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Abstract
Material independent integrated nonlinear components (MIINC) based on nonlinear polarization evolution (NPE) play an important role in the emerging quantum computing, integrated photonics and ultrafast science. However, to our knowledge, no one has yet employed ultrafast laser direct writing for NPE-based MIINC. Here, for the first time, we finish the MIINC direct writing based on NPE using an ultrafast laser, and we suggest a multi-slice (MS) approach to in-fiber waveplate direct writing that allows for flexible adjustment of the phase difference, the waveplate fast and slow axis, and the stress birefringence value. To complete the measurement of the nonlinear transmittance curve, a polarization-splitter prism is attached to the output light path's back end. The measurement results agree with the theoretical calculation. MIINC based on NPE with arbitrary nonlinear transmittance curves are fabricated via the direct writing method, which is expected to be used in optical chips in the future.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Material independent integrated nonlinear components (MIINC) play important role in emerging quantum computing [1,2], integrated photonics [3,4] and ultrafast science [5], and is inherently present in most widely utilized photonic platforms [6], such as silicon nitride [7,8], silicon [9], gallium phosphide [10], tantala [11], silicon carbide [12,13] and lithium niobate [14,15], mode-locked laser [16], optical neurons [17], and entangled photon pairs [18]. Nonlinear polarization evolution (NPE) is one of the very important physical foundations of passive mode-locked lasers [19]. NPE mode-locking laser has the advantages of adjustable wavelength, large modulation depth and quick response time [20]. Therefore, in the future, NPE-based MIINC will be essential in several key domains.
However, to our knowledge, no one has yet employed ultrafast laser direct writing for MIINC based on NPE. Wave plate and material nonlinearity make up MIINC, which is based on NPE. Using an optical fiber carrier as an example, it is required to directly write multiple low-loss internal waveplates at both ends of an optical fiber with a nonlinear and particular length, along with slow axes and angles. The success of the MIINC based on NPE is therefore correlated with the internal waveplate's exact control.
Few direct writing studies on the interior waveplate have been conducted recently. In 2013, the issue of significant birefringence tuning in optical waveguides was thoroughly examined by L.A. Fernandes et al. [21] from the University of Toronto in Canada. The highest amount of birefringence that was produced was $2 \times {10^{ - 3}}$, and it was suggested that writing overlapping stress trajectories directly could boost birefringence. The internal fiber waveplates of quarter and half with a slow axis of 90 degrees are finished. however, because of the overlap region, this method is not suitable for adjusting the slow axis angle. A cuboid stress rods direct writing method was proposed in 2016 by Lei Yuan [22] of Clemson University in the United States. This method finished the direct writing of the quarter waveplate in the fiber. The following are this method's drawbacks. First, there is a space between neighboring stress slices, necessitating precise alignment and position control. Second, 200 direct writing repetitions in a single stress rod necessitate more frequent scanning and a longer processing time. Zhi-Dong Shi et al. [23] from Shanghai University completed an optimization design of a composite tangential spinning rate fiber plate in 2019. However, in actual processing, this type of optical fiber plate requires precise control over both the displacement platform and the optical fiber's rotation, which makes it more challenging in practice.
Here, we provide a multi-slice (MS) approach of in-fiber waveplate direct writing to finish the NPE-based MIINC. This method allows for flexible adjustment of the phase difference, the fast and slow axis of the waveplate, and the stress birefringence value. The low-loss in-fiber quarter waveplate and in-fiber half waveplate are finished after the size of birefringence is reduced to 5.15×${10^{ - 4}}$. Theory compliance is observed in the NPE-based MIINC transmittance curves. Its processing method is straightforward and controllable, requiring no rotation of the fiber, overlapping scans, or excessively repetitive scans to produce any desired NPE-based MIINC transmittance curve.
