Abstract

Stokes vector modulation and direct detection (SVM/DD) has immense potentiality to reduce the cost burden for the next-generation short-reach optical communication networks. In this paper, we propose and demonstrate an InGaAsP/InP waveguide-based polarization-analyzing circuit for an integrated Stokes vector (SV) receiver. By transforming the input state-of-polarization (SOP) and projecting its SV onto three different vectors on the Poincare sphere, we show that the actual SOP can be retrieved by simple calculation. We also reveal that this projection matrix has a flexibility and its deviation due to device imperfectness can be calibrated to a certain degree, so that the proposed device would be fundamentally robust against fabrication errors. A proof-of-concept photonic integrated circuit (PIC) is fabricated on InP by using half-ridge waveguides to successfully demonstrate detection of different SOPs scattered on the Poincare sphere.

© 2017 Optical Society of America

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 S=[S1,S2,S3]T, where S1 = |aTE|2 - |aTM|2, S2 = 2Re(aTE*aTM), and S3 = 2Im(aTE*aTM). Here, aTE and aTM 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).

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While the PC sections on OW2 and OW3 with a length LPC 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<θ45o) with respect to the horizontal or vertical axis [19]. Location of PC section in OW3 is offset by a length Lsym 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 Sref= MMMIS, where S is the SOP at the input of the device and MMMI is a 3 × 3 orthogonal matrix. The role of the section located at right hand side of the reference plane is to transform Sref 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 S1', S2' and S3'. 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

V[V1V2V3]=[S1'.SrefS2'.SrefS3'.Sref]MPS,
where we define MP=[S1',S2',S3']TMMMI as the projection matrix. Since MP is known and fixed, we can retrieve the actual Stokes vector of light at the input of the device by

S=MP1V.

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 Sout = MSin, where Sin 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

M=[cos22θ+cos(ΔβL)sin22θ{1cos(ΔβL)}cos2θsin2θsin(ΔβL)sin2θ{1cos(ΔβL)}cos2θsin2θsin22θ+cos(ΔβL)cos22θsin(ΔβL)cos2θsin(ΔβL)sin2θsin(ΔβL)cos2θcos(ΔβL)]
where L is the length of the birefringent waveguide. Δβ is the difference in propagation constants for two eigenmodes and defined as Δβ2π(n1n2)/λ, where λ is wavelength of light, n1 and n2 are the effective refractive indices of two eigenmodes. Detailed derivation of M can be found in Chapter 6 of [22].

Equation (3) indeed represents rotation in 3D space around a vector b=(cos2θ,sin2θ,0)T with an angle ΔβL. We can therefore design θ and L appropriately, such that three different vectors S1', S2', and S3' 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 LPC [L in Eq. (3)] appropriately, such that a vector S2' 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 S3' on S2-S3 plane first experiences a rotation about S1-axis as it travels through the symmetric waveguide of length Lsym, due to the difference of effective refractive indices between TE (nTE) and TM (nTM) modes, and transformed into a vector S2' on the same plane [see Fig. 1(b)]. This transformation can be understood by inserting θ = 0o in the Eq. (3). Then, S2'experiences a similar rotation as in OW2 to finally arrive at S1-axis. Consequently, we can detect S3' component by TE-PD at OW3.

Since the functionality of PC section is to convert a vector S2', 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 Si' may not necessarily be perfectly orthogonal to calculate S. When Si' are orthogonal, |det(MP)| = 1 (since |det(MMMI)|=1); but even in a non-ideal cases with non-orthogonal S1', we can still retrieve S by calculating Eq. (2) as long as det(Mp) ≠ 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 Mp. As a result, the distances between S1', S2', and S3' decrease on the Poincare sphere, which may result in power penalty. For a device with det(Mp) = 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(Mp)| degrades from 1, the unique flexibility and the ability of calibrating Mp 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 Lsym and LPC 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.

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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.

