1. Introduction

Internet-based services are now ubiquitous and expanding in rapid pace. Consequently, short-reach optical networks need to be upgraded for higher data capacity. Coherent communication is still not a cost-effective option for short/medium reach optical links as it involves a local light source and high-speed complex digital signal processing (DSP) at the receiver. To meet the strict cost requirements for short-reach optical networks, there is a growing interest of utilizing advanced modulation formats based on intensity modulation and direct detection (IM/DD), such as 4-level pulse amplitude modulation (PAM-4) [1].

Since PAM formats are only one dimensional (1D) intensity modulation, huge portion of the four-dimensional signal space remains unutilized. Number of modulation levels in IM/DD can be further increased in a more power-efficient manner by using three-dimensional (3D) Stokes vector modulation (SVM) formats as proposed in [2,3]. One of the key advantages of using SVM with respect to coherent formats is that information is not encoded on the absolute optical phase, therefore relatively simple direct detection (DD) scheme can be employed at the receiver site. Feasibility of multi-level polarization modulation and detection has been demonstrated in the past using discrete optical components [4–6]. Recently, number of high-speed subsystem experiments on SVM have been demonstrated by using discrete polarization optics [7–9].

For the SVM/DD system to be a cost-effective solution in the high-speed short-reach links, optical components for SVM/DD need to be substantially simpler and cheaper as compared with coherent transceivers. To this end, compact and simple SV modulators based on integrated waveguide have been proposed and demonstrated [10,11]. At the detector side, silicon-photonic SV receiver has been reported, which contained dual polarization optical hybrid and six germanium photodetectors [12]. To simplify the receiver further, we have recently proposed a novel compact integrated SV analyzer on InP [13]. The basic concept resembles that of the conventional polarization analyzer using bulky optics [3,6], which splits the light into four branches and detect each Stokes parameter. Unlike the previous integrated devices, our proposed device has substantially simple interferometer-free configuration that would reduce the cost, footprint, and power consumption.

In this paper, we generalize the concept presented in [13] and provide more comprehensive theoretical and experimental studies on the polarization-analyzing photonic integrated circuit (PIC). We demonstrate that arbitrary states-of-polarization (SOPs) scattered on Poincare sphere can be retrieved by using a 3 × 3 projection matrix, which is realized on a compact InP-based PIC by integrating half-ridge waveguide structure. More importantly, we show that this projection matrix has flexibility and its deviation due to device imperfectness can be calibrated to a certain degree, which would greatly relax the fabrication requirement of the proposed device.

The manuscript is organized in the following manner: In Section 2, we explain the key concept and working principle of the proposed device to show its flexibility. Section 3 provides description of proof-of-concept device fabrication and experimental results to support the theory. Finally, we conclude the work in Section 4.

2. Concept and working principle of proposed Stokes vector analyzer

2.1 Device structure

The Stokes vector (SV) used in this paper is defined as $\text{S}={[S_1,S_2,S_3]}^T$, where S₁ = |a_TE|² - |a_TM|², S₂ = 2Re(a_TE*a_TM), and S₃ = 2Im(a_TE*a_TM). Here, a_TE and a_TM are the complex amplitudes of the electric field for transverse electric (TE) and transverse magnetic (TM) modes, respectively, propagating inside the device. Since we can assume that x- and y-polarized light would dominantly excite the TE and TM components when edge-coupled to the PIC, our definition would be consistent with the SV generally defined in free space [14].

Figure 1(a) depicts the schematic layout of the proposed integrated SV analyzer. The device consists of a 1 × 4 polarization-independent multimode interference (MMI) splitter, ridge waveguide with symmetrical cross-section [Fig. 1(b)], polarization converter (PC) with asymmetrical waveguide cross-section [Fig. 1(c)], and polarization-dependent photodetector (PD) that measures S₁ parameter (i.e., TE component) of light [TE-PDs in Fig. 1(a)]. Waveguides lying between the output ports of the MMI and PDs are denoted as output waveguide (OW).

 

Fig. 1 Schematic (a) layout of proposed integrated Stokes vector analyzer, cross-section view of (b) symmetric waveguide and (c) asymmetric waveguide (PC).

