1. Introduction

Resonant optical gyroscopes (ROGs) [1,2] based on Sagnac effect [3] are commonly used for the angular velocity measurement within inertial space, showing high precision, large dynamic range, and high reliability advantages for extensive applications (such as inertial navigation, aircraft attitude control, robot control, and smart vehicles). Low cost, size, weight, and power (CSWaP) requirements for ROGs promote upgrade of resonant integrated optical gyroscopes (RIOGs) that can integrate multiple components at the micro to nano scale as high-performance and monolithic miniature ROGs. Generally, wafer-level-integration is the primary concern. A typical RIOG system is composed of passive components (resonator, coupler, and beam splitter) and active components (modulator, laser, and detector). Thereinto, modulator and resonator are the core components. A modulator loads the modulation signal and tunes the phase of the signal that transmits in-out a resonator. The resonator converts the rotational angular velocity to the frequency difference in either clockwise (CW) or counterclockwise (CCW) directions. For decades, the quality factor of resonators has been improved by several orders of magnitude [4–8] by employing materials which can reduce the propagation losses of the optical waveguides and enhance of the accuracy of ROGs, such as polymer [4,5,9,10], silica [6,11], and silicon nitride [7,8,12,13]. Especially, silica and silicon nitride with ultralow loss are the excellent medium for passive device integration. Furthermore, ROGs with smaller footprint and higher stability were demonstrated by partial integration of passive components including coupler and resonator [4,14–20]. The limitation of ROG thereafter relies on the extraction of high-precision gyroscope signals. The necessity emerges in the idea of integration of modulators with resonator because of the problematic direct detection of gyroscope signals. For example, the frequency difference induced by an angular velocity of 1 $^{\circ }$/h is about 0.043 Hz for a resonator of 2 cm in diameter, while such frequency difference has to be distinguished from a laser carrier wave with 10 ${^{14}}$ Hz of magnitude in frequency. The incidental noises in the optical circuits also deteriorate the detection signal to noise ratio. One solution of this problem is to extract high-precision angular velocity signals using phase modulation spectroscopy technique [19,20] combined with weak signal detection technology in the manner of integration of both phase modulator and resonator.

Lithium niobate (LiNbO${_3}$) [21–23], indium phosphide (InP) [24], and organic polymer [4,5,25–32] are excellent and versatile materials for integrated high-performance electro-optic modulators (EOMs), regarded as the most promising candidates for the photonics integrated circuits including gyroscopes. Unfortunately, the integrated optical gyroscopes co-integrating modulator and resonator were rarely reported. In the cases of modulator and resonator based on LiNbO${_3}$ and InP, it is likely due to the high cost of material preparation and the high requirement of fabrication processes. More specific limitations are located in the material contamination for LiNbO${_3}$ devices [21], and multi-step complicated processes and relatively high loss for InP [16] devices, leading to consequent high cost. Previous study on modulator made of silicon nitride [33] indicated the prospect for the integration of modulator and resonator. Alternatively, polymer with facile and low-cost process can provide a more cost-effective and flexible way to achieve the RIOG. A simple poling process in fabrication can generate nonlinear effects for EOM regardless of the crystal axis of the polymer. The stronger nonlinearity of the electro-optic (EO) polymer than LiNbO${_3}$ material can contribute to lower half-wave voltage V${_{\pi }}$ for EOM. Such simple manufacture for EOM is compatible with other linear optical components. The building blocks in RIOG including EOMs and resonator can be therefore integrated by polymer leveraging basic semiconductor processes (such as spin coating and ultraviolet (UV) photolithography) which are readily accessible, low cost, and short preparation period, making the polymer platform suitable for large-scale manufacture. What’s more, polymer waveguides with the ultralow loss of 4 dB/m have been reported previously [10], showing the potential for the realization of the high-performance RIOG by polymers.

In this paper, we proposed an all-polymer RIOG chip, which monolithically integrated passive components (resonator, beam splitter, and couplers) and active building blocks (EOMs). The side-chain EO polymer was synthesized and used as the core materials of EOMs after poling. Low loss fluorinated polymer was employed in passive parts to obtain high Q factor. The RIOG chip prototype was fabricated by optical integration techniques and characterized by rotation measurement.

