Compact, High Extinction Ratio, and Low-Loss Polarization Beam Splitter on Lithium-Niobate-On-Insulator Using a Silicon Nitride Nanowire Assisted Waveguide and a Grooved Waveguide

Abstract

We propose a compact, high extinction ratio, and low-loss polarization beam splitter (PBS) on a lithium-niobate-on-insulator (LNOI) platform, based on an asymmetrical directional coupler and using a silicon nitride nanowire assisted waveguide (WG) and a grooved WG. By properly designing ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowires and grooved LN WGs, TE polarization meets the phase matching condition, while significant mismatching exists for TM polarization. Numerical simulations show that the PBS has an ultra-high extinction ratio (ER) of ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ (larger than 40 dB and 50 dB, respectively). The device extinction ratios are larger than 10 dB over 100 nm wavelength ranges. Moreover, the device has an ultra-low insertion loss (IL less than 0.05 dB) at the wavelength of 1550 nm and maintains ILs less than 0.4 dB over 100 nm wavelength ranges.

1. Introduction

Lithium niobate (LN) is known as an excellent optical material in the field of communication technology because of its excellent performance in electro-optic, acousto-optic, and nonlinear optics. Due to the low refractive index difference between the core and cladding (n < 0.02), the traditional ion diffusion ln waveguides (WGs) have weak restrictions on the optical field and are difficult to reduce the device size. Thanks to the progress of thin film lithium-niobate (LN) manufacturing technology [1], lithium niobate on insulator (LNOI) can achieve sub-wavelength light limitation, which has broad application prospects for photonic integrated circuits (PIC) [2]. Similar to the other high-index-contrast platforms, LNOI suffers from the polarization-dependent problem due to the birefringence caused by the asymmetrical waveguide structures and the inherent anisotropy property of LN [3]. Therefore, polarization diversity systems are needed to solve these problems in PICs.

Recently, adiabatic coupler [4], Mach Zehnder interferometer [5,6], and subwavelength grating [7] have been used to realize wideband PBS on LNOI platform. However, these PBSs have a large footprint and limited application.

Asymmetric directional coupler (ADC) has been proved to be a simple method to realize compact PBS on other platforms, such as silicon on insulator (SOI) [8]. It is well known that the refractive index difference between fundamental transverse electric mode (${\mathrm{TE}}_0$) and fundamental transverse magnetic mode (${\mathrm{TM}}_0$) of quasi-single mode silicon WG with a typical thickness of 220 nm is about 0.7. With high birefringence, compact PBS based on the on-chip ADC can be achieved on SOI by using different widths WGs [9,10,11]. However, LNOI waveguide birefringence is much smaller than SOI [12,13,14]. For example, the refractive index difference between ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ of LN single-mode waveguide with a height of 400 nm is usually less than 0.2. Therefore, this kind of design may not be suitable for LNOI.

Hybrid plasmonic waveguide (HPW) [15,16] is another effective way to enhance birefringence to realize compact PBS [17,18,19]. Depositing metal on the waveguide can change the refractive index of TM polarization. This design significantly enhances the birefringence of the waveguide, to split TE and TM mode. However, due to the inherent metallic absorption, the insertion loss of HPW is high.

In this paper, we propose a PBS consisted of a silicon nitride nanowire assisted waveguide and a grooved waveguide, which realizes compact, high extinction ratio, and low loss on LNOI platform.

Table 1. Comparison of PBSs based on the LNOI platform.

Source	PER (dB)	IL (dB)	Length (μm)	BandWidth (nm)	Cut
[4]	~21 (TE)	<1 (TE&TM)	>6000	150 (>20 dB, TE)	x-cut
	~45 (TM)			250 (>40 dB, TM)
[5]	-	~2.8 (TE)	51000	140 (>20 dB, TE)	z-cut
		~1.3 (TM)		140 (>18 dB, TM)
[6]	47.7 (TE)	0.9 (TE)	~430	over 200 (>17.8 dB, TE)	x-cut
	48 (TM)	0.6 (TM)		over 200 (>22.8 dB, TM)
[7]	~24 (TE)	0.3 (TE)	160	185 (>20 dB, TE)	z-cut
	~31 (TM)	1.0 (TM)		85 (>20 dB, TM)
[12]	22.8 (TE)	0.12 (TE)	61.5	38 (>20 dB, TE&TM)	z-cut
	26.2 (TM)	0.47 (TM)
[13]	26.7 (TE)	<0.05 (TE&TM)	16	140 (>10 dB, TE&TM)	z-cut
	21.3 (TM)
[14]	~36(TE)	1.10 (TE)	~180	50 (>10 dB, TE)	z-cut
	~35(TM)	1.24(TM)		50 (>35 dB, TM)
This work	40.7 (TE)	<0.05 (TE&TM)	46	100(>10 dB, TE)	x-cut
	50.7 (TM)			100(>45 dB, TM)

