Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Current Optics and Photonics 2020; 4(3): 229-237
Published online June 25, 2020 https://doi.org/10.3807/COPP.2020.4.3.229
Copyright © Optical Society of Korea.
Zhiying Liu^{*}, Xin Jiang, and Mingyu Li
Corresponding author: lzycccccc@126.com
In this study, a beam-coupling system is designed to improve the coupling efficiency of achip-integrated spectrometer when the waveguide is arranged in a linear and discrete manner. In the proposed system the beam is shaped to be anti-Gaussian, to deposit adequate energy in the edge waveguides. The beam is discretely coupled to the corresponding waveguide by a microlens array, to improve the coupling efficiency, and is compressed by a toroidal lens to match the linear discrete waveguides. Based on the findings of this study, the coupling efficiency of the spectrometer is shown to increase by a factor of 2.57. Accordingly, this study provides a reference basis for the improvement of the coupling efficiency of other similar spectrometers.
Keywords: Chip-integrated spectrometer, Integrated optics, Coupling system, Beam shaping, Microlens array
Chip-integrated spectrometers are used extensively in scientific experiments, biomedicine, and in industrial and agricultural production. They realize the transmission of light through an optical waveguide. Optical waveguides typically include one-dimensional waveguides (planar waveguides) and two-dimensional waveguides (such as channel waveguides and ridge waveguides) [1, 2]. Experts have found that when a spectrometer comprises a single-mode ridge waveguide via etching on silicon, it can realize a higher resolution at the same pixel pitch, compared to traditional spectrometers. Such a system is composed of an array of Mach-Zehnder interferometers (MZIs), with the arm-length differences among the MZI array varying linearly. When light is incident upon the waveguide, it is divided by the splitter and enters into the two arms of differing length of the MZI, then interferes by means of the coupler to form an interference pattern. The optical-path difference depends on the difference in arm lengths of the MZI. Compared to traditional spectrometers, the chipintegrated spectrometer contains multiple MZIs and splitters, and the energy of the incident light affects the number of MZIs which can work properly, the free spectral range, and the resolution of the spectrometer [3].
The transmission of the beam depends on the optical fiber, and the coupling efficiency of the fiber determines the transmission rate of the spectral information. Thus, it is important and beneficial to improve the spectral coupling efficiencies of these instruments [4-7].
The chip-integrated spectrometer and optical fiber may be associated with horizontal, grating, or direct couplings. Horizontal coupling expands the mode field of the singlemode waveguide by a spot-size converter, and changes the fiber endface to form a lens fiber for coupling [8]. Grating coupling uses a grating coupler to join the fiber and the spectrometer, but requires matching of the transverse width of the grating to the core size of the fiber [9]. Direct coupling is achieved by aligning the endface of the optical fiber with the single-mode waveguide, but the fiber needs to be in contact with the waveguide. At this point, mismatch between the fiber and single-mode waveguide leads to energy losses, as shown in Fig. 1. Coupling of the beams cannot be achieved, based on the aforementioned methods, when numerous single-mode waveguides receive light simultaneously [10, 11].
The traditional coupling method involves transmission of a Gaussian beam, such that the energy is concentrated in its central part. The chip-integrated spectrometer waveguide is a 1 ×
In this study, a beam-coupling system is designed for a chip-integrated spectrometer with a discrete linear waveguide. The system couples the beam to each waveguide, thus improving the energy and coupling efficiencies.
A beam-coupling system for an on-chip spectrometer with a discrete linear waveguide consists of beam shaping, beam spreading, and discrete-beam and linear-matching subsystems, as shown in Fig. 2. First, the Gaussian beam is reshaped by a beam-shaping subsystem, to improve the utilization rate of the edge energy. Second, the beam diameter is expanded by the beam-spreading subsystem, to match the size of the waveguide. Beam separation is then realized by the discrete-beam subsystem, which utilizes energy at the waveguide gap. Finally, the beam is compressed in the y direction by a linear-matching subsystem, to match the waveguide array. These four subsystems work together to improve the coupling efficiency of the chip-integrated spectrometer with a discrete linear waveguide.