2. Structure and design

Figure 1(a) depicts the proposed RIOG chip with integrated passive building blocks (resonator, beam splitter, and couplers) and active EOMs. The incident laser was coupled into the RIOG chip and then splitted into two optical beams through the beam splitter. These two beams were loaded modulation signal by the EOMs in the individual path. Subsequently, by means of the couplers the beams entered into the ring resonator and propagated along the CW and CCW directions. After multi-beam interference, the resonant signals were generated in the resonator and then outputted through the couplers.

 

Fig. 1. Integrated optical gyroscope. a) Schematic of a typical ROG system including laser and detectors, an all-polymer monolithic RIOG chip integrated resonator, EOMs, beam splitter, and couplers; b) The cross-section sketch of EOM; c) The mode distribution of LFR waveguide; d) The mode distribution of DR19-PUI waveguide; e) The fabricated RIOG chip on a 4-inch wafer.

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The proposed RIOG was fabricated in an organic polymer material system on a 4-inch wafer as shown in Fig. 1(e). The passive components (including beam splitter, couplers and resonator) and EOMs were prepared by the low-loss fluorinated polymer [9] waveguide and side chain bonded polyurethane imide DR19-PUI [29] waveguide, respectively (parameters were shown in Table 1). For the passive parts, the core and cladding materials were LFR 392 and LFR 372 with refractive index of 1.392 and 1.372 at the wavelength of 1550 nm, respectively. EOMs were made of DR19-PUI (Fig. 2), LFR 372, and aluminum materials which were used for the fabrication of cores, claddings, and electrodes, respectively. The refractive indexes of DR19-PUI film after poling were measured to be 1.6104 (transverse electric, TE) and 1.6059 (transverse magnetic, TM) at the wavelength of 1550 nm. Figure 1(b) illustrated the cross-sectional layout of EOM. The brown square shown in the center of Fig. 1(b) presents the core layer of DR19-PUI waveguide with a size of $4\;{\mu }\textrm {m}{\times }4\;{\mu }\textrm {m}$ which is the same with that of the LFR waveguide. By using finite element method, the effective mode refraction indexes of LFR and DR19-PUI waveguides were evaluated as 1.3810 and 1.5935. Due to a larger diversity of refractivity between the core and cladding in DR19-PUI waveguide, the mode in this waveguide (Fig. 1(d)) showed stronger mode confinement and smaller mode size than those of LFR waveguide (Fig. 1(c)). Therefore, when the mode coupling occurred between the LFR waveguide in beam splitter and the DR19-PUI waveguide in EOMs, the coupling loss originating from mode mismatch was calculated as 1.16 dB by mode overlap integral.

 

Fig. 2. Optical performance measurement. a) Molecule structure of EO polymer DR19-PUI; b) The propagation loss of the DR19-PUI optical waveguide. Inset: the output optical beam of the DR19-PUI-based EOMs; c) EO response of the EOM at the sawtooth wave. The triangular wave produced by the signal generator is loaded on MZI through the electrodes by probes; d) Response of the modulator at a square wave driving signal of 5 MHz; e) Response of the modulator at a sine wave driving signal of 30 MHz.

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Table 1. Parameters for LFR and DR19-PUI waveguides

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3. Fabrication and measurement

Organic EO polymer used for the nonlinear material of phase modulators in RIOG was synthesized by using the esterification reaction according to Reference 28 [29]. As shown in Fig. 2(a), chromophore DR19 was bonded to the main chain of PUI in the form of side chain by esterification reaction. A suitable external poling electric field of 5.5 KV was applied to DR19-PUI film to align the intrinsic dipole moment of DR19 along the direction of electric field. After poling, DR19-PUI exhibited the second-order nonlinear optical effect macroscopically. The corresponding EO coefficient of DR19-PUI film was measured as 56.31 pm/V by the simple reflection technique, which is significantly higher than that of LiNbO${_3}$ (up to 33 pm/V) [22]. Hence, the DR19-PUI is possible to serve as EO material for EO modulation.

