Abstract

We fabricated waveguide resonators with high thermal stability using tantalum pentoxide thin film covered with PECVD silicon dioxide cladding. Without complex athermal design, low temperature dependence of 7.4 pm/°C and 8.15 pm/°C were measured in waveguide Bragg gratings (WBG) and Fabry-Perot resonator sandwiched by a pair of identical WBG mirrors, respectively. Suggested by semi-analytical perturbation calculations, the athermal properties of tantalum pentoxide waveguide grating are attributed not only to the low thermo-optical coefficient in tantalum pentoxide thin film but also to the strong chromatic dispersion of the guided modes. Guidelines are proposed to design waveguide-based frequency devices of low thermo-optical effect without complex athermal design.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Waveguide resonators are important devices for integrated optics and silicon photonics. Their sensitive spectral response to the environments makes waveguide resonators applicable to sensor devices for detections of refractive indices [1,2], temperatures [3] and strains [4] the shifts in resonant wavelength. Such high sensitivity to environments also enables simultaneous retrieval of many environmental parameters such as temperature and refractive index [5] or temperature and strain [6]. However, such high sensitivity turns out to be a major drawback as spectral selective devices or optical filters embedded in communication systems for example arrayed waveguide grating (AWG) for wavelength division multiplexing (WDM). In particular, silicon or silica waveguides suffer from large thermo-optical effect so that standard AWG can only achieve temperature sensitivity as low as tens of pm/°C without athermal designs [7]. For even lower temperature sensitivity, complicated resonator structures were proposed that can improve the temperature dependence down to 1 pm/°C at the expanse of not being compatible to silicon photonics fabrication routes [1]. The idea of athermal design originated from compensated temperature diode laser using externally coupled cavity with negative thermo-optical effect [8]. This concept has been adopted to waveguide devices by using polymer (MMA) cladding with negative thermo-optical coefficient so the effective refractive index of guiding mode is insensitive to temperature dependence [9]. Several reports on athermal waveguide design using cladding material with negative thermo-optical coefficient have been proposed [10] and is also applied to optical add-drop multiplexers down to within 1 pm/°C for TM polarized mode at C band [11]; yet the athermal property holds only for a specific temperature range [12]. Recently high quality waveguide devices based on a large band gap (~5 eV.) material, Tantalum Pentoxide (Ta2O5) which has very low linear and nonlinear absorption in visible to infrared wavelength are reported [13]. By virtue of large band gap, Ta2O5 is free from free carrier absorption and two photon absorptions in near infrared wavelengths which are widely utilized in optical communications. Its large nonlinear coefficient (10−14 W/cm2), high refractive index (2.08 at 1550 nm) and CMOS-compatible property make Ta2O5 a promising material for developing integrated optoelectronic devices [13]. Moreover the thermo-optical effect of Ta2O5 is 2.3 × 10−6 K−1 [14], which is an order of magnitude smaller than that of silica (1.3 × 10−5 K−1 [15]) and is almost two order of magnitude smaller than that of silicon (1.8 × 10−4K−1 [15]). Without a doubt, Ta2O5 should be better core material for fabricating athermal integrated optical devices. In this work, we report the fabrication and characterization of athermal Ta2O5 waveguide Bragg grating (WBG) resonator for silicon photonics. In addition, guidelines based on semi-analytical approaches are proposed to design the waveguide-based device of low thermo-optical effects. We believe the athermal Ta2O5 WBG resonator should be of significant contribution in extending the frequency selection functionality for silicon photonics.

2. Device design and fabrication

Schematic of the WBG is shown in Fig. 1(a). The WBG fabrication follows the routes described below. First a 400 nm-thick Ta2O5 thin film was sputtered on 3 μm-thick thermal oxide grown over silicon substrate using home-made radio-frequency magnetron sputter equipped with a 2-inch magnetron gun. In the sputtering process, the RF power level was 100 W and mixture of Ar and O2 gases at a composition of 4:1 was given at 2 mtorr. On the thin film, a 200 μm-long distributed Bragg reflector (DBR) mirror made of surface corrugated gratings was fabricated using e-beam lithography with Inspect F50 thermal field emission scanning electron microscope system. The acceleration voltage and dose of e-beam for photoresist patterning were 30 keV and 20 μC cm−2, respectively. The period of the gratings was designed to be 470 nm with 50% duty cycle and the surface corrugation is 30 nm and 20 nm in depth for the DBR mirror and Fabry-Perot (FP) resonator. It was then dry etched in CHF3 plasma at 80W and 2 mtorr using the Oxford Plasmalab 80 + RIE etcher. After the grating is defined, waveguide core of 700 nm in width is patterned also by e-beam lithography route. Finally, the Ta2O5 core was covered with commercially available organic spin on glass (SOG) or PECVD oxide as cladding. The PECVD oxide claddings were prepared by Oxford Plasmalab 100 PECVD system at 13.56 MHz and 1.2 torr with a substrate temperature of 350 °C and an RF power of 250 W.

 figure: Fig. 1

Fig. 1 (a) plot the schematics of the fabricated WBG device and (b) illustrates the top view of SEM image after dry etching to show the waveguides and Bragg gratings in which the blow-ups are also presented in (d) and (e), respectively. SEM image (c) pictures the trapezoid cross section (850 base angle) of the fabricated waveguide.

