Optical Design of an LCoS-Based 1 × 10 WSS with High Coupling Efficiency and Compact Light Paths

Abstract

In the field of communication, the utilization of Liquid Crystal On Silicon (LCoS) in Wavelength Selective Switch (WSS) systems holds great promise. However, the lack of research on the optical path design of LCoS-based WSS makes it challenging to realize high-port-count and perfect performance with a compact structure. In this paper, the conceptual optical path design method of a compact LCoS-based 1 × 10 WSS system working in C-band (1529 nm–1568 nm) is proposed, where there exists 1 input port and 10 output ports in the same array. The optical powers in both the wavelength and deflection directions have been meticulously considered separately, while the polarization-independent structure has been designed novelty, which boost system compactness and lowers manufacturing costs. Finally, a high fiber-to-fiber coupling efficiency of an idealized system ranging from 95.07 to 99.18% with only five components is achieved. Furthermore, a brief tolerance analysis to demonstrate the instrumentation feasibility is also conducted and the additional losses that will be introduced by real experiments are discussed. Our work is pioneering in providing a more straightforward methodology and conceptual model for WSS system design and offering reference significant for high-port-count systems.

1. Introduction

In response to the growing demand for information transmission, optical fiber communication based on dense wavelength division multiplexing (WDM) technology has emerged to achieve higher network resource utilization. The core of next-generation communication networks is comprised of multi-dimensional optical cross-connects (OXCs) and reconfigurable optical add-drop multiplexers (ROADMs). The optical wavelength selective switches (WSSs), as the central device of ROADM, make it possible to match any input wavelength to any output port for the suggested input ports. The information bandwidth per channel in a WDM system is typically 50 to 100 GHz [1], and wavelength demultiplexing or multiplexing is accomplished using a diffraction grating. One of the WSS design trends is moving towards building M × N WSS system based on 1 × N WSS and additional parts like couplers and optical switches [2,3,4]. Since convergence of these discrete components results in systems becoming more complicated and unstable [1,5], the research on new type of the 1 × N WSS with higher compactness and lower loss plays a significant role to develop more complex and effective M × N WSS systems.

Commercially, micro-electromechanical systems (MEMS) and liquid crystal on silicon (LCoS) spatial light modulator (SLM) switches are two primary competing technologies used in 1 × N WSS systems [6,7,8]. As early as in 2002, American researchers at Bell Laboratories combined multiplexer, demultiplexer, optical attenuator, and other optical components to create WSS based on planar lightwave circuit(PLC) [9]. The system can output from 9 ports and has 1 input port, with an insertion loss of less than 7 dB. In 2004, Metconnex from Canada combined PLC and MEMS technology to develop WSS based on PLC and MEMS [10]. In 2008, Finisar, the world’s largest manufacturer of optical communication devices, announced that they had developed the first LCoS-based WSS with a frequency interval of 50 GHz [11]. The isolation degree of adjacent ports is greater than 25 dB, the insertion loss of polarized light is 8 dB, and the flexible configuration of ports is also supported. Nowadays, as a programmable diffractive optical element, LCoS SLM allows WSS systems to handle high-port-count networks and flex grid technology-enabled networks with good performance due to its high flexibility and structural stability [12]. Considering that the unpolarized light transmitted in fibers is not applicable to LCoS, polarization splitter elements are usually introduced into the WSS system to achieve polarization splitting, modulation and polarization combination. They linearly polarize an input beam in the direction of the liquid-crystal director, modulating its phase in response [13]. In this way, parallel-aligned LCoS devices are more widely employed to display phase-only patterns. Specifically, the reflective LCoS has many advantages such as integration of high performance driving circuitry on a silicon chip, high pixel fill factor and high quality process technology for excellent pixel mirror reflectivity [14]. In a 1 × N WSS system, the input and output ports are often in the same array, corresponding to the same regions of LCoS, which increases the difficulty of optical path layout to a certain extent. Therefore, it is crucial for the design to consider how to eliminate the occlusion of the structure, which is why the off-axis structure is employed.

