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Abstract
The polarization extinction ratio (PER) of the multifunction integrated optic circuit (MIOC) is significant in maintaining polarization reciprocity in the fiber-optic gyroscope (FOG), and a high PER value is required, particularly in high-precision FOGs. Practically, the value of the PER decreases owing to the recoupling of the TM mode to the output port, thereby degrading the performance of the FOG. To improve the PER, the propagation of the leaking TM mode in the substrate is analyzed first. The variation of the PER with the chip structure is simulated based on the overlap integral algorithm of the optical mode. According to the analysis results, a structure of double absorption trenches at the bottom of the MIOC is proposed to block the TM mode from reflecting to the output port. In comparison with the traditional design, the optimized MIOC exhibits a higher PER that increases by approximately 25 dB and the average value of the PER reaches 75 dB. The MIOC design proposed in this study has good potential for application in high-precision FOGs.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The fiber-optic gyroscope (FOG) is one of the most successful rotation rate sensors, currently being used across various platforms, such as satellites, vehicles, and submarines [1,2]. With the expansion of FOG applications, the demand for high-precision FOGs has increased. However, the phase nonreciprocal error caused by polarization cross coupling increases noise level and degrades the drift stability of the FOG output, which limits the precision of the FOG [3–6]. Thus, the polarization cross-coupling should be tightly controlled. Generally, a multifunction integrated optical circuit (MIOC) is used to control the state of polarization, which can suppress the polarization cross coupling in the FOG, owing to the inherent single-polarization guidance of the annealed proton exchange (APE) waveguide [7–9]. Furthermore, previous studies have shown that the polarization-cross-coupling-induced nonreciprocal error is proportional to the polarization rejection of the MIOC [1,5,10,11]. However, in practice, the rejection of the unguided polarization of the MIOC is not ideal.
In MIOCs, the rejection of the unguided polarization is quantified as the polarization extinction ratio (PER) that is expressed as the ratio of the power of the guided TE mode to the unguided TM mode at the output of the chip. A higher PER indicates a lower power of the unguided polarization light reaching the output port, which is equivalent to a higher polarization rejection. To improve the PER, some studies adjusted the structure of the MIOC. For instance, numerous varying types of deep grooves (as deep as 95% of the thickness of the chip) were constructed at the bottom of the MIOC, and the PER was likely to be improved by more than 70 dB [12–14]. However, the mechanical strength of the chip was reduced significantly such that a cover was required to be mounted at the top of the chip. Compared with the traditional MIOC, the process of constructing such deep grooves, mounting the cover and polishing the covered chip increase the manufacturing complexity and the cost of the MIOC fabrication. Furthermore, a cut-off-bonded method was proposed [15], in which the MIOC was cut off before the Y-junction and recoupled after coating with the absorption material. Although this method can increase the PER by more than 80 dB, the process of cutting chip, coating of the absorption material, and polishing the cutting facet result in a significant increase in the manufacturing complexity and it needs more labor. Furthermore, the alignment errors are likely to be introduced during the recoupling of the chip, yielding an increase in the insertion loss of the MIOC. In addition, some studies modify the pattern of the waveguide, such as constructing the scattering or polarization filter regions at the top of the chip to alter the direction of the surface-propagating light [16,17]. For these existing methods, problems remain in improving the PER during practical manufacturing.
In this study, the reason for the PER degradation is investigated theoretically based on the divergence of the TM mode in the substrate, and a simple and effective method of constructing double absorption trenches at the bottom to improve the PER is proposed. Using the proposed method, the PER of MIOC is significantly improved. Additionally, this approach is easy to implement and it promotes the practical availability of MIOCs in high-precision FOGs.