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In Fig. 1(b), the top view of scanning electron microscopy (SEM) image covers the WBG region and straight waveguide regions. Details of the fabricated WBG and waveguides are shown in Fig. 1(c) and Fig. 1(d), respectively to reveal the periodic corrugation of the WBG and good quality of the sidewalls of the waveguide. The period of the fabricated WBG is determined to be 473 nm at 45% duty cycle, which slightly deviates from the designed values. Taking an SEM image from the polished end surface of the fabricated sample, the core region of the waveguide has a trapezoidal cross section with a base angle of 85°.

To get the knowledge of the optical property of the fabricated WBG device, we calculate the transverse electric (TE) polarized mode and their corresponding effective index by solving eigenvalue equation for the guided modes without gratings. At the wavelength of 1533.6 nm, which matches the WBG resonance condition to be revealed later, the intensity profile of fundamental mode of the trapezoidal waveguide in TE polarization is shown in Fig. 2(a). The waveguide core shown in Fig. 2(a) is 700 nm in base width and 400 nm in thickness and cladding is PECVD oxide. Taking into the material dispersion characterized by Wu et al. [13], the effective indices of the fundamental modes as a function of wavelength are plotted in Fig. 2(b) for waveguides of core thickness of 400 nm and 370 nm, respectively with two different cladding materials, i.e. PECVD SiO2 and SOG accordingly. It is clear that smaller core thickness results in smaller effective index because of evanescent wave penetrate deeper in the cladding region from the interface. Moreover, with SOG cladding, the change in waveguide thickness results in greater effective index contrast than that with PECVD SiO2 cladding. It is also interesting to see that the group indices of these guided modes are very large when compared to their effective indices. This infers strong dispersion in waveguides of Tantalum-Pentoxide core.

 figure: Fig. 2

Fig. 2 (a) Intensity profile of transverse electrical (TE) polarized fundamental guided mode at a wavelength of 1533.5 nm in the trapezoidal waveguide with 850 base angle. The calculated (b) effective index and (c) group index of the TE polarized fundamental guided mode as a function of wavelength.

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The WBG with surface corrugation can then be modeled by effective index method and coupled mode equation [16], in which the effective index of thicker and thinner straight waveguide represent the thicker and thinner portion of the WBG, respective. The stacking of high effective index in thicker portion and of low effective index in thinner portion of WBG forms almost periodic variation in the refractive index for electromagnetic waves guided in WBG as shown in Fig. 3(a). For small index change, coupled mode theory can be applied and yields analytical expressions to the transmitted and reflected fields of the WBG working as DBR mirror [16].

t=mmcosh[mLd]+psinh[mLd]
r=κsinh[mLd]mcosh[mLd]+psinh[mLd]
in which without loss of generality,m=p2+κ2,p=iδ+γ and δ=12(β1+β2)πΛ is the detune and γ is the loss in the DBR region. Λ is the grating period and β1=2πλn1 and β2=2πλn2 are the propagation constant of guided waves in the high and low index region, respectively and n1, n2 are their effective index accordingly. The coupling coefficient of the forward and backward waves is κ=2(β1β2)Λ(β1β2) standing for the amount of field reflected per unit length as waves incidents the interface along normal direction twice in a one grating period. The resonance wavelength, λDBF of the DBR mirror is determined by applying Bragg condition β1(λ,T)+β2(λ,T)=2π/Λ where T refers to the waveguide temperature and λ is the wavelength. When temperature drifts, the resonance wavelength can easily be obtained by perturbation approach. To the first order, it writes,
dλdT=β1T+β2T+α2πΛβ1λ+β2λ
in which α is the thermal expansion coefficient of the waveguide.

 figure: Fig. 3

Fig. 3 (a) Illustration of the WBG structure with periodic effective indices following periodic propagation constant β1and β2, respectively. (b) plots the effective index of the guided waves 400 nm thick core cladded with PECVD SiO2 (solid line in blue); 370 nm thick core cladded with PECVD SiO2 (dashed line in blue); 400 nm thick core cladded with SOG (solid line red); 370 nm thick core cladded with SOG (dashed line in red). Thermo-optical coefficients of different core thickness (400 nm or 370 nm) and of different cladding materials are calculated and labeled in (b).