However, there was very few research of the 1 × N WSS system design from the standpoint of optical paths in earlier works [15,16]. Instead, the majority of the attention is placed on developing and testing them to obtain the desired performance, and only then the system structure altered to provide the best possible transmission performance, including insert loss and crosstalk [17]. Skipping the design stages of the system creation is often blind, expensive, and inefficient.

Therefore, in this paper, a conceptual design method of a new type of LCoS-based WSS from the perspective of pure optical path simulation is proposed. This paper innovatively introduces a practical simulation method for WSS optical path design, providing detailed optical design principles for both the wavelength direction and LCoS deflection direction (which will be explained in detail later). Unlike previous polarization-related optical paths, a unique polarization-independent structure is ingeniously designed for the LCoS beam polarization requirement, simplifying the optical path by eliminating the need to polarize the light in the beginning. The entire system uses a minimal number of components, minimizing manufacturing costs and equipment weight, which is favorable for large-scale implementation. Through the detailed design description of the optical path simulation part and the error analysis of the designed optical system, the perfect performance with high pot-to-port coupling efficiency of the simulated system can be seen clearly.

The full paper frame is as follows. The design specifications for the WSS optical system are given in Section 2, along with a detailed explanation of the design concept of the 2-f and 4-f systems described. In addition, the parameters of the system and optical components are also analyzed. Then, in Section 3, we provide the design methods and detailed analysis of three key devices and give the calculation method of the crucial parameters of system performance evaluation. We also demonstrate the feasibility of employing ideal planar mirrors as substitutes for diffraction elements in the simulation of LCoS in this study. The design process and final performance of the 1 × 10 WSS optical system design with optical design software are shown at length in Section 4. In Section 5, a tolerance analysis of all configurations is displayed and the final section includes a summary of the WSS system design and a discussion on the unresolved issues that need further investigation.

2. Designing Principle and System Components

2.1. 4-f and 2-f Optical System

The specifications of the WSS system in this paper are listed in

Table 1. Specifications of Designed WSS system.

Parameter	Specification
Input NA	0.095
Waist Radius	5.2 $\mathsf{\mu }$m
Wavelength	1529 nm–1568 nm
Channel spacing	100 GHz
Optical Volume	<75 mm × 40 mm × 6.4 mm (H)
Number of Optical Elements	≤5
Coupling efficiency of idealized Simulation	≥90%

. The input light source is Gaussian light with determined numerical aperture(NA) and the waist radius.

According to the following loss calculation formula as Equation (1), the simulation coupling efficiency is more than 90%, which corresponds to a simulation coupling loss of at most −0.46 dB. It should be noted that the design and simulation presented in this paper are based on ideal diffraction elements and idealized analysis from an optical path perspective. Therefore, the coupling efficiency requirements are extremely strict, aiming to achieve a level of 90% or higher. In practical experiments, factors such as insertion loss, crosstalk, and diffraction efficiency cannot be replicated exactly as in the ideal design. This is precisely why such a high coupling efficiency is necessary, to allow for sufficient margin in the face of these unavoidable losses.

$$\mathrm{Loss}=-10lg\frac{{\mathrm{P}}_{\mathrm{out}}}{{\mathrm{P}}_{\mathrm{in}}}.$$

(1)

In simple terms, WSS is the WDM signal input to the fiber port, which is divided by a grating and subsequently focused on the focal plane of the lens, where LCoS is located. The wavelength direction (y-axis) and the switching direction (x-axis) describe two dimensions of the WSS system, and these two dimensions are based on different design strategy. The wavelength direction refers to the direction in which the light beam is spread and the switching direction refers to the arrangement direction of input/output single-mode fibers. These two directions are perpendicular to each other in the three-dimensional space of the system.