2. Device principle and theoretical analysis
Because of the photo-elastic effect, mechanical stresses are known to create extra refractive index changes in optical materials. In actuality, axial stress slices are purposefully implanted along commercially available Panda and Bow-tie PM fibers. The fiber's cross section is given an asymmetric index profile by the stress slices, which causes a systematic birefringence along the fiber. In this article, we present a novel method for fabricating six parallel stress slices in the fiber cladding of a single mode fiber (SMF, HI1060, Corning Inc.) to produce birefringence. The beam delivery was changed to pass through a fused silica plate with a thickness of 0.16-0.19 mm that was parallel to and in close contact with the fiber in order to prevent astigmatic focusing of the fiber. The space between the fiber cladding and the glass slide was filled with refractive index matching oil (SHINHO, 1.47). According to one experiment, a top-plate surface aberration should cause the depth of focus to be stretched by around 30 $\mu $m, creating a beam profile that is similar to that of a quasi-non-diffracting Bessel beam [24].
Based on the same idea, we are able to manufacture controlled birefringence along a single-mode optical fiber by using ultrafast laser micromachining to distribute six parallel stress slices in the cladding region of the fiber. Two stress groups that exert direct pressure on the optical fiber core are created by the six parallel stress slices created by ultrafast laser direct writing, as shown in Fig. 1. The ablative pattern's radially asymmetric cross section results in an asymmetric refractive index profile inside the fiber, which cause the light traveling along the fiber to exhibit birefringence.
Fig. 1. The schematically of stress slices produced by ultrafast laser micromachining inside an optical fiber: cross-sectional view (a) and top view (b).
Three parallel stress slices make up each stress group. The central stress slice and the fiber core are separated by a distance of D, the adjacent stress slice is separated by a distance of d, the width of the stress slice is w (the diameter of the ultrafast laser direct writing spot), and the length is H (the depth of the ultrafast laser write spot). The length (L) of six parallel stress slices or the distance (D) between the ablated region and the fiber core's center will determine how much birefringence is present. A smaller D frequently causes a huge stress, but it can also result in a large loss.
We are able to create inner-fiber waveplates with the necessary polarization rotations thanks to the birefringence caused by laser ablation. The stress region per unit length of the six parallel stress slices will result in a specific rotation of polarization, as shown in Fig. 1(b). Thus, it is possible to construct waveplates with the appropriate polarization rotations by adjusting the amount of polarization rotation.
3. Device fabrication
The experimental setup for creating inner-fiber waveplates is shown in Fig. 2. An ultrafast laser with a center wavelength of 1030 nm, a pulse width of 3 ps, and a repetition frequency of 200 kHz was used in our experiment. A segment of three-dimensional motor stage (Newport) with 0.1 ${\mathrm{\mu} \mathrm{m}}$ resolution is fixed to a section of striped SMF (Corning, HI1060). Using an objective lens (Olympus LCPlan N, 50x, NA 0.65), the laser beam is sharply focused into the fiber cladding. The fiber was submerged in index matching oil to reduce the fiber surface's lens effect. At a speed of 100 ${\mathrm{\mu} \mathrm{m}}/\textrm{s}$, the concentrated ultrafast laser beam is scanned parallel to the fiber axis during manufacture in order to introduce each stress slice. The focused beam's spot size was approximately 4 ${\mathrm{\mu} \mathrm{m}}$. The energy of the pulse is 2.08 $\mathrm{\ \mu J}$. The ultrafast laser's polarization direction is perpendicular to the fiber's direct writing direction.
Fig. 2. Experiment setup for fabrication of inner-fiber polarization devices using the ultrafast laser irradiation technique. HWP, half wave plate; BP, beam splitter; M, mirror; PM, power meter; DM, dichroic mirror; PC, polarization controller; Obj, objective lens; SMF, single mode fiber; PA, polarization analyzer; TAS, three-axis stage; CW, continuous wave.
The performance of the polarization devices during the micromachining procedure was observed using in-situ monitoring equipment, as depicted in Fig. 2. For in-situ monitoring of the polarization states as the stress zone of the six parallel stress slices was being added, a continuous wave (CW) laser (1032 nm), a polarization controller, and a polarization analyzer (Thorlabs, TXP5004) were utilized.
