Simultaneous evaluation of two branches of a multifunctional integrated optic chip with an ultra-simple dual-channel configuration

Yonggui Yuan; Chuang Li; Jun Yang; Ai Zhou; Shuai Liang; Zhangjun Yu; Bing Wu; Feng Peng; Yu Zhang; Zhihai Liu; Libo Yuan

doi:10.1364/PRJ.3.000115

1. INTRODUCTION

The multifunctional integrated optic chip (MFIOC) is an important component for fiber-optic sensing applications ^[1–3] due to its multiple functions in beam splitting, optical polarization, and electro-optical phase modulation. A MFIOC is usually characterized with the polarization extinction ratio (PER) of the chip and local cross-couplings at connection points between the chip and its polarization maintaining (PM) pigtails. Accurately measuring these parameters is very important for fabrication and application of the MFIOC. Optical coherence domain polarimetry (OCDP) based on white light interferometry is a useful technique for measuring distributed polarization couplings in PM fibers ^[4–6] and optical devices ^[7]. It has been successfully used for one-channel evaluation of the MFIOCs ^[8–10].

In practical situation, there exists more or less difference between the two branches of the MFIOC. For some high-precision applications such as inertial measurement with fiber optic gyroscope (FOG) ^[11,12], the PER of the MFIOC is generally required to be higher than 80 dB. For such a high PER, a small difference, especially the transient response difference between the two branches of the MFIOC, will cause a significant impact on the performance such as random walk and zero drift of the FOG ^[13]. Therefore, for high-precision application, the difference of the parameters and their transient variation between the two branches of the MFIOC should be as small as possible. To obtain the transient response difference between the branches of the MFIOC, the two branches should be simultaneously evaluated. However, traditional OCDP method is just a single-channel testing configuration which cannot achieve two-branch simultaneous measurement. The full parameters of the MFIOC can only be obtained by evaluating one branch after the other, which means that two separate measurements are needed. In this case, the parameters of the two branches are not obtained simultaneously, and therefore the transient difference between the two branches cannot be accurately detected.

In this paper, we propose and demonstrate an ultra-simple dual-channel configuration for simultaneously evaluating the two branches of a MFIOC. Different from previous single-channel evaluation methods in which the MFIOC just is a device under test (DUT), the MFIOC in the present method acts not only as a DUT but also as an important component of the demodulation interferometer. The proposed configuration can accomplish simultaneous dual-channel evaluation with $- 90 dB$ resolution just using the same number of components as the single-channel configuration, which means that the ultra-simple configuration is cost effective and has high stability and reliability. To the best of our knowledge, this is the first time two branches of a MFIOC have been evaluated simultaneously.

2. SETUP AND ANALYSIS

The configuration of the dual-channel evaluating system is shown in Fig. 1. In the configuration, the beam splitting function of the MFIOC is utilized to construct the demodulation Mach–Zehnder interferometer together with a $2 \times 2$ fiber coupler. The linearly polarized light output from the 45° rotated polarizer is launched into the lead-in pigtail of the MFIOC and split into its two branches. The orthogonal beams output from branch 1 transmit through the 45° rotated analyzer 1 and the optical path scanning mechanism. The beams output from branch 2 pass through the 45° rotated analyzer 2 and the polarization controller (PC). The beams from the two branches are finally combined by the $2 \times 2$ coupler and detected by the detectors. When the optical path length including branch 1 matches that including branch 2 by tuning the position of the scanning mirror, interference occurs. Different from the single-channel evaluation system in which the interference happens between the orthogonal polarization modes in the same fiber branch, in the present two-channel configuration, the modes in the same branch do not interfere, and the interference takes place between beams traveling along different branches. Therefore, for the single-channel configuration, the interference fringes arise in pairs and locate symmetrically around the central interference peak. Each pair of fringes corresponds to a cross-coupling point, and the parameters of the MFIOC can be obtained from the fringes on any side of the central peak. For the dual-channel configuration, the interference fringes do not appear symmetrically, and the fringes at different sides of the central peak present cross-coupling points in different paths.

Figure 1.Schematic diagram of the ultra-simple dual-channel configuration for simultaneously evaluating the MFIOC. GRIN, graded index.

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For the sake of analysis, we use A, F, G, H, and I to represent the positions of the input polarizer, analyzer 1, analyzer 2, the scanning mirror, and the output coupler, respectively. The paths A-B-E-G-H-I and A-B-D-F-I are defined as path 1 and path 2, respectively. Points B, E, and D stand for the interfaces between the PM pigtails and the input end, output end 1, and output end 2 of the MFIOC, respectively. The cross-couplings at the interfaces are expressed as $ρ_{B}$ , $ρ_{E}$ , and $ρ_{D}$ , respectively. The points a, e, and d denote the splice points between the pigtails of the MFIOC and the pigtails of the polarizer, analyzer 1, and analyzer 2, respectively. All the PM pigtails are spliced with 0° axis alignment, and the cross-couplings at these points are expressed as $ρ_{a}$ , $ρ_{e}$ , and $ρ_{d}$ , respectively.