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In Fig. 3(b), effective indices of guided wave are shown for the temperature ranging from 40 to 100 degree Celsius for waveguide with PECVD SiO2 cladding (in blue) and SOG cladding (in red). n1 is the effective index of waveguide device of 400 nm in core thickness and corresponds to the propagation constant β1 marked in Fig. 3(a). n2 is the effective index of waveguide device of 370 nm in core thickness and corresponds to the propagation constant β2 marked in Fig. 3(a). The fitted slope of each line in Fig. 3(b) gives the thermo-optical coefficients of the guided wave in each structure and can be used together with the dispersion relation given in Fig. 2(b) to calculate according to Eq. (3) the temperature sensitivity. Table 1 lists the temperature dependence and dispersion relations near the designed resonance wavelength at 1533.5 nm and 1526 nm for the two devices. For WBG with PECVD SiO2 cladding, the resonance wavelength shifts at a rate of 6.134 pm/°C. But the WBG with SOG cladding experiences blue shift of −7.221 pm/°C. It is seen from Table 1 that the two WBG have commensurate dispersion but SOG cladded WBG suffers from large negative thermo-optical effect due to the intrinsic thermo-optical coefficient of SOG is in magnitude much larger than that of Ta2O5. In this case the size-dependent athermal design [10–12] will conflict with desired single mode operation for the WBG. Moreover, the organic contents in SOG might also bring issues related to long-term reliability and not being CMOS compatible in fabrication processes [17].

Tables Icon

Table 1. Temperature Dependence of the Resonance Wavelength Shift

The calculation listed in Table 1 utilizes the structure parameter described in Fig. 1(a). The resonant wavelengths are λ = 1533nm and λ = 1526nm when Ta2O5 core is cladded by PECVD SiO2 and SOG, respectively. Refractive index of Ta2O5 follows the dispersion relation in REF [13] and its thermo-optical coefficient is 2.3×10−6 K−1 [14]; the refractive index of PECVD SiO2.follows the reported dispersion-equation [18]; the refractive indices and thermo-optical coefficient of SOG are 1.4 and −60×10−6 K−1, respectively [19]; the thermal expansion coefficient of Ta2O5,α=3.6×106 K−1 is adopted [20].

Next we examine a FP resonator made of a 200-μm straight waveguide sandwiched by PECVD-SiO2 cladded WBG as DBR mirrors. Each DBR mirror has a physical length of 200 μm as shown in Fig. 4(a), which is capable of reflecting 97.18% of incident power at resonance wavelength and the full width half maximum (FWHM) spans over 4.54 nm according to the calculation using Eq. (1) and Eq. (2). The transmission and reflection spectrum of the WBG are plotted in Fig. 4(b) using solid line and dashed line in red, respectively. The transmission of FP resonator with DBR mirrors can be described by a standard mathematical expression [21],

Γ=(1R)2(1R)2+4Rsin2[β1L0+(β1+β2)Leff]
in which R=|r|2 and LWBG is the length of the WBGs working as DBR mirrors. An effective length
Leff=12κtanh(κLWBG)
is introduced in additional to the FP resonator length L0 because of the rapid phase change near the band edge of the DBR response. It results in the reduction of free spectral range than that of FP resonator with metallic mirrors. The transmission spectrum of the FP resonator is depicted in Fig. 4(b) with solid line in black. In wavelength covered by the high reflectance band of the DBR (WBG) mirror, there are two high transmission peaks separating by 1.86 nm which can also be obtained by the approximate expression,
ΔλFSR=λ22ng(L0+2Leff)
in which ng is the group index calculated in the resonator region. Notably the exact resonance wavelength may vary due to a slight variation to the cavity length and resonance peak separation become smaller near the DBR band edge due to the rapid phase change mentioned above. The shift in the resonance wavelength caused by temperature variation can be estimated by keeping the round trip phase in the FP resonator constant,
(β1 L0+(β1+β2 )Leff)TΔT+ (β1L0+(β1+β2)Leff)λΔλ=0 
It gives that

 figure: Fig. 4

Fig. 4 (a) is a schematic of the FP resonator with two WBGs as DBR mirrors. The surface corrugation of the grating is 20 nm. The reflection spectrum of a single WBG is calculated by taking the square of Eq. (2) and is plotted in (b) using dashed line in red. The maximum reflectance is 90.6% and its FWHM bandwidth is 4.54 nm around 1533.5 nm. (b) also shows the spectral response of the FP resonator with a central resonance wavelength at 1534.3 nm. Three resonance wavelengths within the DBR bandwidth are shown and free spectral range of the FP resonator is around 1.86 nm.

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dλdT=L0β1T+Leff(β1T+β2T)+(β1+β2)LeffT+L0αβ1L0(β1λ)+Leff(β1λ+β2λ)+(β1+β2)Leffλ
in which

Leffλ=LeffκκλLeffT=LeffκκT+αLWBGsech2(κLWBG)2Leffκ=tanh(κLWBG)2κ2+LWBGsech2(κLWBG)2κκλ=Λ2[dβ1dλdβ2dλβ1+ β2β1β2(β1+ β2)2(dβ1dλ+dβ2dλ)]κT =Λ2[dβ1dTdβ2dTβ1+β2β1β2(β1+β2)2(dβ1dT+dβ2dT)+α(β1β2β1+β2)]Given the parameters described in Fig. 4 and Table 1, a shift of 4.952 pm/°C in resonant wavelength is calculated.

