- Email: [email protected]
Transmission of a dark hollow beam by hollow-core anti-resonant fiber
Optics Communications 462 (2020) 125239
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Transmission of a dark hollow beam by hollow-core anti-resonant fiber Xiaobin Xu, Zhao Di ∗, Fuyu Gao, Yitong Song, Jixun Liu School of Instrumentation and Opto-electronic Engineering, Beihang University, 100183, China
ARTICLE
INFO
Keywords: Dark hollow beam Anti-resonant hollow-core fiber Guiding atoms
ABSTRACT Transmission of dark hollow beams is crucial for blue-detuned guiding of cold atoms, which is fundamental for cold-atom interferometers. We propose an anti-resonant hollow-core fiber and successfully demonstrate ∼13-cm guiding of a dark hollow beam. The intensity profile of the dark hollow beam can be well maintained during transmission through the hollow-core fiber, which is necessary and important for the high-quality guiding of cold atoms. A large fiber core of ∼40-𝜇m diameter facilitate high coupling efficiencies of cold atoms. Moreover, the hollow-core fiber has such a simple structure that fabrication becomes very easy.
1. Introduction Interferometers based on cold atoms show significantly higher precision than conventional optical interferometers because the wavelength of an atomic matter wave is much shorter than that of an optical wave [1]. They have broad applications in precision measurement instruments, such as the atomic gyroscope [2], atomic gravimeter [3] and so on. In interferometers based on cold atoms, blue-detuned guiding of cold atoms is one of the most important techniques, that can minimize the degradation of the coherence of the cold atom matter wave by guiding [4]. Euser et al. [5] reported control of LG01 whose intensity profile is a hollow beam in hollow-core photonic crystal fibers (HC-PCF), but the core diameters of the HC-PCF were only 12 ± 0.2 μm, which is too small to improve both the guiding efficiency and coupling efficiency. Poulin et al. [6] discovered the coupling efficiency of atoms would improve as the fiber core diameter increased. Pechkis et al. [7] demonstrated transmission of a dark hollow beam and guiding of cold 85 Rb atoms through a hollow-core dielectric waveguide having a core diameter of 100 μm, however, the dielectric waveguide was only 3 cm long. Hollow-core anti-resonant fiber confines the light within the air core through anti-resonant effect, and it has been applied in areas such as high power, ultrafast laser delivery [8,9], optofluidic [10] and polarizers [11]. Hollow-core anti-resonant fiber has a large core and simple structure [12,13], which may be beneficial to improve the efficiency of atomic guidance, and makes the fabrication process become very easy. In this paper, we design and fabricate an anti-resonant hollow-core fiber, and successfully implement 13-cm guiding of a dark hollow beam, which will be applied cold atom gravimeter. The fiber has such a simple structure that fabrication becomes facile. Moreover, the large fiber core diameter of 40 μm facilitates high coupling efficiencies of cold atoms in the future. Therefore, the work provides a foundation for blue-detuned guiding of cold 87 Rb atoms.
Fig. 1. Structure of the anti-resonant fiber.
2. Fiber design and fabrication The fiber is used in blue-detuned guiding of 87 Rb, thus, the operating wavelength must be around 780 nm, and the fiber core must be large enough to guarantee coupling efficiency of cold atoms[]. Further, the fabrication should be as simple as possible. Consequently, the fiber structure we designed is shown in Fig. 1, in which the core radius R is 19 μm, the thickness of the core wall t is 0.46 μm, and the size (D) and radius of the fillet (𝑅0 ) of the cladding air hole are 12 μm and 1 μm, respectively. The six modes supported by the fiber, as shown in Fig. 2, including the fundamental mode HE11 (Fig. 2(a)), higher order modes TE01 (Fig. 2(b)), HE21 (Fig. 2(c)), HE31 (Fig. 2(d)), EH21 (Fig. 2(e)) and
∗ Corresponding author. E-mail addresses: [email protected] (Z. Di), [email protected] (F. Gao).
https://doi.org/10.1016/j.optcom.2020.125239 Received 2 September 2019; Received in revised form 26 December 2019; Accepted 2 January 2020 Available online 20 January 2020 0030-4018/© 2020 Elsevier B.V. All rights reserved.
