검색
검색 팝업 닫기

Ex) Article Title, Author, Keywords

Article

Split Viewer

Research Paper

Curr. Opt. Photon. 2024; 8(1): 56-64

Published online February 25, 2024 https://doi.org/10.3807/COPP.2024.8.1.56

Copyright © Optical Society of Korea.

Design and Analysis of Multi Beam Space Optical Mixer

Lian Guan, Zheng Yang

School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun, Jilin 130022, China

Corresponding author: *747421565@qq.com, ORCID 0000-0003-2407-9887

Received: August 9, 2023; Revised: November 20, 2023; Accepted: November 27, 2023

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.

In response to the current situation where general methods cannot effectively compensate for the phase delay of ordinary optical mixers, a multi-layer spatial beam-splitting optical mixer is designed using total reflection triangular prisms and polarization beam splittings. The phase delay is generated by the wave plate, and the mixer can use the existing parallel plates in the structure to individually compensate for the phase of the four output beams. A mixer model is established based on the structure, and the influence of the position and orientation of the optical components on the phase delay is analyzed. The feasibility of the phase compensation method is simulated and analyzed. The results show that the mixer can effectively compensate for the four outputs of the optical mixer over a wide range. The mixer has a compact structure, good performance, and significant advantages in phase error control, production, and tuning, making it suitable for free-space coherent optical communication systems.

Keywords: Coherent optical communication, Multi-beam splitting, Phase compensation, Spatial optical mixer

OCIS codes: (060.1660) Coherent communications; (060.2605) Free-space optical communication; (060.4510) Optical communications; (200.2605) Free-space optical communication

Free space coherent optical communication has emerged as an essential means of improving receiver sensitivity, achieving long-distance, high-capacity, and high bit-rate laser communication [1]. In coherent optical communication terminals, the optical mixer is a key component that divides and combines the beams of signal light and local oscillator light. An optical mixer manufactured based on the Costas phase-locked loop principle generates four mixed beams with relative phase shifts of 0°, 90°, 180°, and 270°, which facilitates the processing of subsequent coherent detection information. Its performance has a significant impact on subsequent coherent reception [2].

The current mature design scheme of spatial light mixers mainly achieves beam splitting and coupling through beam splitters while achieving phase differences between output beams using wave plates [3, 4]. While this approach utilizes fewer components and has a simpler structure, it also has limitations. For instance, compensation must be made at the expense of parameters like splitting ratio to address phase delay errors caused by processing, assembly, and adjustment.

Several researchers have proposed methods for compensating phase delay in rotating optical mixers. Zheng et al. [5] suggested compensating for phase delay in the crystal of a rotating optical mixer, whereas Zhao [6] developed a simulation of the relationship curve between the rotation angle of the 1/4 wave plate and the compensation phase, as well as the relationship with the I and Q path splitting ratio, although they did not provide any measures to adjust the I and Q path splitting ratio. Cao et al. [7] proposed adding a 1/2 wave plate to the signal light branch to compensate for changes in the I and Q path splitting ratio caused by rotating the 1/4 wave plate to address phase differences. These solutions, however, still have limited compensation ranges. Meanwhile, Ke and Han [8] proposed a crystal-type optical mixer, but the required wave plate components are difficult to produce with the current processing size and accuracy, and it is also hard to compensate for phase delay errors caused by installation and adjustment. Although Du et al. [9] designed a new symmetrical optical mixer, its structure requires high processing requirements and lacks a proposed compensation method.

This article addresses the challenges of compensating optical mixers and limited compensation ranges. A multibeam spatial optical mixer was designed, which utilizes its structural components to compensate for phase delay in a large range. We established a model based on the optical mixer and analyzed the impact of the position and orientation of the optical components on the phase delay. We also conducted simulations and analyses to assess the feasibility of the phase compensation process.

2.1. Structural Design

Firstly, the designed optical mixer is introduced in terms of component composition and position. The optical mixer designed in this article is shown in Fig. 1, which can be mainly divided into:

Figure 1.Structure diagram of multi-beam space optical mixer.

(1) A beam splitting and combining part composed of four PBS with a total reflection triangular crystal, where PBS1 and PBS2 act as signal light and local oscillator light for beam splitting, and PBS3 and PBS4 recombine the already split light;

(2) The part where several wave plates were located between PBS1 and PBS2 generates phase delay, including three 1/2 wave plates and one 1/4 wave plate. The 1/2 wave plate 1 acts to change the direction of polarized light, while the 1/4 wave plate and 1/2 wave plates 2 and 3 act to introduce a phase difference of 90° and 180°, respectively;

(3) The rest consists of several parallel plates forming the optical path compensation and phase delay compensation parts. Among them, parallel plates 1–3 are located in the middle of PBS1 and mainly compensate for the optical path difference generated by the wave plate. Parallel plates 4–9 are located between PBS2, PBS3, and PBS4 and mainly serve to compensate for the optical path difference that PBS generates. These parallel plates can rotate left and right with the geometric center in the vertical direction as the axis when needed. At the same time, the above parallel plates are also an indispensable part of this mixer to achieve separate and large-scale phase compensation between the four output lights.

Secondly, the schematic diagram of the fast axis direction of the wave plate included in the mixer is shown in Fig. 2. The fast axis directions of each wave plate are parallel to the front surface of the wave plate, so that the direction of light propagation is in the positive z-axis direction, horizontally to the right is in the positive x-axis direction, and vertically to the top is in the positive y-axis direction. Therefore, the angle between the fast axis direction of 1/2 wave plate 1 and the x-axis is 22.5°, and the fast axis direction of 1/4 wave plate is in the positive x-axis direction. The fast axis direction of 1/2 wave plate 2 is along the negative y-axis direction, and the fast axis direction of 1/2 wave plate 3 is along the positive y-axis direction.

Figure 2.Schematic diagram of the optical axis direction of the wave plates.

