Open Access
Add to BibSonomy
Abstract
In this work, thermo-optic (TO) tunable chirped waveguide Bragg gratings based on organic-inorganic hybrid PMMA material are achieved using the metal-print-defining technique. The molecular structural characteristics and thermal stabilities of the polymer grafting materials are analyzed. Structural parameters of the chirped waveguide gratings and self-electrode heaters are designed and performances of the entire device are simulated. The contrast value of the reflection band is about 15 dB between 1530 and 1570 nm. The actual thermo-optic sensitivity of the chirped grating is 0.2 nm/K. The time delay is obtained as 112 ps and the group velocity dispersion is measured as 2.1 ps/nm. This technique is very beneficial for achieving the dispersion-compensating optical communication system.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The waveguide Bragg grating (WBG) plays a key note in photonic integrated circuits and has been utilized widely as an important functional element for optical systems [1–5]. The multi-functional grating chips can be widely expanded to apply for large-capacity optical communications, high-resolution temporal/spatial measurements and fast-information processing [6-7]. Compared with the conventional WBG, the chirped waveguide Bragg grating (CWBG) can enhance spectral widths efficiently and realize temporal shifting, spectral slicing, non-uniform time delays and frequency to-time mapping [8–10]. For wavelength division multiplexing (WDM) communications, the wide bandwidth of the CWBG can be beneficial to dispersion compensation because continuous wavelengths in the broadband will be reflected at different locations. The characteristic of the wide reflecting spectrum is indispensable for an edge filter that converts the wavelengths to the intensity encoded signals. Furthermore, in contrast to the chirped fiber Bragg gratings (CFBG), the CWBG has more advantages such as compact size of device structure, ease of large scale integration and low cost of the demodulation system [11–14].
At present, different waveguide materials have been used for the preparation of waveguide Bragg gratings, such as InP, GaAs, silica and polymer. Compared with these pure organic or inorganic material systems, the organic-inorganic hybrid materials can exhibit combining characteristics including of silica and polymer. Furthermore, the comprehensive advantages of organic–inorganic hybrid materials are focused on integrated optics for low loss, flexible process and good compatibility [15–17]. Now several fabricating techniques for organic-inorganic hybrid materials such as ICP etching, nano imprinting and laser writing have been applied to form waveguide structure in lateral optical mode confinement [18–22]. But these manufacturing processes tend to damage the thin film of the material and cause extra waveguide loss.
In this work, we proposed a new metal-print-defining approach to directly realize a TO tunable chirped waveguide Bragg grating based on novel organic-inorganic hybrid PMMA materials. The sol-gel waveguide material was synthesized by employing nano-inorganic network into epoxy cross-linking P(MMA-GMA) with grafting composed techniques. The properties of the hybrid PMMA materials were analyzed. Structural parameters of metal-print-defining chirped waveguide Bragg grating and self-electrodes were analyzed and optimized. The contrast and thermo-optic tuning characteristics of the device were measured. The technique is easy to realize large-scale photonic integrated waveguide chip.
2. Experimental section
2.1 Organic-inorganic grafting PMMA waveguide material
Currently PMMA has been used as the main optical material for fabrication of economic POFs applications [23-24]. However, poor thermal stability and high transmission losses of pure polymer prohibit commercial development of the devices. To overcome these limitations, we synthesized the novel grafting hybrid PMMA material. The material system of flexible chain polymer grafted on a silica based inorganic network improves chemical, mechanical and optical properties of sol-gel coatings, and crack-free thick films can be easily obtained. In addition, the relatively high negative TO coefficient and low processing temperature make the hybrid materials suitable for TO waveguide device application.