Download Full Size | PDF

While the PC sections on OW2 and OW3 with a length L_PC could be of any type having asymmetric sections [15–18], we depict in Fig. 1(c) a half-ridge waveguide structure [19] as an example. The electric field of TE and TM modes are oriented along x- and y- directions [as illustrated in Fig. 1(b)], respectively in a symmetric waveguide. In contrast, a waveguide with asymmetric cross-section could generally have the eigenmodes with the electric field effectively tilted by an angle θ ($0<\theta \le {45}^o$) with respect to the horizontal or vertical axis [19]. Location of PC section in OW3 is offset by a length L_sym as compared to the location of PC in OW2. Due to this positional offset of PC in OW3, SOP of light in OW3 experiences an additional transformation before the PC section. Each output port is finally terminated by a polarization-dependent photodetector (PD), which ideally detects only TE component of light. Such PDs could be realized either by implementing multi-quantum-well (MQW) structure and/or integrating on-chip polarizer.

The proposed device configuration resembles conventional polarization analyzer that uses bulky optics [3,6]. The major difference is that, our scheme implements waveguide-based PC section to rotate the SOP of incident light, instead of rotating polarizer. This potentially allows us to integrate all the components monolithically on an InP chip and enables high-speed SV detection. We should also note that for simplicity, we assume in this work an input signal with perfect degree-of-polarization (DOP), so that OW4 is not used to retrieve the SOP. The fourth port, however, will be necessary to detect signal with degraded DOP.

2.2 Principle of operation

Working principle of the device is explained in the following. The incident light is divided into four parts by the MMI section and propagates through four output waveguides from OW1 to OW4. For the ease of explanation, let us consider a reference plane in Fig. 1(a). We assume that the SOP of light at the reference plane is identical for all MMI ports, and can be represented as $S_{ref}=M_{MMI}S$, where $S$ is the SOP at the input of the device and $M_{MMI}$ is a 3 × 3 orthogonal matrix. The role of the section located at right hand side of the reference plane is to transform $S_{ref}$ by using three different rotational matrices (Muller matrix) before launched at TE-PDs. As we explain in the following section, this could be achieved by appropriately designing the location and length of asymmetric PC section in each arm. Since only TE component (namely S₁ Stokes component) is detected at TE-PDs, we could retrieve the projection of S onto three different vectors ${\text{S}}_{\text{1}}^{\text{'}}$, ${\text{S}}_{\text{2}}^{\text{'}}$ and ${\text{S}}_{\text{3}}^{\text{'}}$. If we define V₁, V₂, and V₃ as the measured signals by the PDs at OW1, OW2 and OW3, respectively, they can be expressed as

We now explain how we could transform S by different Muller matrices at each output port of the MMI splitter. As light propagates inside a waveguide supporting two polarization modes, the SV rotates around a fixed birefringence vector b defined in the Stokes space [20,21]. The vector b coincides with the S₁-axis for a symmetric waveguide, whereas it lies on the S₁-S₂ plane making an angle 2θ with respect to S₁-axis for the asymmetric PC waveguide, where θ is the effective tilt angle of the eigenmode as shown in Fig. 1(c). More specifically, the SV of the light after travelling thorough a lossless birefringent waveguide is described as S_out = MS_in, where S_in is incident SV and M is a 3 × 3 rotating matrix. The matrix M is the 3 × 3 components of 4 × 4 Muller matrix without the first row and first column [21,22], and can be expressed as