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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 (Mp) and then retrieve arbitrary SOP using Mp. 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, Mp is derived as

Mp=[0.98-0.04-0.130.100.370.930.44-0.840.08],
with det(MP) = 0.79. We should note that the residual variation in insertion loss among the ports is calibrated when deriving Mp. We estimate the excess on-chip loss to be 9-12 dB depending on the port, after subtracting the inherent 6-dB loss at the 1 × 4 MMI coupler and 6-dB coupling losses at each facet (which is estimated from independent measurement) from the total loss. We attribute this large on-chip loss to the MMI design, which was not optimal in terms of loss. We thus expect loss should be reduced by optimizing the MMI coupler.

By using the derived Mp 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.

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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 (Sre) 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 (Sre = Sin).

 

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

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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.

Funding

Grant-in-Aid of Japan Society for the Promotion of Science (26000010, 15H03985).

References and links

1. J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015). [CrossRef]  

2. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27(22), 5115–5126 (2009). [CrossRef]  

3. K. Kikuchi and S. Kawakami, “Multi-level signaling in the Stokes space and its application to large-capacity optical communications,” Opt. Express 22(7), 7374–7387 (2014). [CrossRef]   [PubMed]  

4. S. Betti, G. De Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992). [CrossRef]  

5. S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994). [CrossRef]  

6. S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995). [CrossRef]  

7. D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “160-Gb/s stokes vector direct detection for short reach optical communication,” in Optical Fiber Communications Conference (Optical Society of America, 2014), paper Th5C.7. [CrossRef]  

8. D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “Stokes vector direct detection for short-reach optical communication,” Opt. Lett. 39(11), 3110–3113 (2014). [CrossRef]   [PubMed]  

9. M. Chagnon, M. Morsy-Osman, and D. Plant, “Single wavelength multi-dimensional modulation with self-beating direct detection,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1A.1.

10. Y. Kawabata, M. Zaitsu, T. Tanemura, and Y. Nakano, “Proposal and experimental demonstration of monolithic InP/InGaAsP polarization modulator,” in Proceedings of the European Conference on Optical Communications (IEEE, 2014), paper Tu.4.4.4. [CrossRef]  

11. M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015). [CrossRef]  

12. P. Dong, X. Chen, K. Kim, S. Chandrasekhar, Y. K. Chen, and J. H. Sinsky, “128-Gb/s 100-km transmission with direct detection using silicon photonic Stokes vector receiver and I/Q modulator,” Opt. Express 24(13), 14208–14214 (2016). [CrossRef]   [PubMed]  

13. S. Ghosh, Y. Kawabata, T. Tanemura, and Y. Nakano, “Integrated Stokes vector analyzer on InP,” in Proceedings of the 21st Optoelectronics and Communications Conference / International Conference on Photonics in Switching (OECC-PS, 2016), paper WD4–4.

14. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 2000).

15. H. E. Refaei, D. Yevick, and T. Jones, “Slanted-rib waveguide InGaAsP-InP polarization converters,” J. Lightwave Technol. 22(5), 1352–1357 (2004). [CrossRef]  

16. B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated passive waveguide mode converters,” IEEE Photonics Technol. Lett. 18(1), 43–45 (2006). [CrossRef]  

17. L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007). [CrossRef]  

18. J. Pello, J. van der Tol, S. Keyvaninia, R. van Veldhoven, H. Ambrosius, G. Roelkens, and M. Smit, “High-efficiency ultrasmall polarization converter in InP membrane,” Opt. Lett. 37(17), 3711–3713 (2012). [CrossRef]   [PubMed]  

19. M. Zaitsu, T. Tanemura, A. Higo, and Y. Nakano, “Experimental demonstration of self-aligned InP/InGaAsP polarization converter for polarization multiplexed photonic integrated circuits,” Opt. Express 21(6), 6910–6918 (2013). [CrossRef]   [PubMed]  