According to the distribution of optical power shown in Figure 1a, the optical system in the wavelength direction can be regarded as a 4-f optical system where exist two lenses with the same optical power of $f_y$. The input Gaussian beam is firstly collimated by microlens array which is represented by Lens 1 in Figure 1a, and the grating is located at the co-focal point of Lens 1 and Lens 2 as a dispersion elements. Then the light beam of different wavelengths is focused by Lens 2.

Similarly, the switching direction is a 2-f optical system as demonstrated in Figure 1b. The input light beam is collimated by lens 3 with a focal length of $f_x$.

In this way, we can place the LCoS at the image plane, which is located at the exit pupil plane in the wavelength direction, and also is the focal plane in the switching direction. By this means, the channel conversion of the beam in the switching direction can be achieved without changing the conjugate position in the wavelength direction. As the length of the system is equal in both directions, the optical power of the element in the wavelength direction should be half of that in the switching direction, namely $f_y$ = 1/2$f_x$.

2.2. System Parameter Analysis

The optical fiber we used in the simulation is the common single-mode fiber with a diameter of 250 $\mathsf{\mu }$m, and the ports are densely packed. So the fiber pitch is also 250 $\mathsf{\mu }$m. The beam waist is located at the exit end of the fiber.

According to the transmission properties of the Gaussian beam, the relationship between Gaussian beam power transmittance and aperture is listed in

Table 2. The relationship between Gaussian beam power transmittance and aperture.

Aperture radius	$\omega$/2	$\omega$	3$\omega$/2	2$\omega$
power transmission ratio/%	39.3	86.5	98.89	99.99

. Therefore, in order to guarantee a high transmission efficiency of the system(greater than 98%), the beam waist radius of the Gaussian beam of each surface should not be greater than 1/3 of the surface aperture.

One of the challenges in this design is to reduce the number of components to make the system as compact as possible. We find that the two elements of the 4-f system, Lens 1 and Lens 2 in Figure 1a, have the same optical power and the same distance from the grating, so they can be used for simplification. We replace them with a cylindrical mirror, which provides optical power and bends the light path as well.

Corresponding to this change, the grating is also replaced by a reflection one, which reflects the light beam back to the cylindrical mirror. As a result, the reflection system needs to be off-axis to eliminate light obscuration which will introduce greater aberrations and difficulty in assembly and make the system more complicated. Besides, we replace the plane diffraction grating with grating prism (hereinafter referred to as Grim) to maximize the dispersion angle differences of the light with different wavelengths. The detailed design method will be described in Section 3.

Based on the foregoing discussion, there are 48 wavelength channels in the C-band with a wavelength interval of 100 GHz. The relationship between the LCoS deflection angle and the power of switching direction is shown in Figure 2, $\gamma$ is the LCoS deflection angle difference between every two adjacent channels, and $step$ refers to the beam reflection angle difference between every two adjacent channels, which satisfies $step$ = 2$\gamma$. We have the geometric relationship:

$$pitch=tan\left(step\right)·f_x,$$

(2)

where the pitch is the distance between the centers of adjacent fibers, which is equal to the fiber diameter of 250 $\mathsf{\mu }$m.

The maximum number of ports $N_{port}$ can be calculated from the step value and the maximum diffraction angle ${\theta }_{max}$:

$$N_{port}={\theta }_{max}·f_x/pitch.$$

(3)

The beam focused on the LCoS through the cylindrical mirror forms a rectangular dispersion pattern in the entire active area of the chip. Phase grating holograms of different periods are uploaded on the pixel areas corresponding to different wavelength channels of the LCoS to complete the direction adjustment of the diffracted beams for the wavelength channels. Since the maximum deflection angle of LCoS cannot be too large, we take the total angle between the input port and the farthest output port within 1.2${}^{\circ }$ [18,19]. After calculation we set the focal length of the element in the switching direction to 120 mm, then the corresponding power of the lens in the wavelength direction is 60 mm.

2.3. Components of the WSS System

According to the above analysis, all elements except for the microlens array are cylindrical surfaces in the WSS system to control the optical power in two directions independently. Starting from the fiber output position, the components of this system are as shown in

Table 3. Components of the LCoS-based WSS.