lists the comparison between LNOI-based PBSs proposed recently and work in this paper. Our device is very competitive, especially in the x-cut platform. Most importantly, we can finely adjust the refractive index of TE mode to achieve a high extinction ratio (>40 dB) of TE mode. Moreover, with the help of silicon nitride nanowires, the refractive index of TM polarization increases significantly, while the refractive index of TM polarization in the grooved waveguide is low [20]. Therefore, when TE polarization meets the phase matching condition, the TM polarization coupling mismatch is large to achieve a high extinction ratio (>50 dB) of TM mode. The results show that the compact PBS based on silicon nitride nanowire assisted waveguide and grooved waveguide has excellent performance on LNOI platform. And this PBS can tolerate large manufacturing errors.

2. Materials and Methods

Figure 1a,b respectively present schematics of the top and cross-sectional views of the proposed PBS. The device consists of two WGs (WG1, WG2) with coupling gap G. WG1 is a ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowire assisted waveguide and it ends with a through-output port. WG2 is a grooved-waveguide ending with a cross output port. The S-shaped curved waveguide with length ${\mathrm{L}}_{\mathrm{s}}$ is used to decouple WG1 and WG2. The thickness of LN layer is 500 nm and embedded ${\mathrm{SiO}}_2$ layer (box) is 2 μm. The waveguide height ${\mathrm{h}}_{\mathrm{w}}$ is 300 nm, and ${\mathrm{SiO}}_2$ is covered on the upper layer to protect WGs. The refractive indices of LN, ${\mathrm{Si}}_3{\mathrm{N}}_4$ and ${\mathrm{SiO}}_2$ are ${\mathrm{n}}_{\mathrm{LN}}$ = 2.21, ${\mathrm{n}}_{{\mathrm{Si}}_3{\mathrm{N}}_4}$= 2.46 (which is relatively larger as the fabrication of film deposition is PEVED) and ${\mathrm{n}}_{{\mathrm{SiO}}_2}$= 1.44 at the wavelength of 1550 nm, respectively.

Although the Z-cut platform is more advantageous to design PBS, the existing LNOI electro-optic modulators are generally manufactured based on the X-cut platform to take advantage of the high electro-optic coefficient of the Z-axis. Considering that PBS will be integrated with modulators in the future, our design is based on X-cut LNOI platform [21]. LN WGs can be patterned with high resolution using Electron Beam Lithography (EBL) and Inductively Coupled Plasma Reactive Ion Etching (ICP-RIE). Limited by the manufacturing process, the side wall of LN WG manufactured by ICP-RIE inclines about 75° [22]. Therefore, we set the sidewall corner (θ) at 75° to match the manufacturing process.

By optimizing the geometric parameters (${\mathrm{w}}_{\mathrm{a}}$, ${\mathrm{h}}_{\mathrm{a}}$) of ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowires, the effective refractive index (Neff) of ${\mathrm{TM}}_0$ mode can be significantly improved, while the Neff of ${\mathrm{TE}}_0$ mode can be slightly improved. Then, by optimizing the parameters (${\mathrm{w}}_1$, ${\mathrm{w}}_2$, ${\mathrm{w}}_3$) of grooved LN WG, the TE polarization can meet the phase matching condition, and there is a large phase mismatch of TM polarization, to significantly inhibit the cross-coupling of TM polarization. In this case, TE and TM can be separated after going through a short coupling region.