Finally, the schematic diagram of the optical circuit of the optical mixer is shown in Fig. 3. The signal and the local lights are both linearly polarized at a 45° angle, emitted from the bottom side of PBS1. When passing through PBS1, the horizontal component is reflected on the first reflecting surface, and the vertical component undergoes total reflection on the rear reflecting surface. When the signal light and the local oscillator light pass through the wave plate between PBS1 and PBS2, the vibration direction and phase change differently, and then further beam splitting through PBS2. The horizontal component of the signal light passes through 1/2 wave plate 1, 1/4 wave plate, and 1/2 wave plate 2 in sequence. The signal light’s vertical components pass through 1/2 wave plate 1, 1/4 wave plate, and parallel plate 3 in sequence. The horizontal components of the local oscillator light pass through 1/2 wave plate 1, parallel plate 1, and parallel plate 2 in sequence. The vertical components of the local oscillator light pass through 1/2 wave plate 1, parallel plate 1, and 1/2 wave plate 3 in sequence. Subsequently, the horizontal components of the local and signal light components that emit changes in phase and vibration direction are reflected on the first reflecting surface, while the vertical components are reflected on the rear reflecting surface. Then, after passing through the optical path compensation part between PBS2 and PBS3–4, the beam is recombined between PBS3 and 4. Finally, an output beam with a phase difference of 0°, 90°, 180°, and 270° between the signal light and the local oscillator light is generated.

Figure 3.Schematic diagram of the optical path of a multi-beam space optical mixer.

All parallel plates in the structure are designed to compensate for optical path differences, and their thickness can be calculated based on the optical path differences generated by the compensated components. The first parallel plate compensates for the optical path of the 1/4 wave plate. The second and third parallel plates compensate for the optical path of the two 1/2 wave plates. The remaining parallel plates are used to compensate for the optical path generated by all PBS.

2.2. Formula Derivation

If the incident light is both 45° linearly polarized light, the signal light ES and the local light EL can be represented as

ES=22ESx,y,z11expiϕt,
EL=22ELOx,y,z11expiψ.

Under ideal conditions, the transmission matrix and reflection matrix of PBS are expressed as

T=0001,
R=1000.

The matrix representation of a quarter wave plate is

Q=100i.

The matrix representations of three 1/2 wave plates are

H1=221111,
H2=1001,
H3=1001.

The final two PBS reflect S- and P-waves respectively

S=1000,
P=0001.

The output light can be expressed in the multiplication form of the Jones matrix as

E0=S×R×Q×H1×T×ES+H3×H1×T×EL,
E90=P×T×Q×H1×T×ES+H3×H1×T×EL,
E180=S×R×H2×Q×H1×R×ES+H1×R×EL,
E270=P×T×H2×Q×H1×R×ES+H1×R×EL.

The calculation result is

E0=12ESx,y,z10expiϕt+12ELOx,y,z10expiψ,
E90=i2ESx,y,z 0 1expiϕt+12ELOx,y,z 0 1expiψ=12ESx,y,z 0 1expiϕtexp(i3π2)+12ELOx,y,z 0 1expiψ,
E180=12ESx,y,z 1 0expiϕt+12ELOx,y,z 1 0expiψ=12ESx,y,z 1 0expiϕtexp(iπ)+12ELOx,y,z 1 0expiψ,
E270=i2ESx,y,z 0 1expiϕt+12ELOx,y,z 0 1expiψ=12ESx,y,z 0 1expiϕtexp(iπ2)+12ELOx,y,z 0 1expiψ,
δ0=ψϕt,
δ90=ψϕt3π2,
δ180=ψϕtπ,
δ270=ψϕtπ2.

Suppose the phase of the signal light is subtracted from the phase of the local oscillator light as the reference. In that case, the phase delays of the signal light and the local oscillator light in the four output lights are 0°, 90°, 180°, and 270°, respectively, and within the same cycle.

The positions and orientations of various components in the design structure can significantly impact on phase and error analysis. In addition to errors resulting from component processing, incorrect positioning, and posture during component assembly can also lead to significant errors that must be analyzed.

To illustrate this point, we first consider the influence of parallel plates. Under ideal conditions of complete perpendicularity to the incident light, the optical path difference is consistent with the compensated wave plate and the optical path generated by PBS. However, any deviation from this ideal position during installation can cause a phase change. Figure 4 illustrates the schematic diagram of parallel plates. By establishing a coordinate system based on the surface of the incident component, we can approximate the change in component position and orientation as a deflection of the incident light angle. The magnitude of the deflection angle can then be represented by the azimuth and pitch angles. It is evident that the phase change is only related to the pitch angle and not the azimuth angle.

Figure 4.Schematic diagram of the influence of parallel plate position and posture on phase.

The phase difference generated by parallel plates is

Δp=2πλnpdpcosθn0dp.

In the formula, dp is the thickness of the parallel plate, np is the refractive index of the parallel plate, and θ is the incident angle of the parallel plate.

Figure 5 shows the error calculated with MATLAB simulation. As the material of the selected parallel plate is not fixed, its thickness can change with the refractive index. Therefore, parallel plates with a refractive index of approximately 1.5 and thicknesses ranging from 2 mm to 10 mm were selected for simulation calculations. The results show that errors generated by several parallel plates vary proportionally with the thickness within a deviation range of 1° in pitch angles. Specifically, the phase delay for the 2.5 mm parallel plate is within 2.32°, the phase delay for the 5 mm parallel plate is within 4.64°, and the phase delay for the 10 mm parallel plate is within 9.28°.

Figure 5.Phase variation with pitch angle and thickness of the parallel plate.

The next component we analyzed is the wave plate. During the adjustment process, the surface of the crystal is often not completely perpendicular to the direction of light propagation, which is similar to that of a parallel flat plate. To analyze this effect, we use the crystal surface as the coordinate system equivalent to a deflection of the incident angle, as shown in Fig. 6.

Figure 6.Schematic diagram of crystal birefringence.

It can be obtained from the Fresnel formula and the law of refraction

n1sinθ1=nosinθo=ne(θe)sinθe,
ne(θe)=no2ne2no2sin2θe +ne2cos2θe .