No.	Elements	Description
1	Input & output array	One input port and 10 output ports with 250 $\mathsf{\mu }$m pitches
2	Microlens array (MLA)	Spherical lens array corresponding to input & output array
3	Cylindrical mirror at y-axis	60 mm focal length at wavelength direction
4	Cylindrical lens at x-axis	120 mm focal length at switching direction
5	Grim	1.71 lines/$\mathsf{\mu }$m; N-SK2 material
6	Polarization conversion element	Convert light beam to single polarized light
7	LCoS chip	Pixel-pitch size: 3.74 $\mathsf{\mu }$m; Resolution: 4160 × 2464

and Figure 3.

Polarization conversion element are needed due to the polarization-independent operating characteristics of LCoS. Only S-polarized light can be received and modulated by LCoS, so we need to convent P-polarized light into S-polarized light before LCoS. At the same time, it is necessary to control the optical paths in two directions to be consistent, so that S-polarized light and P-polarized light can be recombined into one when the optical path of the system returns. We combine the polarization conversion element and LCoS as Polarization Independent Structure (PIS) and the specific design scheme will be described in the next section.

3. Design and Analysis of Key Components

3.1. Grim Design

Grim consists of a reflection grating and a triangular prism as shown in Figure 4, which are glued together and both made of N-SK2 glass with a refractive index of 1.589 at the central wavelength of 1548 nm. According to the grating equation,

$$n(sini+sin\theta )=\frac{m\lambda }{d}.$$

(4)

where n is the refractive index corresponding to the wavelength, i is the incident angle fixed at 53.8${}^{\circ }$, $\theta$ is the exit angle, m is the diffraction order, $\lambda$ is the wavelength, and d is the number of grating lines per unit length, and in this context, it is taken as 1.71 lines/$\mathsf{\mu }$m. To achieve higher diffraction efficiency, we use the +1st diffraction order. According to Equation (3), the exit light angle range from 56.96${}^{\circ }$ to 61.67${}^{\circ }$ with a spectral band of 1529 nm–1568 nm, which means the dispersion angle is less than 5${}^{\circ }$. However, after adding the dispersion effect prim, the dispersion angle can be expended and the different wavelengths can be separated completely. In the design stage, we set $\alpha$ as a variable and control the difference of the exit angles to be more than 10${}^{\circ }$ to obtain a grim that meets the requirements.

3.2. LCoS Analysis

LCoS devices utilize the electro-optical properties of liquid crystals to modulate the amplitude, phase, or polarization of incident light. Commercially available LCoS devices are reflective in nature and consist of pixels with aluminum mirrors deposited on a silicon backplane. The application of voltage to each pixel is individually controlled by integrated drive circuits situated beneath the aluminum mirror on the silicon backplane.

The LCoS chip we choose is the GAEA phase modulator, which is based on reflective LCoS microdisplays with 4160 × 2464 pixel resolution and 3.74 $\mathsf{\mu }$m pixel pitch. The choice of higher resolution in LCoS offers increased modulation flexibility, while smaller pixel sizes contribute to reduced twist loss. In the study conducted by Mi Wang etc. [4], they conducted relevant tests using the same type of LCoS chip. The experiments demonstrated the significant impact of voltage profile optimization method in mitigating diffraction losses, particularly at smaller diffraction angles. Data from this research indicates that diffraction losses remain within 0.6 dB when diffraction angles are below 1${}^{\circ }$ as shown in Figure 5 in Reference [4].

Conversely, although the performance of LCoS-based optical switches is also dependent on optical design, in general, a minimum of 7-pixel periods is required to maintain reasonable high efficiency (>90%) and low crosstalk [20]. As the grating period decreases, losses tend to increase. Achieving uniformity in losses can be accomplished by programming phase patterns to attenuate the output signal. In other words, adjusting phase patterns on the LCoS allows for the reduction of output signal intensity, thereby ensuring uniformity in losses between different output ports. This strategy enhances overall system performance. For instance, when the grating period reaches around 20 pixels, twist losses decrease to within 0.025 dB as shown in Figure 6 in Reference [4].