X. Xu, Z. Di, F. Gao et al.
Optics Communications 462 (2020) 125239
Fig. 2. Six modes supported by the designed anti-resonant hollow-core fiber. (a) HE11 , (b) TE01 , (c) HE21 , (d) HE31 , (e) EH21 , (f) HE41 .
Fig. 3. Confinement loss of different core modes. Fig. 4. Scanning electron micrograph of the fabricated anti-resonant hollow-core fiber.
HE41 (Fig. 2(f)). All of these modes, except for the fundamental mode, are hollow. The confinement losses of the HE11 , TE01 , HE21 , HE31 , EH21 , and HE41 are 0.72 dB/m, 0.034 dB/m, 1.985 dB/m, 1.5978 dB/m, 19.038 dB/m, 20.642 dB/m at 780 nm, respectively. The loss spectrums of the three low-order modes (HE11 , TE01 , HE21 ,) are given in Fig. 3, which shows that the loss of TE01 is always smaller than HE11 for the wavelength between 770 nm and 785 nm. Therefore, the hollow TE01 is dominant around 780 nm, and this makes transmission of dark hollow beams with low loss possible [14]. The anti-resonant hollow-core fibers were fabricated using a conventional stack-and-draw process [15]. Silica tubes were first drawn to obtain capillaries of the desired diameter. The capillaries were stacked and inserted into a jacked tube to create a preform. The form and size of the core and cladding air holes were controlled through different Argon gas pressures. Fig. 4 shows a scanning electron micrograph of the structure of the fabricated anti-resonant fiber. The core diameter R = ∼40 μm, the thickness of core wall t = ∼0.4 μm, 𝑅0 = ∼2 μm and D = ∼13.2 μm. These parameters are inevitably a little different from the designed values, so optical performance is also simulated for these fiber samples. The simulation results show that the confinement loss of the
fiber samples gets larger as compared to the excepted value, but there are only four modes in the fiber samples, as shown in Fig. 5. What is more, TE01 has the lowest confinement loss (∼6.38 dB/m) as compared to HE11 (∼49.34 dB/m), HE21 (∼44.4 dB/m) and TM01 (∼261.31 dB/m) at 780 nm. 3. Experimental results An experimental setup is established to verify the transmission of the dark hollow beam in the fabricated anti-resonant hollow-core fiber, as shown in Fig. 6. A Gaussian beam emitted by a laser having a wavelength of ∼780 nm, is linearly polarized, and expanded by 3× to 6-mm diameter to ensure that the focal spot (A) is small enough (∼31 μm) for mode field matching, and improve the coupling efficiency of the beam to the ∼13-cm long hollow-core fiber. The dark hollow beam incident into the anti-resonant hollow-core fiber is generated by a vortex retarder with fast axes that continuously rotate, so that its polarization state continuously rotates. Adjustment of the half wave plate is necessary to obtain the desired optical intensity profile in the hollowcore fiber. CCD1 and CCD2 are respectively used to monitor intensity 2
X. Xu, Z. Di, F. Gao et al.
Optics Communications 462 (2020) 125239
Fig. 5. Four modes supported by the anti-resonant hollow-core fiber sample. (a) TE01 , (b) HE11 , (c) HE21 , (d) TM01 .
Fig. 6. Experimental setup. P: linear polarizer. HWP: half wave plate. A: focal spot.
Although polarization state is not as important as intensity profile for the atom guiding, we also compare the input and output polarization state and investigate whether the output dark hollow beam is TE01 . First, a polarizer is placed at position A before the dark hollow beam enters the fiber, and its intensity profiles (the second row in Fig. 9) are recorded by CCD1 when the polarizing axis is 0◦ , 45◦ , 90◦ , 135◦ . Second, the polarizer at position A is removed and placed after the BS in Fig. 6. CCD3 is used to record intensity profile of the output dark hollow beam when the polarizing axis is also 0◦ , 45◦ , 90◦ , 135◦ , as shown in the third row in Fig. 9. Obviously, the output polarization state of the dark hollow beam is the same with the incident polarization state. Moreover, the output polarization state is consistent with the TE01 mode. Therefore, the dark hollow beam generated by vortex has successfully excited the TE01 mode in the anti-resonant fiber sample.
