Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Curr. Opt. Photon. 2021; 5(3): 250-260
Published online June 25, 2021 https://doi.org/10.3807/COPP.2021.5.3.250
Copyright © Optical Society of Korea.
Jianping Shen^{1} , Siwei Zhang^{1}, Wei Wang^{1}, Shuguang Li^{2}, Song Zhang^{2}, Yujun Wang^{2}
Corresponding author: ^{*}jianpingshen@njupt.edu.cn, ORCID 0000-0002-7669-6046
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
A tapered As_{2}S_{3} photonic crystal fiber (PCF) with four layers of air holes in a hexagonal array around the core is designed in this paper. Numerical simulation shows that the dispersion D decreases and the nonlinearity coefficient γ increases from the thick to the thin end along the tapered PCF. We simulate the midinfrared pulse compression in the tapered As_{2}S_{3} PCF using the adaptive split-step Fourier method. Initial Gaussian pulses of 4.4 ps and a central wavelength of 2.5 μm propagating in the tapered PCF are located in the anomalous dispersion region. With an average power of assumed input pulses at 3 mW and a repetition frequency of 81.0 MHz, we theoretically obtain a pulse duration of 56 fs and a compression factor of 78 when the pulse propagates from the thick end to the thin end of the tapered PCF. When confinement loss in the tapered PCF is included in the simulation, the minimum pulse duration reaches 72 fs; correspondingly, the maximum compression factor reaches 61. The results show that in the anomalous-dispersion region, midinfrared pulses can be efficiently compressed in a dispersion-decreasing and nonlinearity-increasing tapered As_{2}S_{3} PCF. Due to confinement loss in the tapered fiber, the efficiency of pulse compression is suppressed.
Keywords: As_{2}S_{3} photonic crystal fiber, Mid-infrared, Pulse compression
OCIS codes: (060.5295) Photonic crystal fibers; (230.4320) Nonlinear optical devices; (260.2030) Dispersion; (260.3060) Infrared
Photonic crystal fiber (PCF) [1, 2], also known as microstructure optical fiber [3], has recently attracted wide interest in scientific research. Typically, a PCF is sa ingle-material-based optical fiber, with air-filled holes surrounding the core along the fiber’s entire length, to provide strong confinement of the light field, long interaction lengths, and customizable wavelength dispersion. Tapered single-mode fibers [4], tapered microstructure fibers [5], and tapered photonic crystal fibers [6, 7] exhibit many novel characteristics, such as mode coupling and high nonlinearity. In the fiber-tapering process, the nonlinearity is enhanced by reducing the core size and modulating dispersion along the fiber’s length. With the rapid development of fiber-optic technology, high-quality ultrashort pulses will play a very important role in modern communication. Recently, compression of an ultrashort pulse has been developed using waveguide techniques [8] or optical fibers [9, 10]. Arnold
An infrared laser is an important tool in scientific research [29]. For example, a midinfrared laser was recently shown to cut a variety of tissues effectively, with minimal injury to adjacent structures [30]. Sources of broadband midinfrared light attract considerable attention from many researchers, due to their broad application potential [31] in optical frequency metrology, astronomical spectroscopy, optical tomography, tunable wavelength conversion, and infrared imaging. Compared to other non-silica glasses, chalcogenide glasses—in particular, As_{2}Se_{3} [32, 33] and As_{2}S_{3} [34, 35]—exhibit a larger refractive index and a higher nonlinear index, providing larger mode confinement and higher nonlinearity. Highly nonlinear multimaterial chalcogenide spiral PCF has been prepared by Kalra
In this paper, we design a tapered As_{2}S_{3} PCF. The dispersion, nonlinearity coefficient, confinement loss, and other parameters of the tapered As_{2}S_{3} PCF are numerically simulated using the finite-element method. The propagation of a midinfrared pulse in the tapered As_{2}S_{3} PCF is simulated numerically using the adaptive split-step Fourier method. The potential for pulse compression in the tapered fiber is studied, and the influence of fiber confinement loss on pulse compression is analyzed.
In this paper, we design a tapered As_{2}S_{3} PCF with four layers of air holes in a hexagonal array around the core. We assume that the air-hole pitch Λ, air-hole diameter
The air-hole pitch of the tapered PCF with a linearly tapered structure can be expressed as follows [23]:
where Λ(
where
For the As_{2}S_{3}-tapered PCF simulated in this paper, we set Λ(0) = 2.26 μm, Λ(
To achieve the dispersion-decreasing and nonlinearity-increasing tapered fiber, we select the ratio of the air-hole diameter to the pitch
The variation of dispersion and confinement loss with the structure parameters of a PCF is a complex process affected by multiple parameters, such as the air-hole diameter
To realize some design tolerance, we include Fig. 5 to illustrate that small variations in
Maintaining the air holes is a difficult problem in the preparation of a photonic crystal fiber. In the process of preparing a PCF, an appropriate pressure is applied to the preform rod to keep the air holes from collapsing, and the adiabatic tapering method is used to keep the air-hole diameter proportional to the tapered region during the tapering process [41]. In addition, as shown in Fig. 5, the performance of the fiber has a certain tolerance to the preparation parameters.