In the formula, n1, no, and ne represent the refractive indices of air and the refractive indices of the medium containing o and e light, respectively. θ1 is the incident angle, while θo and θe denote the refracted angles of o and e light, respectively. Additionally, θe represents the angle between the e-light and the fast axis direction.

If the length of the crystal is d, then the phase change generated by o light and e light in the crystal is ∆o and ∆e, the phase difference ∆ generated by the wave plate is

Δ=Δoe=2πλno dcosθo ne dcosθe .

Figure 7(a) shows the phase change of a 1/4 wave plate, while Fig. 7(b) shows the phase change of a 1/2 wave plate. The simulation results shows that slight angle position deviations of the wave plate due to birefringence have a relatively minor impact on phase variation within 1°, which can be almost ignored. However, since wave plate deflection has a similar effect on the optical path as that of a parallel plate, its value is almost equal to the phase difference generated by parallel plate deflection when the thickness and refractive index are similar.

Figure 7.Schematic diagram of the influence of wave plate position and posture on phase. (a) 1/4 wave plate phase delay, (b) 1/2 wave plate phase delay.

During the processing of wave plates, simulation has also been conducted due to the high possibility that the optical axis direction is not parallel to the crystal surface. Figure 8 shows the schematic diagram of phase delay when the optical axis elevation angle is 89° and the azimuth angle is 0°. As shown in Fig. 8, the phase delay of the wave plate also has a small change. Specifically, when the light is incident perpendicular to the crystal surface, the phase delay of the 1/4 wave plate is about 0.02° different from the phase delay when the optical axis is parallel to the crystal surface, while the phase delay of the 1/2 wave plate is about 0.05° different from the phase delay when the optical axis is parallel to the crystal surface.

Figure 8.Schematic diagram of phase delay with optical axis angle error. (a) 1/4 wave plate phase delay, (b) 1/2 wave plate phase delay.

When a parallel plate rotates, the energy of the light also changes. The vibration direction of the light is different from the rotation direction of the parallel plate, and the amplitude change of the light is also different. The amplitude of light with respect to angle can be calculated using the Fresnel formula:

ts=2sinθ2cosθ1sin(θ1+θ2),
tp=2sinθ2cosθ1sin(θ1+θ2)cos(θ1θ2).

In the formula, ts and tp are the projected amplitude coefficients of S- and P-waves, and θ1 and θ2 are the incident angle and refractive angle, respectively.

Figure 9 shows the image of the attenuation ratio of transmitted light amplitude with incident angle when S- and P-waves pass through a parallel plate. It can be seen from the figure that the influence of the rotation angle of the parallel plate within 6° on the amplitude of S- and P-waves is less than 0.2%, which can be almost ignored.

Figure 9.Attenuation ratio of transmitted light amplitude of S-wave and P-wave with incident angle.

The phase error generated by parallel plates is uniform, and can be compensated using the same approach as for parallel plate deflection. As the signal light and local oscillator light in the optical mixer are initially separated before final coupling, the phase delay in this branch can be adjusted by rotating a separate parallel plate in both the signal and local oscillator light branches simultaneously. It changes the optical path difference between the signal and local oscillator light, allowing for phase compensation.

Figure 10(a) shows the phase delay generated by parallel plates as a function of the rotation angle of the parallel plates between 0–6° and the thickness of the parallel plates between 2–10 mm; Fig. 10(b) shows the corresponding curve of the phase compensation range with rotation angle in Fig. 10(a) for the fixed parallel plate thickness used in the structure of this article. By rotating the parallel plate by 0.1° within this range, the phase change variable is less than 5°, which meets the phase requirements of the phase-locked loop. The smaller the rotation angle of a parallel plate, the higher the phase accuracy that can be controlled by rotating the same angle. When the rotation angle is within 2°, the phase delay difference that can be controlled for each 0.1° rotation is within 1°. With minor errors and higher component operation levels, the control accuracy of the mixer can be further improved. The parallel plates with thicknesses of 2.612 mm, 5 mm, and 5.22 mm used in this article for phase compensation can compensate for a maximum range of 83.73°, 167.47°, and 174.84° within a range of 6°, respectively.

Figure 10.Schematic diagram of phase compensation range for parallel flat plates. (a) Phase delay variation with parallel plate thickness and incident angle, (b) curve of phase delay variation with pitch angle for a given thickness of parallel plate.

Because parallel plates were initially added to this structure to compensate for the optical path difference between the wave plate and PBS, their branch for phase compensation is consistent with the compensated component, except for the opposite direction of the phase change. If the compensation range of the compensation plate exceeds the error generated by its compensation component, complete compensation for the phase delay can be achieved. Table 1 lists all components compensated by parallel plates and their corresponding phase compensation ranges at a pitch angle 6°. Table 1 indicates that the compensation range of the parallel plates is significantly greater than errors resulting from incorrect positioning and attitude, as well as phase delays caused by beam splitting film and processing errors of the polarization beam splitter. Therefore, the parallel plates can effectively compensate for these effects.

TABLE 1 Parallel plate phase compensation range table

ComponentsCompensated ComponentPhase Compensation Branch and DirectionElement Reference Thickness (mm)Reference Compensation Range (°)
E(0°)E(90°)E(180°)E(270°)
Parallel Plate 11/4 Wave Plate2.61283.73
Parallel Plate 21/2 Wave Plate 2--5.22174.84
Parallel Plate 31/2 Wave Plate 3--5.22174.84
Parallel Plate 4PBS1----10-
Parallel Plate 5PBS2----10-
Parallel Plate 6PBS3---5167.47
Parallel Plate 7PBS3---5167.47
Parallel Plate 8PBS4---5167.47
Parallel Plate 9PBS4---5167.47

Firstly, in the initial stage of structural design, this paper selects a multi-level structure to avoid highly degenerate structures. This selection aims to effectively separate the beams of each branch, enabling independent adjustment of each branch.