Fig. 7. Intensity profiles obtained by CCD1 and CCD2. Intensity profiles of (a) the incident dark hollow beam (CCD1), and (b) the beam measured at the end-face of the fiber (CCD2).
profile of the dark hollow beam before and after transmission through the hollow-core fiber, the results of which are shown in Fig. 7(a) and (b). CCD3 is used to monitor the polarization state of the output dark hollow beam.
4. Conclusions A simple hollow core anti-resonant fiber was proposed to transmit dark hollow beams. The fiber core has a diameter of ∼40 μm, and a cladding composed of a ring of 12 air holes enclosed by silica rings was used to support the fiber core. An experimental setup was established to verify the transmission of the dark hollow beam through the fabricated hollow core fiber. The experimental results showed that the relative intensity ratio is ∼3.32% and ∼3.89%, before and after the dark hollow beam passed through the fabricated hollow-core fiber, respectively, and that the corresponding relative sizes are ∼0.56 and ∼0.6. Therefore, the intensity profile of the dark hollow beam can be well maintained through the ∼13-cm long hollow-core fiber, which is vital for the high-quality guiding of cold atoms.
Stable transmission of the dark hollow beam within the fiber is crucial for guidance of cold atoms. Relative intensity ratio (𝜂) and relative size (𝜀) of the dark hollow beam are designed and used to evaluate the quality of dark hollow beam. 𝜂 is defined as 𝜂 = 𝐼min ∕𝐼max , where 𝐼max and 𝐼min are, respectively, the maximum and minimum of light intensity in radius r. Relative size 𝜀 is defined as DP/𝑊DHB , where DP is the peak-to-peak beam width, and 𝑊DHB [16] is defined as the width at 1/e2 of the peak intensity. As shown in Fig. 8, the black spots are the experimental data of the dark hollow beam intensity along the x-axis of the intensity profile shown in Fig. 7, and the red line is the intensity after double-Gaussian fitting in order to accurately obtain DP and 𝑊DHB . The relative intensity ratio 𝜂 is, respectively, ∼3.32% and ∼3.89% before and after the dark hollow beam passes through the hollow-core fiber. In addition, the relative size 𝜀 is, respectively, ∼0.56 and ∼0.6 before and after the dark hollow beam passes through the hollow-core fiber. Therefore, the dark hollow beam is well maintained and transmitted through the hollow-core fiber, which is necessary and important for the high-quality guiding of cold atoms.
CRediT authorship contribution statement Xiaobin Xu: Writing - review & editing, Funding acquisition, Supervision. Zhao Di: Software, Investigation, Writing - original draft, Writing - review & editing. Fuyu Gao: Methodology, Software. Yitong Song: Conceptualization, Formal analysis, Project administration. Jixun Liu: Resources, Methodology. 3
X. Xu, Z. Di, F. Gao et al.
Optics Communications 462 (2020) 125239
Fig. 8. Intensity profile along the x-axis (a) before and (b) after the dark hollow beam passes through the hollow-core fiber.
Fig. 9. Intensity profile of input beam and output beam through the polarizer.
Acknowledgments
[7] J.A. Pechkis, F.K. Fatemi, Cold atom guidance in a capillary using blue-detuned, hollow optical modes, J. Opt. Express 20 (2012) 13409. [8] E. Lee, J. Luo, B. Sun, et al., Flexible single-mode delivery of a high-power 2μm pulsed laser using an antiresonant hollow-core fiber, Opt. Lett. 43 (12) (2018) 2732–2735. [9] M. Michieletto, J.K. Lyngso, C. Jakobsen, et al., Hollow-core fibers for high power pulse delivery, Opt. Express 24 (7) (2016) 7103–7119. [10] Y. Hao, L. Xiao, F. Benabid, Optimized design of unsymmetrical gap nodeless hollow core fibers for optofluidic applications, J. Lightwave Technol. 36 (16) (2018) 11. [11] L. Li, L. Xiao, Plasmonic nodeless hollow-core photonic crystal fibers for in-fiber polarizers, J. Lightwave Technol. 37 (20) (2019) 5199–5211. [12] I. Hasan, N. Akhmediev, W. Chan, Positive and negative curvatures nested in an antiresonant hollow-core fiber, Opt. Lett. 42 (4) (2017) 703–706. [13] F. Poletti, Nested antiresonant nodeless hollow core fiber, Opt. Express 22 (20) (2014) 23807–23828. [14] L. Li, L. Xiao, Second-order vector mode propagation in hollow-core antiresonant fibers, Micromachines 10 (6) (2019) 381–394. [15] M.R. Taghizadeh, A.J. Waddie, R. Buczynski, J. Nowosielski, A. Filipkowski, D. Pysz, Nanostructured micro-optics based on a modified stack-and-draw fabrication technique, Adv. Opt. Technol. 1 (3) (2012) 171–180. [16] Y. Yin, L. Chunnan, X. Yong, Y. Min, The generation of hollow beam and its application in modern optics, J. Prog. Phys. 24 (2004) 336–380.