When the ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowires are loaded on LN WGs, the electric fields of TE polarization (whose main electrical field is horizontal) and TM polarization (whose main electrical field is vertical) will be affected differently. Figure 2a shows the Neff of ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ in ${\mathrm{Si}}_3{\mathrm{N}}_4$ assisted LNWG at the wavelength of 1.55 μm. We use Lumerical Finite Difference Eigenmode (FDE) solver to calculate their Neff. In the calculation, ${\mathrm{w}}_{\mathrm{b}}$ is fixed at 600 nm. It can be seen that for both polarizations, Neff increases with ${\mathrm{w}}_{\mathrm{a}}$ and ${\mathrm{h}}_{\mathrm{a}}$. However, with the increase of ${\mathrm{h}}_{\mathrm{a}}$, Neff of ${\mathrm{TM}}_0$ will approach and exceed Neff of ${\mathrm{TE}}_0$ eventually. According to Figure 2b, we choose (${\mathrm{w}}_{\mathrm{a}}$, ${\mathrm{h}}_{\mathrm{a}}$) = (400, 500) nm, to match the Neff of ${\mathrm{TE}}_0$ of grooved WG (~1.93), and to significantly increase Neff of ${\mathrm{TM}}_0$. Figure 2c shows the relevant electric field distribution of ${\mathrm{TM}}_0$ and ${\mathrm{TE}}_0$ modes in the case of (${\mathrm{w}}_{\mathrm{a}}$, ${\mathrm{h}}_{\mathrm{a}}$) = (400, 500) nm.

When the LN WGs are grooved, ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ will also be affected differently. Figure 3a shows the Neff of ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ modes in grooved LNWG at 1.55 μm wavelength. We also use the Lumerical FDE solver to calculate their Neff. In the calculation, ${\mathrm{w}}_1$ is fixed at 1μm. And we assume that when ${\mathrm{w}}_2$ is narrow, WG cannot be etched completely, but small pits are formed on the WG [23]. It can be seen that for both modes, Neff of grooved waveguide first increases and then decreases with the increase of ${\mathrm{w}}_2$, and gradually approaches Neff of single-mode WG with the width ${\mathrm{w}}_1$. So it is convenient for us to design Neff of TE polarization. According to Figure 3a, we select (${\mathrm{w}}_2$, ${\mathrm{w}}_3$) as (200, 100) nm to exact match Neff of ${\mathrm{TE}}_0$ mode. Figure 3b shows the electric field of ${\mathrm{TM}}_0$ and ${\mathrm{TE}}_0$ modes in the case of (${\mathrm{w}}_2$, ${\mathrm{w}}_3$) = (200, 100) nm.

Then, we calculate the Neff as a function of the width of WG at 1.55 μm wavelength, as shown in Figure 3 We choose ${\mathrm{w}}_1$ as 1μm and ${\mathrm{w}}_{\mathrm{b}}$ as 600 nm. As expected, the ${\mathrm{TE}}_0$ meets the phase matching condition, while the Neff of ${\mathrm{TM}}_0$ is significantly different.

3. Results

Lumerical 3D finite-difference time-domain (FDTD) is applied to further simulate the light transmission characteristics of the proposed structure. Cross-coupling length of ${\mathrm{TE}}_0$ mode is determined by G. The smaller G is, the smaller coupling length of the DC is. However, undesired TM polarization cross-coupling will also increase due to the insufficient phase-mismatch caused by smaller G. Therefore, G is optimized to 1380 nm. ${\mathrm{w}}_{\mathrm{a}}$ is optimized to 393 nm to obtain the maximum ER of ${\mathrm{TE}}_0$. Considering the complete coupling of ${\mathrm{TE}}_0$ mode, ${\mathrm{L}}_{\mathrm{c}}$ is optimized to 36 μm. And ${\mathrm{G}}_{\mathrm{out}}$ is set to 2 μm to avoid accidental coupling between two WGS. ${\mathrm{L}}_{\mathrm{s}}$ is set to 10μm to ensure a low bending loss.