4. Results
4.1 A 90° slow axis quarter waveplate in fiber
The stress slices that were manufactured inside of a single-mode fiber are depicted in microscopic detail in Fig. 3(a) and 3(b). The six stress slices were constructed symmetrically inside the fiber's cladding. The dimensions of the design are D = 18 ${\mathrm{\mu} \mathrm{m}}$ and d = 8 ${\mathrm{\mu} \mathrm{m}}$. Experimental measurements are D = 20 - 24 ${\mathrm{\mu} \mathrm{m}}$ and d = 9 - 10 ${\mathrm{\mu} \mathrm{m}}$, respectively, as shown in Fig. 3(a). The six stress slices are evenly placed in two regions of the core, as can be seen in Fig. 3(b), which shows the top view of the CCD. As a result, the experimental findings closely match the theory.
Fig. 3. Microscopic images of the end face of six stress slices fabricated inside a SMF using ultrafast laser irradiation: (a) end face view and (b) top view.
The device's performance may be impacted by a crucial parameter called offset D. The fiber core would typically experience high levels of stress as a result of a tiny D, leading to high levels of index modulation and birefringence. The stress patterns could cause a significant optical loss to the light traveling inside the fiber core, though, if D is set too low.
In order to create a fiber inner quarter waveplate with a slow axis of + 90°, the polarization direction must first be changed by an external polarization controller to line polarized light with a + 45° angle, and then the length must be written directly in accordance with Fig. 3. As demonstrated in Fig. 4, you may view the polarization changes caused by each straight write stress slice on the polarization analyzer in real time. The Stokes vector on the Poincare sphere was (0.01, 0.99, 0.02), and the initial polarization state visible at the polarization analyzer was adjusted at about + 45° linear polarization in the equator by modifying the polarization controller. The polarization state upon direct writing of each stress slice is also shown in Fig. 4. The measured Stokes vectors were as follows: (-0.30, 0.69, -0.65), (-0.31, 0.41, -0.85), (-0.40, 0.24, -0.88), (-0.11,0.18, -0.97), (-0.04, 0.08, -0.99), and (0.08, 0.08, -0.99).
The polarization state shifted from the initial roughly + 45° linear polarization to the approximate left-handed circular polarization following the implantation of six stress slices. To put it another way, Fig. 3 shows that writing six 0.5 mm long stress slices immediately results in the creation of a quarter waveplate inside the single-mode fiber. After including six stress slices, the insertion loss was calculated to be 0.2479 dB. It's interesting to observe that the polarization states may be roughly accurately regulated and gradually changed during the ultrafast laser irradiation process, as indicated by the designated places along the longitude of the Poincare sphere.
Our experiment uses light with a wavelength of 1030 nm, stress slices with a length of 0.5 mm, and a phase delay of pi/2. This is,
where L is equal to 0.5 mm, $\lambda $ is 1030 nm, and ${B_f}$ is the fiber's birefringence caused by the stress zone, defined as [25], where ${n_x}$ and ${n_y}$ are the two orthogonal polarization modes’ respective effective refractive indices.The stress-induced birefringence ${B_f}$ was approximately $5.15 \times {10^{ - 4}}$, according to Eqs. (1). The six stress slices made with an ultrafast laser have a higher birefringence than standard polarization maintaining fibers (PMFs) [26,27], like the panda fiber and the bow-tie fiber ($3.1 \times {10^{ - 4}}$ and $3.8 \times {10^{ - 4}}$, respectively).
4.2 Half waveplate in fiber with a 45° slow axis
There is, as far as we are aware, no literature on direct writing of inner-fiber waveplates with a 45° slow axis. Therefore, this paper conducted a half waveplate experiment with a slow axis of 45° to confirm the accuracy of direct writing of waveplate. The direct write location has altered, as illustrated in Fig. 5, but the processing light route is the same as 4.1. The values for the design theory are D = 28 $\mu $m and d = 8 $\mu $m. Experimental measurements are D = 28 $\mu $m and d = 8 - 9 $\mu $m, respectively, as shown in Fig. 5(a). A trace is immediately written at the core location in Fig. 5(a) in order to more accurately depict the positioning accuracy, and the results demonstrate that the positioning of the initial position is extremely consistent with the core center. The six stress slices are evenly distributed in two regions of the core, as can be seen in the top view of the CCD in Fig. 5(b). As a result, the experimental findings closely match the theoretical values.