The light transmitting through the MFIOC demodulation configuration can be described with the Jones matrix method ^[10]. The light fields output from the analyzers 1 and 2 can be written as where $T_{pol}$ , $T_{ana 1}$ , and $T_{ana 2}$ are transfer matrices of the polarizer and analyzers 1 and 2, respectively; $T_{45 °}$ is the matrix of the 45° rotation angle of the polarizers; $T_{f_{A a}}$ , $T_{f_{a B}}$ , $T_{f_{D d}}$ , $T_{f_{d F}}$ , $T_{f_{E e}}$ , and $T_{f_{e G}}$ are transfer matrices of the PM pigtails with length of $l_{A a}$ , $l_{a B}$ , $l_{D d}$ , $l_{d F}$ , $l_{E e}$ , and $l_{e G}$ , respectively; and $T_{ρ_{a}}$ , $T_{ρ_{B}}$ , $T_{ρ_{D}}$ , $T_{ρ_{d}}$ , $T_{ρ_{E}}$ , and $T_{ρ_{e}}$ are transfer matrices of the coupling points a, B, D, d, E, and e, respectively; $T_{Y} T_{ξ}$ and $T_{Y} T_{ζ}$ present the transfer matrices of branch 1 and branch 2 of the MFIOC, respectively, where $ξ : ζ$ is the splitting ratio of the output coupler.

The output light fields $E_{out 1}$ and $E_{out 2}$ interfere at the coupler after transmitting through the optical path scanning mechanism and the PC, respectively. Neglecting the higher order terms of the interference signal, and only considering the constant and linear terms, the envelope of the interference signal can be expressed as where $R (τ)$ is the autocorrelation function of the light source; $ε_{1}$ and $ε_{2}$ are PERs of branch 1 and branch 2 of the MFIOC, respectively; and $τ_{A a}$ , $τ_{A B}$ , $τ_{E G}$ , $τ_{e G}$ , $τ_{D F}$ , and $τ_{d F}$ are time-delay differences between two polarization modes in PM fibers of $l_{A a}$ , $l_{A B}$ , $l_{E G}$ , $l_{e G}$ , $l_{D F}$ , and $l_{d F}$ , respectively. $τ_{1}$ , $τ_{2}$ , and $τ_{3}$ are time delay differences between beams transmitting along different paths, which are written as where $t_{n_{i}}^{M N}$ ( $M = B$ , $E$ , $G$ , $H$ , $D$ or $F$ , $N = E$ , $G$ , $H$ , $I$ , $D$ or $F$ , $i = x, y$ , or 0) is transit time of the light in the waveguides between points $M$ and $N$ . For PM fibers, $n_{x} = n_{slow}^{fiber}$ and $n_{y} = n_{fast}^{fiber}$ ; for the MFIOC, $n_{x} = n_{fast}^{chip}$ and $n_{y} = n_{slow}^{chip}$ ; for single mode fiber, the refractive index is expressed as $n_{0}$ .

In Eq. (3), the first item on the right-hand side denotes the central interference peak which serves as reference for getting the amplitude (cross talk) and location [optical path difference (OPD)] of other interference peaks. The second to sixth items present the cross-couplings at points a, B, E, and e and the PER of branch 1, respectively. The interference peaks corresponding to these items appear on the left side of the central interference peak. The last five items stand for the cross-couplings at points a, B, D, and d and the PER of branch 2, respectively, and their corresponding interference peaks arise on the right side of the central peak.

3. RESULTS AND DISCUSSION

A two-branch MFIOC was tested by using the proposed dual-channel configuration as shown in Fig. 1. The light source used in the experiment is a superluminescent diode (PSDD1502, InPhenix, Inc., USA) with a central wavelength of 1550 nm and bandwidth of $\sim 50 nm$ . The splitting ratio of the output coupler is $50 ∶ 50$ . The circulator has 1 dB insertion loss and 55 dB return loss. The polarizer and analyzers have 30 dB PER and $< 1 dB$ insertion loss. The scanning mirror has a $\sim 100 mm$ scanning range, $> 92 %$ reflectivity, 1.5 dB insertion loss, and $\pm 0.1 dB$ loss fluctuation. The photodetectors have a working range of 1100–1700 nm and responsivity of $> 0.85$ . The lengths and estimated OPD of the PM pigtails and the tested MFIOC are presented in Table 1. The length and birefringence of the PM fibers and MFIOC are approximate values that are used for roughly estimating the OPD in each waveguide. According to these estimated OPDs, we can confirm the characteristic peak positions of the cross-coupling points and the PERs of the MFIOC.

Table 1. Length and Estimated OPD of the MFIOC

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Table 1. Length and Estimated OPD of the MFIOC

MFIOC Length (m) Approximate Birefringence Estimated OPD (mm)
lAa 19.0 5×10−4 9.50
laB 1.22 5×10−4 0.61
lBE/lBD 0.02 8×10−2 1.60
lEe 1.20 5×10−4 0.60
lDd 1.59 5×10−4 0.80
leG 4.7 5×10−4 2.35
ldF 3.6 5×10−4 1.80

The measured interference pattern of the MFIOC is shown in Fig. 2. The central peak corresponding to the first item of Eq. (3) is caused from the interference between the paths $A B_{x} \to B E_{x} \to E G_{x}$ and $A B_{x} \to B D_{x} \to D F_{x}$ . The peaks on the left sides of the central peak represent the cross-coupling points in path 1, and those on the right side denote the cross-couplings in path 2. From the figure, the PER of the MFIOC is nearly $- 90 dB$ , and the dynamic range is about 90 dB, which are as high as those of the single-channel evaluation configuration ^[10].