20. R. Ulrich, “Representation of codirectional coupled waves,” Opt. Lett. 1(3), 109–111 (1977). [CrossRef]   [PubMed]  

21. J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).

22. D. H. Goldstein, Polarized Light (CRC Press, 2016).

23. M. Zaitsu, T. Tanemura, and Y. Nakano, “Numerical study on fabrication tolerance of half-ridge InP polarization converters,” IEICE Trans. Electron. 97(7), 731–735 (2014). [CrossRef]  

References

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  1. J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
    [Crossref]
  2. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27(22), 5115–5126 (2009).
    [Crossref]
  3. K. Kikuchi and S. Kawakami, “Multi-level signaling in the Stokes space and its application to large-capacity optical communications,” Opt. Express 22(7), 7374–7387 (2014).
    [Crossref] [PubMed]
  4. S. Betti, G. De Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
    [Crossref]
  5. S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
    [Crossref]
  6. S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
    [Crossref]
  7. D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “160-Gb/s stokes vector direct detection for short reach optical communication,” in Optical Fiber Communications Conference (Optical Society of America, 2014), paper Th5C.7.
    [Crossref]
  8. D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “Stokes vector direct detection for short-reach optical communication,” Opt. Lett. 39(11), 3110–3113 (2014).
    [Crossref] [PubMed]
  9. M. Chagnon, M. Morsy-Osman, and D. Plant, “Single wavelength multi-dimensional modulation with self-beating direct detection,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1A.1.
  10. Y. Kawabata, M. Zaitsu, T. Tanemura, and Y. Nakano, “Proposal and experimental demonstration of monolithic InP/InGaAsP polarization modulator,” in Proceedings of the European Conference on Optical Communications (IEEE, 2014), paper Tu.4.4.4.
    [Crossref]
  11. M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
    [Crossref]
  12. P. Dong, X. Chen, K. Kim, S. Chandrasekhar, Y. K. Chen, and J. H. Sinsky, “128-Gb/s 100-km transmission with direct detection using silicon photonic Stokes vector receiver and I/Q modulator,” Opt. Express 24(13), 14208–14214 (2016).
    [Crossref] [PubMed]
  13. S. Ghosh, Y. Kawabata, T. Tanemura, and Y. Nakano, “Integrated Stokes vector analyzer on InP,” in Proceedings of the 21st Optoelectronics and Communications Conference / International Conference on Photonics in Switching (OECC-PS, 2016), paper WD4–4.
  14. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 2000).
  15. H. E. Refaei, D. Yevick, and T. Jones, “Slanted-rib waveguide InGaAsP-InP polarization converters,” J. Lightwave Technol. 22(5), 1352–1357 (2004).
    [Crossref]
  16. B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated passive waveguide mode converters,” IEEE Photonics Technol. Lett. 18(1), 43–45 (2006).
    [Crossref]
  17. L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
    [Crossref]
  18. J. Pello, J. van der Tol, S. Keyvaninia, R. van Veldhoven, H. Ambrosius, G. Roelkens, and M. Smit, “High-efficiency ultrasmall polarization converter in InP membrane,” Opt. Lett. 37(17), 3711–3713 (2012).
    [Crossref] [PubMed]
  19. M. Zaitsu, T. Tanemura, A. Higo, and Y. Nakano, “Experimental demonstration of self-aligned InP/InGaAsP polarization converter for polarization multiplexed photonic integrated circuits,” Opt. Express 21(6), 6910–6918 (2013).
    [Crossref] [PubMed]
  20. R. Ulrich, “Representation of codirectional coupled waves,” Opt. Lett. 1(3), 109–111 (1977).
    [Crossref] [PubMed]
  21. J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).
  22. D. H. Goldstein, Polarized Light (CRC Press, 2016).
  23. M. Zaitsu, T. Tanemura, and Y. Nakano, “Numerical study on fabrication tolerance of half-ridge InP polarization converters,” IEICE Trans. Electron. 97(7), 731–735 (2014).
    [Crossref]

2016 (1)

2015 (2)

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

2014 (3)

2013 (1)

2012 (1)

2009 (1)

2007 (1)

L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
[Crossref]

2006 (1)

B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated passive waveguide mode converters,” IEEE Photonics Technol. Lett. 18(1), 43–45 (2006).
[Crossref]

2004 (1)

1995 (1)

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

1994 (1)

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

1992 (1)

S. Betti, G. De Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[Crossref]

1977 (1)

Agrell, E.

