Integrated gallium phosphide-waveguide polarization rotator based on rotating a horizontal slot by 45 degree for 700 nm wavelength

Abstract

Polarization manipulation elements operating at visible wavelengths represent a critical component of quantum communication sub-systems, equivalent to their telecom wavelength counterparts. The method proposed involves rotating the optic axis of the polarized input light by an angle of 45 degree, thereby converting the fundamental transverse electric (TE₀) mode to the fundamental transverse magnetic (TM₀) mode. This paper outlines an integrated gallium phosphide-waveguide polarization rotator, which relies on the rotation of a horizontal slot by 45 degree at a wavelength of 700 nm. This will ultimately lead to the conception of a mode hybridization phenomenon in the waveguide. The simulation results demonstrate a polarization conversion efficiency of 99.99% (99.98%) for TE₀-to-TM₀ (TM₀-to-TE₀) mode conversion, with an extinction ratio of 46.14 (39.62) dB and insertion loss below 1.6 dB at the specified wavelength. Additionally, the fabrication tolerance with regard to the width, height, and half-beat length of the proposed structure is investigated.

Introduction

Photonic integrated circuits (PIC) based on silicon on insulator platforms are now widely used in a variety of applications such as optical telecommunication, optical sensing, and optical interconnection due to high index contrast and complementary-metal–oxide–semiconductor compatibility [1]. By utilizing the high index contrast property, the size of integrated photonic devices can be reduced due to high optical mode confinement, which minimizes the dimension of the PICs by several orders of magnitude [2]. In contrast, this feature introduces high birefringence which causes polarization mode dispersion and polarization-dependent loss [3]. To overcome this problem, polarization diversity systems have been proposed such as polarization beam splitters (PBSs) [4], polarization rotators (PRs) [5], and polarization splitter-converters (PSCs) [6].

PRs convert TE (TM) mode to TM (TE) mode by rotating the optical axis at an angle relative to the x-axis resulting in hybridized modes. Rotation is achieved after the propagation of hybridized modes for a distance equal to the conversion length [7]. The PRs can be obtained by breaking the symmetry of the waveguide either by introducing different materials as upper cladding or by using an asymmetric waveguide structure [8]. There are four mechanisms of PRs, mode evolution [9], mode coupling [2], mode hybridization [10], and surface plasmon effects [11].

Recently, there has been a considerable demand to develop PIC at visible wavelengths that require polarization manipulation, particularly for chip-scale atomic systems and qubit state preparation [12]. A polarization rotator at visible wavelength plays an important role in information processing similar to the polarization rotators at telecom wavelengths [13]. Polarization control components are crucial for quantum communication sub-systems including quantum key distribution transmitter and receiver chips as well as quantum repeaters [14]. In addition, shorter wavelength operation would enable polarization rotators more compatible with a variety of single photon emitter sources [15], and several free space transmission systems [16].

In this paper, we design a gallium phosphide-waveguide polarization rotator operating at 700 nm wavelength. Thus, the symmetry of the cross section of the rotator is broken by using air as the upper cladding which is a different material from hydrogen silsesquioxane and a 45-degree tilted slot structure.

Design and operation

Figure 1a shows the 3D view of the proposed structure. It consists of input and output parts that are regular gallium phosphide (GaP) strip waveguides. The input GaP strip waveguide is followed by a rotator waveguide. The cross section of the rotator waveguide is shown in Fig. 1b. It has a slot of hydrogen silsesquioxane (HSQ) tilted by 45º to break the symmetry of the waveguide. The structure is covered by air. The light is propagated in the GaP waveguide in the y-direction. The refractive indices of GaP, HSQ, and air are 3.2543, 1.41, and 1, respectively, at a wavelength of 700 nm. The structure was designed by using COMSOL Multiphysics. The physical principle of polarization rotation in the rotator waveguide is based on the conversion between the two orthogonal fundamental modes.