Fig. 5. Microscopic images of the end face of six stress slices fabricated inside a SMF using ultrafast laser irradiation: (a) end face view and (b) side view.
In order to create a fiber inner half waveplate with a slow axis of + 45°, the polarization direction must first be changed by an external polarization controller to + 0° linear polarization light, and then the fiber must be written directly in accordance with Fig. 5 with a length of 1 mm. As demonstrated in Fig. 6, you can view the polarization variations caused by each straight write stress slice in real time on the polarization analyzer. With the Stokes vector at (0.99, 0.09, -0.06) on the Poincare sphere, the initial polarization state seen at the polarization analyzer was tuned to about 0 degrees linear polarization in the equator by changing the polarization controller. The polarization state upon direct writing of each stress slice is also shown in Fig. 6. The calculated Stokes vectors were as follows: (0.36, 0.12, -0.92), (-0.04, 0.12, -0.99), (-0.25, -0.11, -0.96), (-0.53, -0.07, -0.83), (-0.83, -0.20, -0.50), and (-0.98, 0.05, 0.14).
The polarization state changed from the initial nearly 0° linear polarization to the subsequent approximately 90° linear polarization after the implantation of six stress slices, suggesting a 90° rotation in polarization. To put it another way, Fig. 5 shows that six stress slices with the length of 1 mm can be directly written to form a half waveplate inside the SMF. After including six stress slices, the insertion loss was calculated to be 0.1425 dB. It's interesting to observe that the polarization states may be roughly accurately regulated and gradually changed during the ultrafast laser irradiation process, as indicated by the designated places along the longitude of the Poincare sphere.
The stress-induced birefringence was also about $5.15 \times {10^{ - 4}}$, according to Eqs. (1). The same processing parameters are used for the second half waveplate. The incident light has a linear polarization of about 90°. The measured experiment yielded the following Stokes vector parameters: (0.99, 0.01, -0.13), (-0.43, 0.81, 0.38), (-0.01, 0.96, 0.25), (0.10, 0.98, 0.12), (0.30, 0.94, -0.06), (0.60, 0.74, -0.26), and (0.78, 0.16, -0.60). The insertion loss is 0.0959 dB. The fabrication procedure was repeatable, as evidenced by the little changes in stokes parameters.
4.3 MIINC based on NPE
In this paper, the optical path diagram depicted in Fig. 7 is proposed to achieve an MIINC based on NPE. The length of NF1, NF2, NF3 and YDF is 0.15 m, 0.30 m, 0.50 m, and 0.30 m respectively
Fig. 7. Nonlinear transmission rate curve measuring device. PM1, power meter 1; PM2, power meter 2; PBS, polarizing beam splitter; C1, collimator 1; NF1, nonlinear fiber 1; NF2, nonlinear fiber 2; NF3, nonlinear fiber 3; NF4 nonlinear fiber 4; HWP2, half wave plate 2; YDF, ytterbium-doped fiber; HWP1, half wave plate 1; C2, collimator 2; C3, collimator 3; PMF, polarization maintain fiber.
A 90° of slow axis inner-fiber half wave plate and a 45° of slow axis inner-fiber half waveplate are directly written in this work, respectively. The pump current is then regulated, and when the pump current is increased, the power ratio of PM1 and PM2 or the nonlinear transmissivity will alter nonlinearly. Figure 8 depicts the nonlinear transmissivity curve and spectrum diagram using the PM1 output power as an example.
Fig. 8. The (a) nonlinear transmissivity curve and (b) spectral diagram of the inner-fiber waveplate after direct writing.
Figure 8(a) makes it abundantly evident that as the overall output power rises, the transmissivity of PM1 exhibits a nonlinear variation. The signal light spectrum is widened and the pump light is nearly undetectable when the pumping strength is at its maximum, as shown in Fig. 8(b). As a result, the signal light (1030 nm) is produced using the majority of the energy of pump light (976 nm).