In our design within this study, we controlled the LCoS diffraction angles to be within approximately ±1${}^{\circ }$, with the dispersion direction spot covering approximately 20 pixels, aiming to achieve minimal diffraction loss and twist loss. Based on the aforementioned analysis, to simplify simulations, LCoS can be approximated as a series of rectangular mirrors. Each sub-mirror has a monochromatic spot at its center, enabling free deviation of the corresponding angle to redirect different output ports. For each monochromatic spot, in addition to constraining the size in the wavelength direction, we also controlled the center-to-center distance of spots with a frequency spacing of 100 GHz to be at least 5 times the spot radius. In-depth explanations and additional details will also be elucidated in Section 3.3.

3.3. PIS Design

In this paper, the polarization conversion element is composed of a Polarizing Beam Splitter (PBS) prim, a right angle (RA) prism, a quarter-wave plate and a mirror. As shown in Figure 5, the beam is separated in the PBS prim with the S-polarized light transmitted and the P-polarized light reflected to the direction of the quarter-wave plate. While the P-polarized light returns to the PBS prism, it passes through the quarter-wave plate twice and is converted to S-polarized light.

The deflection of the LCoS occurs at the switching direction. For the rays in the two regions of LCoS-A and LCoS-B as shown in Figure 6, the corresponding beam deflection directions are opposite, and the values are the same. For the light beams that need to enter different return ports, the deflection angle $\gamma$ of the LCoS is different, and the vertical position of the return beam paths exiting from the PBS prism are different, so as to complete the switching of different ports. In the optical design process, we set the LCoS as a plane mirror to simulation in each channel configuration.

The light spots of different wavelengths on the LCoS are arranged in two columns in the y-direction, which are located in the A and B regions respectively. The active area of the LCoS chip we used is 15.32 mm × 9.622 mm, corresponding to switching direction and wavelength direction respectively. This means that 48 light spots should be arranged within the length of 9.622 mm, and the width of the two light spot should not exceed 15.32 mm. In the wavelength direction, the center distance of adjacent spots in each column is denoted as d, and we specify that d is at least 5 times the beam waist radius ${\omega }_y$ which is set less than 40 $\mathsf{\mu }$m to reduce the transmission loss caused by channel crosstalk. The beam waist radius ${\omega }_x$ in the x-direction is specified to be less than 1.5 mm to meet the Gaussian beam transmission efficiency.

Considering the active area of LCoS and system space thickness requirements, the size of the PIS is set as shown in Figure 7. It should be noted that the thickness of the plane mirror does not participate in the light transmission, so it is not marked here.

4. Simulation Results and Performance Analysis

4.1. The Systematic Level of the WSS System

In the simulation of this paper, we utilized the ZEMAX OpticStusio 2022 optical design software (compatible with version 2017 and later). When constructing the initial structure in ZEMAX, we should consider the arrangement of the input and output ports firstly. In Section 2 we have discussed that the maximum deflection angle of LCoS is no more than 1.2${}^{\circ }$. If the input port is placed in the center of the array, as shown in Figure 8a, more output ports can be obtained by deviating 1.2${}^{\circ }$ in opposite directions, but this will cause the reflected light in different directions to be aliased and reduce the modulation efficiency of LCoS and isolation. Therefore, we place the input ports at the edge of the input and output arrays as shown in Figure 8b, thereby avoiding crosstalk caused by anomalous reflections of the beams. In this way, when the input light reaches the LCoS, it is not vertically incident in the switching direction, and returns to the farthest output port when the LCoS is not deflected.