The EOM is the key component for phase modulation spectroscopy in the RIOG. According to the scheme in Fig. 1, the EOMs were prepared by DR19-PUI waveguides with a propagation loss measured as 2.69 dB/cm via cut-back method (Fig. 2(b)). The output light spots from the EOM in the inset of Fig. 2(b) showed well mode transmission quality. Because the output parameter of an EOM was the phase of light, a Mach-Zehnder interferometer architecture with the assistance of polarization maintaining fiber couplers was used to convert the phase signal to intensity signal which could be easily detected by commercially available photodiodes (PDs). One decisive indicator of an EOM is the voltage-induced phase difference, the half-wave voltage V${_{\pi }}$. From the measured EO response shown in Fig. 2(c), V${_{\pi }}$ of the DR19-PUI-based EOM was less than 2 V, which is half of EOM with LiNbO${_3}$. This is consistent with the fact that V${_{\pi }}$ of the EOM is inversely proportional to the EO coefficient whereby the higher EO coefficient of DR19-PUI leads to a lower V${_{\pi }}$, which contributes to high modulation efficiency and low power consumption.

The modulation frequency of an EOM should be taken into account of RIOG because in the measurement of the gyroscope signal, the optimal phase modulated signal loaded by EOM depended on the performance of the resonator specifically involved in the full width at half maximum (FWHM) [20]. A RIOG with better FWHM typically requires a lower modulation frequency. As shown in Fig. 2(d), the proposed EOM can well-withstand a sine wave signal of 30 MHz with a clear response. The fabricated EOM also exhibited a fast response time as shown in Fig. 2(e). The 10-90% rise time and fall time of the response signal were 14.4 ns and 15.2 ns respectively under a square wave signal with the frequency of 5 MHz. Compared with the previous reports [14], the DR19-PUI based EOMs are sufficient to satisfy the modulation requirements for a gyroscope.

In terms of the passive parts of RIOG chip, the propagation loss of LFR optical waveguide was evaluated approximately 0.118 dB/cm through a cut-back method by monitoring the output powers of LFR waveguides with different lengths. The resonator acts as the core sensing unit of gyroscopes. The bending radius of the resonator is critical because too small bending radius (<0.5 cm) will give rise to the energy leakage of the guided mode and high bending loss. Furthermore, the quality factor of a resonator rises along with increase of the radius. Nevertheless, the large dimension violates the miniaturization of RIOG. Thus, the resonator was designed with a radius of 1 cm in compromise to the performance and size. The coupling ratio of the couplers was optimized through the simulation on the shot-noise-limited sensitivity of the proposed RIOG. Optimized coupling ratio is typically obtained at the critical coupling state to achieve the best sensitivity. Therefore, the coupling ratios of the two couplers were optimized to make the resonator work at the critical coupling state.

The resonance properties of the fabricated RIOG chip under TM and TE polarization states were performed through frequency swept laser signal which was tuned by the sawtooth wave signal, as illustrated in Fig. 3. Firstly, the resonance properties are affected by the polarization state of the optical signal. The results indicated that the resonance depth and the FWHM in TM polarization state were better than those in TE polarization state. Such polarization dependence of the resonator was mainly derived from the difference of the refractive indexes of polymer in TM and TE polarization state and the fabrication errors of optical waveguides. Secondly, since the output signals in CW and CCW directions were exported from the two couplers respectively, the deviations between the resonance spectra in CW and CCW directions mainly stemmed from the variance of the coupling ratios between the two couplers caused by the fabrication errors (side wall roughness, surface roughness, dimensional error). Combined with these multi-factors, the RIOG chip exhibited optimal characteristics in CCW direction under TM polarization state with the FWHM of 1.62 pm, the fitness of 17, and the quality factor of approximately 10$^{6}$ (see Fig. 3(e)). In contrast, for TE polarization state, the FWHM is 1.97 pm in CW direction with a fitness of 14 and a quality factor of $7.81{\times }10^{5}$ (see Fig. 3(c)). The free spectral range (FSR) were measured as a constant 27.6 pm in each cycle, which is independent on the resonator direction and polarization state. Moreover, limited by the shot noises of the photodiodes, the sensitivity [4] of the fabricated RIOG system was estimated as 0.0139 $^{\circ }$/s in TM polarization state by assuming that the laser output power was 10 mW, and the measurement bandwidth of the photodiodes were 1 Hz.