Secondly, previous studies by Zhao [6] proposed the rotation 4/λ wave plate method, which can only compensate for phase between I/Q paths (I: 0° and 180°, Q: 90° and 270°) with a splitting ratio ranging from 0.57 to 1.75. Cao et al. [7] compensation methods added splitting ratio compensation to [6], with a phase compensation range between I/Q channels of −14° to 29°, requiring pre-calculation. Ke and Han [8] compensation method is essentially the same as [7], with similar phase and spectral ratio compensation ranges. In contrast, the structure proposed in this article is relatively symmetrical, where the splitting ratio of each output light is ideally 1:1. The phase compensation is not limited to between I/Q branches but can be continuously and freely compensated for all four output lights. During the phase compensation process, calculations based on the Fresnel refraction amplitude formula indicate that the amplitude reduction of each polarized light within a 6-degree rotation of the parallel plate is less than 0.2%, and the changes in light intensity and spectral ratio can be almost ignored. The compensation range is also much larger than the 45° compensation range of [7] and others, reaching over 300°, making it more practical and adaptable for practical use.

Additionally, from a processing and production perspective, the proposed structure in this article consists mainly of regular cubes or rectangles, without separating components that do not require compensation. It allows most processed crystals and parallel plates to be directly attached to the bottom plate without installation and adjustment steps, and simplifies the production process to a certain extent. The wide range of phase compensation in the structure of this article means that the accuracy requirements for processing and producing some of the components can be reduced, and more cost-effective component materials can be selected, significantly reducing the production cost of optical mixers. The mixer designed in this article also has great advantages for the future trend of commercializing and generalizing of spatial coherent optical communication.

This article proposes a multi-beam spatial light mixer that utilizes a parallel flat plate to compensate for phase delay, overcoming the challenges associated with conventional optical mixers in compensating for phase delays resulting from machining errors, tuning, and other factors. This compensation method makes complete compensation for the phase delay almost achievable. Especially, it can achieve separate compensation for each of the four output lights which was not possible in the past.

The compensation method and scope were simulated and calculated. The overall phase adjustment range of the optical mixer is −83.73° to 0°. The phase compensation range of the branch is 0° to −342.31°; The phase compensation range of the branch is −167.47° to −174.84°; The phase compensation range of the branch is −174.84° to −167.47°; The phase compensation range of the branch is −342.31° to 0°, and the output light compensation range of each channel is much higher than the previously achievable 45°. The position and attitude errors of the structure were analyzed; The error caused by a 5 mm deflection of the parallel plate within a 1° range is less than 4.64°, while the phase delay errors generated by a 1/2 wave plate and a 1/4 wave plate deflection within 1° of the optical axis direction are less than 0.05° and 0.02°, respectively. The compensation range is far greater than various error ranges.

The results show that this structure has great potential in multi branch phase compensation and reducing machining accuracy and cost. Meanwhile, this structure has significant innovation potential and can be effectively used in spatial coherent optical communication applications.

Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.

  1. C. J. Wu, C. X. Yan, and Z. L. Gao, “Overview of space laser communications,” Chin. Opt. 6, 670-680 (2013).
    CrossRef
  2. A. Banerjee and B. N. Biswas, “BPSK homodyne receivers based on modified balanced optical phase-locked loop,” Optik 124, 994-997 (2013).
    CrossRef
  3. Y. Zhou, L. Y. Wan, Y. N. Zhi, Z. Luan, J. F. Sun, and L. R. Liu, “Polarization-splitting 2×4 90° free-space optical hybrid with phase compensation,” Acta Opt. Sin. 29, 3291 (2009).
    CrossRef
  4. J. Li, M. R. Billah, P. C. Schindler, M. Lauermann, S. Schuele, S. Hengsbach, U. Hollenbach, J. Mohr, C. Koos, W. Freude, and J. Leuthold, “Four-in-one interferometer for coherent and self-coherent detection,” Opt. Express 21, 13293-13304 (2013).
    Pubmed CrossRef
  5. Y. Zheng, H. Jiang, Y. Hu, S. Tong, and Z. Li, “Opto-mechanical structure design of the space optical hybrid,” in Proc. 2012 International Conference on Optoelectronics and Microelectronics (Changchun, China, Aug. 23-25, 2012), pp. 303-307.
    KoreaMed CrossRef
  6. Y. Zhao, “Study on the optical system of space coherent optical communication terminal,” Ph. D. dissertation, Xi'an Institute of Optics and Precision Mechanics Chinese Academy of Science, China (2015).
  7. H.-S. Cao, L. Jiang, P. Zhang, H. Nan, S.-F. Tong, and L.-Z. Zhang, “Power ratio adjustment and 90° phase difference compensation method of space optical hybrid,” Acta Photonica Sin. 46, 0606001 (2017).
    CrossRef
  8. X. Ke and J. Han, “Analysis and design of 2×4 90° crystal space optical hybrid for coherent optical communication,” Am. J. Opt. Photonics 8, 33-39 (2020).
    CrossRef
  9. Y. Du, Y. Zheng, S. Xie, and X. Bo, “Mathematical modelling of a crystal spatial light mixer,” J. Opt. 22, 025704 (2020).
    CrossRef

Article

Research Paper

Curr. Opt. Photon. 2024; 8(1): 56-64

Published online February 25, 2024 https://doi.org/10.3807/COPP.2024.8.1.56

Copyright © Optical Society of Korea.

Design and Analysis of Multi Beam Space Optical Mixer

Lian Guan, Zheng Yang

School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun, Jilin 130022, China

Correspondence to:*747421565@qq.com, ORCID 0000-0003-2407-9887

Received: August 9, 2023; Revised: November 20, 2023; Accepted: November 27, 2023

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.

Abstract

In response to the current situation where general methods cannot effectively compensate for the phase delay of ordinary optical mixers, a multi-layer spatial beam-splitting optical mixer is designed using total reflection triangular prisms and polarization beam splittings. The phase delay is generated by the wave plate, and the mixer can use the existing parallel plates in the structure to individually compensate for the phase of the four output beams. A mixer model is established based on the structure, and the influence of the position and orientation of the optical components on the phase delay is analyzed. The feasibility of the phase compensation method is simulated and analyzed. The results show that the mixer can effectively compensate for the four outputs of the optical mixer over a wide range. The mixer has a compact structure, good performance, and significant advantages in phase error control, production, and tuning, making it suitable for free-space coherent optical communication systems.