The authors express their gratitude to the National Natural Science Foundation of China (NSFC) (61575012, 61575013) for the funding that made this project possible. References [1] T.L. Gustavson, A. Landragin, M.A. Kasevich, Rotation sensing with a dual atom-interferometer Sagnac gyroscope, J. Class. Quantum Gravity 17 (2000) 2385–2398. [2] D.S. Durfee, Y.K. Shaham, M.A. Kasevich, Long-term stability of an areareversible atom-interferometer Sagnac gyroscope, J. Phys. Rev. Lett. 97 (2006) 240801. [3] Q. Bodart, S. Merlet, N. Malossi, F.P. Dos Santos, A. Landragin, A cold atom pyramidal gravimeter with a single laser beam, J. Appl. Phys. Lett. 96 (2010) 134101. [4] M.J. Renn, E.A. Donley, E.A. Cornell, C.E. Wieman, D.Z. Anderson, Evanescentwave guiding of atoms in hollow optical fibers, J. Phys. Rev. A 53 (1996) R648. [5] T.G. Euser, G. Whyte, M. Scharrer, J.S.Y. Chen, P.S.J. Russell, Dynamic control of higher-order modes in hollow-core photonic crystal fibers, J. Opt. Express 16 (2008) 17972–17981. [6] J. Poulin, P.S. Light, R. Kashyap, A.N. Luiten, Optimized coupling of cold atoms into a fiber using a blue-detuned hollow-beam funnel, J. Phys. Rev. A 84 (2011) 053812.
4
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Transmission of a dark hollow beam by hollow-core anti-resonant fiber Xiaobin Xu, Zhao Di ∗, Fuyu Gao, Yitong Song, Jixun Liu School of Instrumentation and Opto-electronic Engineering, Beihang University, 100183, China
ARTICLE
INFO
Keywords: Dark hollow beam Anti-resonant hollow-core fiber Guiding atoms
ABSTRACT Transmission of dark hollow beams is crucial for blue-detuned guiding of cold atoms, which is fundamental for cold-atom interferometers. We propose an anti-resonant hollow-core fiber and successfully demonstrate ∼13-cm guiding of a dark hollow beam. The intensity profile of the dark hollow beam can be well maintained during transmission through the hollow-core fiber, which is necessary and important for the high-quality guiding of cold atoms. A large fiber core of ∼40-𝜇m diameter facilitate high coupling efficiencies of cold atoms. Moreover, the hollow-core fiber has such a simple structure that fabrication becomes very easy.
1. Introduction Interferometers based on cold atoms show significantly higher precision than conventional optical interferometers because the wavelength of an atomic matter wave is much shorter than that of an optical wave [1]. They have broad applications in precision measurement instruments, such as the atomic gyroscope [2], atomic gravimeter [3] and so on. In interferometers based on cold atoms, blue-detuned guiding of cold atoms is one of the most important techniques, that can minimize the degradation of the coherence of the cold atom matter wave by guiding [4]. Euser et al. [5] reported control of LG01 whose intensity profile is a hollow beam in hollow-core photonic crystal fibers (HC-PCF), but the core diameters of the HC-PCF were only 12 ± 0.2 μm, which is too small to improve both the guiding efficiency and coupling efficiency. Poulin et al. [6] discovered the coupling efficiency of atoms would improve as the fiber core diameter increased. Pechkis et al. [7] demonstrated transmission of a dark hollow beam and guiding of cold 85 Rb atoms through a hollow-core dielectric waveguide having a core diameter of 100 μm, however, the dielectric waveguide was only 3 cm long. Hollow-core anti-resonant fiber confines the light within the air core through anti-resonant effect, and it has been applied in areas such as high power, ultrafast laser delivery [8,9], optofluidic [10] and polarizers [11]. Hollow-core anti-resonant fiber has a large core and simple structure [12,13], which may be beneficial to improve the efficiency of atomic guidance, and makes the fabrication process become very easy. In this paper, we design and fabricate an anti-resonant hollow-core fiber, and successfully implement 13-cm guiding of a dark hollow beam, which will be applied cold atom gravimeter. The fiber has such a simple structure that fabrication becomes facile. Moreover, the large fiber core diameter of 40 μm facilitates high coupling efficiencies of cold atoms in the future. Therefore, the work provides a foundation for blue-detuned guiding of cold 87 Rb atoms.