The novel grafting hybrid PMMA material was polymerized by 3-methacryloxy-proyltrimethoxysilane (MAPTMS, KH570; 98%), methylmethacrylate (MMA; 99.5%) and epoxypropylmethacrylate (GMA; 97%). MAPTMS (1.50 g, 6.00 mmol), MMA (6.00 g, 60.00 mmol), GMA (1.50 g, 11.00 mmol), Tetrahydrofuran (THF) (25 mL) and Azobisisbutyronitrile (AIBN) (0.018 g, 0.10 mmol, 2 wt‰) as radical initiator were added into a three-neck round-bottom flask equipped with a mechanical stirrer, nitrogen in inlet, and reflux condenser [25]. The mixture was stirred at the temperature of 70 °C for 5 hours in blocking reaction situation. Then the copolymer was formed and tetraethylorthosilicate (TEOS; 98%) was added to be hydrolyzed to obtain sol-gel hybrid material. In this process, TEOS (Si(OC2H5)4, 1.50 g, 7.00 mmol) in THF (15 ml) was dropped into the copolymer solution little by little with acidic water (CH3COOH, pH = 1, 0.50 g, 8.00 mmol) used as catalyst. The hybrid material solution was stirred at the temperature of 30 °C for 12 h before reaching homogenization. The SiO2 network was generated by prehydrolyzing MAPTMS and TEOS. It is mainly that TEOS has C2H5O-Si-groups which could react with the CH3O-Si-groups in MAPTMS. Finally, 2-methylimidazole (DMM, 98%) (0.05 g, 0.70 mmol, 5 wt‰) in THF (5 ml) used as a curing agent could achieve epoxy cross-linking network from the organic component of GMA. The synthesis process of the organic-inorganic hybrid P(MMA-GMA) material was given as Fig. 1.
The root mean square (RMS) of surface roughness for the hybrid film is measured around 1.56 nm by Atomic Force Microscope (AFM). Pure PMMA and hybrid PMMA material solutions are cured thermally on Si substrate, then the solid PMMA and hybrid PMMA materials are scraped off and collected for FTIR measuring. The FTIR spectra of the organic-inorganic hybrid PMMA material and pure PMMA are shown as Fig. 2. Compared to pure PMMA, some typical bands of the grafting PMMA are given in the spectrum. Asymmetric stretching vibrations of Si-O groups in inorganic component and symmetric stretching vibrations of C-O-C groups in mono-substituted epoxy rings produce the characteristic peaks at 1090 and 830 cm−1, respectively.
Figure 3 shows that the glass transition temperature (Tg) of the organic-inorganic hybrid PMMA material in different cross-linked states are measured with a modulated differential scanning calorimeter (DSC). Specially, the polymerization and the SiO2 cross-linked networks can enhance the Tg of the hybrid film. When the copolymers only form organic epoxy cross-linked network structure, the Tg of the material is 126 °C, which is higher than pure PMMA as 100 °C. Furthermore, when the copolymers form both organic epoxy and inorganic SiO2 cross-linking networks, the Tg of the material comes to 153 °C. Compared to the hybrid PMMA with only organic epoxy cross-linked network, the Tg of the hybrid PMMA with the inorganic networks is increased by 27 °C. The reason may be that the high Tg of SiO2 networks is helpful to increase that of the overall hybrid PMMA material.
2.2 Theoretical analysis and simulation
The schematic diagram of metal-print-defining chirped waveguide Bragg gratings with self-electrode structure is shown in Fig. 4(a). The thin gold films with chirped waveguide grating patterns are formed on organic–inorganic hybrid PMMA core layer [26]. The metal-print-defining chirped waveguide Bragg grating can produce non-uniform periodic structure so that the mode effective index perturbation of the grating may be continuously changed. Compared with conventional waveguide Bragg gratings, the chirp waveguide Bragg gratings have a wider reflection spectrum with dispersion compensation characteristics. Self-electrode heater structures are set and configured on the metal gratings. The tunable function of Bragg reflecting spectrum can be achieved by applying the electric signal to adjust the optical wavelengths by TO effect. Figure 4(b) gives the cross-sectional profile of the metal-print-defining chirped waveguide Bragg gratings. The hybrid PMMA thin film is spin-coated and cured onto Si substrate with 5 μm width SiO2 lower cladding. The Au strips are shaped as metal-defining upper claddings by deposition and photolithography technique. The core waveguide area is directly confined with air-upper cladding during the Au strips. The refractive indices of SiO2, organic-inorganic hybrid PMMA material, Au and air are 1.444 [27], 1.476, 0.56 + 11.21i [28] and 1.00 at 1550-nm wavelength, respectively. The fundamental transverse magnetic (TM) mode of the waveguide was analyzed by the effective index method. The width and thickness of the core waveguide are designed as 5 µm and 3 µm, respectively. The width and the height of the metal strips are defined as 25 µm and 60 nm, respectively.
Fig. 4 The structure of the chirped gratings (a) Schematic diagram of metal-print-defining chirped waveguide Bragg gratings (b) Cross-sectional profile of the waveguide designed.