2. Mechanical analysis of PER degradation
In the MIOC, the polarization rejection of the unguided TM mode is due to light leaking into the substrate [1]. Some portion of the unguided TM mode leaking from the input port is potentially recoupled back into the output fiber, thereby reducing the PER of the MIOC. Generally, the TM mode in the substrate can be recoupled into the output fiber in two ways: one is that light diverges from the input port directly recoupling into the output fiber, whereas the other is that light is reflected at the polished bottom and top faces of the substrate and reaches the output fiber. The theoretical deduction of the recoupling intensity of the aforementioned two cases is as follows:
The first case of recoupling can be analyzed using the interferometric Lloyd’s mirror effect of the top interface of the substrate. When the light is injected into the MIOC, the unguided TM mode pattern becomes half of the second-order antisymmetric mode profile of the fiber because of Lloyd’s mirror interferometer, and then diverges in the substrate, as shown in Fig. 1 [1]. The TM mode diverges at a divergence angle of φd = λ/(πω0no), where λ denotes the working wavelength of the MIOC, no is the refractive index of the TM mode in the substrate, and ω0 is the mode radius of the input fiber. After attainment of the chip length Lc, the mode diameter becomes 2ωL = φd Lc at the output port, and the center of the mode field deviates 200–300 µm in the z-direction owing to the profile of the Y-junction, as shown in Fig. 1. According to the field profile of the second-order antisymmetric mode and the principle of mode overlap, the recoupling coefficient cd can be expressed as follows [18]:
Fig. 1. Optical mode propagating in the APE waveguide and the substrate of the MIOC. The coordinate axis represents the crystal orientation.
Taking the parameters of the MIOC working at 1550 nm utilized in the FOG as an example, the height of the MIOC chip is 1 mm and the refractive index no for the TM mode in the LiNbO3 substrate is 2.21 [1]. Three fiber pigtails with a mode-field diameter of 2ω0∼6.5 µm are coupled to the MIOC chip. Assuming that the unguided TM mode is leaked in a uniform medium, the divergence angle φd is approximately 0.07 rad. Based on Eq. (1), the variation of the PER with the length of the MIOC chip owing to the direct coupling of the divergence light can be represented by the blue line in Fig. 2. The simulation results in Fig. 2 also consider the attenuation of the TE mode, including the propagation and coupling losses of approximately 3 dB, and 3 dB splitting in the junction. Because the energy distribution of the TM mode propagating to the output port becomes divergent, the overlap with the mode in the output fiber is reduced, thereby improving the PER of the MIOC with the increase in the chip length Lc.
In the second case, since both the bottom and top facets of the substrate are polished, the light in the TM mode leaking from the input port into the substrate is reflected on the bottom and top facets and thereafter reaches the output port. When the reflected TM mode overlaps with the propagation light in the output fiber at the output port of the MIOC, recoupling occurs. Similar to the simulation in the first case, the recoupling coefficient cr can be obtained using the imaged input fiber core, and the variation in the PER due to the reflection-induced recoupling is illustrated by the green line in Fig. 2. As the divergence length increases, the energy center of the reflected TM mode approaches the foundational mode in the output fiber and subsequently moves away, whereas the energy distribution continuously diverges, resulting in a maximum overlap at a certain chip length. Therefore, as the chip length increases, the variation in the PER due to reflection-induced recoupling initially decreases and thereafter exhibits a slight increase.
Based on the above analysis, the theoretical value of the PER of the MIOC without additional treatment can be represented by the red dashed line in Fig. 2. Since the PER in the second case is significantly lower than that in the first case as the chip length increases, the change of the theoretical PER is almost the same as the variation in PER due to reflection-induced recoupling, which significantly weakens the single-polarization advantage of the APE waveguide. In Fig. 2, when the chip length is close to 16 mm, the PER of the MIOC can reach approximately 75 dB. However, the length of 16 mm is not always the best choice. It is necessary to combine the properties and fabrication requirements of the MIOC to determine the chip length, such as the half-wave voltage, propagation loss, and manufacturing tolerance. Generally, within the allowable space, a relatively long chip is preferred. Therefore, as an essential factor that degrades the PER, the surface-reflection-induced recoupling of the TM mode should be suppressed at different chip lengths. To suppress the recoupling of the TM mode and improve the PER of the MIOC, the propagation path of the TM mode in the substrate should be predicted first and then blocked.
Combined with the divergence of the TM mode and the boundary conditions of the light propagating in the substrate, the path of the TM mode in the substrate can be predicted. To clarify the propagation path of the TM mode without sacrificing the accuracy of the simulation, the 10% value of the maximum amplitude of the TM mode is regarded as the mode boundary in this study. Since the boundary beam has the largest divergence angle, it reaches the surface of the MIOC first. When the boundary of the TM mode reaches the surface of the MIOC, reflection occurs, and the reflected light is potentially recoupled into the output, thereby reducing the PER of the MIOC. Taking the aforementioned parameters of the MIOC, as shown in Fig. 3, the blue and red lines represent the divergence path of the upper and lower boundaries of the TM mode, respectively. As the divergence of the TM mode, the upper boundary does not reach the surface of the substrate within a 60-mm long chip, and it propagates as a straight line. The lower boundary reaches the bottom facet of the substrate after propagating for approximately 10.55 mm, and it is totally internally reflected back into the substrate. Thereafter, as the TM mode propagates, the lower boundary is totally internally reflected at 21.08 mm, 31.6 mm, 42.14 mm, and 52.67 mm, respectively. According to the aforementioned reflection points, when the length of the chip is longer than 21.08 mm, the light reflected at the center of the chip will recouple into the output, which is known as the primary reflection. When the length of the chip is longer than 42.14 mm, the second reflection point appears.
