Polarization-diversity Loop Structure Research Articles

광섬유 빗살 필터의 사분파장 지연기 연속 조합을 이용한 협대역 다파장 스펙트럼의 연속 주파수 조정에 관한 연구

We propose an optical fiber comb filter based on a polarization-diversity loop structure, which can continuously adjust the narrowband multiwavelength spectrum. The proposed comb filter consists of a polarization beam splitter(PBS), a successive combination of quarter-wave retarders(QWRs), a set of a half-wave retarder and a QWR, and two polarization-maintaining fiber(PMF) segments of equal length. For the convenient adjustment of the narrowband multiwavelength spectrum, the successive combination of QWRs was located between the PBS and the first PMF segment. The transmittance function of the proposed filter was theoretically derived using the Jones calculus. Based on the filter transmittance, we theoretically predicted the orientation angle sets of four wave retarders, which allow the extra phase difference φ of the transmittance function to vary from 0˚ to 315˚ with increments of 45˚. Then, the proposed filter successfully demonstrated the predicted results by obtaining ∼0.0915 ㎚ average wavelength shift and a high linearity of 0.99878.

대역 평탄화된 빗살 스펙트럼의 간단한 연속 파장 조정을 위한 이종 파장 지연기 조합 기반 광섬유 1차 빗살 필터에 관한 연구

In this paper, we propose an optical fiber first-order comb filter based on a polarization-diversity loop structure(PDLS), whose passband-flattened comb spectrum can be continuously wavelength-tuned in a convenient way through heterogeneous wave retarder combination. The proposed filter consists of a polarization beam splitter, two equal-length polarization-maintaining fiber(PMF) segments, three quarter-wave retarders(QWRs) and one half-wave retarder(HWR). For convenient wavelength control, we inserted a set of a QWR and an HWR between two PMF segments. Using the filter transmittance theoretically derived with Jones calculus, we found the azimuth angle(AA) sets of four wave retarders, which enable the additional phase difference ø to change from 0° to 360° On the basis of these AA sets, we theoretically calculated passband-flattened transmittance spectra spaced with a wavelength interval of 0.1nm. Then, we experimentally demonstrated theoretical results.

Frequency-tunable optical fiber passband-squeezed birefringence filter based on quarter-wave polarization conversion

A polarization-diversified loop structure (PDLS) formed by a four-port polarizing beam splitter has been employed to establish the input polarization independence of optical devices. Here we report a PDLS-based optical fiber birefringence filter, which can provide continuous frequency tunability in passband-squeezed comb spectra by harnessing quarter-wave polarization conversion. The birefringence filter is composed of a four-port PBS, two high birefringence fiber (HBF) segments whose lengths are equal, the first polarization controller (PC) comprised of a quarter-wave retarder (QWR) and a half-wave retarder (HWR), which is located in front of the first HBF segment, and a set of two QWRs as the second PC that lies before the second HBF segment. The dual QWRs, chosen for the second PC, are the simplest form of a PC that can convert arbitrary input polarization into desired polarization. The slow axis of the second HBF segment is oriented at 22.5° with respect to the horizontal axis of the PBS. Through the Jones matrix formulation, we derived the sinusoidal passband-squeezed transmittance function of the filter, whose absolute phase (ϕ) should be continuously varied for the contiguous wavelength tuning of filter spectra. Then, using this filter transmittance, we found the possible loci of the orientation angles (OAs) of the four wave retarders as the functions of ϕ. By utilizing the OA loci of the wave retarders, the theoretical passband-squeezed transmission spectra of the filter were calculated for eight equally spaced values of ϕ from 0° to 315° (with an increment of 45°). This theoretical calculation was also verified by measuring the wavelength-tuned passband-squeezed spectra of the fabricated filter. We theoretically and experimentally confirmed that our filter could provide the wavelength tunability of the polarization-independent passband-squeezed comb spectrum by appropriately controlling the OAs of the wave retarders.

Passband-Flattened Frequency-Tunable Optical Fiber Multiwavelength Filter with Composite Combination of Waveplates.