Keywords: Coherent optical communication, Multi-beam splitting, Phase compensation, Spatial optical mixer

I. INTRODUCTION

Free space coherent optical communication has emerged as an essential means of improving receiver sensitivity, achieving long-distance, high-capacity, and high bit-rate laser communication [1]. In coherent optical communication terminals, the optical mixer is a key component that divides and combines the beams of signal light and local oscillator light. An optical mixer manufactured based on the Costas phase-locked loop principle generates four mixed beams with relative phase shifts of 0°, 90°, 180°, and 270°, which facilitates the processing of subsequent coherent detection information. Its performance has a significant impact on subsequent coherent reception [2].

The current mature design scheme of spatial light mixers mainly achieves beam splitting and coupling through beam splitters while achieving phase differences between output beams using wave plates [3, 4]. While this approach utilizes fewer components and has a simpler structure, it also has limitations. For instance, compensation must be made at the expense of parameters like splitting ratio to address phase delay errors caused by processing, assembly, and adjustment.

Several researchers have proposed methods for compensating phase delay in rotating optical mixers. Zheng et al. [5] suggested compensating for phase delay in the crystal of a rotating optical mixer, whereas Zhao [6] developed a simulation of the relationship curve between the rotation angle of the 1/4 wave plate and the compensation phase, as well as the relationship with the I and Q path splitting ratio, although they did not provide any measures to adjust the I and Q path splitting ratio. Cao et al. [7] proposed adding a 1/2 wave plate to the signal light branch to compensate for changes in the I and Q path splitting ratio caused by rotating the 1/4 wave plate to address phase differences. These solutions, however, still have limited compensation ranges. Meanwhile, Ke and Han [8] proposed a crystal-type optical mixer, but the required wave plate components are difficult to produce with the current processing size and accuracy, and it is also hard to compensate for phase delay errors caused by installation and adjustment. Although Du et al. [9] designed a new symmetrical optical mixer, its structure requires high processing requirements and lacks a proposed compensation method.

This article addresses the challenges of compensating optical mixers and limited compensation ranges. A multibeam spatial optical mixer was designed, which utilizes its structural components to compensate for phase delay in a large range. We established a model based on the optical mixer and analyzed the impact of the position and orientation of the optical components on the phase delay. We also conducted simulations and analyses to assess the feasibility of the phase compensation process.

II. MODEL ESTABLISHMENT

2.1. Structural Design

Firstly, the designed optical mixer is introduced in terms of component composition and position. The optical mixer designed in this article is shown in Fig. 1, which can be mainly divided into:

Figure 1. Structure diagram of multi-beam space optical mixer.

(1) A beam splitting and combining part composed of four PBS with a total reflection triangular crystal, where PBS1 and PBS2 act as signal light and local oscillator light for beam splitting, and PBS3 and PBS4 recombine the already split light;

(2) The part where several wave plates were located between PBS1 and PBS2 generates phase delay, including three 1/2 wave plates and one 1/4 wave plate. The 1/2 wave plate 1 acts to change the direction of polarized light, while the 1/4 wave plate and 1/2 wave plates 2 and 3 act to introduce a phase difference of 90° and 180°, respectively;

(3) The rest consists of several parallel plates forming the optical path compensation and phase delay compensation parts. Among them, parallel plates 1–3 are located in the middle of PBS1 and mainly compensate for the optical path difference generated by the wave plate. Parallel plates 4–9 are located between PBS2, PBS3, and PBS4 and mainly serve to compensate for the optical path difference that PBS generates. These parallel plates can rotate left and right with the geometric center in the vertical direction as the axis when needed. At the same time, the above parallel plates are also an indispensable part of this mixer to achieve separate and large-scale phase compensation between the four output lights.

Secondly, the schematic diagram of the fast axis direction of the wave plate included in the mixer is shown in Fig. 2. The fast axis directions of each wave plate are parallel to the front surface of the wave plate, so that the direction of light propagation is in the positive z-axis direction, horizontally to the right is in the positive x-axis direction, and vertically to the top is in the positive y-axis direction. Therefore, the angle between the fast axis direction of 1/2 wave plate 1 and the x-axis is 22.5°, and the fast axis direction of 1/4 wave plate is in the positive x-axis direction. The fast axis direction of 1/2 wave plate 2 is along the negative y-axis direction, and the fast axis direction of 1/2 wave plate 3 is along the positive y-axis direction.

Figure 2. Schematic diagram of the optical axis direction of the wave plates.

Finally, the schematic diagram of the optical circuit of the optical mixer is shown in Fig. 3. The signal and the local lights are both linearly polarized at a 45° angle, emitted from the bottom side of PBS1. When passing through PBS1, the horizontal component is reflected on the first reflecting surface, and the vertical component undergoes total reflection on the rear reflecting surface. When the signal light and the local oscillator light pass through the wave plate between PBS1 and PBS2, the vibration direction and phase change differently, and then further beam splitting through PBS2. The horizontal component of the signal light passes through 1/2 wave plate 1, 1/4 wave plate, and 1/2 wave plate 2 in sequence. The signal light’s vertical components pass through 1/2 wave plate 1, 1/4 wave plate, and parallel plate 3 in sequence. The horizontal components of the local oscillator light pass through 1/2 wave plate 1, parallel plate 1, and parallel plate 2 in sequence. The vertical components of the local oscillator light pass through 1/2 wave plate 1, parallel plate 1, and 1/2 wave plate 3 in sequence. Subsequently, the horizontal components of the local and signal light components that emit changes in phase and vibration direction are reflected on the first reflecting surface, while the vertical components are reflected on the rear reflecting surface. Then, after passing through the optical path compensation part between PBS2 and PBS3–4, the beam is recombined between PBS3 and 4. Finally, an output beam with a phase difference of 0°, 90°, 180°, and 270° between the signal light and the local oscillator light is generated.

Figure 3. Schematic diagram of the optical path of a multi-beam space optical mixer.