A theoretical model is created in accordance with the experimental module to demonstrate the accuracy and logic of the nonlinear transmissivity curve (Fig. 9.). Three nonlinear fiber segments are positioned in the middle of two polarizers (P1 and P2), two half waveplates (HWP1 and HWP2), and two polarizers (P1 and P2). Using the vertical as a point of reference, the polarization angles of P1, HWP1, HWP2, and P2 are as follows: 40° for P1, 45° for HWP1, 90° for HWP2, and 0° for P2. The y direction and the vertical direction also correspond. The nonlinear fiber is analogous to a waveplate, and there are two types of phase delays: linear and nonlinear.
Fig. 9. A nonlinear fiber placed between two polarizers with two half-wave plates. P1, polarizer 1; NF1, nonlinear fiber 1; HWP1, half wave plate 1; NF2, nonlinear fiber 2; HWP2, half wave plate 2; NF3, nonlinear fiber 3; P2, polarizer 2.
The nonlinear refractive index of nonlinear fiber (NF) is $2.5 \times {10^{ - 20}}$, the wavelength is 1030 nm, the length of NF1, NF2 and NF3 is 0.30 m, 0.80 m, and 0.15 m, and the effective mode field diameter of NF is 6.2 ${\mathrm{\mu} \mathrm{m}}$ in the experimental data. The maximum total average power is 223 mW. $2.86 \times {10^{ - 7}}$ is the theoretical value of fiber birefringence. The nonlinear transmittance curve identical to the experiment can be produced, once the Jones matrix has been calculated, as illustrated in Fig. 10. This nonlinear transmittance curve is achieved when the slow axes of NF1, NF2 and NF3 are -7°, 20° and 30°, respectively.
The successful realization of the MIINC based on NPE is demonstrated by Fig. 10, which shows how closely theory and experiment match. Additionally, the theory allows for the highly exact determination of the corresponding slow axis angle of the actual fiber, which will offer strong theoretical direction for any MIINC based on NPE transmittance curve in a waveguide can be designed.
5. Discussion
First of all, there were some poor results from the direct writing of quarter waveplate and half waveplate. According to this paper, there are several contributing factors. One is that the incident light's polarization direction is elliptically polarized, which is close to linear polarization, and another is that there is a positioning error of 1-2 $\mu $m in the optical fiber, which is brought on by the failure to achieve very accurate positioning. Therefore, the subsequent stage might be taken into consideration in terms of orientation and incidence polarization direction in order to get better outcomes. Second, due to the ease of experimental clamping, the two internal waveplates are not placed at each end of the fiber in the all-fiber saturable absorber experimental apparatus. The fiber's left and right ends are roughly 0.15 m and 0.35 m, respectively. The theoretical calculations show that the gain fiber has just a small effect on the entire NPE process. In the subsequent experiment, the optical fiber clamping device may be enhanced, and the inner waveplate of the fiber can be directly written on both ends of the fiber to better play the role of nonlinear fiber, increasing the implementation of integrated nonlinear element NPE. Finally, it is important to make sure that the fiber is in a normal straightening state and that the tension is not too high since too high tension will generate false birefringence in the experiment of NPE. The theoretical model presented in this work has all of its parameters within a respectable range, making it compatible with the experimental findings. Writing the internal waveplate directly on the two ends of the fiber also helps to simplify the theoretical procedure. In addition, the slow axis angle of the fiber that was determined is only one of several possible possibilities. Next, on the basis of our existing, we will integrate the polarization splitting prism into the fiber to complete the full fiber saturable absorber.
6. Conclusion
To complete the NPE-based MIINC, we propose a multi-slice (MS) method of in-fiber waveplate direct writing, which can flexibly adjust the stress birefringence value, the waveplate fast and slow axis and the phase difference. the size of birefringence is controlled to 5.15×${10^{ - 4}}$, and then the low-loss in-fiber quarter waveplate, in-fiber half waveplate and MIINC based on NPE are completed. This method can design and generate any desired NPE-based MIINC transmittance curve. Next, on the basis of our existing, we will integrate the polarization splitting prism into the fiber to complete the full fiber saturable absorber.
Acknowledgments
First of all, I would like to thank Dr. Xiangyu Chen and Mingming Wang of Wuhan Hongtuo New Technology Co., Ltd. for their careful guidance. Secondly, I would like to thank Qingdao Free Trade Technology Co., Ltd. for providing ultrafast lasers for this project.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the author upon reasonable request.
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