Fig. 1. Structure of the anti-resonant fiber.
2. Fiber design and fabrication The fiber is used in blue-detuned guiding of 87 Rb, thus, the operating wavelength must be around 780 nm, and the fiber core must be large enough to guarantee coupling efficiency of cold atoms[]. Further, the fabrication should be as simple as possible. Consequently, the fiber structure we designed is shown in Fig. 1, in which the core radius R is 19 μm, the thickness of the core wall t is 0.46 μm, and the size (D) and radius of the fillet (𝑅0 ) of the cladding air hole are 12 μm and 1 μm, respectively. The six modes supported by the fiber, as shown in Fig. 2, including the fundamental mode HE11 (Fig. 2(a)), higher order modes TE01 (Fig. 2(b)), HE21 (Fig. 2(c)), HE31 (Fig. 2(d)), EH21 (Fig. 2(e)) and
∗ Corresponding author. E-mail addresses: [email protected] (Z. Di), [email protected] (F. Gao).
https://doi.org/10.1016/j.optcom.2020.125239 Received 2 September 2019; Received in revised form 26 December 2019; Accepted 2 January 2020 Available online 20 January 2020 0030-4018/© 2020 Elsevier B.V. All rights reserved.
X. Xu, Z. Di, F. Gao et al.
Optics Communications 462 (2020) 125239
Fig. 2. Six modes supported by the designed anti-resonant hollow-core fiber. (a) HE11 , (b) TE01 , (c) HE21 , (d) HE31 , (e) EH21 , (f) HE41 .
Fig. 3. Confinement loss of different core modes. Fig. 4. Scanning electron micrograph of the fabricated anti-resonant hollow-core fiber.
HE41 (Fig. 2(f)). All of these modes, except for the fundamental mode, are hollow. The confinement losses of the HE11 , TE01 , HE21 , HE31 , EH21 , and HE41 are 0.72 dB/m, 0.034 dB/m, 1.985 dB/m, 1.5978 dB/m, 19.038 dB/m, 20.642 dB/m at 780 nm, respectively. The loss spectrums of the three low-order modes (HE11 , TE01 , HE21 ,) are given in Fig. 3, which shows that the loss of TE01 is always smaller than HE11 for the wavelength between 770 nm and 785 nm. Therefore, the hollow TE01 is dominant around 780 nm, and this makes transmission of dark hollow beams with low loss possible [14]. The anti-resonant hollow-core fibers were fabricated using a conventional stack-and-draw process [15]. Silica tubes were first drawn to obtain capillaries of the desired diameter. The capillaries were stacked and inserted into a jacked tube to create a preform. The form and size of the core and cladding air holes were controlled through different Argon gas pressures. Fig. 4 shows a scanning electron micrograph of the structure of the fabricated anti-resonant fiber. The core diameter R = ∼40 μm, the thickness of core wall t = ∼0.4 μm, 𝑅0 = ∼2 μm and D = ∼13.2 μm. These parameters are inevitably a little different from the designed values, so optical performance is also simulated for these fiber samples. The simulation results show that the confinement loss of the
fiber samples gets larger as compared to the excepted value, but there are only four modes in the fiber samples, as shown in Fig. 5. What is more, TE01 has the lowest confinement loss (∼6.38 dB/m) as compared to HE11 (∼49.34 dB/m), HE21 (∼44.4 dB/m) and TM01 (∼261.31 dB/m) at 780 nm. 3. Experimental results An experimental setup is established to verify the transmission of the dark hollow beam in the fabricated anti-resonant hollow-core fiber, as shown in Fig. 6. A Gaussian beam emitted by a laser having a wavelength of ∼780 nm, is linearly polarized, and expanded by 3× to 6-mm diameter to ensure that the focal spot (A) is small enough (∼31 μm) for mode field matching, and improve the coupling efficiency of the beam to the ∼13-cm long hollow-core fiber. The dark hollow beam incident into the anti-resonant hollow-core fiber is generated by a vortex retarder with fast axes that continuously rotate, so that its polarization state continuously rotates. Adjustment of the half wave plate is necessary to obtain the desired optical intensity profile in the hollowcore fiber. CCD1 and CCD2 are respectively used to monitor intensity 2