All parallel plates in the structure are designed to compensate for optical path differences, and their thickness can be calculated based on the optical path differences generated by the compensated components. The first parallel plate compensates for the optical path of the 1/4 wave plate. The second and third parallel plates compensate for the optical path of the two 1/2 wave plates. The remaining parallel plates are used to compensate for the optical path generated by all PBS.

2.2. Formula Derivation

If the incident light is both 45° linearly polarized light, the signal light ES and the local light EL can be represented as

ES=22ESx,y,z11expiϕt,
EL=22ELOx,y,z11expiψ.

Under ideal conditions, the transmission matrix and reflection matrix of PBS are expressed as

T=0001,
R=1000.

The matrix representation of a quarter wave plate is

Q=100i.

The matrix representations of three 1/2 wave plates are

H1=221111,
H2=1001,
H3=1001.

The final two PBS reflect S- and P-waves respectively

S=1000,
P=0001.

The output light can be expressed in the multiplication form of the Jones matrix as

E0=S×R×Q×H1×T×ES+H3×H1×T×EL,
E90=P×T×Q×H1×T×ES+H3×H1×T×EL,
E180=S×R×H2×Q×H1×R×ES+H1×R×EL,
E270=P×T×H2×Q×H1×R×ES+H1×R×EL.

The calculation result is

E0=12ESx,y,z10expiϕt+12ELOx,y,z10expiψ,
E90=i2ESx,y,z 0 1expiϕt+12ELOx,y,z 0 1expiψ=12ESx,y,z 0 1expiϕtexp(i3π2)+12ELOx,y,z 0 1expiψ,
E180=12ESx,y,z 1 0expiϕt+12ELOx,y,z 1 0expiψ=12ESx,y,z 1 0expiϕtexp(iπ)+12ELOx,y,z 1 0expiψ,
E270=i2ESx,y,z 0 1expiϕt+12ELOx,y,z 0 1expiψ=12ESx,y,z 0 1expiϕtexp(iπ2)+12ELOx,y,z 0 1expiψ,
δ0=ψϕt,
δ90=ψϕt3π2,
δ180=ψϕtπ,
δ270=ψϕtπ2.

Suppose the phase of the signal light is subtracted from the phase of the local oscillator light as the reference. In that case, the phase delays of the signal light and the local oscillator light in the four output lights are 0°, 90°, 180°, and 270°, respectively, and within the same cycle.

III. THE INFLUENCE OF COMPONENT POSITION AND ATTITUDE ON PHASE AND ERROR ANALYSIS

The positions and orientations of various components in the design structure can significantly impact on phase and error analysis. In addition to errors resulting from component processing, incorrect positioning, and posture during component assembly can also lead to significant errors that must be analyzed.

To illustrate this point, we first consider the influence of parallel plates. Under ideal conditions of complete perpendicularity to the incident light, the optical path difference is consistent with the compensated wave plate and the optical path generated by PBS. However, any deviation from this ideal position during installation can cause a phase change. Figure 4 illustrates the schematic diagram of parallel plates. By establishing a coordinate system based on the surface of the incident component, we can approximate the change in component position and orientation as a deflection of the incident light angle. The magnitude of the deflection angle can then be represented by the azimuth and pitch angles. It is evident that the phase change is only related to the pitch angle and not the azimuth angle.

Figure 4. Schematic diagram of the influence of parallel plate position and posture on phase.

The phase difference generated by parallel plates is

Δp=2πλnpdpcosθn0dp.

In the formula, dp is the thickness of the parallel plate, np is the refractive index of the parallel plate, and θ is the incident angle of the parallel plate.

Figure 5 shows the error calculated with MATLAB simulation. As the material of the selected parallel plate is not fixed, its thickness can change with the refractive index. Therefore, parallel plates with a refractive index of approximately 1.5 and thicknesses ranging from 2 mm to 10 mm were selected for simulation calculations. The results show that errors generated by several parallel plates vary proportionally with the thickness within a deviation range of 1° in pitch angles. Specifically, the phase delay for the 2.5 mm parallel plate is within 2.32°, the phase delay for the 5 mm parallel plate is within 4.64°, and the phase delay for the 10 mm parallel plate is within 9.28°.

Figure 5. Phase variation with pitch angle and thickness of the parallel plate.

The next component we analyzed is the wave plate. During the adjustment process, the surface of the crystal is often not completely perpendicular to the direction of light propagation, which is similar to that of a parallel flat plate. To analyze this effect, we use the crystal surface as the coordinate system equivalent to a deflection of the incident angle, as shown in Fig. 6.

Figure 6. Schematic diagram of crystal birefringence.

It can be obtained from the Fresnel formula and the law of refraction

n1sinθ1=nosinθo=ne(θe)sinθe,
ne(θe)=no2ne2no2sin2θe +ne2cos2θe .

In the formula, n1, no, and ne represent the refractive indices of air and the refractive indices of the medium containing o and e light, respectively. θ1 is the incident angle, while θo and θe denote the refracted angles of o and e light, respectively. Additionally, θe represents the angle between the e-light and the fast axis direction.

If the length of the crystal is d, then the phase change generated by o light and e light in the crystal is ∆o and ∆e, the phase difference ∆ generated by the wave plate is

Δ=Δoe=2πλno dcosθo ne dcosθe .

Figure 7(a) shows the phase change of a 1/4 wave plate, while Fig. 7(b) shows the phase change of a 1/2 wave plate. The simulation results shows that slight angle position deviations of the wave plate due to birefringence have a relatively minor impact on phase variation within 1°, which can be almost ignored. However, since wave plate deflection has a similar effect on the optical path as that of a parallel plate, its value is almost equal to the phase difference generated by parallel plate deflection when the thickness and refractive index are similar.

Figure 7. Schematic diagram of the influence of wave plate position and posture on phase. (a) 1/4 wave plate phase delay, (b) 1/2 wave plate phase delay.