 

Fig. 3. Passive RIOG chip measurement. a) The sawtooth signal applied on the tuned laser when measuring the transmission under TE polarization state. b) The resonance spectrum of the RIOG chip in CCW under TE polarization state. Inset: the optical path sketch in CCW direction. c) The resonance spectrum in CCW under TM polarization state. d) The sawtooth signal applied on the tuned laser when measuring the transmission under TM polarization state. e) The resonance spectrum in CW under TE polarization state. Inset: the optical path sketch in CW direction. f) The resonance spectrum in CW under TM polarization state. The measurement cycles of the resonance spectra were divided by the dash lines.

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Leveraging the commonly used integrated optical processes (Fig. 4) including spin coating, UV lithography, and reactive ion etching (RIE), the proposed all-polymer on-chip RIOG system (Fig. 1(e)) integrated the both EO modulators and resonator. An adhesive layer, two 5-$\mu$m-thick LFR 372 films (lower cladding) and a 4-$\mu$m-thick LFR 392 film (the core layer of LFR waveguide) were successively spin coated on a silicon substrate. Electron beam evaporation was performed to deposit an 80 nm of aluminum film as the mask for the core of EOMs. Positive photoresist was spin coated and exposed according to the pattern of lithography mask plate, and then developed to obtain a groove structure. Then the aluminum film was etched by the mixed aqueous solution of phosphoric acid and hydrogen peroxide. RIE was utilized to etch the LFR 392 film under the flow of a mixture of oxygen and sulfur hexafluoride gas. After removing the residual photoresist and aluminum, the groove structure was transferred to the LFR 392 film. A 2-$\mu$m-thick DR19-PUI film was spin coated followed by RIE etching. Thus, we obtained a LFR 392 film with the embedded DR19-PUI. Subsequently, another aluminum film and positive photoresist were prepared as the mask for the core of the RIOG chip. Through similar exposing, developing, etching and removing procedures, the core layers of the LFR waveguide and DR19-PUI waveguide were obtained. Then the upper cladding was completed up by the spin coating of two 5-$\mu$m-thick LFR 372 films. Finally, aluminum electrodes for EOMs were prepared upon the cladding layer, which were aligned to the core layer of DR19-PUI waveguide.

 

Fig. 4. The fabrication process of the RIOG chip. The preparation of a) the film preparation of adhesive layer, the bottom cladding layer LFR 372, and the core layer LFR 392 of the LFR waveguide; b) the Al and photoresist; c) the preparation of groove profile structure of the EOMs (electro optical modulators) on photoresist film; d) the groove structure on the core layer LFR 392; e) the core layer PUI-DR19 of the EOMs; f) the LFR 392 layer containing the core layer PUI-DR19 of EOMs waveguide; g) core layers of the resonator, EOMs, beam splitter, and couplers; h) the upper cladding LFR 372 and the Al electrodes.

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To evaluate the performance of RIOG, the measurement system of gyroscope signal based on phase modulation spectroscopy technique was performed as shown in Fig. 5(a). For realizing the optimal performance, the input light was adjusted to TM polarization state by utilizing polarization controller (PC). In the CW loop of the resonator, the lock-in amplifier (LIA) 1 demodulated the signal detected by PD 1, which was treated by proportional integral (PI) and then acted on the laser. Subsequently, the center frequency of the laser was adjusted according to the resonance properties of the resonator, and real time locked at the resonance frequency of the CW loop. In this case, when the RIOG chip rotated in its normal direction relative to the inertial space, the resonance frequency of the CCW loop deviated from the resonance frequency of CW loop, namely the laser frequency. This frequency difference was reflected by LIA2 as the changes of output of the demodulation signal. Therefore, the amplitude of the demodulation output of LIA2 is proportional to the rotation speed, and the plus or minus sign indicates the direction of rotation. When the RIOG chip was stationary relative to the inertial space the CCW loop output of LIA2 was also zero. Through locking the laser frequency, the noises caused by the fluctuations of the laser frequency can be effectively reduced, improving the measurement accuracy of the RIOG chip. In addition, in the phase modulation spectroscopy technique, the setup of the modulation signals directly affected the detection accuracy and noises. The modulation signals were set according to the resonance properties in CW and CCW directions to suppress the backscattering noises. While the amplitudes of the modulation signals were determined by the V${_{\pi }}$ to inhibit the carrier signals. Therefore, sine wave modulation signals for CCW and CW loops with modulation frequencies of 26.2 MHz and 29.2 MHz and amplitudes of 1.47 V and 1.44 V were loaded on the corresponding EOMs.