We propose a passband-flattened frequency-tunable optical multiwavelength filter with a composite combination of waveplates, which is realized by harnessing a polarization-diversified loop structure. The proposed filter comprises a polarization beam splitter (PBS), two polarization-maintaining fiber (PMF) segments of equal length, an ordered waveplate combination (OWC) of a half-wave plate (HWP) and a quarter-wave plate (QWP) before the first PMF segment, and an OWC of a QWP and an HWP before the second PMF segment. The second PMF segment is butt-coupled to one port of the PBS so that its slow axis is oriented at 22.5° for the horizontal axis of the PBS. Based on the filter transmittance derived through the Jones calculus, we found the orientation angle (OA) sets of the four waveplates, which could induce an extra phase shift Φ from 0° to 360° in the passband-flattened transmittance function. From the transmission spectra calculated at the eight selected OA sets, which caused Φ to increase from 0° to 315° by steps of 45°, it was confirmed that the passband-flattened multiwavelength spectrum can be continuously tuned by properly controlling the OAs. This indicates continuous wavelength tunability based on composite OWCs. Then, this theoretical prediction was verified by experimental demonstration.

편광 상이 고리 구조 내 복합 파장판 조합을 이용한 협대역 빗살 스펙트럼의 연속 파장 제어에 관한 연구

In this paper, we propose a novel birefringence filter based on polarization-diversity loop structure(PDLS) for continuous wavelength controlling of narrowband transmission spectrum. This filter consists of a polarization beam splitter(PBS), two high-birefringence fiber(HBF) of the same length, two half-wave plates(HWPs), and two quarter-wave plates(QWPs). We found a combination of the orientation angles of the four waveplates which could induce an additional phase difference φ from 0° to 360° to the narrowband transmittance function by considering the filter transmittance derived from Jones matrices. Then, we experimentally exhibited eight narrowband transmission spectra measured with a channel spacing of ∼0.1nm based on these theoretical calculations. As a result, we verified the effectiveness of the narrowband multiwavelength filter capable of continuously tuning its wavelength position when properly adjusting the combination of the orientation angles.

편광 상이 고리 구조 내 복합 파장판 조합을 이용한 평탄 대역 다파장 스펙트럼의 연속적인 파장 조정에 관한 연구

편광 상이 고리 구조 내 복합 파장판 조합을 이용한 평탄 대역 다파장 스펙트럼의 연속적인 파장 조정에 관한 연구

Arbitrary Phase Modulation of General Transmittance Function of First-Order Optical Comb Filter with Ordered Sets of Quarter- and Half-Wave Plates

Here we theoretically and experimentally demonstrated the arbitrary phase modulation of a general transmittance function (GTF) of the first-order optical comb filter based on a polarization-diversity loop structure, which employed two ordered waveplate sets (OWS’s) of a quarter-wave plate (QWP) and a half-wave plate (HWP). The proposed comb filter is composed of a polarization beam splitter (PBS), two equal-length polarization-maintaining fiber (PMF) segments, and two OWS’s of a QWP and an HWP with each set located before each PMF segment. The second PMF segment is butt-coupled to one port of the PBS so that its principal axis should be 22.5° away from the horizontal axis of the PBS. First, we explained a scheme to find four waveplate orientation angles (WOA’s) allowing the phase of a GTF to be arbitrarily modulated, using the way each component of the filter, such as a waveplate or PMF segment, affects its input or output polarization. Then, with the WOA finding method, we derived WOA sets of the four waveplates, which could give arbitrary phase retardations ϕ’s from 0° to 360° to a GTF chosen here arbitrarily. Finally, we showed phase-modulated GTF’s calculated at eight selected WOA sets allowing ϕ’s to be 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, and then the predicted results were verified by experimentally measured results. It is concluded from the theoretical and experimental demonstrations that the GTF of our filter based on the OWS of a QWP and an HWP can be arbitrarily phase-modulated by properly controlling the WOA’s of the four waveplates.

Tapered Length Dependence of Pressure Sensitivity in Polarimetric Fiber Pressure Sensor Based on Tapered High Birefringence Fiber