Ambrosius, H.

Augustin, L. M.

L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
[Crossref]

Benedetto, S.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

Betti, S.

S. Betti, G. De Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[Crossref]

Chandrasekhar, S.

Che, D.

Chen, X.

Chen, Y. K.

Cheng, Q.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Cunningham, D. G.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

De Marchis, G.

S. Betti, G. De Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[Crossref]

Djupsjobacka, A.

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

Dong, P.

Gaudino, R.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

Geluk, E. J.

L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
[Crossref]

Haji, M.

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

Higo, A.

Holmes, B. M.

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated passive waveguide mode converters,” IEEE Photonics Technol. Lett. 18(1), 43–45 (2006).
[Crossref]

Hu, Q.

Hutchings, D. C.

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated passive waveguide mode converters,” IEEE Photonics Technol. Lett. 18(1), 43–45 (2006).
[Crossref]

Iannone, E.

S. Betti, G. De Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[Crossref]

Jones, T.

Karlsson, M.

Kawakami, S.

Kelly, A. E.

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

Keyvaninia, S.

Kikuchi, K.

Kim, K.

Lagerstrom, B.

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

Li, A.

Marsh, J. H.

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

Mijic, G.

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

Naeem, M. A.

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

Nakano, Y.

M. Zaitsu, T. Tanemura, and Y. Nakano, “Numerical study on fabrication tolerance of half-ridge InP polarization converters,” IEICE Trans. Electron. 97(7), 731–735 (2014).
[Crossref]

M. Zaitsu, T. Tanemura, A. Higo, and Y. Nakano, “Experimental demonstration of self-aligned InP/InGaAsP polarization converter for polarization multiplexed photonic integrated circuits,” Opt. Express 21(6), 6910–6918 (2013).
[Crossref] [PubMed]

Paoletti, R.

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

Pello, J.

Penty, R. V.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Poggiolini, P.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

Refaei, H. E.

Roelkens, G.

Shieh, W.

Sinsky, J. H.

Smit, M.

Smit, M. K.

L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
[Crossref]

Tanemura, T.

M. Zaitsu, T. Tanemura, and Y. Nakano, “Numerical study on fabrication tolerance of half-ridge InP polarization converters,” IEICE Trans. Electron. 97(7), 731–735 (2014).
[Crossref]

M. Zaitsu, T. Tanemura, A. Higo, and Y. Nakano, “Experimental demonstration of self-aligned InP/InGaAsP polarization converter for polarization multiplexed photonic integrated circuits,” Opt. Express 21(6), 6910–6918 (2013).
[Crossref] [PubMed]

Ulrich, R.

van der Tol, J.

van der Tol, J. J. G. M.

L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
[Crossref]

van Veldhoven, R.

Wang, Y.

Wei, J.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

White, I. H.

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

Yevick, D.

Zaitsu, M.

M. Zaitsu, T. Tanemura, and Y. Nakano, “Numerical study on fabrication tolerance of half-ridge InP polarization converters,” IEICE Trans. Electron. 97(7), 731–735 (2014).
[Crossref]

M. Zaitsu, T. Tanemura, A. Higo, and Y. Nakano, “Experimental demonstration of self-aligned InP/InGaAsP polarization converter for polarization multiplexed photonic integrated circuits,” Opt. Express 21(6), 6910–6918 (2013).
[Crossref] [PubMed]

IEEE Commun. Mag. (1)