To simulate the transmission of laser pulses in the As_{2}S_{3} tapered PCF, we further calculate the high-order dispersion of the As_{2}S_{3} tapered PCF from β_{3} to β_{15}. Second-order dispersion β_{2} and third-order dispersion β_{3} at a wavelength of 2.5 μm, as functions of distance
The generalized nonlinear Schrödinger equation for pulse propagation in a tapered PCF with nonuniform parameters should be expressed as in Eq. (3) [42]:
where α
while the nonlinear response function is defined as
For Gaussian-shaped pulses, the input pulses are given by [41] as follows:
where
The decrease in dispersion acts as effective amplification, because it precisely compensates for the decrease in soliton energy caused by fiber loss. Equation (7) shows that pulse compression could be achieved during propagation along a fiber with either
Higher-order compression in the dispersion-decreasing fiber is a process of transforming a higher-order soliton into a highly compressed pulse that propagates almost the same as a fundamental soliton. The width of an
where
In this paper, we simulate pulse transmission by pumping the active mode locking of a Cr^{2+}:ZnSe laser [37] into a tapered PCF. The central wavelength of this laser is nearly 2.5 μm, located in the As_{2}S_{3} weak-absorption window of 0.78–5.5 μm, and the absorption wavelength is 2.5 μm, corresponding to minimum material loss for As_{2}S_{3}. The laser produces 4.4-ps transform-limited Gaussian-shaped pulses. The average power of the input pulses is 3 mW in the simulation conducted for the current study, the repetition frequency is 81.0 MHz, the corresponding peak pulse power is 12 W, and the energy of a single pulse is approximately 0.037 nJ. In this simulation, an adaptive split-step Fourier method [23] is numerically applied to study pulse propagation in the tapered PCF. We compare without fiber loss with total fiber loss under two operating modes.
The pulse propagation in the tapered As_{2}S_{3} PCF is simulated numerically using the adaptive split-step Fourier method, and the corresponding program is written by our research group in the FORTRAN language. The temporal profile as a function of propagation distance z is shown in Fig. 7. The horizontal ordinate is the normalized time
To describe pulse compression we use the pulse compression factor, defined as the ratio of the FWHM pulse duration at the beginning and at a given transmission distance in the fiber. Figure 9 shows the pulse width and compression factor as functions of propagation distance
As shown in Fig. 9, the pulse compression mainly occurs over the propagation-distance range of 0–0.7 m, becoming slow after 0.7 m. By analyzing the data in Fig. 9, we can see that the pulse width changed from 252 fs to 56 fs and the compression factor changed from 17.5 to 78.6 when the pulse propagates from 0.7 m to 1.0 m in the tapered PCF. When the transmission distance is greater than 0.7 m, the pulse compression slows because the spectrum is widened and the energy corresponding to the peak wavelength of the pulse decreases, which weakens the nonlinear effect.
A degree of loss in the fiber always exists. In a tapered PCF, the loss coefficient α increases from the thin to the thick end, as shown in Fig. 4(b). The confinement loss is roughly 16 dB/m at the thin end of the tapered PCF. A comparison of the temporal profile with and without loss, as a function of propagation distance
Compared to silica or Poly methyl methacrylate, As_{2}S_{3} glass has higher refractive index and nonlinear refractive index, the values being
From the numerical simulation results, we find that loss reduces the compression factor when the pulse propagates in the tapered PCF. Pulse compression is a nonlinear optical process related to pulse energy, and the existence of loss will make the pulse energy gradually diminish in the transmission process. As a result, the decrease of pulse energy leads to the decrease of the nonlinear effect, and the compression factor of the pulse is reduced. Equation (7) is the theoretical basis of pulse compression using a tapered PCF. The factor
Li
In this paper, a tapered As_{2}S_{3} PCF with four air-hole layers in a hexagonal array around the core was designed. For structural parameters Λ(0) = 2.26 μm, Λ(
This study was supported in part by the Program of the Natural Science Foundation of Hebei Province (Grant No. F2017203193), and in part by Nanjing University of Posts and Telecommunications Foundation under Grants JUH219002, JUH219007, NY215007, and NY215113. This work was supported in part by the Research Center of Optical Communications Engineering & Technology, Jiangsu Province Foundation, under Grant ZXF20170102.