Figure 2 shows the transmission of the beam in the
A Gaussian beam is input to the system. The energy distribution of the Gaussian beam, as shown in Fig. 3, is focused in its central part, and only a small fraction of the energy is associated with the edges. A Gaussian beam is not beneficial for coupling efficiency. The Gaussian distribution is expressed by Eq. (1)
where
Most existing studies have shaped Gaussian beams into flat-topped beams. However, compared to a flat-topped beam, an anti-Gaussian beam, with low central energy and a significant energy distribution at the edges, offers higher edge energy after longitudinal compression by the linear-matching subsystem. Therefore, the beam-shaping subsystem reshapes the Gaussian distribution into an anti-Gaussian distribution, as shown in Fig. 4.
The equation of the intensity distribution of the anti-Gaussian beam can be deduced based on Eq. (2)
where
where
substitution of Eqs. (1) and (2) into (4) leads to
Substitution of Eq. (5) into (2) allows us to deduce the intensity distribution equation of the anti-Gaussian beam. Accordingly,
By substituting different values in the range of 0-1, the
When the incident beam’s diameter does not match the width of the optical-waveguide array of the spectrometer, it is necessary to design a beam-spreading subsystem. Based on a telescopic system structure, this subsystem needs to shorten the total length. Thus, the subsystem adopts the inverted Galileo structure, as shown in Fig. 5.
The single-mode ridge waveguide of the spectrometer is formed by etching on the silicon-on-insulator (SOI) platform. However, to show the matching between the waveguide array and the discrete-beam subsystem, a single module is used to represent a single-mode ridge waveguide, as shown in Fig. 6. The optical-waveguide structure of the chip-integrated spectrometer is a linearly distributed array with a specific spacing between each waveguide. If the light is compressed directly through the toroidal lens, the light energy at the waveguide gap still will be wasted. When the waveguide’s spacing is wide, only a fraction of the light can be utilized, causing a significant reduction in coupling efficiency.
If the number of waveguides is
If the waveguide gap
In this study, the discrete-beam subsystem can reduce the (
Therefore, if the energy losses in the transmission process are neglected, the entire beam energy of the optical fiber will be used in the waveguide.
To concentrate the energy on the waveguide, the discrete-beam subsystem needs to converge the light to
The circular beam is divided into
The microlens array structure is shown in Fig. 7. A ray is converged independently by each microlens in the first array, and is diverged independently in the second microlens array, to ensure that light is emitted in parallel directions [16].
The optical-waveguide structure of the chip-integrated spectrometer is linearly distributed in a 1 ×
The design parameters of this system are listed in Table 1.
TABLE 1. System design parameters
As shown in Fig. 9, the refraction directions of rays at each position are different when the Gaussian beam is refracted through the lens. The central rays should be diverged, and the edge rays should be kept along the original direction of propagation. Therefore, the radius of lens curvature is different at each position. The farther away one is from the optical axis, the greater the radius of the curvature is. Thus, the lens surface adheres to the mathematical formulation of an aspheric surface, as expressed by Eq. (9)
Figure 10 is the structure of the beam-shaping subsystem. Referring to the Galileo structure, it should consist of a concave and a convex aspheric lens. However, the asphericity of the two lenses is exaggerated. Considering the processing of the aspheric lens, the concave lens can be divided into two other lenses.
As shown in Fig. 11, the spots in the central region are sparse, while the edge spots are dense. Figure 12 is the energy distribution of the beam-shaping subsystem. As can be observed, the central region takes up less energy, while the edges take up more. Based on Figs. 11 and 12, the emitted light from the beam-shaping subsystem has an anti-Gaussian distribution, and thus achieves the subsystem’s requirements.
As shown in Fig. 13, the beam-spreading subsystem references the inverted Galileo structure. Because the diameter of a microlens-array element in the discrete beam subsystem is (
where
Figure 15 is the structure of the microlens-array element that converts the beam’s diameter (23 μm)—the sum of the waveguide length and spacing—to the waveguide length (3 μm). It can be clearly seen in Fig. 16 that the light spot distribution is uniform. A 201 × 201 microlens array was defined with the “User Defined” command in ZEMAX. Eventually, the beam was divided into 201 × 201 smaller beams to achieve the subsystem’s requirements.