J. Wei, Q. Cheng, R. V. Penty, I. H. White, and D. G. Cunningham, “400 Gigabit Ethernet using advanced modulation formats: Performance, complexity, and power dissipation,” IEEE Commun. Mag. 53(2), 182–189 (2015).
[Crossref]

IEEE J. Sel. Areas Comm. (1)

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm. 13(3), 531–542 (1995).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

M. A. Naeem, M. Haji, B. M. Holmes, D. C. Hutchings, J. H. Marsh, and A. E. Kelly, “Generation of high speed polarization modulated data using a monolithically integrated device,” IEEE J. Sel. Top. Quantum Electron. 21(4), 207–211 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (3)

S. Benedetto, A. Djupsjobacka, B. Lagerstrom, R. Paoletti, P. Poggiolini, and G. Mijic, “Multilevel polarization modulation using a specifically designed LiNbO3 device,” IEEE Photonics Technol. Lett. 6(8), 949–951 (1994).
[Crossref]

B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated passive waveguide mode converters,” IEEE Photonics Technol. Lett. 18(1), 43–45 (2006).
[Crossref]

L. M. Augustin, J. J. G. M. van der Tol, E. J. Geluk, and M. K. Smit, “Short polarization converter optimized for active–passive integration in InGaAsP–InP,” IEEE Photonics Technol. Lett. 19(20), 1673–1675 (2007).
[Crossref]

IEICE Trans. Electron. (1)

M. Zaitsu, T. Tanemura, and Y. Nakano, “Numerical study on fabrication tolerance of half-ridge InP polarization converters,” IEICE Trans. Electron. 97(7), 731–735 (2014).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (3)

Opt. Lett. (3)

Other (7)

M. Chagnon, M. Morsy-Osman, and D. Plant, “Single wavelength multi-dimensional modulation with self-beating direct detection,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper W1A.1.

Y. Kawabata, M. Zaitsu, T. Tanemura, and Y. Nakano, “Proposal and experimental demonstration of monolithic InP/InGaAsP polarization modulator,” in Proceedings of the European Conference on Optical Communications (IEEE, 2014), paper Tu.4.4.4.
[Crossref]

D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “160-Gb/s stokes vector direct detection for short reach optical communication,” in Optical Fiber Communications Conference (Optical Society of America, 2014), paper Th5C.7.
[Crossref]

J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).

D. H. Goldstein, Polarized Light (CRC Press, 2016).

S. Ghosh, Y. Kawabata, T. Tanemura, and Y. Nakano, “Integrated Stokes vector analyzer on InP,” in Proceedings of the 21st Optoelectronics and Communications Conference / International Conference on Photonics in Switching (OECC-PS, 2016), paper WD4–4.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 2000).

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Figures (5)

Fig. 1
Fig. 1 Schematic (a) layout of proposed integrated Stokes vector analyzer, cross-section view of (b) symmetric waveguide and (c) asymmetric waveguide (PC).
Fig. 2
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.
Fig. 3
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.
Fig. 4
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.
Fig. 5
Fig. 5 (a) Retrieved and input SOPs on Poincare sphere, (b) scattered plot of retrieved (Sre) and input (Sin) Stokes parameters together with ideal case straight line, Sre = Sin (dotted line).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

V [ V 1 V 2 V 3 ] = [ S 1 ' . S ref S 2 ' . S ref S 3 ' . S ref ] M P S,
S= M P 1 V.
M=[ cos 2 2θ+cos(ΔβL) sin 2 2θ {1cos(ΔβL)}cos2θsin2θ sin(ΔβL)sin2θ {1cos(ΔβL)}cos2θsin2θ sin 2 2θ+cos(ΔβL) cos 2 2θ sin(ΔβL)cos2θ sin(ΔβL)sin2θ sin(ΔβL)cos2θ cos(ΔβL) ]
M p =[ 0.98 -0.04 -0.13 0.10 0.37 0.93 0.44 -0.84 0.08 ],

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