Here we investigated the tapered length dependence of the pressure sensitivity in a temperature-independent polarimetric fiber-optic pressure sensor (FPS) based on tapered high birefringence fiber (HBF) and a fiber Bragg grating (FBG) for three different tapered lengths of 200, 300, and 400 $\mu \text{m}$ . The investigation on the tapered length dependence was also done for three different types of HBF including one panda type fiber (PM-1550XP) and two bow-tie type fibers (HB1250T and HB1500). The polarimetric FPS was constructed by incorporating a polarization-diversified loop structure composed of a polarization beam splitter, polarization controllers, and a sensor head comprised of a 10.0-cm-long tapered HBF segment and a 1.8-cm-long FBG. The tapered HBF was used as a birefringence element to create polarization interference (PI). A pressure-induced change in the HBF birefringence leads to the wavelength shift of the PI spectrum. The FBG, which is sensitive to an ambient temperature change but nearly insensitive to a pressure change, was utilized to compensate for the temperature cross-sensitivity of the tapered HBF. From the investigation, the pressure sensitivity of the tapered HBF was found out to be proportional to the tapered length irrespective of the fiber type. Moreover, for the same tapered length, HB1500 showed the largest pressure sensitivity. In consequence, the maximum pressure sensitivity of approximately−35.46 nm/MPa could be obtained using bow-tie type HBF (HB1500) with a tapered length of $400~\mu \text{m}$ . Its adjusted ${R} ^{{{2}}}$ value representing the sensor linearity was measured as ~0.9973 in an applied pressure measurement range of 0–0.5 MPa.

Universal Wavelength Tuning Scheme for a First-Order Optical Fiber Multiwavelength Filter Based on a Polarization-Diversified Loop Structure.

In this paper, we propose a universal wavelength tuning scheme for a first-order optical fiber multiwavelength filter based on a polarization-diversified loop structure (PDLS), which is comprised of a polarization beam splitter, two sets of a half-wave plate (HWP) and a quarter-wave plate (QWP), and two polarization-maintaining fiber (PMF) segments. First, the polarization conditions, which should be satisfied to continuously tune the absolute wavelength of a transmittance function with an arbitrary transmission spectrum, are explained based on the continuous wavelength tuning mechanism of the flat-top band transmittance, which was previously reported in the PDLS-based passband-flattened first-order multiwavelength filter. Then, by considering the effect of the four waveplates (i.e., two HWPs and two QWPs) and two PMF segments on the output polarization of each element comprising the filter, we suggest a systematic scheme to find the azimuth angles of the four waveplates for continuous wavelength tuning of the arbitrary transmittance function. Three hundred sixty sets of the four waveplate azimuth angles, which give additional phase shifts of 1-360° (with a step of 1°) to an arbitrarily chosen transmittance function, are obtained with the suggested angle finding approach. Wavelength-tuned transmission spectra are displayed at eight waveplate angle sets, which are chosen from among the above angle sets so that they can induce extra phase shifts of 0, 45, 90, 135, 180, 225, 270, and 315° to the original transmittance function. These spectra prove that the proposed scheme can be applied to the wavelength tuning of every transmittance function of the PDLS-based first-order multiwavelength filter.

Tunable Narrowband Fiber Multiwavelength Filter Based on Polarization-Diversified Loop Structure.

In this paper, we propose a wavelength-tunable narrowband fiber multiwavelength filter based on polarization-diversified loop structure. The proposed filter consists of a polarization beam splitter, three half-wave plates (HWPs), two quarter-wave plates (QWPs) and two polarization-maintaining fiber (PMF) segments. The lengths of the two PMF segments are equal with each other. Among the five waveplates within the filter, a pair of an HWP and a QWP and the other pair of an HWP and a QWP are located in front of each PMF segment. The last HWP is placed after the second PMF and used to adjust the effective azimuthal angle of the second PMF. Azimuthal angle sets of the five waveplates, which can give additional phase shifts from 0 to 360° to the narrowband transmittance function derived from the Jones matrix formula, were theoretically found. Narrowband transmission spectra were calculated at eight waveplate angle sets selected among the angle sets derived above, which were designated as sets I, II, III, IV, V, VI, VII, and VIII that induced additional phase shifts from 0 to 315° (step: 45°) in the transmittance function. The calculated multiwavelength spectra clearly show that the narrowband multiwavelength spectrum can be wavelength-tuned by 0.1 nm as the waveplate angle set switches from set I to set VIII. This theoretical prediction was experimentally verified by appropriately controlling the azimuthal angle of each waveplate.

Polarization-Diversity-Loop-Based Optical Fiber Comb Filter with Polarization-Controlled Dual Transmission Channel Spacings.