The TM mode index of core and cladding layers are simulated. The effective index of core layer denoted as Ncore and the effective index of cladding layer denoted as Nclad are defined, respectively. Based on effective index method, the relations between the core thickness b and TM mode effective refractive indices of the core and the cladding for the signal wavelengths are given in Fig. 5(a) and (b), respectively. It can be found that when the core thickness b is chosen to be 3 μm, there is only TM0 mode in the core waveguide, and TM0 mode in the cladding is cut-off. TM-1 mode in the cladding belongs to the surface plasmon polariton (SPP) mode in the Au cladding structure. The effective refractive index of TM-1 mode in the cladding is larger than that of TM0 mode in the core waveguide, so there is no mode coupling between them.
Fig. 5 The relationship between the core thickness b and TM mode effective refractive indices of (a) Ncore and (b) Nclad for resonant wavelengths; (c) The absorption loss curves for different metal claddings (Au and Al) simulated.
The absorption loss coefficient for corresponding metal cladding structure is simulated. The relationships between the core thickness b and the loss factor for Au and Al are shown in Fig. 5(c). It can be found that compared with the large loss coefficient of Al, the value of Au is smaller than 0.02 dB/cm. This is mainly because the imaginary part of the dielectric constant of Au is small, resulting in less absorption loss. By choosing Au as a cladding material, it can be relatively effective to reduce the transmission loss of the waveguide.
The optical and thermal distributions are simulated by software COMSOL multiphysics. Figure 6(a) shows the single-mode optical field distribution for the transverse magnetic (TM) mode simulated by the effective index method for the metal-print-defining waveguide structure. Figure 6(b) gives thermal field distribution characteristics of Au self-electrodes in the cross-sectional waveguide profile.
Fig. 6 Optical and thermal field simulated (a) Optical field distribution for the TM waveguide (b) thermal field distribution in the waveguide cross-section.
The proposed CWBG is made by axially altering the grating period (Λ) with linear increment to adjust effective refractive index (neff) difference. According to the Bragg phase-matching condition, λB = 2 × neff × Λ/m, where m is the grating order and neff is the mode effective refractive index. The Bragg wavelength λB along the grating is continuously changing, and the chirped effect can be formed. The initial grating period is designed to be 20 μm with a duty cycle of 50%. The periodic modulation equation of chirped waveguide grating is given as [29–34]
The transfer matrix method is applied to obtain the reflection spectrum as where C = dλ/dz is the chirping coefficient as 0.2 nm/mm. Λ0 is the initial grating period, which is defined as 20 μm. The length of the grating L is 4200 μm. The coupling coefficient κ is 2 × 10−3 µm−1, R is the reflectivity of the chirped grating.The characteristic equations for the time delay τ(λ) and dispersion D(λ) are shown as
where θ is the dispersion angle and is related to the reflectivity R as eiθ.Figure 7(a) shows the simulating reflection spectrum of the CWBG for TM mode and the group time delay of the metal-print-defining CWBG, respectively. Figure 7(b) gives the calculating reflection spectrum and dispersion curve, respectively. The maximum contrast of the reflection bandwidth is about 20 dB at room temperature. It can be found that the chirped grating gives the group time delay of 120 ps and the dispersion of 3.2 ps/nm during 1530-1565 nm. It is important that the broad reflection bandwidth of the CWBG is derived from the enhancing refractive index (RI) modulation, which is superior to that of a conventional CFBG. When the self-electrodes are applied with certain electric power, the tunable resonant wavelength function of the chirped grating with group time delay and dispersion varying by different temperature is realized based on TO effect as shown in Fig. 7(c) and (d), respectively. The resonant wavelengths with group time delay and dispersion for TM polarization exhibit red shift with the temperature increasing. The temperature dependences of the filter rejection and reflection are derived from the change of the effective refractive index (neff) of the waveguide from Eq. (1), (2) and (3) based on thermo-optic effect. The sensitivity of the chirped grating is obtained as 0.5 nm/K approximately.
Fig. 7 The simulating performances of the chirped gratings (a) Reflection spectrum (red) and group time delay (blue) (b) Reflection spectrum (red) and dispersion curve (c) Tunable resonant wavelengths of the chirped grating.
The frequency characteristic of the device is depended on the switching time. The switching time τ can be determined by τ = 0.47L2/γ, γ = keff/ρeff Cpeff [35], where keff is the effective thermal conductivity, ρeff is the effective density, Cpeff is the effective heat capacity, and L2 is the square of the slab thickness. The parameters of the waveguide materials are given in Table 1. The switching time can be estimated to be hundreds of microseconds.