Considering the fabrication difficulty of microlens array, planar-convex spherical lens array is used in the design. This system is different from the traditional imaging optical system for we do not pay much attention to the beam aberrations returning to the output ports. Hence, we chose the readily available commercial components, using fused silica for the microlens array, N-SK2 for the Grim, PBS prism and RA prim, and H-LAF3 for the cylindrical lens.

According to the previous discussion, the system structure is constructed as shown in Figure 9. At this time, the system has only one input port and one output port in the other end of the array with no deflection of LCoS. According to the size of the optical fiber, the center distance between the two can be calculated as 2.5 mm. Adjust the angle $\alpha$ and size of the Grim, and the eccentric distance of mirror 3 to make the light be able to return to the output port with the ignoration of return efficiency at this time.

Following the previous stage, more parameters are set as variables, including the distances between elements and the thickness of the lens. Preliminary optimization is performed by setting the optimization functions of back coupling efficiency and the spot limit on each surface. Specifically, the radius of the Gaussian beam spot should not be greater than 1/3 of the diameter of the surface to pass through, ensuring that the transmission efficiency of the Gaussian beam on each surface is higher than 98%.

When the coupling efficiency of all channels is not lower than 95%, we set different angles of deflection for LCoS to complete the wavelength selection. Since the output port farthest from the input port does not deflect corresponding to the LCoS, the closer it is to the input port, the greater the deflection angle. Twenty configurations are constructed in ZEMAX, among which the first ten are the original S-polarized light paths, and the last ten are the original P-polarized light paths. The 3D schematic diagram of all channels is shown in Figure 10. Similar to the foregoing single-channel return optimization method, we firstly ensure that the beam of each port can be deflected at a certain angle to return, and then increase the variables, including but not limited to element distance, element power, element eccentricity and tilt, to improve the coupling efficiency.

The final optimized parameters of the system are shown in

Table 4. Parameters of surfaces.

Element	Radius/mm	Distance/mm	Glass	Size/mm	Decenter/mm	Tilt/${}^{\circ }$
1 Input	-	0.095	-	-	0	0
2 MLA	Infinity	0.90	F_SILICA	$\varphi$0.125	1.25 (x)	0
	−0.35	52.46
3 Mirror	−88.92 (y)	−19.53	-	18 × 3.2	-	24.50 (x)
4 Lens	42.40 (x)	−1.00	H-LAF3	2 × 3.2	22.46 (y)	75.00 (x)
	26.81 (x)	−8.12			24.22 (y)	75.00 (x)
5 Grim	Infinity	−11.00	N-SK2	4.23 × 3.2	33.56 (y)	−23.44 (x)
	Infinity	11.00		4.5 × 3.2	-	67.25 (x)
	Infinity	28.53		4.23 × 3.2	-	−23.44 (x)
3 Mirror	−88.92 (y)	−22.83	-	18 × 3.2	-	24.50 (x)
6 PIS	-	-	N-SK2	-	12.7 (y)	−25.73 (x)

. It should be noted that the tilts in last column are all in the global coordinate system with the input surface as a reference, that is, each surface returns to the opposite angle value after tilting, and then tilts the next surface. The size of the designed system is 65 mm × 40 mm × 6.4 mm (H), which meets the design requirements.

Taking the original S-polarized light as an example, the deflection angles of the mirror simulation LCoS in different configurations are shown in

Table 5. LCoS deflection angle corresponding to different ports.

Configuration	Center Distance	LCoS Deflection Angle/${}^{\circ }$
Config. 1/11	2.50	0
Config. 2/12	2.25	±0.084
Config. 3/13	2.00	±0.162
Config. 4/14	1.75	±0.247
Config. 5/15	1.50	±0.325
Config. 6/16	1.25	±0.398
Config. 7/17	1.00	±0.474
Config. 8/18	0.75	±0.566
Config. 9/18	0.50	±0.638
Config. 10/20	0.25	±0.722

. As mentioned above, the configurations 11–20 correspond to the opposite angle of the configurations 1–10, respectively.