3. Experimental measurement and discussion

To characterize the fabricated WBG and FP resonator devices, experimental setup for the test bed is implemented following the schematics in Fig. 5. Our light source is a tunable laser modeled Agilent HP 8164A Mainframe equipped with 81642A and 81689A laser modules. It spans radiation wavelength from 1510 nm to 1640 nm from amplified spontaneous emission. A set of polarization controller is installed before a tapered fiber that couples tunable laser into the WBG and FP resonator devices. The device samples are placed on a temperature-controlled plate driven by thermoelectric cooler. Varying temperature from 20 to 80 degrees Celsius, output laser transmitting through the device is received by a tapered fiber that connects to either an Optical Spectral Analyzer (OSA) or a power meter to take the transmission spectrum and to evaluate the insertion loss accordingly.

 figure: Fig. 5

Fig. 5 Schematics of the device test and measurement system. Coherent radiation from a polarization controlled tunable laser is coupled to device sample placed on a temperature-controlled plate. The transmission spectrum is measured by an Optical Spectral Analyzer (OSA) modeled ANDO 6317 and insertion loss is evaluated by power measurement with a power meter.

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The insertion loss of the 700-μm WBG device that includes 200μm WBG section sandwiched by two 200μm-long straight waveguides is 10.6 dB including the coupling loss and propagation loss. Employing the same fabrication route for the waveguides [13], low propagation loss of 1.5 dB/cm in our waveguide is expected and the contribution of propagation loss is as low as 0.105 dB corresponding to power loss of 3.4%. Yet without the inverse-taper design, large coupling loss should be responsible for the insertion loss of the fabricated WBG device. Notably the loss in the surface corrugated grating appears to be small as it will be discussed later. The measured transmission spectrum is plotted in Fig. 6(a) together with the theoretical calculation using Eq. (1). The calculation is in good agreement with the measurement in the stop band near the DBR resonance. In the experiments, however, oscillation fringes are recorded particularly at the high transmission region. By taking the Fourier transform of the measured spectrum as shown in Fig. 6(b), one clearly sees a peak at 1.17 nm−1, which is confirmed to result from a low finesse FP resonant fringes of a cavity length of 700 μm that matches the length of our device length. Assuming the FWHM bandwidth of the DBR structure remain unchanged, which is confirmed by experiments, we plot in Fig. 7(a) the variations in resonance frequency as a function of device temperature and a linear function that best fit experimental data. The slopedndλ=7.4 pm/°C refers to the temperature stability of the WBG device with PECVD SiO2 cladding. It is slightly greater than theoretical value of 6.134 pm/°C calculated by a semi-analytical approach discussed in Sec. II. When this value is compared to standard WBG device with silicon core, our device has a better temperature stability that is greater an order of magnitude improved [22]. For the WBG device with SOG claddings, dndλ=19.4 pm/°C can be retrieved from the experiments shown in Fig. 7(b). It is also comparable to the theoretical calculated value of −7.221 pm/°C when the athermal design is not adopted. Athermal design requires a larger core size of the waveguide and may conflict to single mode operation for the WBG with SOG cladding. Moreover, a discrepancy of 10 nm in the resonating wavelength is observed in Fig. 6(a) and Fig. 7(a) because the measurements are taken by two distinct fabricated WBG devices with PECVD SiO2 cladding. We believe such a discrepancy lies in the possible fabrication error of the e-beam lithography. The change in DBR resonance approximates to the expression,

δλ=2πΛλ(β1+β2)(δΛΛ+δβ12β1+δβ22β2)
For example, at the designed resonance wavelength of 1533.5 nm, even 0.6% errors corresponding to 2.76 nm in fabricating gratings using e-beam lithography causes a 10 nm shift in resonance wavelength.

 figure: Fig. 6

Fig. 6 (a) plots the transmission spectrum as a function of wavelength measured by the setup illustrated in Fig. 5 in solid line along with theoretical calculation in dashed line. The Fourier transform of measured transmittance is plotted in (b).

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 figure: Fig. 7

Fig. 7 The shift in resonance wavelength of WBG device with (a) PECVD SiO2 cladding and (b) SOG cladding.

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In Fig. 8(b), the resonance wavelength of the FP resonator is recorded as a function of device temperature controlled by thermo-electric cooler. The resonance wavelength experiences a red shift as the temperature increases shown in the inset of Fig. 8(b) and temperature stability dndλ=8 pm/oC can be fitted which is slightly higher than dndλ=5.12 pm/oC obtained by semi-analytical calculation adopting the grating corrugation of 15.5 nm obtained from experiment. Nevertheless, the fabricated FP resonator of low temperature depending drift in resonance wavelength already match the industrial requirement using fabrication process that is completely CMOS compatible [11,17].

 figure: Fig. 8

Fig. 8 (a) shows the measured spectrum of the FP resonator and the shift in resonance wavelength of the FP resonator with PECVD SiO2 cladding is plotted in (b). The inset in (b) illustrates the red shift in resonance peak as temperature increases.