Table 1. Parameters of the waveguide materials
2.3 Device fabrication and measurement
This chirped Bragg grating using the hybrid PMMA material is realized by deposition and photolithography fabrication process forming Au-print-defining waveguide structure. Figure 8(a) gives CBWG patterns defined by Au cladding layers using microscope ( × 500). It is illustrated that the actual structural parameters of this device can fit well with the values designed. Precise control of the waveguide size can be achieved. Figure 8(b) gives the surface profile of Au cladding patterns measured by Atomic force microscope (AFM). The thickness is about 60 nm and the surface roughness is less than 1.5 nm. The total resistance of the self-electrode is measured as 2 kΩ.
Fig. 8 The profiles of the chirped waveguide gratings (a) Structural patterns of CBWG region observed by microscope ( × 500) (b) Surface profile of the Au cladding layer measured by AFM.
Figure 9 gives the schematic diagrams of the measurement system. The metal-print-defining tunable chirped waveguide Bragg grating was characterized by coupling signal wavelengths in a range from 1510 to 1590 nm by an amplified spontaneous emission (ASE) laser into the device using a standard single-mode fiber. The electrical modulating power from a signal generator is loaded on the self-electrodes of the gratings by needle probes. The reflecting signals are fed back into an optical spectrum analyzer (OSA) by a circulator. The light signals from the output fibers are divided into two parts by a splitter. One part is monitored by an infrared camera with an optical power meter, and the other part is launched into a photo detector and then converted to electrical signals into an oscilloscope compared to the reference signals from the signal generator. Compared with the other organic-inorganic hybrid waveguide [36], the absorption loss of the hybrid materials is similar. However, due to the absorption loss of the metal cladding and mode mismatch loss between the coupling fiber and effective waveguide size, the transmission loss of the waveguide was obtained as 1.2 dB/cm through a cut-back method. But the waveguide structure and the direct effect of the metal heater on the core layer are advantageous for high integration and fast TO response speed.
Figure 10 (a) shows the actual TO tunable reflection spectrum measured for the TM polarization. It can be described that when the electrical signal power is strengthened by 1 mW with the temperature of the self-electrode increasing by 5 K, the actual entire resonant wavelength band will generate red shift as 1 nm. The actual sensitivity of the chirped gratings is 0.2 nm/K. The contrast of the whole reflecting band from 1530 to 1565 nm is about 15 dB. The actual group time-delaying response of the device is measured by an optical vector analyzer (LUNA OVA CTe). The group time delay is obtained as 112 ps and the dispersion as 2.1 ps/nm during the reflection wavelength range. When only the center reflecting wavelength as 1550 nm is coupled into the waveguide by the fiber, the TO switching response is measured in Fig. 10(b). Figure 10(b) shows the TO tunable response observed by loading square-wave driving voltage at a frequency as 500 Hz. The measuring switching rise and fall times were obtained as 467.0 μs and 225.6 μs, respectively. The actual electric power required for the chirped grating achieving maximum contrast value was about 25 mW.
Fig. 10 Functional characteristics of the actual CBWG device (a) TO tunable reflection spectrum (b) TO switching response curves.
3. Conclusion
In summary, the TO tunable chirped waveguide Bragg gratings based on the novel organic-inorganic hybrid PMMA materials are designed and fabricated by metal-print-defining waveguide technique. The contrast value of the reflection band for the device is about 15 dB between 1530 and 1565 nm. The actual thermo-optic sensitivity of the chirped grating is 0.2 nm/K. The time delay is obtained as 112 ps and the group velocity dispersion is measured as 2.1 ps/nm. The technique will be very suitable for optical wavelength division multiplexing (WDM) communication system integrated with dispersion compensation functions.
Funding
National Key R&D Program of China (2016YFB0402504); National Natural Science Foundation of China (No. 61575076, 61675087); and Jilin Provincial Industrial Innovation Special Fund Project (2016C019).