Figure 2.Measured interference pattern of the MFIOC by using the dual-channel evaluating system. The left-side pattern expresses the cross-couplings of path 1, and the right-side pattern denotes the cross-couplings of path 2.

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The intensity and position of the characteristic peaks in Fig. 2 are shown in Table 2. Comparing the left peaks with the right ones, we can see that peaks III and IV have almost the same intensities as peaks ${III}^{'}$ and ${IV}^{'}$ , respectively, whereas the intensities of peaks I, II, and V are quite different from those of peaks $I^{'}$ , ${II}^{'}$ , and $V^{'}$ , respectively. The nearly identical intensities between peaks III and ${III}^{'}$ and peaks IV and ${IV}^{'}$ verify the consistency between the performances of the two measuring paths. The differences in the other three peak pairs apparently indicate the difference between the two branches of the MFIOC. To verify the measurement repeatability of the two-channel configuration, the MFIOC was repeatedly measured 20 times at room temperature. The results are plotted in Fig. 3. The largest standard deviation of the crosstalk is 0.13 dB (3σ), which confirms that the evaluation system has good repeatability.

Table 2. Measurement Results of the MFIOC

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Table 2. Measurement Results of the MFIOC

Peak	Position (mm)	Cross Talk (dB)	Corresponding Waveguide OPD
I (ρd)	1.962	−37.2	ldF
I′ (ρe)	−2.924	−43.1	leG
II (ρD)	2.928	−38.8	lDF
II′ (ρE)	−3.646	−44.1	lEG
III (ρa)	9.362	−32.4	lAa
III′ (ρa)	−9.354	−32.5	lAa
IV (ρB)	10.070	−47.5	lAB
IV′(ρB)	−10.065	−47.5	lAB
V(ε2)	11.383	−55.7	lAB−lBD+lDF
V′ (ε1)	−12.098	−53.6	lAB−lBE+lEG

Figure 3.Cross talk distribution of 20 measurements at room temperature.

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The MFIOC was then put into a temperature chamber to investigate the effect of temperature on the characteristics of the two branches of the MFIOC. The inconsistency of the temperature responses between the two branches can be directly obtained. In the experiment, the coupling points B, D, and E were in the temperature chamber, and points a, d, and e were out of the chamber. The temperature was increased from $- 40$ to 80°C with a step of 5°C. The intensity variation of peaks II, ${II}^{'}$ , IV, ${IV}^{'}$ , V, and $V^{'}$ are presented in Fig. 4. From the figure, we can see that intensities of peaks IV and ${IV}^{'}$ which represent the cross talk at the same point B, have the same variation tendency. Such a phenomenon demonstrates that the two channels of the evaluating configuration have the same response to temperature variation. The fluctuation of the intensity of peak $V^{'}$ ( $ε_{1}$ ) is much smaller than that of peak V ( $ε_{2}$ ), which indicates that branch 1 has better temperature stability than branch 2. The intensities of peaks II ( $ρ_{D}$ ) and ${II}^{'}$ ( $ρ_{E}$ ) change greatly with temperature variation, and the variation tendencies are quite different. The strong variations of $ρ_{D}$ and $ρ_{E}$ are due to the deformation of the optical adhesive for connecting the MFIOC and PM pigtails. The deformation of the adhesive will introduce stress on the PM pigtails and may cause slight rotation of the PM pigtails. Such temperature-caused stress and rotation mainly depend on the amount and shape of the adhesive; therefore the temperature response of the cross talks at the connections between the MFIOC and its pigtails is random for different MFIOCs.

Figure 4.Temperature responses of the two branches of the MFIOC.

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4. CONCLUSIONS

In conclusion, we proposed an ultra-simple dual-channel configuration for simultaneously evaluating two branches of a MFIOC. We employed the MFIOC as a beam splitter to construct the demodulation interferometer. The beams transmitting through different branches of the MFIOC interfere with each other, and the characteristic peaks corresponding to each branch locate on opposite sides with respect to the central interference peak. The resolution and dynamic range of the dual-channel configuration are as high as $- 90$ and 90 dB, respectively, which are comparable with those of the single-channel configuration. The temperature responses of the two branches were simultaneously measured, and results verify the simultaneous high-precision transient evaluation ability of the dual-channel configuration.

Category: Integrated Optics

Received: Mar. 20, 2015

Accepted: Feb. 24, 2015

Published Online: Jan. 6, 2016

The Author Email: Jun Yang (yangjun141@263.net)

DOI:10.1364/PRJ.3.000115

Table 1. Length and Estimated OPD of the MFIOC

Table 1. Length and Estimated OPD of the MFIOC

Table 2. Measurement Results of the MFIOC

Table 2. Measurement Results of the MFIOC