A partial enlargement of the microlens array is shown in Fig. 17. The beam is divided into individual, smaller beams to achieve the subsystem’s requirements. Given that the first microlens array concentrates the smaller beams, there is no light at the lens unit’s connection.
Substitution of the parameters listed in Table 1 into Eq. (7) yields the value of the maximum coupling efficiency of the traditional coupling method
As shown in Fig. 18, the ray is compressed in the
Splicing the four subsystems described in Section 3 yields the results shown in Fig. 20. Effectively, this is the structure of the system in the
Because the incident light of the microlens array is not perfectly parallel in the actual optical design. After the light passes through the micro lens array and the toroidal lens, each discrete spot formed is different. And the actual spots are larger than the waveguide, the energy cannot be fully utilized. The actual coupling efficiency can be calculated based on the sampling spots according to Eq. (11)
where
According to Table 2, the average actual coupling efficiency of the system is 0.352, which is 2.57 times as large as the
TABLE 2. Spot sampling data
The maximum actual coupling efficiency is 0.522, which is 3.81 times as large as the ideal efficiency of the traditional method, while the minimum actual coupling efficiency is 0.228, which is still higher than the ideal coupling efficiency of the traditional method (0.137). Therefore, it is feasible to improve beam-coupling efficiency based on the use of the beam-coupling system proposed in this study.
In this study, we design a beam-coupling system for a chip-integrated spectrometer with a discrete linear waveguide to ensure that the waveguide can receive sufficient response energy at the edges. Furthermore, the system matches light with the 201 × 1 linear waveguide array of the spectrometer. It does not need contact between the optical fiber and the chip-integrated spectrometer, which avoids wear. The system can improve the coupling efficiency by a factor of 2.57. Its structure is simple, it is easy to set up, and it does not require manual adjustments. It solves the problem of beam coupling in the case of the discrete linear waveguide of a chip-integrated spectrometer, provides a reference for beam coupling for that type of spectrometer, and is practically useful.
Current Optics and Photonics 2020; 4(3): 229-237
Published online June 25, 2020 https://doi.org/10.3807/COPP.2020.4.3.229
Copyright © Optical Society of Korea.
Zhiying Liu^{*}, Xin Jiang, and Mingyu Li
Correspondence to:lzycccccc@126.com
In this study, a beam-coupling system is designed to improve the coupling efficiency of achip-integrated spectrometer when the waveguide is arranged in a linear and discrete manner. In the proposed system the beam is shaped to be anti-Gaussian, to deposit adequate energy in the edge waveguides. The beam is discretely coupled to the corresponding waveguide by a microlens array, to improve the coupling efficiency, and is compressed by a toroidal lens to match the linear discrete waveguides. Based on the findings of this study, the coupling efficiency of the spectrometer is shown to increase by a factor of 2.57. Accordingly, this study provides a reference basis for the improvement of the coupling efficiency of other similar spectrometers.
Keywords: Chip-integrated spectrometer, Integrated optics, Coupling system, Beam shaping, Microlens array
Chip-integrated spectrometers are used extensively in scientific experiments, biomedicine, and in industrial and agricultural production. They realize the transmission of light through an optical waveguide. Optical waveguides typically include one-dimensional waveguides (planar waveguides) and two-dimensional waveguides (such as channel waveguides and ridge waveguides) [1, 2]. Experts have found that when a spectrometer comprises a single-mode ridge waveguide via etching on silicon, it can realize a higher resolution at the same pixel pitch, compared to traditional spectrometers. Such a system is composed of an array of Mach-Zehnder interferometers (MZIs), with the arm-length differences among the MZI array varying linearly. When light is incident upon the waveguide, it is divided by the splitter and enters into the two arms of differing length of the MZI, then interferes by means of the coupler to form an interference pattern. The optical-path difference depends on the difference in arm lengths of the MZI. Compared to traditional spectrometers, the chipintegrated spectrometer contains multiple MZIs and splitters, and the energy of the incident light affects the number of MZIs which can work properly, the free spectral range, and the resolution of the spectrometer [3].