References and links
1. Z. y. Zhang, A. M. Novo, D. Liu, N. Keil, and N. Grote, “Compact and tunable silicon nitride Bragg grating filters in polymer,” Opt. Commun. 321, 23–27 (2014). [CrossRef]
2. M. Thiel, G. Flachenecker, and W. Schade, “Femtosecond laser writing of Bragg grating waveguide bundles in bulk glass,” Opt. Lett. 40(7), 1266–1269 (2015). [CrossRef] [PubMed]
3. C. Porzi, G. Serafino, P. Velha, P. Ghelfi, and A. Bogoni, “Integrated SOI high-Order phase-shifted Bragg Grating for microwave photonics signal processing,” J. Lightwave Technol. 35(20), 4479–4487 (2017). [CrossRef]
4. H. Okamoto and K. Kusaka, “Low Loss Plasmonic Bragg Gratings with a Trench Plasmonic Waveguide,” Plasmonics 12(5), 1481–1485 (2017). [CrossRef]
5. C. Klitis, G. Cantarella, M. J. Strain, and M. Sorel, “High-extinction-ratio TE/TM selective Bragg grating filters on silicon-on-insulator,” Opt. Lett. 42(15), 3040–3043 (2017). [CrossRef] [PubMed]
6. S. H. Park, J. K. Seo, J. Park, H. K. Lee, J. S. Shin, and M. C. Oh, “Transmission type tunable wavelength filters based on polymer waveguide Bragg reflectors,” Opt. Commun. 362, 96–100 (2016). [CrossRef]
7. P. A. Cooper, L. G. Carpenter, C. Holmes, C. Sima, J. C. Gates, and P. G. R. Smith, “Power-Efficiency enhanced thermally tunable Bragg grating for silica-on-silicon photonics,” IEEE Photonics J. 7(2), 1 (2015). [CrossRef]
8. B. Yun, G. Hu, R. Zhang, and Y. Cui, “Fabrication of a third-order polymer chirped waveguide Bragg grating with tapered core size by contact lithography,” Appl. Opt. 54(3), 467–471 (2015). [CrossRef]
9. P. Bettini, E. Guerreschi, and G. Sala, “Development and experimental validation of a numerical tool for structural health and usage monitoring systems based on chirped grating sensors,” Sensors (Basel) 15(1), 1321–1341 (2015). [CrossRef] [PubMed]
10. A. Bostani, M. Ahlawat, A. Tehranchi, R. Morandotti, and R. Kashyap, “Tailoring and tuning of the broadband spectrum of a step-chirped grating based frequency doubler using tightly-focused Gaussian beams,” Opt. Express 21(24), 29847–29853 (2013). [CrossRef] [PubMed]
11. W. Zhang and J. Yao, “Silicon-based on-chip electrically-tunable spectral shaper for continuously tunable linearly chirped microwave waveform generation,” J. Lightwave Technol. 34(20), 4664–4672 (2016). [CrossRef]
12. W. Zhang and J. Yao, “Photonic generation of linearly chirped microwave waveforms using a silicon-based on-chip spectral shaper incorporating two linearly chirped waveguide Bragg gratings,” J. Lightwave Technol. 33(24), 5047–5054 (2015). [CrossRef]
13. T. Tiess, C. Chojetzki, M. Rothhardt, H. Bartelt, and M. Jäger, “Fiber-integrated concept to electrically tune pulsed fiber lasers based on step-chirped fiber Bragg grating arrays,” Opt. Express 23(15), 19634–19645 (2015). [CrossRef] [PubMed]
14. A. V. Tokarev, G. G. Anchutkin, S. V. Varzhel, A. I. Gribaev, A. V. Kulikov, I. K. Meshkovskiy, M. Rothhardt, T. Elsmann, M. Becker, and H. Bartelt, “UV-transparent fluoropolymer fiber coating for the inscription of chirped Bragg gratings arrays,” Opt. Laser Technol. 89, 173–178 (2017). [CrossRef]
15. Q. q. Wang, X. Zhang, and J. Li, “Synthesis and evaluation of organic–Inorganic hybrid molecularly imprinted monolith column for selective recognition of acephate and phosphamidon in Vegetables,” Adv. Polym. Technol. 36, 21620 (2015).
16. X. y. Jia, Z. y. Hu, Y. Zhu, T. Weng, J. Wang, J. Zhang, and Y. Zhu, “Facile synthesis of organic-inorganic hybrid perovskite CH3NH3PbI3 microcrystals,” J. Alloys Compd. 725, 270–274 (2017). [CrossRef]
17. G. Roviello, C. Menna, O. Tarallo, L. Ricciotti, F. Messina, C. Ferone, D. Asprone, and R. Cioffi, “G.a Roviello, C. Menna, O. Tarallo, “Lightweight geopolymer-based hybrid materials,” Compos., Part B Eng. 128, 225–237 (2017). [CrossRef]
18. G. Semwal and V. Rastogi, “Design optimization of long period waveguide grating devices for refractive index sensing using adaptive particle swarm optimization,” Opt. Commun. 359, 336–343 (2016). [CrossRef]
19. P. A. Cooper, L. G. Carpenter, and C. Holmes, “Power-Efficiency Enhanced Thermally Tunable Bragg Grating for Silica-on-Silicon Photonics,” Photonics Journal 7, 7800411 (2015).