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Without any athermal design using material compensation or complicated structure, WBG device using Ta2O5 as core material enjoys not only the smaller thermo-optic coefficient but also stronger chromatic dispersion in the waveguide. As can be perceived from Eq. (3) and Eq. (8), strong chromatic dispersion makes the denominator large and consequently the temperature stability of the device is enhanced. It infers that the athermal design of a spectral device might not necessarily resort to low thermo-optic effect solely. Either by strong materials dispersion or design of waveguide to high dispersion configuration may improve the temperature stability of frequency device. In contrast, frequency devices designed near the zero dispersion point could suffer from severe frequency shift as the device temperature varies subject to absorption or environmental effects. Regarding to large chromatic dispersion, issues like pulse broadening and bandwidth limitation might degrade the performance and limit the propagation range of some optical communication system. Such application is apparently not suitable to apply our design scenario for temperature stability. However, for frequency devices such as AWG for WDM, add-drop filters, add-drop multiplexors, FP resonators and the like, large chromatic dispersion is essential for them to function properly. Enhancing their temperature stability by adopting large chromatic dispersion is straightforward and significantly effective. In particular, the desired functionality and performance of these frequency devices are not sacrificed.

4. Conclusion

To conclude, we reported the fabrication and characterization of frequency devices including WBG and FP resonator using Ta2O5 as core material to achieve high thermal stability. The reflectivity of WBG of greater than 90% was obtained and the insertion loss of the 700 μm-long WBG was 10.6 dB at 1550 nm. The center wavelength-to-temperature shifts of the WBG with the SiO2 and SOG cladding were 7.4 pm/oC and −16.8 pm/oC, respectively and were both with high thermal stability. The fabricated FP resonator has a quality factor greater than 9,000 and a WBG corrugation of 15.5 nm can be fitted by semi-analytical calculations. The resonance wavelength of the FP resonator experiences red shifts by 8 pm/oC. Such thermal stability in resonant wavelength are attributed to not only low thermo-optical coefficient of Ta2O5 thin film but also its large chromatic dispersion supported by the semi-analytical calculations. The semi-analytical expressions utilized in this work further provide guidelines to design waveguide-based frequency device of low thermo-optical effect without complex athermal configuration.

Funding

Ministry of Science and Technology, Tawaiin (MOST) (107-2112-M-110-004).

Acknowledgments

The authors thank Prof. Chao-Kuei Lee, Prof. Yung-Jr Hung, Prof. Yu-Ju Hung, and Dr. Chung-Lun Wu for their technical supports and valuable suggestions.

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References

  • View by:

  1. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
    [Crossref]
  2. A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
    [Crossref]
  3. Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
    [Crossref] [PubMed]
  4. W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
    [Crossref]
  5. R. M. André, S. C. Warren-Smith, M. Becker, J. Dellith, M. Rothhardt, M. I. Zibaii, H. Latifi, M. B. Marques, H. Bartelt, and O. Frazão, “Simultaneous measurement of temperature and refractive index using focused ion beam milled Fabry-Perot cavities in optical fiber micro-tips,” Opt. Express 24(13), 14053–14065 (2016).
    [Crossref] [PubMed]
  6. A. Zhou, B. Qin, Z. Zhu, Y. Zhang, Z. Liu, J. Yang, and L. Yuan, “Hybrid structured fiber-optic Fabry-Perot interferometer for simultaneous measurement of strain and temperature,” Opt. Lett. 39(18), 5267–5270 (2014).
    [Crossref] [PubMed]
  7. L. Wang, W. Bogaerts, P. Dumon, S. K. Selvaraja, J. Teng, S. Pathak, X. Han, J. Wang, X. Jian, M. Zhao, R. Baets, and G. Morthier, “Athermal arrayed waveguide gratings in silicon-on-insulator by overlaying a polymer cladding on narrowed arrayed waveguides,” Appl. Opt. 51(9), 1251–1256 (2012).
    [Crossref] [PubMed]
  8. K. Tada, Y. Nakano, and A. Ushirokawa, “Temperature compensated coupled cavity diode lasers,” Opt. Quantum Electron. 16(5), 463–469 (1984).
    [Crossref]
  9. Y. Kokubun, N. Funato, and M. Takizawa, “Athermal Waveguides for Temperature-Independent Lightwave Devices,” IEEE Photonics Technol. Lett. 5(11), 1297–1300 (1993).
    [Crossref]
  10. W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal High-Index-Contrast Waveguide Design,” IEEE Photonics Technol. Lett. 20(11), 885–887 (2008).
    [Crossref]
  11. S. Namnabat, K.-J. Kim, A. Jones, R. Himmelhuber, C. T. DeRose, D. C. Trotter, A. L. Starbuck, A. Pomerene, A. L. Lentine, and R. A. Norwood, “Athermal silicon optical add-drop multiplexers based on thermo-optic coefficient tuning of sol-gel material,” Opt. Express 25(18), 21471–21482 (2017).
    [Crossref] [PubMed]
  12. M. M. Milošević, N. G. Emerson, F. Y. Gardes, X. Chen, A. A. D. T. Adikaari, and G. Z. Mashanovich, “Athermal waveguides for optical communication wavelengths,” Opt. Lett. 36(23), 4659–4661 (2011).
    [Crossref] [PubMed]
  13. C.-L. Wu, B.-T. Chen, Y.-Y. Lin, W.-C. Tien, G.-R. Lin, Y.-J. Chiu, Y. J. Hung, A. K. Chu, and C. K. Lee, “Low-loss and high-Q Ta(2)O(5) based micro-ring resonator with inverse taper structure,” Opt. Express 23(20), 26268–26275 (2015).
    [Crossref] [PubMed]
  14. A. K. Chu, H. C. Lin, and W. H. Cheng, “Temperature Dependence of Refractive Index of Ta2O5 Dielectric Films,” J. Electron. Mater. 26(8), 889–892 (1997).
    [Crossref]
  15. J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
    [Crossref]
  16. K. A. Winick, “Effective-index method and coupled-mode theory for almost-periodic waveguide gratings: a comparison,” Appl. Opt. 31(6), 757–764 (1992).
    [Crossref] [PubMed]
  17. D. Melati, P. G. Verly, A. Delâge, P. Cheben, J. H. Schmid, S. Janz, and D.-X. Xu, “Athermal echelle grating filter in silicon-on-insulator using a temperature-synchronized input,” Opt. Express 26(22), 28651–28660 (2018).
    [Crossref] [PubMed]
  18. G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
    [Crossref]
  19. H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
    [Crossref]
  20. C.-L. Tien, C.-C. Lee, K.-P. Chuang, and C.-C. Jaing, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681–1691 (2000).
  21. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006).
    [Crossref] [PubMed]
  22. N. N. Klimov, S. Mittal, M. Berger, and Z. Ahmed, “On-chip silicon waveguide Bragg grating photonic temperature sensor,” Opt. Lett. 40(17), 3934–3936 (2015).
    [Crossref] [PubMed]