4.2. Performance of the Final Designed System

In the designed WSS system of this paper, the parameters we mainly focus on are the size of the system, the performance of the light spot on the LCoS and the coupling efficiency of the output ports. In addition, the beam-splitting capabilities of Grim are also listed. The difference between the beam angles emitted from the Grim is 11.507${}^{\circ }$, the radius of the spot of the reading beam in the y-direction of the grating surface is 1.182 mm.

The light spot trace with 12 sampling wavelengths on LCoS is as in Figure 11. It can be seen that the light spots of different wavelengths are distributed in a column, the width of the light spot in the x direction is uniform and the center is aligned, the light spot radius is 1.015 mm. The light spot radius in the y direction is 35 $\mathsf{\mu }$m and the coverage length is 8.5 mm. The average distance d in the y-direction center of adjacent wavelength spots with spacing of 100 GHz is 0.18 mm, and the ratio of d to ${\omega }_y$ is 5.2 $\mathsf{\mu }$m, which meets the design requirement of no less than 5 times. The average difference between the deflection angles of adjacent channels in LCoS is 0.0722${}^{\circ }$ from Table 5, so the step is 0.1444${}^{\circ }$.

Through the physical optical propagation of ZEMAX, we obtained the ideal coupling efficiencies of different configurations ranging from 95.07 to 99.18% (corresponding to −0.220 to −0.036 dB of coupling loss according to Equation (1)) as shown in

Table 6. Idealized simulation coupling efficiency of different configurations.

Config.	1529 nm	1548 nm	1567 nm	Config.	1529 nm	1548 nm	1567 nm
1	96.92%	99.18%	97.14%	11	96.08%	99.17%	96.37%
2	96.80%	99.06%	96.91%	12	95.96%	99.06%	95.15%
3	96.78%	99.11%	97.02%	13	95.93%	99.09%	96.22%
4	96.31%	98.50%	96.23%	14	95.48%	98.50%	95.47%
5	96.37%	98.59%	96.34%	15	95.55%	98.56%	95.54%
6	96.66%	99.05%	97.01%	16	96.08%	99.17%	96.37%
7	96.57%	98.94%	96.95%	17	95.80%	99.03%	96.20%
8	96.01%	98.13%	95.80%	18	95.18%	98.13%	95.07%
9	96.64%	99.00%	96.94%	19	95.78%	98.98%	96.17%
10	96.35%	98.54%	96.29%	20	95.52%	98.54%	95.59%

. Also, the average coupling efficiency of these three characteristic wavelengths can be obtained in all configurations as 97.07%, and the average loss is −0.129 dB. Figure 12 shows the physical optical morphology of the central wavelength (1548 nm) of different configurations returning to the output port position. It can be seen that the beam basically maintains the characteristics of a Gaussian beam, which further indicates that the physical optical transmission effect of the system is good.

5. Tolerance Analysis

The conceptual optical design of WSS system in this paper contains fewer components which are easy to obtain as well. However, this design employs an off-axis layout which is more difficult in fabrication and alignment than the ordinary coaxial optical system. Hence a detailed tolerance analysis should be implemented to demonstrated the feasibility of WSS system. The coupling efficiency of the output channels is selected as the performance criterion in tolerance analysis, and LCoS deflection angle is selected as compensator in Monte-Carlo analysis, since LCoS can be modulated by computer.

By comparison the data in Table 6, we found that the performance of S-polarized light and P-polarized light for the same output channel is basically the same, that is, there is little difference with configurations 11–20 corresponding to configurations 1–10. Therefore, the error analysis for the first ten structures is reasonable to show the tolerance sensitivity of the whole system. In this paper, three representative configurations are selected from 1–10 configurations, namely, Config.1 with no deflection of LCoS, Config.5 with the middle deflection angle and Config.10 with the largest deflection angle. After sensitivity analysis, 500 trails of Monte Carlo analysis were performed to predict the average coupling efficiency of the as-built WSS system. The analysis results shows that the probable performance degradation in coupling efficiency is only 1%. The detailed tolerance allocation is listed in

Table 7. Component Tolerance Settings in ZEMAX.