In this paper, we propose an optical comb filter based on a polarization-diversity loop structure, whose two transmission channel spacings (TCS's) can be alternately switched between two principal axes of the filter by controlling waveplates contained in the filter. The proposed filter consists of a polarization beam splitter (PBS), three half-wave plates (HWPs), one Faraday rotator (FR), and two polarization-maintaining fiber (PMF) segments with different lengths (L and 2L) and equal birefringence (B). As the PMF segments are utilized as birefringence elements, the TCS of the filter is determined by the product of their effective length Le and birefringence B. For an input signal introduced into each principal axis of the filter, Le can be the sum of or difference between the two lengths (L and 2L) of the two PMF segments, that is, L or 3L, resulting in a TCS of S1 or S₂, respectively, according to angular combination of the orientation angles of the three HWPs. At a specific set of the three HWP angles, the proposed filter can create two sinusoidal transmittance functions with different TCS's (S1 and S₂) at the two principal axes, respectively. Also, the two TCS's (S1 and S₂) are switchable with each other depending on three HWP angles for each principal axis. With the fabricated filter, the flexible switching between S1 and S₂ could be successfully implemented for two orthogonally polarized input signals aligned along the two principal axes of the filter by properly controlling the three HWPs, without any modification of the filter configuration.

편광상이 고리 구조 기반 1차 광섬유 복굴절 필터의 임의 스펙트럼 파장 연속 조절을 위한 편광 조건 연구

편광상이 고리 구조 기반 1차 광섬유 복굴절 필터의 임의 스펙트럼 파장 연속 조절을 위한 편광 조건 연구

Dual-wavelength fiber Bragg grating laser with independently controllable output polarization

By incorporating an inline filter based on a polarization-diversified loop structure composed of two fiber Bragg gratings (FBGs) with different resonant wavelengths and three quarter-wave plates (QWPs), we propose a dual-wavelength FBG laser that can independently control the output polarization of dual-lasing lines oscillating at two Bragg resonances. At a special combination of the orientation angles of the QWPs, the inline filter can be arranged so that its transmittance depends on input polarization, and it can also select the output polarization states of reflection spectra of two FBGs independently according to its input polarization. For example, their reflection spectra chosen by the inline filter can be linear horizontally polarized at one Bragg wavelength and linear vertically polarized at the other Bragg wavelength, and vice versa. Moreover, linear horizontally or vertically polarized reflection spectra at both Bragg resonances can also be realized. By controlling the QWPs and a cavity polarizer used as an input polarizer of the filter, switching operation among four possible output polarization sets (i.e., two kinds of orthogonal output polarization sets and two kinds of parallel ones at two Bragg resonances) could be implemented in the proposed fiber laser with the measured polarization extinction ratio of each lasing line more than 20.0 dB.

Poincaré sphere-based technique for tuning flat-top fiber comb filter

We propose a universal method for designing flat-top passband and wavelength tuning of transmission spectrum of a fiber comb filter based on a polarization-diversified loop structure using Poincaré sphere representation. The proposed method gives a clear visualization of the evolution of polarization state through birefringent optical elements comprising the filter, and the design results are experimentally verified. Our method can also suggest which optical components are necessary for a specifically desired transmission spectrum of the comb filter.

Continuously wavelength-tunable passband-flattened fiber comb filter based on polarization-diversified loop structure

Continuous wavelength tuning of optical comb filters, which is an essential functionality for flexible signal processing in reconfigurable optical systems, has been challenging in high order filter structures with two birefringent elements (BEs) or more due to cumbersomeness in finding a combination of waveplates and BEs and complexity in determining their individual azimuthal orientations. Here, we propose a continuously tunable polarization-independent passband-flattened fiber comb filter with two BEs using a polarization-diversified loop structure for the first time. The proposed filter consists of a polarization beam splitter and two groups of a half-wave plate, quarter-wave plate, and polarization-maintaining fiber (PMF). The azimuthal orientation of PMF in the second group is fixed as 22.5°. Orientation angle sets of the four waveplates, which can induce an arbitrary phase shift from 0 to 2π in the passband-flattened transmittance function, are found from the filter transmittance derived using Jones matrix formulation. From theoretical spectral analysis, it is confirmed that passband-flattened comb spectra can be continuously tuned. Theoretical prediction is verified by experimental demonstration. Moreover, the wavelength-dependent evolution of the output state of polarization (SOP) of each PMF is investigated on the Poincare sphere, and the relationship between wavelength tuning and SOP evolution is also discussed.