2018 (2)

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

D. Melati, P. G. Verly, A. Delâge, P. Cheben, J. H. Schmid, S. Janz, and D.-X. Xu, “Athermal echelle grating filter in silicon-on-insulator using a temperature-synchronized input,” Opt. Express 26(22), 28651–28660 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (1)

2015 (2)

2014 (2)

A. Zhou, B. Qin, Z. Zhu, Y. Zhang, Z. Liu, J. Yang, and L. Yuan, “Hybrid structured fiber-optic Fabry-Perot interferometer for simultaneous measurement of strain and temperature,” Opt. Lett. 39(18), 5267–5270 (2014).
[Crossref] [PubMed]

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

2012 (2)

2011 (1)

2008 (1)

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal High-Index-Contrast Waveguide Design,” IEEE Photonics Technol. Lett. 20(11), 885–887 (2008).
[Crossref]

2006 (1)

2005 (1)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

2004 (1)

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
[Crossref]

2001 (1)

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

2000 (1)

C.-L. Tien, C.-C. Lee, K.-P. Chuang, and C.-C. Jaing, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681–1691 (2000).

1999 (1)

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
[Crossref]

1997 (1)

A. K. Chu, H. C. Lin, and W. H. Cheng, “Temperature Dependence of Refractive Index of Ta2O5 Dielectric Films,” J. Electron. Mater. 26(8), 889–892 (1997).
[Crossref]

1993 (1)

Y. Kokubun, N. Funato, and M. Takizawa, “Athermal Waveguides for Temperature-Independent Lightwave Devices,” IEEE Photonics Technol. Lett. 5(11), 1297–1300 (1993).
[Crossref]

1992 (1)

1984 (1)

K. Tada, Y. Nakano, and A. Ushirokawa, “Temperature compensated coupled cavity diode lasers,” Opt. Quantum Electron. 16(5), 463–469 (1984).
[Crossref]

Adikaari, A. A. D. T.

Ahmed, Z.

André, R. M.

Andrés, M. V.

Baets, R.

Barmenkov, Y. O.

Bartelt, H.

Becker, M.

Berger, M.

Bernini, R.

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
[Crossref]

Bogaerts, W.

Cheben, P.

Chen, B.-T.

Chen, X.

Chen, Z.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Cheng, W. H.

A. K. Chu, H. C. Lin, and W. H. Cheng, “Temperature Dependence of Refractive Index of Ta2O5 Dielectric Films,” J. Electron. Mater. 26(8), 889–892 (1997).
[Crossref]

Chiu, Y.-J.

Chu, A. K.

Chuang, K.-P.

C.-L. Tien, C.-C. Lee, K.-P. Chuang, and C.-C. Jaing, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681–1691 (2000).

Cruz, J. L.

Cusano, A.

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
[Crossref]

Cutolo, A.