X. Xu, Z. Di, F. Gao et al.
Optics Communications 462 (2020) 125239
Fig. 5. Four modes supported by the anti-resonant hollow-core fiber sample. (a) TE01 , (b) HE11 , (c) HE21 , (d) TM01 .
Fig. 6. Experimental setup. P: linear polarizer. HWP: half wave plate. A: focal spot.
Although polarization state is not as important as intensity profile for the atom guiding, we also compare the input and output polarization state and investigate whether the output dark hollow beam is TE01 . First, a polarizer is placed at position A before the dark hollow beam enters the fiber, and its intensity profiles (the second row in Fig. 9) are recorded by CCD1 when the polarizing axis is 0◦ , 45◦ , 90◦ , 135◦ . Second, the polarizer at position A is removed and placed after the BS in Fig. 6. CCD3 is used to record intensity profile of the output dark hollow beam when the polarizing axis is also 0◦ , 45◦ , 90◦ , 135◦ , as shown in the third row in Fig. 9. Obviously, the output polarization state of the dark hollow beam is the same with the incident polarization state. Moreover, the output polarization state is consistent with the TE01 mode. Therefore, the dark hollow beam generated by vortex has successfully excited the TE01 mode in the anti-resonant fiber sample.
Fig. 7. Intensity profiles obtained by CCD1 and CCD2. Intensity profiles of (a) the incident dark hollow beam (CCD1), and (b) the beam measured at the end-face of the fiber (CCD2).
profile of the dark hollow beam before and after transmission through the hollow-core fiber, the results of which are shown in Fig. 7(a) and (b). CCD3 is used to monitor the polarization state of the output dark hollow beam.
4. Conclusions A simple hollow core anti-resonant fiber was proposed to transmit dark hollow beams. The fiber core has a diameter of ∼40 μm, and a cladding composed of a ring of 12 air holes enclosed by silica rings was used to support the fiber core. An experimental setup was established to verify the transmission of the dark hollow beam through the fabricated hollow core fiber. The experimental results showed that the relative intensity ratio is ∼3.32% and ∼3.89%, before and after the dark hollow beam passed through the fabricated hollow-core fiber, respectively, and that the corresponding relative sizes are ∼0.56 and ∼0.6. Therefore, the intensity profile of the dark hollow beam can be well maintained through the ∼13-cm long hollow-core fiber, which is vital for the high-quality guiding of cold atoms.
Stable transmission of the dark hollow beam within the fiber is crucial for guidance of cold atoms. Relative intensity ratio (𝜂) and relative size (𝜀) of the dark hollow beam are designed and used to evaluate the quality of dark hollow beam. 𝜂 is defined as 𝜂 = 𝐼min ∕𝐼max , where 𝐼max and 𝐼min are, respectively, the maximum and minimum of light intensity in radius r. Relative size 𝜀 is defined as DP/𝑊DHB , where DP is the peak-to-peak beam width, and 𝑊DHB [16] is defined as the width at 1/e2 of the peak intensity. As shown in Fig. 8, the black spots are the experimental data of the dark hollow beam intensity along the x-axis of the intensity profile shown in Fig. 7, and the red line is the intensity after double-Gaussian fitting in order to accurately obtain DP and 𝑊DHB . The relative intensity ratio 𝜂 is, respectively, ∼3.32% and ∼3.89% before and after the dark hollow beam passes through the hollow-core fiber. In addition, the relative size 𝜀 is, respectively, ∼0.56 and ∼0.6 before and after the dark hollow beam passes through the hollow-core fiber. Therefore, the dark hollow beam is well maintained and transmitted through the hollow-core fiber, which is necessary and important for the high-quality guiding of cold atoms.