Continuously tunable polarization-independent zeroth-order fiber comb filter based on polarization-diversity loop structure

By selecting some optimal wave retarder combination (WRC) groups, we propose and experimentally implement a continuously tunable polarization-independent zeroth-order fiber comb filter based on a polarization-diversity loop structure. The selected WRC groups contain a set of two quarter-wave retarders (QWRs), a set of a QWR and a half-wave retarder (HWR), and a set of an HWR and a QWR. The filter was formed using a polarization beam splitter (PBS), one of the three selected WRC groups, and high birefringence fiber (HBF). One end of HBF was butt-coupled to the PBS so that its slow axis should be oriented at 45° for the horizontal axis of the PBS, and the other end was connected to the WRC group. Three kinds of comb filters were fabricated with the three selected WRC groups. Through theoretical analysis on light polarization conditions for continuous spectral tuning and filter transmittances, eight special azimuth angle sets of two wave retarders, which gave the transmittance function eight different phase shifts of 0 to –7π/4 with a –π/4 step, were found for each WRC group. Theoretical prediction was verified by experimental demonstration. It was also confirmed that the filter could be continuously tuned by the appropriate control of wave retarders.

Polarization-Interference-Based Fiber Vibration Sensor Incorporating Polarization-Diversity Loop Structure

We demonstrate a polarization-interference-based fiber vibration sensor by incorporating a Sagnac interferometer based on a polarization-diversity loop structure composed of a polarization beam splitter, polarization-maintaining photonic crystal fiber, and polarization controllers. A laser diode and a photodetector were used to implement a high-speed intensity-based sensor. By using a piezoelectric transducer, we performed single frequency vibration measurement over 1-3000 Hz, resulting in a cutoff frequency of ~2100 Hz, a phase shift per unit length and unit strain of ~3.48 mrad/(με · m), and a minimum detectable strain perturbation of ~0.46 nε/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at 2000 Hz. Naturally, damped vibration response was also investigated using a metal cantilever, and the relationship between the sensor output and applied impulse was analyzed.

편광상이 고리 구조 기반 Lyot형 고차 광섬유 빗살 필터의 출력 편광 분석에 관한 연구

In this paper, we investigated the output polarization of a Lyot-type optical fiber comb filter based on a polarization-diversity loop structure. It was found that the output state of polarization (SOP) of the filter made a wavelength-dependent evolution, and the spectral periods of the output SOP variation in flat-top and lossy flat-top band modes were the channel separation of the filter and its half, respectively. For a certain input SOP, the filter could pass or reject specific spectral sections by adding and controlling an output analyzer. In particular, it was theoretically anticipated that the filter with the output polarizer could provide the fine continuous tuning of its pass band center in a wavelength range corresponding to the ±9.5% of channel spacing(0.8㎚) when the input SOP was properly adjusted. It is expected that this tuning function can be effectively applied to suppress unwanted spectral portions in modulated optical signals.

Study on Transmission and Output Polarization Characteristics of a First-Order Lyot-Type Fiber Comb Filter Using Polarization-Diversity Loop

A first-order Lyot-type fiber comb filter was fabricated by incorporating a polarization-diversity loop structure composed of a polarization beam splitter, two half-wave plates (HWPs), and two polarization-maintaining fiber (PMF) segments. One of the two PMF segments was two times longer than the other, and they were concatenated with a 60 $^{\circ} $ offset between their principal axes. The transmission spectra and output polarization characteristics of the filter were theoretically predicted and experimentally verified. By proper control of the two HWPs, first-order transmission spectra could be obtained, including flat-top and lossy flat-top band modes, and the interleaving operation of the respective spectrum could be also achieved. This flat-top band mode spectrum showed a higher attenuation rate at the cutoff level, in comparison with that of the Solc-type filter. In particular, it was revealed that the output state of polarization of the filter was a periodical function of wavelength and that the evolution period was different, according to transmission band modes. With the help of a linear output polarizer, the specific portion of a passband could be passed or rejected by controlling input polarization. It was also theoretically predicted that the fine tuning of the passband center was possible within a specific wavelength range.

편광 상이 루프 구조 기반 Lyot형 고차 광섬유 빗살 필터

In this paper, we propose a Lyot-type optical fiber comb filter based on a polarization-diversity loop structure (PDLS), which has flat-top pass bands and multiwavelength switching capability. Generally, the PDLS can remove the dependency of the filter on input polarization. The proposed filter is composed of a polarization beam splitter, two half-wave plates (HWPs), and two polarization-maintaining fiber loops concatenated with a 60° offset between their principal axes. By controlling two HWPs, it can operate in a flat-top band mode or a lossy flat-top band mode with an inherent insertion loss of ∼3.49dB. In particular, flat-top bands can be interleaved in both modes, which cannot be realized in a Lyot-Sagnac comb filter based on a fiber coupler. Compared with Solc-type high-order comb filters with the same order, the proposed filter shows sharper transition between pass and stop bands.