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
[Crossref]

Delâge, A.

Dellith, J.

DeRose, C. T.

Dumon, P.

Emerson, N. G.

Feng, Y.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Frazão, O.

Funato, N.

Y. Kokubun, N. Funato, and M. Takizawa, “Athermal Waveguides for Temperature-Independent Lightwave Devices,” IEEE Photonics Technol. Lett. 5(11), 1297–1300 (1993).
[Crossref]

Gao, S.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Gardes, F. Y.

Ghosh, G.

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
[Crossref]

Giordano, M.

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
[Crossref]

Han, X.

Heinert, D.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
[Crossref]

Himmelhuber, R.

Hofmann, G.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
[Crossref]

Homma, T.

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

Huang, B.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Huang, X.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Huang, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Hung, Y. J.

Iadicicco, A.

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, “Thinned fiber Bragg gratings as high sensitivity refractive index sensor,” IEEE Photonics Technol. Lett. 16(4), 1149–1151 (2004).
[Crossref]

Inohara, K.

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

Jaing, C.-C.

C.-L. Tien, C.-C. Lee, K.-P. Chuang, and C.-C. Jaing, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681–1691 (2000).

Janz, S.

Jian, X.

Jones, A.

Kim, K.-J.

Kimerling, L. C.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal High-Index-Contrast Waveguide Design,” IEEE Photonics Technol. Lett. 20(11), 885–887 (2008).
[Crossref]

Klimov, N. N.

Kokubun, Y.

Y. Kokubun, N. Funato, and M. Takizawa, “Athermal Waveguides for Temperature-Independent Lightwave Devices,” IEEE Photonics Technol. Lett. 5(11), 1297–1300 (1993).
[Crossref]

Komma, J.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
[Crossref]

Kondo, H.

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

Latifi, H.

Lee, C. K.

Lee, C.-C.

C.-L. Tien, C.-C. Lee, K.-P. Chuang, and C.-C. Jaing, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681–1691 (2000).

Lee, R. K.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Leinders, S. M.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Lentine, A. L.

Li, Z.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Liang, W.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Lin, G.-R.

Lin, H. C.

A. K. Chu, H. C. Lin, and W. H. Cheng, “Temperature Dependence of Refractive Index of Ta2O5 Dielectric Films,” J. Electron. Mater. 26(8), 889–892 (1997).
[Crossref]

Lin, Y.-Y.

Liu, W.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Liu, Z.

Marques, M. B.

Mashanovich, G. Z.

Melati, D.

Michel, J.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal High-Index-Contrast Waveguide Design,” IEEE Photonics Technol. Lett. 20(11), 885–887 (2008).
[Crossref]

Miloševic, M. M.

Mittal, S.

Morthier, G.

Muilwijk, P. M.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Nakahata, J.

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

Nakano, Y.

K. Tada, Y. Nakano, and A. Ushirokawa, “Temperature compensated coupled cavity diode lasers,” Opt. Quantum Electron. 16(5), 463–469 (1984).
[Crossref]

Namnabat, S.

Nawrodt, R.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
[Crossref]

Norwood, R. A.

Pathak, S.

Pomerene, A.

Pozo, J.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Qin, B.

Rothhardt, M.

Schmid, J. H.

Schwarz, C.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
[Crossref]

Selvaraja, S. K.

Starbuck, A. L.

Tada, K.

K. Tada, Y. Nakano, and A. Ushirokawa, “Temperature compensated coupled cavity diode lasers,” Opt. Quantum Electron. 16(5), 463–469 (1984).
[Crossref]

Takahashi, H.

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

Takizawa, M.

Y. Kokubun, N. Funato, and M. Takizawa, “Athermal Waveguides for Temperature-Independent Lightwave Devices,” IEEE Photonics Technol. Lett. 5(11), 1297–1300 (1993).
[Crossref]

Taniguchi, Y.

H. Kondo, K. Inohara, Y. Taniguchi, J. Nakahata, T. Homma, and H. Takahashi, “Thermo-optic switch using fluorinated silicon oxide and organic spin-on-glass films,” Opt. Rev. 8(5), 323–325 (2001).
[Crossref]

Teng, J.

Tien, C.-L.

C.-L. Tien, C.-C. Lee, K.-P. Chuang, and C.-C. Jaing, “Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry,” J. Mod. Opt. 47, 1681–1691 (2000).

Tien, W.-C.

Torres-Peiró, S.

Trotter, D. C.

Urbach, H. P.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Ushirokawa, A.

K. Tada, Y. Nakano, and A. Ushirokawa, “Temperature compensated coupled cavity diode lasers,” Opt. Quantum Electron. 16(5), 463–469 (1984).
[Crossref]

van den Dool, T. C.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Verly, P. G.

Verweij, M. D.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Wan, L.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Wang, J.

Wang, L.

Warren-Smith, S. C.

Westerveld, W. J.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Winick, K. A.

Wu, C.-L.

Xiong, S.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Xu, D.-X.

Xu, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Yang, J.