During the processing of wave plates, simulation has also been conducted due to the high possibility that the optical axis direction is not parallel to the crystal surface. Figure 8 shows the schematic diagram of phase delay when the optical axis elevation angle is 89° and the azimuth angle is 0°. As shown in Fig. 8, the phase delay of the wave plate also has a small change. Specifically, when the light is incident perpendicular to the crystal surface, the phase delay of the 1/4 wave plate is about 0.02° different from the phase delay when the optical axis is parallel to the crystal surface, while the phase delay of the 1/2 wave plate is about 0.05° different from the phase delay when the optical axis is parallel to the crystal surface.

Figure 8. Schematic diagram of phase delay with optical axis angle error. (a) 1/4 wave plate phase delay, (b) 1/2 wave plate phase delay.

When a parallel plate rotates, the energy of the light also changes. The vibration direction of the light is different from the rotation direction of the parallel plate, and the amplitude change of the light is also different. The amplitude of light with respect to angle can be calculated using the Fresnel formula:

ts=2sinθ2cosθ1sin(θ1+θ2),
tp=2sinθ2cosθ1sin(θ1+θ2)cos(θ1θ2).

In the formula, ts and tp are the projected amplitude coefficients of S- and P-waves, and θ1 and θ2 are the incident angle and refractive angle, respectively.

Figure 9 shows the image of the attenuation ratio of transmitted light amplitude with incident angle when S- and P-waves pass through a parallel plate. It can be seen from the figure that the influence of the rotation angle of the parallel plate within 6° on the amplitude of S- and P-waves is less than 0.2%, which can be almost ignored.

Figure 9. Attenuation ratio of transmitted light amplitude of S-wave and P-wave with incident angle.

IV. PHASE COMPENSATION ANALYSIS

The phase error generated by parallel plates is uniform, and can be compensated using the same approach as for parallel plate deflection. As the signal light and local oscillator light in the optical mixer are initially separated before final coupling, the phase delay in this branch can be adjusted by rotating a separate parallel plate in both the signal and local oscillator light branches simultaneously. It changes the optical path difference between the signal and local oscillator light, allowing for phase compensation.

Figure 10(a) shows the phase delay generated by parallel plates as a function of the rotation angle of the parallel plates between 0–6° and the thickness of the parallel plates between 2–10 mm; Fig. 10(b) shows the corresponding curve of the phase compensation range with rotation angle in Fig. 10(a) for the fixed parallel plate thickness used in the structure of this article. By rotating the parallel plate by 0.1° within this range, the phase change variable is less than 5°, which meets the phase requirements of the phase-locked loop. The smaller the rotation angle of a parallel plate, the higher the phase accuracy that can be controlled by rotating the same angle. When the rotation angle is within 2°, the phase delay difference that can be controlled for each 0.1° rotation is within 1°. With minor errors and higher component operation levels, the control accuracy of the mixer can be further improved. The parallel plates with thicknesses of 2.612 mm, 5 mm, and 5.22 mm used in this article for phase compensation can compensate for a maximum range of 83.73°, 167.47°, and 174.84° within a range of 6°, respectively.

Figure 10. Schematic diagram of phase compensation range for parallel flat plates. (a) Phase delay variation with parallel plate thickness and incident angle, (b) curve of phase delay variation with pitch angle for a given thickness of parallel plate.

Because parallel plates were initially added to this structure to compensate for the optical path difference between the wave plate and PBS, their branch for phase compensation is consistent with the compensated component, except for the opposite direction of the phase change. If the compensation range of the compensation plate exceeds the error generated by its compensation component, complete compensation for the phase delay can be achieved. Table 1 lists all components compensated by parallel plates and their corresponding phase compensation ranges at a pitch angle 6°. Table 1 indicates that the compensation range of the parallel plates is significantly greater than errors resulting from incorrect positioning and attitude, as well as phase delays caused by beam splitting film and processing errors of the polarization beam splitter. Therefore, the parallel plates can effectively compensate for these effects.

TABLE 1. Parallel plate phase compensation range table.

ComponentsCompensated ComponentPhase Compensation Branch and DirectionElement Reference Thickness (mm)Reference Compensation Range (°)
E(0°)E(90°)E(180°)E(270°)
Parallel Plate 11/4 Wave Plate2.61283.73
Parallel Plate 21/2 Wave Plate 2--5.22174.84
Parallel Plate 31/2 Wave Plate 3--5.22174.84
Parallel Plate 4PBS1----10-
Parallel Plate 5PBS2----10-
Parallel Plate 6PBS3---5167.47
Parallel Plate 7PBS3---5167.47
Parallel Plate 8PBS4---5167.47
Parallel Plate 9PBS4---5167.47

V. DISCUSSION

Firstly, in the initial stage of structural design, this paper selects a multi-level structure to avoid highly degenerate structures. This selection aims to effectively separate the beams of each branch, enabling independent adjustment of each branch.

Secondly, previous studies by Zhao [6] proposed the rotation 4/λ wave plate method, which can only compensate for phase between I/Q paths (I: 0° and 180°, Q: 90° and 270°) with a splitting ratio ranging from 0.57 to 1.75. Cao et al. [7] compensation methods added splitting ratio compensation to [6], with a phase compensation range between I/Q channels of −14° to 29°, requiring pre-calculation. Ke and Han [8] compensation method is essentially the same as [7], with similar phase and spectral ratio compensation ranges. In contrast, the structure proposed in this article is relatively symmetrical, where the splitting ratio of each output light is ideally 1:1. The phase compensation is not limited to between I/Q branches but can be continuously and freely compensated for all four output lights. During the phase compensation process, calculations based on the Fresnel refraction amplitude formula indicate that the amplitude reduction of each polarized light within a 6-degree rotation of the parallel plate is less than 0.2%, and the changes in light intensity and spectral ratio can be almost ignored. The compensation range is also much larger than the 45° compensation range of [7] and others, reaching over 300°, making it more practical and adaptable for practical use.