The transmission of the beam depends on the optical fiber, and the coupling efficiency of the fiber determines the transmission rate of the spectral information. Thus, it is important and beneficial to improve the spectral coupling efficiencies of these instruments [4-7].
The chip-integrated spectrometer and optical fiber may be associated with horizontal, grating, or direct couplings. Horizontal coupling expands the mode field of the singlemode waveguide by a spot-size converter, and changes the fiber endface to form a lens fiber for coupling [8]. Grating coupling uses a grating coupler to join the fiber and the spectrometer, but requires matching of the transverse width of the grating to the core size of the fiber [9]. Direct coupling is achieved by aligning the endface of the optical fiber with the single-mode waveguide, but the fiber needs to be in contact with the waveguide. At this point, mismatch between the fiber and single-mode waveguide leads to energy losses, as shown in Fig. 1. Coupling of the beams cannot be achieved, based on the aforementioned methods, when numerous single-mode waveguides receive light simultaneously [10, 11].
The traditional coupling method involves transmission of a Gaussian beam, such that the energy is concentrated in its central part. The chip-integrated spectrometer waveguide is a 1 ×
In this study, a beam-coupling system is designed for a chip-integrated spectrometer with a discrete linear waveguide. The system couples the beam to each waveguide, thus improving the energy and coupling efficiencies.
A beam-coupling system for an on-chip spectrometer with a discrete linear waveguide consists of beam shaping, beam spreading, and discrete-beam and linear-matching subsystems, as shown in Fig. 2. First, the Gaussian beam is reshaped by a beam-shaping subsystem, to improve the utilization rate of the edge energy. Second, the beam diameter is expanded by the beam-spreading subsystem, to match the size of the waveguide. Beam separation is then realized by the discrete-beam subsystem, which utilizes energy at the waveguide gap. Finally, the beam is compressed in the y direction by a linear-matching subsystem, to match the waveguide array. These four subsystems work together to improve the coupling efficiency of the chip-integrated spectrometer with a discrete linear waveguide.
Figure 2 shows the transmission of the beam in the
A Gaussian beam is input to the system. The energy distribution of the Gaussian beam, as shown in Fig. 3, is focused in its central part, and only a small fraction of the energy is associated with the edges. A Gaussian beam is not beneficial for coupling efficiency. The Gaussian distribution is expressed by Eq. (1)
where
Most existing studies have shaped Gaussian beams into flat-topped beams. However, compared to a flat-topped beam, an anti-Gaussian beam, with low central energy and a significant energy distribution at the edges, offers higher edge energy after longitudinal compression by the linear-matching subsystem. Therefore, the beam-shaping subsystem reshapes the Gaussian distribution into an anti-Gaussian distribution, as shown in Fig. 4.
The equation of the intensity distribution of the anti-Gaussian beam can be deduced based on Eq. (2)
where
where
substitution of Eqs. (1) and (2) into (4) leads to
Substitution of Eq. (5) into (2) allows us to deduce the intensity distribution equation of the anti-Gaussian beam. Accordingly,
By substituting different values in the range of 0-1, the
When the incident beam’s diameter does not match the width of the optical-waveguide array of the spectrometer, it is necessary to design a beam-spreading subsystem. Based on a telescopic system structure, this subsystem needs to shorten the total length. Thus, the subsystem adopts the inverted Galileo structure, as shown in Fig. 5.
The single-mode ridge waveguide of the spectrometer is formed by etching on the silicon-on-insulator (SOI) platform. However, to show the matching between the waveguide array and the discrete-beam subsystem, a single module is used to represent a single-mode ridge waveguide, as shown in Fig. 6. The optical-waveguide structure of the chip-integrated spectrometer is a linearly distributed array with a specific spacing between each waveguide. If the light is compressed directly through the toroidal lens, the light energy at the waveguide gap still will be wasted. When the waveguide’s spacing is wide, only a fraction of the light can be utilized, causing a significant reduction in coupling efficiency.