Element	Tolerance	Value
Mirror	Radius	±0.001 mm
	Decenter in x	±0.2 mm
	Decenter in y	±0.001 mm
	Tilt in x	±0.001${}^{\circ }$
	Tilt in y	±0.0002${}^{\circ }$
	Tilt in z	±0.005${}^{\circ }$
Lens	Radii of both surfaces	±0.01 mm
	Decenter in x	±0.001 mm
	Decenter in y	±0.005 mm
	Tilt in x	±0.005${}^{\circ }$
	Tilt in y	±0.005${}^{\circ }$
	Tilt in z	±0.005${}^{\circ }$
Grim	Decenter in x	±0.1 mm
	Decenter in y	±0.002 mm
	Tilt in x	±0.002${}^{\circ }$
	Tilt in y	±0.002${}^{\circ }$
	Tilt in z	±0.001${}^{\circ }$
PIS	Decenter in x	±0.2 mm
	Decenter in y	±0.2 mm
	Tilt in x	±0.001${}^{\circ }$
	Tilt in y	±0.002${}^{\circ }$
	Tilt in z	±0.1${}^{\circ }$
LCoS (Compensator)	Tilt in y	±0.04${}^{\circ }$

and

Table 8. Distance Tolerance Settings in ZEMAX.

Element-Element	Distance Tolerance
SLA-Mirror	±0.02 mm
Mirror-Lens	±0.01 mm
Lens-Grim	±0.02 mm
Mirror-PIS	±0.02 mm

. The overall analysis results are listed in

Table 9. Monte Carlo Tolerance Analysis Probability Results of Coupling Efficiency Reduction Percentage (500 Trials).

Cumulative Probability	Config.1	Config.5	Config.10
98%	0.1868%	0.2485%	0.2940%
90%	0.0666%	0.2118%	0.2718%
80%	0.0558%	0.1826%	0.2592%
50%	0.0321%	0.1427%	0.2170%
20%	0.0006%	0.1074%	0.2005%
10%	0.0002%	0.0900%	0.1947%
2%	0.0000%	0.0659%	0.1716%

and shown in Figure 13.

6. Discussion and Conclusions

In this paper, a new type of WSS system design is proposed from the perspective of optical path design. In the design approach, independent optical power distribution is carried out according to the 4-f system in the wavelength direction and the 2-f system in the switching direction. For the key devices, the Grim and polarization conversion element, detailed design schemes are described to meet the system performance requirements. Grim is made of a plane grating and a prim glued together, which can increase the maximum angle of light separation of different wavelengths by more than five times. The polarization conversion element is composed of a PBS prism and an RA prism in order to convert P-polarized light into S-polarized light and then modulated by LCoS. Instead of the traditional need for polarization splitting of the beam at the fiber location, the polarization conversion element innovatively provides a polarization-independent optical path solution for the WSS systems. In the simulation, an ideal model of a plane mirror was used to replace the LCoS, with a maximum switching angle of ±0.722${}^{\circ }$, consistent with the maximum angle limitation found in relevant studies.

The WSS system designed in this paper has excellent performance in coupling efficiency ranging from 95.07 to 98.18%, corresponding to the best loss of −0.036 dB and worst loss of −0.220 dB, and the tolerance analysis demonstrates its good achievability. However, it is important to acknowledge the inherent limitations of the simulations presented in this study. LCoS is modeled as a flat mirror, effectively treated as an ideal diffractive element, while in practical experiments, errors and losses due to diffraction are unavoidable. Within the manuscript, we have addressed the LCoS-related errors, and it should be emphasized that the exceptionally high coupling efficiency observed in our simulations allows for a margin to accommodate losses in practical implementations. The optical path model proposed in this work for LCoS-based WSS design serves as an idealized representation, offering a novel perspective for WSS design. This idea and method can better inspire the integration and combination of different disciplines in optics.