550nm was coupled into the BWGs using cleaved SMF28 + fiber mounted on a V-groove chip. The launch fiber was connected with a circulator for collecting the reflection spectrum, while the transmission was collected with a second fiber coupled with the guided mode after the objective as shown in Fig. 2. The signals were recorded on an optical spectrum analyzer (Ando 6317B) for data analysis.
Similarly to the waveguide thermal stability test, Bragg grating waveguides written with 1160 nJ pulses with 300 fs duration were characterized in several heating cycles at 250°C and 350°C for a duration of 1 hour. The samples were cooled down to room temperature after each cycle and observed by optical microscope, and characterized for Bragg resonance wavelength. Figure 8(a) shows a optical microscope image of the 3rd order Bragg grating waveguides viewed from the direction of the incident beam. No visible change was found in grating fringe visibility for all the heating cycles. Figure 8(b) shows reflection spectra of gratings after 250°C and 350°C thermal cycling in comparison with the spectrum before the thermal treatment. All measurements were performed at 25°C. No significant changes were observed in reflection spectra of waveguide gratings after the thermal treatment in terms of grating strength and their resonance wavelength. Given that the resolution of spectral analyzer is 10pm, the refractive index change due to the small cycling is less than 1 × 10−5. These thermal stability results in Bragg grating waveguide are consistent with those of uniform waveguide shown in Fig. 7.
Using the rotating extinction method [31–33], birefringence of the waveguides was measured. For waveguides written by pulse energy of 1000nJ at 300fs with 10mm/s writing speed, waveguide birefringence was measured as 0.45 × 10−5. To further confirm this measurement, Bragg grating waveguides were also used to measure the birefringence. By inserting a polarizer and a half-wave plate in the optical path to control the polarization of the interrogating light source, the polarization-dependent grating reflection spectra can be used to gauge the waveguide birefringence. Figure 9 shows the grating peak for –p and –s polarized light. The waveguide birefringence can be calculated by the resonance wavelength difference using 𝑛𝑝-𝑛𝑠 = (λ𝑝-λ𝑠)/(2𝑣𝑓). The resonance wavelength difference of 3 pm as shown in Fig. 9 yields the birefringence for the Bragg grating waveguide to be 0.58 × 10−5, which is consistent with rotating extinction method for waveguides in flexible glass.
4. Discussion and conclusion
This paper explores an alternative approach for flexible photonics. It replaces material challenges incurred in polymer-based flexible photonic devices with laser manufacturing technology innovations by fabricating flexible photonics components in highly stable flexible glass with proven optical quality using femtosecond ultrafast lasers.
In this work we applied ultrafast laser direct writing techniques to fabricate high-quality waveguides in flexible glass with thicknesses between 25 and 100 μm. The laser processing parameters were optimized for the flexible glass substrates through a combination of temporal pulse width tuning, spatial laser beam shaping, and other laser writing parameter tuning. We report that highly symmetrical waveguides that support single mode operation at the 1550nm telecom wavelength can be formed in flexible glass substrates. The propagation loss of the waveguides was measured as 0.11dB/cm by OFDR. No noticeable increase of insertion loss was observed with bending radii down to 1.5 cm. The realization of high-quality photonic circuits in glass substrates provides engineers new opportunities to develop flexible optoelectronic application with better reliability and longevity.
This work was supported by the National Science Foundation (CMMI-1334763 and CMMI-0923006).
References and links
1. R. Dangel, F. Horst, D. Jubin, N. Meier, J. Weiss, B. J. Offrein, B. W. Swatowski, C. M. Amb, D. J. Deshazer, and W. K. Weidner, “Development of versatile polymer waveguide flex technology for use in optical interconnects,” J. Lightwave Technol. 31(24), 3915–3926 (2013). [CrossRef]
2. H. Ma, A. K. Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: materials, processing, and devices,” Adv. Mater. 14(19), 1339–1365 (2002). [CrossRef]
3. L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000). [CrossRef]
4. S. Garner, “Ultra-slim flexible glass for electronic applications,” in 2012 MRS Fall Meeting & Exhibit, 2012.
5. S. M. Garner, K.-W. Wu, Y. C. Liao, J. W. Shiu, Y. S. Tsai, K. T. Chen, Y. C. Lai, C.-C. Lai, Y.-Z. Lee, J. C. Lin, X. Li, and P. Cimo, “Cholesteric liquid crystal display with flexible glass substrates,” J. Disp. Technol. 9(8), 644–650 (2013). [CrossRef]
6. S. Garner, J. Tosch, J. Matusick, X. Li, D. Marshall, C. Chase, J. Steiner, D. Yepez, J. Switzer, and P. Moschak, “Flexible glass substrates for continuous manufacturing,” in Flexible Electronics and Displays Conference (Phoenix, 2011).
8. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008). [CrossRef]
9. C. Florea and K. A. Winick, “Fabrication and characterization of photonic devices directly written in glass using femtosecond laser pulses,” J. Lightwave Technol. 21(1), 246–253 (2003). [CrossRef]
10. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004). [CrossRef]
11. S. Taccheo, G. D. Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Er:Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29(22), 2626–2628 (2004). [CrossRef] [PubMed]
13. J. R. Liu, Z. Y. Zhang, S. D. Chang, C. Flueraru, and C. P. Grover, “Directly writing in fused of 1-to-N optical waveguide power splitters silica glass using a femtosecond laser,” Opt. Commun. 253(4-6), 315–319 (2005). [CrossRef]
14. E. Bosman, G. Van Steenberge, B. Van Hoe, J. Missinne, J. Vanfleteren, and P. Van Daele, “Highly reliable flexible active optical links,” IEEE Photonics Technol. Lett. 22(5), 287–289 (2010). [CrossRef]
15. R. Keil, M. Heinrich, F. Dreisow, T. Pertsch, A. Tünnermann, S. Nolte, D. N. Christodoulides, and A. Szameit, “All-optical routing and switching for three-dimensional photonic circuitry,” Sci. Rep. 1, 94 (2011). [CrossRef] [PubMed]
16. R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20(7), 1559–1567 (2003). [CrossRef]
18. J. Hu, L. Li, H. Lin, P. Zhang, W. Zhou, and Z. Ma, “Flexible integrated photonics: where materials, mechanics and optics meet [Invited],” Opt. Mater. Express 3(9), 1313–1331 (2013). [CrossRef]
19. S. M. Eaton, H. Zhang, M. L. Ng, J. Li, W.-J. Chen, S. Ho, and P. R. Herman, “Transition from thermal diffusion to heat accumulation in high repetition rate femtosecond laser writing of buried optical waveguides,” Opt. Express 16(13), 9443–9458 (2008). [CrossRef] [PubMed]
20. S. Garner, S. Glaesemann, and X. Li, “Ultra-slim flexible glass for roll-to-roll electronic device fabrication,” Appl. Phys., A Mater. Sci. Process. 116(2), 403–407 (2014). [CrossRef]
21. S. M. Garner, M. He, P. Y. Lo, C. F. Sung, C. W. Liu, Y.-M. Hsieh, R. Hsu, J.-M. Ding, J.-P. Hu, Y.-J. Chan, J. C. Lin, X. Li, M. Sorenson, J. Li, P. Cimo, and K. T. Kuo, “Electrophoretic displays fabricated on ultra-slim flexible glass substrates,” J. Disp. Technol. 8(10), 590–595 (2012). [CrossRef]
22. S. Hoehla, S. Garner, M. Hohmann, O. Kuhls, X. Li, A. Schindler, and N. Fruehauf, “Active matrix color-LCD on 75 mm thick flexible glass substrates,” J. Disp. Technol. 8(6), 309–316 (2012). [CrossRef]
23. H. P. Mahabaduge, W. L. Rance, J. M. Burst, M. O. Reese, D. M. Meysing, C. A. Wolden, J. Li, J. D. Beach, T. A. Gessert, W. K. Metzger, S. Garner, and T. M. Barnes, “High-efficiency, flexible CdTe solar cells on ultra-thin glass substrates,” Appl. Phys. Lett. 106(13), 133501 (2015). [CrossRef]
24. S. Sheehan, P. K. Surolia, O. Byrne, S. Garner, P. Cimo, X. Li, D. P. Dowling, and K. R. Thampi, “Flexible glass substrate based dye sensitized solar cells,” Sol. Energy Mater. Sol. Cells 132, 237–244 (2015). [CrossRef]
25. L. Lan, H. Lin, S. Qiao, Y. Zou, S. Danto, K. Richardson, J. D. Musgraves, N. Lu, and J. Hu, “Integrated flexible chalcogenide glass photonic devices,” Nat. Photonics 8(8), 643–649 (2014). [CrossRef]
26. S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005). [CrossRef] [PubMed]
27. J. M. Burst, W. L. Rance, D. M. Meysing, C. A. Wolden, W. K. Metzger, S. M. Garner, P. Cimo, T. M. Barnes, T. A. Gessert, and M. O. Reese, “Performance of transparent conductors on flexible glass and plastic substrates,” 2014 IEEE-PVSC, Denver, June 9–13, 2014.
28. R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007). [CrossRef]
29. H. Zhang, S. M. Eaton, and P. R. Herman, “Single-step writing of Bragg grating waveguides in fused silica with an externally modulated femtosecond fiber laser,” Opt. Lett. 32(17), 2559–2561 (2007). [CrossRef] [PubMed]
31. H. Jerrard, “Optical compensators for measurement of elliptical polarization,” J. Opt. Soc. Am. 38(1), 35–57 (1948). [CrossRef]
32. R. Plumb, “Analysis of elliptically polarized light,” J. Opt. Soc. Am. 50(9), 892 (1960). [CrossRef]