Fig. 1

a 3D view of the polarization rotator waveguide b cross section of the rotation region

The proposed structure is based on rotating a horizontal slot by 45° resulting in a trapezoid shape and shifted by $46\mathrm{ nm}$ from the upper left corner of the rotator waveguide. This will introduce a mode hybridization in the waveguide. The width of the slot (${\mathrm{w}}_{\mathrm{slot}}$), i.e., the height of the trapezoid was fixed to $20\mathrm{ nm}$. Figure 2a shows the effect of the variation of the width ($\mathrm{w}$) and the height ($\mathrm{h}$) of the waveguide on the electric field distribution components (E_x and E_y) of the fundamental and the first-order modes. The optical rotation angle is defined as the direction of the normal magnetic field to a vertical line in the transversal plane [17]

Fig. 2

a Optical rotation angle as a function of the variation of $\mathrm{w}$ and $\mathrm{h}$. The normal magnetic field distribution of b 1st hybrid mode c 2nd hybrid mode

$$\mathrm{tan\theta }=\frac{\iint n\left(x,y\right){E}_{\mathrm{x}}^{2}\left(\mathrm{x},\mathrm{y}\right)\mathrm{d}x\mathrm{d}y}{\iint n\left(x,y\right){E}_{\mathrm{y}}^{2}\left(\mathrm{x},\mathrm{y}\right)\mathrm{d}x\mathrm{d}y}$$

(1)

where n(x,y) is the refractive index distribution and E_x(x,y) and E_y(x,y) are the horizontal and vertical electrical field components of the fundamental and the first-order modes, respectively.

By choosing the appropriate dimensions (w = 197 nm, h = 190 nm), two orthogonal fundamental modes with effective mode indices of 2.407 and 2.317 that are fully hybridized. Figure 2b and c shows the normal magnetic field profiles and surface arrows with respect to the vertical line in the transversal plane. Each mode has an equal magnitude of the electric field components (E_x and E_y) with a rotation angle of 45°. The polarization of an incoming TE₀ or TM₀ mode is therefore rotated by 90 after a half-beat length as [17]

$${L}_{\uppi }=\frac{\lambda }{2({n}_{\mathrm{eff}1}-{n}_{\mathrm{eff}2})}$$

(2)

where λ is the operating wavelength and n_eff1 and n_eff2 are the effective mode indices of the two hybrid modes.

When the input polarized light (TE₀ or TM₀) is launched at the input of the rotator waveguide, two orthogonal fundamental hybridized modes will be excited equally due to the asymmetry of a cross section of the rotation region. The input polarized light will be converted to (TM₀ or TE₀) after propagating along the waveguide for a half-beat length (L_π = 4.95 µm). Figure 3. shows the electric field distribution of ${\mathrm{TE}}_{0}$ mode at different distances (z = 0 µm, z = 2.78 µm, z = 4.9 µm) of the rotator waveguide. The electric field distribution of E_x and E_y components along the rotator waveguide is observed in Fig. 4.

Fig. 3

The electric field distribution of ${\mathrm{TE}}_{0}$ mode at different distances along the rotator

Fig. 4

Top view of the electric field distribution of ${\mathrm{E}}_{\mathrm{x}}$ and ${\mathrm{E}}_{\mathrm{z}}$ components along the rotator waveguide. a ${\mathrm{E}}_{\mathrm{x}}$ and b ${\mathrm{E}}_{\mathrm{z}}$ for ${\mathrm{TE}}_{0}$ input c ${\mathrm{E}}_{\mathrm{z}}$ and d ${\mathrm{E}}_{\mathrm{x}}$ for ${\mathrm{TM}}_{0}$ input

The performance of the polarization rotator for ${\mathrm{TE}}_{0}$ input is determined by the polarization conversion efficiency (${PCE}_{{TE}_{0}-{TM}_{0}}$), extinction ratio (${ER}_{{TE}_{0}-{TM}_{0}}$), and insertion loss (${\mathrm{IL}}_{{\mathrm{TE}}_{0}-{\mathrm{TM}}_{0}}$) which can be defined as [17]

$${\mathrm{PCE}}_{{\mathrm{TE}}_{0}-{\mathrm{TM}}_{0}}=\frac{{P}_{\mathrm{TM}-\mathrm{out}}}{{P}_{\mathrm{TE}-\mathrm{out}}+{\mathrm{P}}_{\mathrm{TM}-\mathrm{out}}}$$