Curr. Opt. Photon. 2021; 5(3): 250-260
Published online June 25, 2021 https://doi.org/10.3807/COPP.2021.5.3.250
Copyright © Optical Society of Korea.
Jianping Shen^{1} , Siwei Zhang^{1}, Wei Wang^{1}, Shuguang Li^{2}, Song Zhang^{2}, Yujun Wang^{2}
^{1}College of Electronic and Optical Engineering, Nanjing University of Post and Telecommunications, Nanjing 210023, China
^{2}State Key Laboratory of Metastable Materials Science and Technology & Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China
Correspondence to:^{*}jianpingshen@njupt.edu.cn, ORCID 0000-0002-7669-6046
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
A tapered As_{2}S_{3} photonic crystal fiber (PCF) with four layers of air holes in a hexagonal array around the core is designed in this paper. Numerical simulation shows that the dispersion D decreases and the nonlinearity coefficient γ increases from the thick to the thin end along the tapered PCF. We simulate the midinfrared pulse compression in the tapered As_{2}S_{3} PCF using the adaptive split-step Fourier method. Initial Gaussian pulses of 4.4 ps and a central wavelength of 2.5 μm propagating in the tapered PCF are located in the anomalous dispersion region. With an average power of assumed input pulses at 3 mW and a repetition frequency of 81.0 MHz, we theoretically obtain a pulse duration of 56 fs and a compression factor of 78 when the pulse propagates from the thick end to the thin end of the tapered PCF. When confinement loss in the tapered PCF is included in the simulation, the minimum pulse duration reaches 72 fs; correspondingly, the maximum compression factor reaches 61. The results show that in the anomalous-dispersion region, midinfrared pulses can be efficiently compressed in a dispersion-decreasing and nonlinearity-increasing tapered As_{2}S_{3} PCF. Due to confinement loss in the tapered fiber, the efficiency of pulse compression is suppressed.
Keywords: As_{2}S_{3} photonic crystal fiber, Mid-infrared, Pulse compression
Photonic crystal fiber (PCF) [1, 2], also known as microstructure optical fiber [3], has recently attracted wide interest in scientific research. Typically, a PCF is sa ingle-material-based optical fiber, with air-filled holes surrounding the core along the fiber’s entire length, to provide strong confinement of the light field, long interaction lengths, and customizable wavelength dispersion. Tapered single-mode fibers [4], tapered microstructure fibers [5], and tapered photonic crystal fibers [6, 7] exhibit many novel characteristics, such as mode coupling and high nonlinearity. In the fiber-tapering process, the nonlinearity is enhanced by reducing the core size and modulating dispersion along the fiber’s length. With the rapid development of fiber-optic technology, high-quality ultrashort pulses will play a very important role in modern communication. Recently, compression of an ultrashort pulse has been developed using waveguide techniques [8] or optical fibers [9, 10]. Arnold
An infrared laser is an important tool in scientific research [29]. For example, a midinfrared laser was recently shown to cut a variety of tissues effectively, with minimal injury to adjacent structures [30]. Sources of broadband midinfrared light attract considerable attention from many researchers, due to their broad application potential [31] in optical frequency metrology, astronomical spectroscopy, optical tomography, tunable wavelength conversion, and infrared imaging. Compared to other non-silica glasses, chalcogenide glasses—in particular, As_{2}Se_{3} [32, 33] and As_{2}S_{3} [34, 35]—exhibit a larger refractive index and a higher nonlinear index, providing larger mode confinement and higher nonlinearity. Highly nonlinear multimaterial chalcogenide spiral PCF has been prepared by Kalra
In this paper, we design a tapered As_{2}S_{3} PCF. The dispersion, nonlinearity coefficient, confinement loss, and other parameters of the tapered As_{2}S_{3} PCF are numerically simulated using the finite-element method. The propagation of a midinfrared pulse in the tapered As_{2}S_{3} PCF is simulated numerically using the adaptive split-step Fourier method. The potential for pulse compression in the tapered fiber is studied, and the influence of fiber confinement loss on pulse compression is analyzed.
In this paper, we design a tapered As_{2}S_{3} PCF with four layers of air holes in a hexagonal array around the core. We assume that the air-hole pitch Λ, air-hole diameter
The air-hole pitch of the tapered PCF with a linearly tapered structure can be expressed as follows [23]:
where Λ(
where
For the As_{2}S_{3}-tapered PCF simulated in this paper, we set Λ(0) = 2.26 μm, Λ(
To achieve the dispersion-decreasing and nonlinearity-increasing tapered fiber, we select the ratio of the air-hole diameter to the pitch
The variation of dispersion and confinement loss with the structure parameters of a PCF is a complex process affected by multiple parameters, such as the air-hole diameter
To realize some design tolerance, we include Fig. 5 to illustrate that small variations in
Maintaining the air holes is a difficult problem in the preparation of a photonic crystal fiber. In the process of preparing a PCF, an appropriate pressure is applied to the preform rod to keep the air holes from collapsing, and the adiabatic tapering method is used to keep the air-hole diameter proportional to the tapered region during the tapering process [41]. In addition, as shown in Fig. 5, the performance of the fiber has a certain tolerance to the preparation parameters.