3. Method to improve the PER of MIOC
To block the reflection-induced recoupling of the TM mode without giving up the mechanical strength and consistency of the MIOC, a block structure of double trenches with absorption coating is proposed. The two trenches are located on both sides of the reflection area on the bottom facet to block the recoupling of the TM mode that leaks from both the input and output ports. The material of the absorption coating is selected by the working wavelength of the MIOC to absorb the light power diffracting to the trench surface, thereby reducing the reflection intensity of the TM mode.
In this study, the MIOC with a length Lc of 23.5 mm and other parameters similar to those in the simulation, are used to perform the detailed design of the block structure. According to the theoretical analysis in Section 2, as shown in Fig. 3, the chip length is between 21.08 and 42.14 mm, implying that there mainly exists the primary reflection of the TM mode in the substrate, correspondingly, the reflection area is approximately at the center of the chip. As shown in Fig. 4, the block structure is located on both sides of the central primary reflection area.
The positions and domains of the two trenches can be determined by the overlap of the mode field before and after divergence. As shown in Fig. 5, the imaged input fiber core is used to discuss the parameters of the trench near the input port. The blue curve represents the field profile of the TM mode leaking from the input port and diverging to the output, the red curve indicates the field profile of the light propagating in fiber, whereas the red shadow is the overlap of the two modes. To suppress the overlap, the geometric shadow formed by the trench should cover the inherent overlap as much as possible. Considering the imperfect uniformity of the substrate and the impact of the fiber bonding glue, the recoupling of the TM mode in the output is likely to differ from the theoretical analysis. To ensure coverage efficiency, the width of the geometric shadow formed by the trench is set to ten times the fiber mode-field diameter, which is about 20ω0 ∼ 65 µm. Furthermore, since the depth of the trench is proportional to the distance from the reflection area, the distance between the trench and the reflection area should be controlled to avoid damaging the mechanical strength of the chip. Based on the geometric relationship in Fig. 5, if the trench is placed near the left of the primary reflection area, its parameters can be designed as ptr1 = 11462 µm, wtr1 = 200∼250 µm, and dtr1 = 100∼200 µm, where ptr1 represents the distance between the center of the trench and the substrate edge of the input port.
The trench near the output port is close to the right boundary of the primary reflection area, as shown in Fig. 5. Similarly, the parameters of the trench near the output port can also be determined by the imaged output fiber core. The parameters can be designed as ptr2 = 11544 µm, wtr2 = 200∼250 µm, and dtr2 = 100∼200 µm, where ptr2 represents the distance between the center of the trench and the substrate edge of the output port.
For the absorption coating, the material of the coating needs to have strong absorption near the working wavelength of the MIOC, stable physical and chemical properties, and strong adhesion with LiNbO3. For the absorption material of the MIOC working at 1550 nm, graphite is the primary choice, which provides excellent light absorption performance, high chemical stability, and is easy to obtain. Thus, the absorption coating of the MIOC working at 1550 nm is obtained by mixing graphite powder with an adhesive whose refractive index matches that of LiNbO3. To mix evenly, the mixture of the two is stirred at high temperature for half an hour. When coating the absorption material, an optical fiber is used to fill the trench completely, especially the corners of the trench, to prevent the undesirable refraction caused by the filling vacancy. Then the middle of the bottom face is coated, and the coating range needs to completely cover the double trenches to ensure sufficient absorption of the light reflected to the opposite port. After the coating is finished, the chip should be placed in a room environment for several hours to ensure the absorption coating fully cured.
In the proposed method, the block structure is placed on the bottom of the MIOC chip, whose depth is approximately one-fifth of the height of the chip. The APE waveguide is on the top of the chip with the depth less than 10 µm. Theoretically, most of the energy of the propagation light is concentrated in the APE waveguide, and the penetration depth of the evanescent wave that diffuses outside the APE waveguide is usually only a few wavelengths. Therefore, the distance between the propagation light and the block structure is far enough that the block structure hardly affects the light propagation. Therefore, the optical properties of the MIOC, such as the insertion loss, will not be degraded.