Equation (3) indeed represents rotation in 3D space around a vector $b={(\cos 2\theta ,\sin 2\theta ,0)}^T$ with an angle $\Delta \beta L$. We can therefore design θ and L appropriately, such that three different vectors $S_{\text{1}}^{\text{'}}$, $S_{\text{2}}^{\text{'}}$, and $S_{\text{3}}^{\text{'}}$ are transformed into a vector on the S₁-axis in respective OWs. OW1 is just a straight waveguide with symmetric cross-section wherein SV rotates about S₁-axis, hence the S₁ component will remain unchanged throughout its journey and can be detected directly by TE-PD. In OW2, we design θ in the PC sections to be in the range between 22.5° to 45° and L_PC [L in Eq. (3)] appropriately, such that a vector ${\text{S}}_{\text{2}}^{\text{'}}$ on the S₂-S₃ plane gets transformed into a vector on the S₁-axis as shown in Fig. 1(c). The SOP transformation in OW3 is different than OW2 due to the presence of symmetric waveguide before the PC. In OW3, a vector ${\text{S}}_{\text{3}}^{\text{'}}$ on S₂-S₃ plane first experiences a rotation about S₁-axis as it travels through the symmetric waveguide of length L_sym, due to the difference of effective refractive indices between TE (n_TE) and TM (n_TM) modes, and transformed into a vector ${\text{S}}_{\text{2}}^{\text{'}}$ on the same plane [see Fig. 1(b)]. This transformation can be understood by inserting θ = 0^o in the Eq. (3). Then, ${\text{S}}_{\text{2}}^{\text{'}}$experiences a similar rotation as in OW2 to finally arrive at S₁-axis. Consequently, we can detect ${\text{S}}_{\text{3}}^{\text{'}}$ component by TE-PD at OW3.

Since the functionality of PC section is to convert a vector $S_{\text{2}}^{\text{'}}$, which could be anywhere on the S₂-S₃ plane, to a vector on S₁ -axis, its design could be relatively flexible. This is in contrast to the usual usage of PC to convert specific SOP to another specific SOP, where fabrication tolerance is generally strict [23]. Moreover, we notice from Eqs. (1) and (2), that the projection vectors ${\text{S}}_{\text{i}}^{\text{'}}$ may not necessarily be perfectly orthogonal to calculate S. When ${\text{S}}_{\text{i}}^{\text{'}}$ are orthogonal, |det(${\text{M}}_{\text{P}}$)| = 1 (since $\left|\det \left(M_{MMI}\right)\right|=1$); but even in a non-ideal cases with non-orthogonal $S_{\text{1}}^{\text{'}}$, we can still retrieve S by calculating Eq. (2) as long as det(M_p) ≠ 0. In practice, fabrication imperfectness, such as structural variations at the PC section and symmetrical waveguide, residual port dependence at the MMI splitter, etc., degrades the orthogonality of M_p. As a result, the distances between $S_{\text{1}}^{\text{'}}$, $S_{\text{2}}^{\text{'}}$, and ${\text{S}}_{\text{3}}^{\text{'}}$ decrease on the Poincare sphere, which may result in power penalty. For a device with det(M_p) = 0.8, for example, the distance is reduced by up to 20%, corresponding to 1-dB penalty. While we need to pay a cost of receiver sensitivity if |det(M_p)| degrades from 1, the unique flexibility and the ability of calibrating M_p should greatly relax the fabrication tolerance. More accurate quantitative investigation on the impact of fabrication errors to the receiver sensitivity requires detailed assumption of noise sources, which depends on the specific receiver configuration. This is outside the scope of this paper and will be presented elsewhere.

3. Device fabrication and experimental demonstration

3.1 Device design and fabrication

For the proof-of-concept demonstration, the passive PIC section without the PD array [Fig. 1(a)] was fabricated on InP. We employed 2.5-μm-wide ridge InGaAsP/InP waveguide (WG) for the symmetric WG and 0.9-μm-wide half-ridge structure for the PC sections [19]. Half-ridge PC section and symmetric WG section was connected by 20 μm long lateral taper on both sides of the PC. The thickness of the core layer was designed to be 0.5 μm. InGaAsP slab was kept as 300 nm thick on top of the InP bottom clad layer. From the two-dimensional mode analysis and preliminary measurement, we derived L_sym and L_PC to be 35 μm and 70 μm, respectively.

A self-aligned fabrication procedure was employed for the monolithic integration of PC sections with the MMI splitter and the other symmetric waveguides. A detailed explanation on fabrication procedure can be found in [19]. Scanning electron microscope (SEM) images of the fabricated PC section, symmetrical WG cross-section and asymmetrical PC cross-section are shown in Figs. 2(a)-2(c), respectively.

 

Fig. 2 SEM images of PC section (a) angled top view and cross-section view of (b) symmetrical WG section and (c) asymmetrical half-ridge WG section.