Additionally, from a processing and production perspective, the proposed structure in this article consists mainly of regular cubes or rectangles, without separating components that do not require compensation. It allows most processed crystals and parallel plates to be directly attached to the bottom plate without installation and adjustment steps, and simplifies the production process to a certain extent. The wide range of phase compensation in the structure of this article means that the accuracy requirements for processing and producing some of the components can be reduced, and more cost-effective component materials can be selected, significantly reducing the production cost of optical mixers. The mixer designed in this article also has great advantages for the future trend of commercializing and generalizing of spatial coherent optical communication.

VI. CONCLUSION

This article proposes a multi-beam spatial light mixer that utilizes a parallel flat plate to compensate for phase delay, overcoming the challenges associated with conventional optical mixers in compensating for phase delays resulting from machining errors, tuning, and other factors. This compensation method makes complete compensation for the phase delay almost achievable. Especially, it can achieve separate compensation for each of the four output lights which was not possible in the past.

The compensation method and scope were simulated and calculated. The overall phase adjustment range of the optical mixer is −83.73° to 0°. The phase compensation range of the branch is 0° to −342.31°; The phase compensation range of the branch is −167.47° to −174.84°; The phase compensation range of the branch is −174.84° to −167.47°; The phase compensation range of the branch is −342.31° to 0°, and the output light compensation range of each channel is much higher than the previously achievable 45°. The position and attitude errors of the structure were analyzed; The error caused by a 5 mm deflection of the parallel plate within a 1° range is less than 4.64°, while the phase delay errors generated by a 1/2 wave plate and a 1/4 wave plate deflection within 1° of the optical axis direction are less than 0.05° and 0.02°, respectively. The compensation range is far greater than various error ranges.

The results show that this structure has great potential in multi branch phase compensation and reducing machining accuracy and cost. Meanwhile, this structure has significant innovation potential and can be effectively used in spatial coherent optical communication applications.

FUNDING

Jilin Province Science and technology development plan project (No. 20190302098G).

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 maybe obtained from the authors upon reasonable request.

Fig 1.

Figure 1.Structure diagram of multi-beam space optical mixer.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 2.

Figure 2.Schematic diagram of the optical axis direction of the wave plates.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 3.

Figure 3.Schematic diagram of the optical path of a multi-beam space optical mixer.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 4.

Figure 4.Schematic diagram of the influence of parallel plate position and posture on phase.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 5.

Figure 5.Phase variation with pitch angle and thickness of the parallel plate.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 6.

Figure 6.Schematic diagram of crystal birefringence.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 7.

Figure 7.Schematic diagram of the influence of wave plate position and posture on phase. (a) 1/4 wave plate phase delay, (b) 1/2 wave plate phase delay.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 8.

Figure 8.Schematic diagram of phase delay with optical axis angle error. (a) 1/4 wave plate phase delay, (b) 1/2 wave plate phase delay.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 9.

Figure 9.Attenuation ratio of transmitted light amplitude of S-wave and P-wave with incident angle.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

Fig 10.

Figure 10.Schematic diagram of phase compensation range for parallel flat plates. (a) Phase delay variation with parallel plate thickness and incident angle, (b) curve of phase delay variation with pitch angle for a given thickness of parallel plate.
Current Optics and Photonics 2024; 8: 56-64https://doi.org/10.3807/COPP.2024.8.1.56

TABLE 1 Parallel plate phase compensation range table

ComponentsCompensated ComponentPhase Compensation Branch and DirectionElement Reference Thickness (mm)Reference Compensation Range (°)
E(0°)E(90°)E(180°)E(270°)
Parallel Plate 11/4 Wave Plate2.61283.73
Parallel Plate 21/2 Wave Plate 2--5.22174.84
Parallel Plate 31/2 Wave Plate 3--5.22174.84
Parallel Plate 4PBS1----10-
Parallel Plate 5PBS2----10-
Parallel Plate 6PBS3---5167.47
Parallel Plate 7PBS3---5167.47
Parallel Plate 8PBS4---5167.47
Parallel Plate 9PBS4---5167.47

References

  1. C. J. Wu, C. X. Yan, and Z. L. Gao, “Overview of space laser communications,” Chin. Opt. 6, 670-680 (2013).
    CrossRef
  2. A. Banerjee and B. N. Biswas, “BPSK homodyne receivers based on modified balanced optical phase-locked loop,” Optik 124, 994-997 (2013).
    CrossRef
  3. Y. Zhou, L. Y. Wan, Y. N. Zhi, Z. Luan, J. F. Sun, and L. R. Liu, “Polarization-splitting 2×4 90° free-space optical hybrid with phase compensation,” Acta Opt. Sin. 29, 3291 (2009).
    CrossRef
  4. J. Li, M. R. Billah, P. C. Schindler, M. Lauermann, S. Schuele, S. Hengsbach, U. Hollenbach, J. Mohr, C. Koos, W. Freude, and J. Leuthold, “Four-in-one interferometer for coherent and self-coherent detection,” Opt. Express 21, 13293-13304 (2013).
    Pubmed CrossRef
  5. Y. Zheng, H. Jiang, Y. Hu, S. Tong, and Z. Li, “Opto-mechanical structure design of the space optical hybrid,” in Proc. 2012 International Conference on Optoelectronics and Microelectronics (Changchun, China, Aug. 23-25, 2012), pp. 303-307.
    KoreaMed CrossRef
  6. Y. Zhao, “Study on the optical system of space coherent optical communication terminal,” Ph. D. dissertation, Xi'an Institute of Optics and Precision Mechanics Chinese Academy of Science, China (2015).
  7. H.-S. Cao, L. Jiang, P. Zhang, H. Nan, S.-F. Tong, and L.-Z. Zhang, “Power ratio adjustment and 90° phase difference compensation method of space optical hybrid,” Acta Photonica Sin. 46, 0606001 (2017).
    CrossRef
  8. X. Ke and J. Han, “Analysis and design of 2×4 90° crystal space optical hybrid for coherent optical communication,” Am. J. Opt. Photonics 8, 33-39 (2020).
    CrossRef
  9. Y. Du, Y. Zheng, S. Xie, and X. Bo, “Mathematical modelling of a crystal spatial light mixer,” J. Opt. 22, 025704 (2020).
    CrossRef