20. G. Huang, J. S. Shin, W. J. Lee, T. H. Park, W. S. Chu, and M. C. Oh, “Surface relief apodized grating tunable filters produced by using a shadow mask,” Opt. Express 23(16), 21090–21096 (2015). [CrossRef] [PubMed]
21. W. Jin and K. S. Chiang, “Mode switch based on electro-optic long-period waveguide grating in lithium niobate,” Opt. Lett. 40(2), 237–240 (2015). [CrossRef] [PubMed]
22. Q. Liu, Z. Gu, J. S. Kee, and M. K. Park, “Silicon waveguide filter based on cladding modulated anti-symmetric long-period grating,” Opt. Express 22(24), 29954–29963 (2014). [CrossRef] [PubMed]
23. S. Kiesel, K. Peters, T. Hassan, and M. Kowalsky, “Behaviour of intrinsic polymer optical fibre sensor for large-strain applications,” Meas. Sci. Technol. 18(10), 3144–3154 (2007). [CrossRef]
24. W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. H. Rasmussen, F. K. Nielsen, S. Andresen, O. B. Sørensen, K. S. Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber Bragg gratings,” Opt. Commun. 284(1), 176–182 (2011). [CrossRef]
25. Y. Gu, C. Chen, Y. Zheng, Z. Shi, X. Wang, Y. Yi, T. Jiang, X. Sun, F. Wang, Z. Cui, and D. Zhang, “Heat-induced multimode interference variable optical attenuator based on novel organic-inorganic hybrid materials,” J. Opt. 17(8), 1–9 (2015). [CrossRef]
26. Z. Yang, C. m. Chen, and Y. l. Gu, “Metal-cladding directly defined active integrated optical waveguide device based on erbium-containing polymer,” RSC Advances 6, 3224–3230 (2015).
27. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1208 (1965). [CrossRef]
28. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
29. H. Y. Chang, Y. C. Chang, H. J. Sheng, M.-Y. Fu, W.-F. Liu, and R. Kashyap, “An Ultra-Sensitive Liquid-Level Indicator Based on an Etched Chirped-Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 28(3), 268–271 (2016). [CrossRef]
30. K. Markowski, K. Jedrzejewski, and T. Osuch, “Numerical analysis of double chirp effect in tapered and linearly chirped fiber Bragg gratings,” Appl. Opt. 55(17), 4505–4513 (2016). [CrossRef] [PubMed]
31. T. A. Hamdalla, “Wavelength profiles of nonlinear irradiated apodized chirped Bragg grating,” Curr. Appl. Phys. 13(3), 533–536 (2013). [CrossRef]
32. L. y. Wu, L. Pei, C. Liu, and J. Wang, “Research on tunable phase shift induced by piezoelectric transducer in linearly chirped fiber Bragg grating with the V-I transmission matrix formalism,” Opt. Laser Technol. 79, 15–19 (2016). [CrossRef]
33. J. Feng, X. Zhang, S. Wu, H. Xiong, F. Gao, Z. Zhuang, and X. Yuan, “Configuration with four chirped volume Bragg gratings in parallel combination for large dispersion applications,” Opt. Eng. 54(5), 056105 (2015). [CrossRef]
34. A. Hessainiaa, S. El-Akrmi, and H. Triki, “Analysis of fiber Bragg grating with exponential–linear and parabolic taper profiles for dispersion slope compensation in optical fiber links,” Optik (Stuttg.) 125(17), 4642–4645 (2014). [CrossRef]
35. Y. F. Yan, C. T. Zheng, X. Q. Sun, F. Wang, and D. M. Zhang, “Fast response 2×2 thermo-optic switch with polymer/silica hybrid waveguide,” Chin. Opt. Lett. 10(9), 092501 (2012). [CrossRef]
36. C. M. S. Vicente, E. Pecoraro, R. A. S. Ferreira, P. S. Andre, R. Nogueira, Y. Messaddeq, S. J. L. Ribeiro, and L. D. Carlos, “Waveguides and gratings fabrication in zirconium-based organic/inorganic hybrids,” J. Sol-Gel Sci. Technol. 48, 80–85 (2008).