(3)

$${\mathrm{ER}}_{{\mathrm{TE}}_{0}-{\mathrm{TM}}_{0}}=10\mathrm{log }\left(\frac{{P}_{\mathrm{TM}-\mathrm{out}}}{{P}_{\mathrm{TE}-\mathrm{out}}}\right)$$

(4)

$${\mathrm{IL}}_{{\mathrm{TE}}_{0}-{\mathrm{TM}}_{0}}=-10\mathrm{log}\left(\frac{{P}_{\mathrm{TM}-\mathrm{out}}}{{\mathrm{P}}_{\mathrm{in}}}\right)$$

(5)

where P_TM-out and P_TE-out are the output power for TE and TM modes, respectively, and P_in is the input power.

The wavelength dependence transmission spectra, PCE, ER, and IL of the polarization rotator are viewed in Fig. 5. In Fig. 5a, the transmission spectra for the rotation from TE₀-to-TM₀ and TE₀-to-TE₀ are represented by the blue solid and dashed lines, respectively, at the output port. The transmission spectra for the rotation from TM₀-to-TE₀ and TM₀-to-TM₀ are represented by the red solid and dashed lines, respectively, at the output port. The blue and red solid lines overlap giving a transmission value less than -0.63 dB at the operating wavelength. The polarization conversion efficiency to convert TE₀-to-TM₀ (TM₀-to-TE₀), is 99.99% (99.98%) with ER of 46.14 (39.62) and IL less than 1 dB. The bandwidth of the rotator waveguide is 50 nm for ER > 20 dB and IL < 1.6 dB as depicted in Fig. 5b, c.

Fig. 5

a Transmission spectra for ${\mathrm{TE}}_{0}$ -to- ${\mathrm{TM}}_{0}$ mode rotation (blue solid line) and for- ${\mathrm{TM}}_{0}$-to-${\mathrm{TE}}_{0}$ mode rotation (red solid line) b $\mathrm{PCE},\mathrm{ ER},\mathrm{ IL}$ for ${\mathrm{TE}}_{0}$-to ${\mathrm{TM}}_{0}$ mode rotation c $\mathrm{PCE},\mathrm{ ER},\mathrm{ IL}$ for ${\mathrm{TM}}_{0}$-to-${\mathrm{TM}}_{0}$ mode rotation

The proposed polarization rotator can be fabricated by an optical lithography process. The performance of the device is affected by the variation in dimensions that occur during the fabrication process. The fabrication error of Δw, Δh, and ΔL_π are shown in Fig. 6a–f. These fabrication errors have been investigated by varying one parameter, L_π, and keeping the other parameters fixed at their optimum values. To achieve PCE > 98%, ER > 20 dB and IL less than 1.6 dB, the fabrication tolerance analysis for converting TE₀-to-TM₀ mode and vice versa shows that ΔL_π = 750 nm, $\Delta \mathrm{w}=\pm 1\mathrm{ nm}$, $\Delta \mathrm{h}= \pm 1\mathrm{ nm}$.

Fig. 6

The fabrication error of $\Delta \mathrm{w}, \Delta \mathrm{h},$ and $\Delta {\mathrm{L}}_{\uppi }$

Table 1 shows a performance comparison between polarization rotator structures at visible wavelengths. It can be realized that our proposed structure has a better PCE and ER with short L_π compared to the structures in the literature.

Table 1 A performance comparison between polarization rotator structures at visible wavelength

Conclusion

In conclusion, an integrated gallium phosphide-waveguide polarization rotator for 700 nm wavelength is proposed. The results show that the bandwidth is $50\mathrm{ nm}$ with $\mathrm{PCE}$ for TE₀-to-TM₀ (TM₀-to-TE₀) convertor of 99.99% (99.98%) and ER of 46.14 (39.62) $\mathrm{dB}$ and IL less than 1.6 dB with half-beat length of 4.95 µm. Also, the fabrication tolerance is analyzed and discussed.