Figure 4a,b show the light propagation profiles of ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ at 1.55 μm, respectively. It can be seen that ${\mathrm{TE}}_0$ is completely coupled with the cross port, while ${\mathrm{TM}}_0$ has almost no coupling. The Extinction Ratio (ER) of ${\mathrm{TE}}_0$ is 40.7 dB (mainly propagates from the cross port), while ${\mathrm{TM}}_0$ is 50.7 dB (mainly propagates from the through port). For both polarizations, ultra-low Insertion Loss (IL < 0.05 dB) can be achieved. ER and IL are defined as follows:

$${\mathrm{ER}}_{\mathrm{TE}}=10{\log }_{10}\left(\frac{{\mathrm{T}}_{\mathrm{cross},\mathrm{TE}}}{{\mathrm{T}}_{\mathrm{through},\mathrm{TE}}}\right)$$

(1)

$${\mathrm{ER}}_{\mathrm{TM}}=10{\log }_{10}\left(\frac{{\mathrm{T}}_{\mathrm{through},\mathrm{TM}}}{{\mathrm{T}}_{\mathrm{cross},\mathrm{TM}}}\right)$$

(2)

$${\mathrm{IL}}_{\mathrm{TE}}=10{\log }_{10}\left({\mathrm{T}}_{\mathrm{cross},\mathrm{TE}}\right)$$

(3)

$${\mathrm{IL}}_{\mathrm{TM}}=10{\log }_{10}\left({\mathrm{T}}_{\mathrm{through},\mathrm{TM}}\right)$$

(4)

${\mathrm{T}}_{\mathrm{through}}$ and ${\mathrm{T}}_{\mathrm{cross}}$ are the through port and cross port transmission, respectively. Figure 4c,d show ERs and ILs of TE and TM polarization, respectively. It can be observed that for both polarizations, our PBS shows broadband performance with ERs > 10 dB over 100 nm wavelength ranges. In the wavelength range of 100 nm, the IL of TE polarization is less than 0.4 dB, and that of TM polarization is less than 0.05 dB The ILs of TM polarization is mainly caused by bending, which can be further reduced by increasing ${\mathrm{L}}_{\mathrm{s}}$.

The manufacturing tolerance is considered of four parameters, that is, (1) Etching depth error of grooves on LN film δh, (because narrow grooves are difficult to etch), (2) the sidewall angle of WGs δθ, (3) width of WGs δw (assuming that the two WGS have the same change), (4) mask misalignment δm (mask misalignment will cause the horizontal position of ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowires to shift). And Figure 5 shows the transmission spectrum of the corresponding parameters deviating from the optimized value. For both polarizations, When the range of δh/δθ/δw/δm is 30 nm/±3°/±20 nm/±30 nm, ER > 10 dB and IL < 0.5 dB of ${\mathrm{TE}}_0$ and ER > 40 dB and IL < 0.05 dB of ${\mathrm{TM}}_0$ can still be maintained in the 160 nm bandwidth. It is worth noting that ${\mathrm{TM}}_0$ is much less sensitive to fabrication errors and wavelength changes than ${\mathrm{TE}}_0$, which is caused by the large phase mismatch of ${\mathrm{TM}}_0$.

4. Discussion

In fact, single LN WG is easier to manufacture than grooved LN WG. We have tried to use single LN WG instead of grooved waveguide to build PBS as in reference [13]. However, there are few parameters that can be changed for a single LN WG. So it is difficult to design the Neff, resulting in poor extinction ratio. The groove waveguide we propose has three parameters that can be flexibly adjusted (w1, w2 and w3) to precisely design Neff of ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$. Therefore, replacing LN WG with groove waveguide can make Neff of TE match better and Neff of TM difference larger, thus improving extinction ratio.

5. Conclusions

In this paper, we propose a compact, high extinction ratio, and low loss PBS based on an asymmetric directional coupler on LNOI platform. ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowires are deposited on LN waveguides to significantly change birefringence. By properly designing ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanowires and grooved LN WGS, TE polarization meets the phase matching condition. However, TM polarization has an obvious phase mismatch, and the coupling is fully suppressed. We design a PBS with a length of 46 μm (including S-bend). Simulations show that the PBS has an ultra-high extinction ratio (ER) of ${\mathrm{TE}}_0$ and ${\mathrm{TM}}_0$ (larger than 40 dB and 50 dB, respectively). Simulation shows that PBS has the broadband performance of keeping ERs > 10 dB in the 100 nm wavelength range. In addition, PBS shows ultra-low IL (<0.05 dB) and maintains ILs < 0.4 dB in the 100 nm wavelength range. This device has good manufacturing error tolerance. We believe that our work paves the way for the integrated polarization control system on the LNOI platform.