4. Experimental verification
To evaluate the improvement method of the PER of MIOC, four MIOCs at 1550 nm with a chip length of ∼23.5 mm, height of 1 mm, and width of 3 mm are experimented. All the MIOCs are fabricated with the same APE method, and the polarization-maintaining fiber pigtails used in MIOCs are from the same batch. Two of the MIOCs are optimized with the proposed method in this paper, and the other two are traditional MIOCs without any additional treatment for comparison.
Figure 6 illustrates the experimental MIOC with the block structure at the bottom, and the double absorption trenches are fabricated using a dicing saw with a diamond blade. The parameters of the block structure of one of the MIOCs are ptr1 = ∼11472 µm, wtr1 = ∼250 µm, dtr1 = ∼200 µm, ptr2 = ∼10960 µm, wtr2 = ∼250 µm, and dtr2 = ∼200 µm, where subscripts 1 and 2 represent the parameters of the trench near the input and output ports, respectively.
Then, the PER of the MIOC is measured with an optical coherence domain polarimeter (OCDP, FIBERPRO, Inc.). The measuring sensitivity of the OCDP we used is >85 dB, which is sufficient to measure the PER of the MIOC chip in our work. To evaluate the suppression effect of the block structure on the TM mode that can be recoupled, the PERs are measured when the light propagated forward and backward in the MIOC. To express clearly, the three ports of the MIOC are referred to as Y1, Y2, and Y3, as shown in Fig. 4, and (Y3-Y1) represents the light propagating from ports Y3 to Y1. Table 1 lists the measurement results for the PER of the fabricated MIOCs. The MIOCs of No. 1 and No. 2 are in the traditional design, whereas MIOCs of No. 3 and No. 4 are constructed with the block structure at the bottom, as proposed in this study. According to the measured PER, compared with the traditional MIOC, regardless of the direction of light propagation, the PER of the optimized MIOC is significantly improved, that is, the double trenches with the absorption coating at the bottom can block the light propagating both forward and backward, which is likely to be recoupled. In comparison with the traditional design, the PERs of the MIOCs with the block structure are increased by approximately 25 dB, and the average value of the PER is higher than 75 dB. In addition, within the error tolerance, the measured insertion loss of the MIOC after constructing the block structure is similar to that of the MIOC before optimization, which is consistent with the above analysis.
Table 1. Measurement results of the fabricated MIOCs
Figure 7 shows the measurement results of the PERs of MIOCs with and without treatment, and the comparison with the theoretical value of PER. Comparing the measured PER at different chip lengths (black squares) with the theoretical PER of the MIOC without treatment (blue solid line), the measurement result is consistent with the theoretical analysis. After the MIOC is optimized, the value of PER is close to the theoretical value of PER induced by the direct recoupling of the divergence light (green dashed line), indicating that the degradation of the PER caused by reflection-induced recoupling is well suppressed.
Fig. 7. Comparison of measured and theoretical PERs of MIOC with different chip lengths, and improvement of the PER.
5. Conclusion
In this study, the reason for the degradation of the PER is theoretically analyzed by the overlap integral algorithm of the optical mode. The results demonstrate that, compared with the direct-divergence-induced recoupling of the TM mode, the reflection-induced recoupling of the TM mode is the main reason for the degradation of the PER. To prevent the TM mode from recoupling into the opposite port, based on the simulated propagation path of the mode field boundary of the TM mode, a method for constructing a block structure of double absorption trenches at the bottom surface of the MIOC is proposed. Four MIOC samples are fabricated for comparison and verification, two of which are MIOCs with a block structure design, and the other two are traditional MIOCs without additional treatment. The measurement result shows that the double absorption trenches can block the light reflecting on the bottom facet, regardless of whether the light propagates forward or backward in the substrate of the MIOC. In comparison with the traditional MIOC, the PER of the optimized MIOC with the block structure on the bottom can be improved by approximately 25 dB without an increase of the insertion loss of the MIOC, and the average value of the PER is higher than 75 dB, which is especially helpful for the application of high-precision FOGs.
In the future, the proposed method will be applied to MIOCs with longer chips to reduce reflection-induced recoupling and obtain a higher PER, thereby suppressing the effect of polarization nonreciprocal errors in the high-precision FOG.
Funding
National Natural Science Foundation of China (61935002).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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