To simulate the transmission of laser pulses in the As_{2}S_{3} tapered PCF, we further calculate the high-order dispersion of the As_{2}S_{3} tapered PCF from β_{3} to β_{15}. Second-order dispersion β_{2} and third-order dispersion β_{3} at a wavelength of 2.5 μm, as functions of distance
The generalized nonlinear Schrödinger equation for pulse propagation in a tapered PCF with nonuniform parameters should be expressed as in Eq. (3) [42]:
where α
while the nonlinear response function is defined as
For Gaussian-shaped pulses, the input pulses are given by [41] as follows:
where
The decrease in dispersion acts as effective amplification, because it precisely compensates for the decrease in soliton energy caused by fiber loss. Equation (7) shows that pulse compression could be achieved during propagation along a fiber with either
Higher-order compression in the dispersion-decreasing fiber is a process of transforming a higher-order soliton into a highly compressed pulse that propagates almost the same as a fundamental soliton. The width of an
where
In this paper, we simulate pulse transmission by pumping the active mode locking of a Cr^{2+}:ZnSe laser [37] into a tapered PCF. The central wavelength of this laser is nearly 2.5 μm, located in the As_{2}S_{3} weak-absorption window of 0.78–5.5 μm, and the absorption wavelength is 2.5 μm, corresponding to minimum material loss for As_{2}S_{3}. The laser produces 4.4-ps transform-limited Gaussian-shaped pulses. The average power of the input pulses is 3 mW in the simulation conducted for the current study, the repetition frequency is 81.0 MHz, the corresponding peak pulse power is 12 W, and the energy of a single pulse is approximately 0.037 nJ. In this simulation, an adaptive split-step Fourier method [23] is numerically applied to study pulse propagation in the tapered PCF. We compare without fiber loss with total fiber loss under two operating modes.
The pulse propagation in the tapered As_{2}S_{3} PCF is simulated numerically using the adaptive split-step Fourier method, and the corresponding program is written by our research group in the FORTRAN language. The temporal profile as a function of propagation distance z is shown in Fig. 7. The horizontal ordinate is the normalized time
To describe pulse compression we use the pulse compression factor, defined as the ratio of the FWHM pulse duration at the beginning and at a given transmission distance in the fiber. Figure 9 shows the pulse width and compression factor as functions of propagation distance
As shown in Fig. 9, the pulse compression mainly occurs over the propagation-distance range of 0–0.7 m, becoming slow after 0.7 m. By analyzing the data in Fig. 9, we can see that the pulse width changed from 252 fs to 56 fs and the compression factor changed from 17.5 to 78.6 when the pulse propagates from 0.7 m to 1.0 m in the tapered PCF. When the transmission distance is greater than 0.7 m, the pulse compression slows because the spectrum is widened and the energy corresponding to the peak wavelength of the pulse decreases, which weakens the nonlinear effect.
A degree of loss in the fiber always exists. In a tapered PCF, the loss coefficient α increases from the thin to the thick end, as shown in Fig. 4(b). The confinement loss is roughly 16 dB/m at the thin end of the tapered PCF. A comparison of the temporal profile with and without loss, as a function of propagation distance
Compared to silica or Poly methyl methacrylate, As_{2}S_{3} glass has higher refractive index and nonlinear refractive index, the values being
From the numerical simulation results, we find that loss reduces the compression factor when the pulse propagates in the tapered PCF. Pulse compression is a nonlinear optical process related to pulse energy, and the existence of loss will make the pulse energy gradually diminish in the transmission process. As a result, the decrease of pulse energy leads to the decrease of the nonlinear effect, and the compression factor of the pulse is reduced. Equation (7) is the theoretical basis of pulse compression using a tapered PCF. The factor
Li
In this paper, a tapered As_{2}S_{3} PCF with four air-hole layers in a hexagonal array around the core was designed. For structural parameters Λ(0) = 2.26 μm, Λ(
This study was supported in part by the Program of the Natural Science Foundation of Hebei Province (Grant No. F2017203193), and in part by Nanjing University of Posts and Telecommunications Foundation under Grants JUH219002, JUH219007, NY215007, and NY215113. This work was supported in part by the Research Center of Optical Communications Engineering & Technology, Jiangsu Province Foundation, under Grant ZXF20170102.