Download Full Size | PDF

3.2. Measurement setup

The experimental setup used in this work is shown in Fig. 3. A light at 1550-nm wavelength from a tunable light source (TLS) was sent through a polarizer, a half-wave plate (HWP) and a quarter-wave plate (QWP), and coupled into the PIC by using a non-polarization-maintaining (non-PM) lensed fiber. By rotating HWP and QWP, and carefully calibrating the effect of SOP change inside the non-PM fiber, we could deterministically generate arbitrary SOP at the input of PIC. The PIC under test was kept on a temperature-controlled stage to maintain constant temperature throughout the experiment. The output light from each port was coupled sequentially and characterized using a commercial bench-top polarization analyzer (General Photonics PSY-101) to detect the Stokes parameters (S₁, S₂, S₃). The measured S₁ parameters from all output ports (OW1-OW3) were used as V in Eq. (2) to retrieve input SOP.

 

Fig. 3 Experimental setup. A polarization controller (Pol. Ctrl.) and optical power meter (OPM) at the input were used to maximize the power transmitted through the polarizer, whereas OPM at the output was used for alignment.

Download Full Size | PDF

In order to emulate TE-PDs in Fig. 1 and detect S₁ component of the light at the PIC output, the change in SOP at the output fiber and 90:10 splitter was calibrated before the measurement; we sent a TE-mode light and recorded the Stokes parameters at PSY-101, which were used to rotate the rest of the measured data. To define the input SOP, we first removed the PIC and coupled the input light directly to the output fiber. We then rotated HWP and QWP to determine required rotation angles to have desired SOPs. Afterwards, we inserted the PIC and sent the predetermined SOPs to the circuit.

3.3. Measurement results

The experimental procedure is twofold; we first derive the projection matrix (M_p) and then retrieve arbitrary SOP using M_p. The projection matrix of the fabricated PIC is determined by sending three different SOPs: S = (1, 0, 0)^T, (0, 1, 0)^T and (0, 0, 1)^T and measuring S₁ values at three output ports (OW1-OW3) to be used as V for each S. Consequently, M_p is derived as

By using the derived M_p and the measured S₁ values at three output ports (OW1-OW3) V, we could retrieve any arbitrary SOP by Eq. (2). Figure 4(a) depicts the actual input SOP sent to the PIC (blue dots) and the SOP retrieved from the detected signal V (red dots), when the HWP is rotated from 0 to 45° in a step of 5°. Figure 4(b) represents the input and retrieved Stokes parameters for the same data points as shown in Fig. 4(a). We see that the retrieved SV rotates around a great circle and convert from TE mode [S = (1, 0, 0)^T] to TM mode [S = (−1, 0, 0)^T] in agreement with theory.

 

Fig. 4 (a) Retrieved and input SOPs on Poincare sphere when HWP was rotated from 0 to 45°. (b) Stokes parameters plotted as a function of HWP angle for the same data.

Download Full Size | PDF

Next, we generate several different SOPs randomly scattered on the Poincare sphere as the input into the PIC. Figure 5(a) shows both the actual input and retrieved SOPs on Stokes space. The input and the corresponding retrieved SOPs are marked by dotted circles in Fig. 5(a). For quantitative comparison, we plot the retrieved (S^re) and actual input (Sⁱⁿ) Stokes parameters for all the measured cases in Fig. 5(b). It reveals a good agreement with the data lying on ideal straight line (S^re = Sⁱⁿ).

 

Fig. 5 (a) Retrieved and input SOPs on Poincare sphere, (b) scattered plot of retrieved (S^re) and input (Sⁱⁿ) Stokes parameters together with ideal case straight line, S^re = Sⁱⁿ (dotted line).

Download Full Size | PDF

4. Conclusion

A monolithic integrated waveguide-based SV analyzer has been proposed and demonstrated on a compact InP PIC by integrating half-ridge waveguides. Using the 3 × 3 projection matrix realized on the PIC, we have shown that arbitrary SOP can be retrieved from the detected signals. We also clarified that fabrication imperfectness can be calibrated by deriving the projection matrix of the actual device. Monolithic integration of MQW-based photodetectors and/or waveguide-based polarizer would allow on-chip high-speed detection of SOP, which should find plethora of attractive applications in the next generation short-reach communication links. Finally, we should note that although InP-based PIC has been demonstrated in this work, the proposed concept is general and can be implemented in any waveguide platform.