 

Fig. 5. RIOG measurement. a, Measurement system architecture for gyroscope signal. b, Gyroscope out at different rotation rates of ${\pm }500 ^{\circ }/\textrm {s}$, ${\pm }400 ^{\circ }/\textrm {s}$, ${\pm }350 ^{\circ }/\textrm {s}$, ${\pm }300 ^{\circ }/\textrm {s}$, ${\pm }250 ^{\circ }/\textrm {s}$, ${\pm }200 ^{\circ }/\textrm {s}$ and ${\pm }100 ^{\circ }/\textrm {s}$. The dashed line marks the stationary state. The yellow arrow pointed out the fluctuation of the gyroscope out in the stationary state. Inset: the gyroscope out at the rotation rates of ${\pm }500 ^{\circ }/\textrm {s}$ and ${\pm }100 ^{\circ }/\textrm {s}$. c, The Allan deviation based on the stationary gyroscope out of the RIOG chip during 4 hours. d, Gyroscope out versus rotation rate, where the gyroscope out is the average value of the output curve of the oscilloscope, and the error bar represents the peak-to-peak value of the curve fluctuation.

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The simulated rotation test (Fig. 5(b)) was carried out under different rotation rates, showing good linearity at the whole range of rotation rate. As shown in the curve, we also observed a zero drift in stationary state at 100 s as illustrated by the arrow, which may be probably derived from the environmental disturbances during the data collection. The environmental change brought the losing lock and relock of the resonance peak implement by PI circuit, resulting in the difference between the relocked zero point and the original one. When the disturbances disappeared, the stationary state returned back to reference zero point again. The PI circuit needs to be optimized further by the algorithm dynamically locking the baseline in the future to improve accuracy and linearity of RIOG. Based on the stationary property in 4 hours with the integration time of 0.01s, the Allan deviation analysis (Fig. 5(c)) demonstrated the bias instability and the angle random walk of RIOG are $2.8 ^{\circ }/\textrm {s}$ and $182.05 ^{\circ }/{\textrm {h}^{1/2}}$, respectively. Furthermore, the rotational test under different angular velocity was performed on a rotating platform. The output voltage of LIA2 (Fig. 5(d)) showed a linear relationship with the rotational rate. The minimum rotation rate that the RIOG chip could extract from the noises was 20 rpm. The experimental results suggest that the all-polymer RIOG chip we proposed, which integrated resonator, EOMs, beam splitter, and couplers, can realize the measurement of angular velocity.

4. Conclusion

In summary, we utilized the polymeric platform to integrate the two key components, resonator and EOM, on a chip, leading to the achievement of an all-polymer monolithic RIOG. Based on this structure, the EOMs with low half-wave voltage V${_{\pi }}$ less than 2 V were successfully prepared by EO polymer DR19-PUI, and the resonator was fabricated by the low loss fluorinated polymer. Finally, the gyroscopic effect of RIOG was demonstrated by the rotation test. Therefore, this study of RIOG clearly demonstrates the ability to integrate discrete optical components, providing a new and more accessible avenue for the future development of practical high-precision fully integrated optical gyroscopes. Moreover, recent publications show the working frequency of the polymer-based laser [34] and detectors [35] are being gradually extended to infrared communication bands, pretending the possibility of the fully integrated ROG based on polymer in the future.