Yariv, A.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Ye, W. N.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal High-Index-Contrast Waveguide Design,” IEEE Photonics Technol. Lett. 20(11), 885–887 (2008).
[Crossref]

Yousefi, M.

W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, M. Yousefi, and H. P. Urbach, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Topics Quantum Electron. 20(4), 101–110 (2014).
[Crossref]

Yuan, L.

Zalvidea, D.

Zhang, H.

Z. Chen, S. Xiong, S. Gao, H. Zhang, L. Wan, X. Huang, B. Huang, Y. Feng, W. Liu, and Z. Li, “High-Temperature Sensor Based on Fabry-Perot Interferometer in Microfiber Tip,” Sensors (Basel) 18(1), 202 (2018).
[Crossref] [PubMed]

Zhang, Y.

Zhao, M.

Zhou, A.

Zhu, Z.

Zibaii, M. I.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101(4), 041905 (2012).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (1)

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Figures (8)

Fig. 1
Fig. 1 (a) plot the schematics of the fabricated WBG device and (b) illustrates the top view of SEM image after dry etching to show the waveguides and Bragg gratings in which the blow-ups are also presented in (d) and (e), respectively. SEM image (c) pictures the trapezoid cross section (850 base angle) of the fabricated waveguide.
Fig. 2
Fig. 2 (a) Intensity profile of transverse electrical (TE) polarized fundamental guided mode at a wavelength of 1533.5 nm in the trapezoidal waveguide with 850 base angle. The calculated (b) effective index and (c) group index of the TE polarized fundamental guided mode as a function of wavelength.
Fig. 3
Fig. 3 (a) Illustration of the WBG structure with periodic effective indices following periodic propagation constant β 1 and β 2 , respectively. (b) plots the effective index of the guided waves 400 nm thick core cladded with PECVD SiO2 (solid line in blue); 370 nm thick core cladded with PECVD SiO2 (dashed line in blue); 400 nm thick core cladded with SOG (solid line red); 370 nm thick core cladded with SOG (dashed line in red). Thermo-optical coefficients of different core thickness (400 nm or 370 nm) and of different cladding materials are calculated and labeled in (b).
Fig. 4
Fig. 4 (a) is a schematic of the FP resonator with two WBGs as DBR mirrors. The surface corrugation of the grating is 20 nm. The reflection spectrum of a single WBG is calculated by taking the square of Eq. (2) and is plotted in (b) using dashed line in red. The maximum reflectance is 90.6% and its FWHM bandwidth is 4.54 nm around 1533.5 nm. (b) also shows the spectral response of the FP resonator with a central resonance wavelength at 1534.3 nm. Three resonance wavelengths within the DBR bandwidth are shown and free spectral range of the FP resonator is around 1.86 nm.
Fig. 5
Fig. 5 Schematics of the device test and measurement system. Coherent radiation from a polarization controlled tunable laser is coupled to device sample placed on a temperature-controlled plate. The transmission spectrum is measured by an Optical Spectral Analyzer (OSA) modeled ANDO 6317 and insertion loss is evaluated by power measurement with a power meter.
Fig. 6
Fig. 6 (a) plots the transmission spectrum as a function of wavelength measured by the setup illustrated in Fig. 5 in solid line along with theoretical calculation in dashed line. The Fourier transform of measured transmittance is plotted in (b).
Fig. 7
Fig. 7 The shift in resonance wavelength of WBG device with (a) PECVD SiO2 cladding and (b) SOG cladding.
Fig. 8
Fig. 8 (a) shows the measured spectrum of the FP resonator and the shift in resonance wavelength of the FP resonator with PECVD SiO2 cladding is plotted in (b). The inset in (b) illustrates the red shift in resonance peak as temperature increases.

Tables (1)

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Table 1 Temperature Dependence of the Resonance Wavelength Shift

Equations (9)

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t= m mcosh[m L d ]+psinh[m L d ]
r= κsinh[m L d ] mcosh[m L d ]+psinh[m L d ]
dλ dT = β 1 T + β 2 T +α 2π Λ β 1 λ + β 2 λ
Γ= (1R) 2 (1R) 2 +4R sin 2 [ β 1 L 0 +( β 1 + β 2 ) L eff ]
L eff = 1 2κ tanh( κ L WBG )
Δ λ FSR = λ 2 2 n g ( L 0 +2 L eff )
( β 1   L 0 +( β 1 + β 2   ) L eff ) T ΔT+  ( β 1 L 0 +( β 1 + β 2 ) L eff ) λ Δλ=0 
dλ dT = L 0 β 1 T + L eff ( β 1 T + β 2 T )+( β 1 + β 2 ) L eff T + L 0 α β 1 L 0 ( β 1 λ )+ L eff ( β 1 λ + β 2 λ )+( β 1 + β 2 ) L eff λ
δλ= 2πΛ λ( β 1 + β 2 ) ( δΛ Λ + δ β 1 2 β 1 + δ β 2 2 β 2 )

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