If the number of waveguides is
If the waveguide gap
In this study, the discrete-beam subsystem can reduce the (
Therefore, if the energy losses in the transmission process are neglected, the entire beam energy of the optical fiber will be used in the waveguide.
To concentrate the energy on the waveguide, the discrete-beam subsystem needs to converge the light to
The circular beam is divided into
The microlens array structure is shown in Fig. 7. A ray is converged independently by each microlens in the first array, and is diverged independently in the second microlens array, to ensure that light is emitted in parallel directions [16].
The optical-waveguide structure of the chip-integrated spectrometer is linearly distributed in a 1 ×
The design parameters of this system are listed in Table 1.
As shown in Fig. 9, the refraction directions of rays at each position are different when the Gaussian beam is refracted through the lens. The central rays should be diverged, and the edge rays should be kept along the original direction of propagation. Therefore, the radius of lens curvature is different at each position. The farther away one is from the optical axis, the greater the radius of the curvature is. Thus, the lens surface adheres to the mathematical formulation of an aspheric surface, as expressed by Eq. (9)
Figure 10 is the structure of the beam-shaping subsystem. Referring to the Galileo structure, it should consist of a concave and a convex aspheric lens. However, the asphericity of the two lenses is exaggerated. Considering the processing of the aspheric lens, the concave lens can be divided into two other lenses.
As shown in Fig. 11, the spots in the central region are sparse, while the edge spots are dense. Figure 12 is the energy distribution of the beam-shaping subsystem. As can be observed, the central region takes up less energy, while the edges take up more. Based on Figs. 11 and 12, the emitted light from the beam-shaping subsystem has an anti-Gaussian distribution, and thus achieves the subsystem’s requirements.
As shown in Fig. 13, the beam-spreading subsystem references the inverted Galileo structure. Because the diameter of a microlens-array element in the discrete beam subsystem is (
where
Figure 15 is the structure of the microlens-array element that converts the beam’s diameter (23 μm)—the sum of the waveguide length and spacing—to the waveguide length (3 μm). It can be clearly seen in Fig. 16 that the light spot distribution is uniform. A 201 × 201 microlens array was defined with the “User Defined” command in ZEMAX. Eventually, the beam was divided into 201 × 201 smaller beams to achieve the subsystem’s requirements.
A partial enlargement of the microlens array is shown in Fig. 17. The beam is divided into individual, smaller beams to achieve the subsystem’s requirements. Given that the first microlens array concentrates the smaller beams, there is no light at the lens unit’s connection.
Substitution of the parameters listed in Table 1 into Eq. (7) yields the value of the maximum coupling efficiency of the traditional coupling method
As shown in Fig. 18, the ray is compressed in the
Splicing the four subsystems described in Section 3 yields the results shown in Fig. 20. Effectively, this is the structure of the system in the
Because the incident light of the microlens array is not perfectly parallel in the actual optical design. After the light passes through the micro lens array and the toroidal lens, each discrete spot formed is different. And the actual spots are larger than the waveguide, the energy cannot be fully utilized. The actual coupling efficiency can be calculated based on the sampling spots according to Eq. (11)
where
According to Table 2, the average actual coupling efficiency of the system is 0.352, which is 2.57 times as large as the
The maximum actual coupling efficiency is 0.522, which is 3.81 times as large as the ideal efficiency of the traditional method, while the minimum actual coupling efficiency is 0.228, which is still higher than the ideal coupling efficiency of the traditional method (0.137). Therefore, it is feasible to improve beam-coupling efficiency based on the use of the beam-coupling system proposed in this study.
In this study, we design a beam-coupling system for a chip-integrated spectrometer with a discrete linear waveguide to ensure that the waveguide can receive sufficient response energy at the edges. Furthermore, the system matches light with the 201 × 1 linear waveguide array of the spectrometer. It does not need contact between the optical fiber and the chip-integrated spectrometer, which avoids wear. The system can improve the coupling efficiency by a factor of 2.57. Its structure is simple, it is easy to set up, and it does not require manual adjustments. It solves the problem of beam coupling in the case of the discrete linear waveguide of a chip-integrated spectrometer, provides a reference for beam coupling for that type of spectrometer, and is practically useful.