CRediT authorship contribution statement Xiaobin Xu: Writing - review & editing, Funding acquisition, Supervision. Zhao Di: Software, Investigation, Writing - original draft, Writing - review & editing. Fuyu Gao: Methodology, Software. Yitong Song: Conceptualization, Formal analysis, Project administration. Jixun Liu: Resources, Methodology. 3
X. Xu, Z. Di, F. Gao et al.
Optics Communications 462 (2020) 125239
Fig. 8. Intensity profile along the x-axis (a) before and (b) after the dark hollow beam passes through the hollow-core fiber.
Fig. 9. Intensity profile of input beam and output beam through the polarizer.
Acknowledgments
[7] J.A. Pechkis, F.K. Fatemi, Cold atom guidance in a capillary using blue-detuned, hollow optical modes, J. Opt. Express 20 (2012) 13409. [8] E. Lee, J. Luo, B. Sun, et al., Flexible single-mode delivery of a high-power 2μm pulsed laser using an antiresonant hollow-core fiber, Opt. Lett. 43 (12) (2018) 2732–2735. [9] M. Michieletto, J.K. Lyngso, C. Jakobsen, et al., Hollow-core fibers for high power pulse delivery, Opt. Express 24 (7) (2016) 7103–7119. [10] Y. Hao, L. Xiao, F. Benabid, Optimized design of unsymmetrical gap nodeless hollow core fibers for optofluidic applications, J. Lightwave Technol. 36 (16) (2018) 11. [11] L. Li, L. Xiao, Plasmonic nodeless hollow-core photonic crystal fibers for in-fiber polarizers, J. Lightwave Technol. 37 (20) (2019) 5199–5211. [12] I. Hasan, N. Akhmediev, W. Chan, Positive and negative curvatures nested in an antiresonant hollow-core fiber, Opt. Lett. 42 (4) (2017) 703–706. [13] F. Poletti, Nested antiresonant nodeless hollow core fiber, Opt. Express 22 (20) (2014) 23807–23828. [14] L. Li, L. Xiao, Second-order vector mode propagation in hollow-core antiresonant fibers, Micromachines 10 (6) (2019) 381–394. [15] M.R. Taghizadeh, A.J. Waddie, R. Buczynski, J. Nowosielski, A. Filipkowski, D. Pysz, Nanostructured micro-optics based on a modified stack-and-draw fabrication technique, Adv. Opt. Technol. 1 (3) (2012) 171–180. [16] Y. Yin, L. Chunnan, X. Yong, Y. Min, The generation of hollow beam and its application in modern optics, J. Prog. Phys. 24 (2004) 336–380.
The authors express their gratitude to the National Natural Science Foundation of China (NSFC) (61575012, 61575013) for the funding that made this project possible. References [1] T.L. Gustavson, A. Landragin, M.A. Kasevich, Rotation sensing with a dual atom-interferometer Sagnac gyroscope, J. Class. Quantum Gravity 17 (2000) 2385–2398. [2] D.S. Durfee, Y.K. Shaham, M.A. Kasevich, Long-term stability of an areareversible atom-interferometer Sagnac gyroscope, J. Phys. Rev. Lett. 97 (2006) 240801. [3] Q. Bodart, S. Merlet, N. Malossi, F.P. Dos Santos, A. Landragin, A cold atom pyramidal gravimeter with a single laser beam, J. Appl. Phys. Lett. 96 (2010) 134101. [4] M.J. Renn, E.A. Donley, E.A. Cornell, C.E. Wieman, D.Z. Anderson, Evanescentwave guiding of atoms in hollow optical fibers, J. Phys. Rev. A 53 (1996) R648. [5] T.G. Euser, G. Whyte, M. Scharrer, J.S.Y. Chen, P.S.J. Russell, Dynamic control of higher-order modes in hollow-core photonic crystal fibers, J. Opt. Express 16 (2008) 17972–17981. [6] J. Poulin, P.S. Light, R. Kashyap, A.N. Luiten, Optimized coupling of cold atoms into a fiber using a blue-detuned hollow-beam funnel, J. Phys. Rev. A 84 (2011) 053812.
4