Abstract

Monolithically integrated polarization beam splitters (PBSs) are needed to reduce the form-factor and assembly cost of optical coherent receivers. A highly efficient passive polarization rotator and splitter based on mode-evolution is demonstrated. The device is fabricated on InP substrate with a single etch-step and uses an adiabatic mode-converter and an asymmetric Y-coupler. Despite its simple fabrication process, the device shows a polarization extinction ratio (PER) better than 19 dB over 1520 nm to 1620 nm, thus covering both C- and L-band. The peak value of 24 dB is obtained for TE and TM polarizations. Its fabrication tolerance is large, so that even under a width variation of +/− 200 nm the PER remains above 17 dB over the entire C- and L-band.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Polarization handling in photonic integrated circuits (PICs) is of great importance to further decrease the component cost of high-speed optical communication networks. Data is transmitted in fibers in two main polarization states. At the end of a transmission line at the input of an optical receiver, the TE polarization has to be separated from the TM polarization to double the spectral efficiency by polarization-division-multiplexing. This requires a pair of identical photonic sub-circuits in parallel for each of the two polarization states [1–3]. The planar geometry of a PIC often causes different behavior for the two orthogonally polarized modes because of different boundary conditions, leading to different propagation constants and confinement factors. To overcome this problem, different approaches can be applied. One is to remove polarization dependence by changing the properties of the material [4] or the geometry of the waveguides [5]. This can be challenging and will always be compromising with respect to optimal performance for one of the polarization states. An alternative solution is having only one type of polarization at each sub-circuit by converting orthogonal polarizations to identical ones, e.g., TE polarizations. For the implementation of polarization demultiplexing at the receiver, a PBS and optionally a polarization rotator (PR) are needed. One option to implement the polarization demultiplexing stage is based on discrete polarization components, usually implemented in free-space optics [6,7]. The other approach is based on monolithically integrating the polarization components together with the receiver in a PIC [8–11]. Therefore, the integrated PBS and polarization rotator-splitter (PRS) are key devices to realize such on-chip polarization control. Many approaches have been proposed to implement PBS and PRS in different material platforms [10–26]. The PBS and PRS can mainly be categorized in mode-coupling and mode-evolution types. Mode-coupling-based polarization handling devices use the mode beating behavior resulting from controlled waveguide birefringence and their performance is often wavelength-dependent. To solve this problem, several novel asymmetric directional coupler (DC) designs and cascaded bend DC structures have been proposed in recent years [19–21]. However, one major barrier for this type is its tight fabrication tolerance of often not more than ± 20 nm [20]. On the contrary, mode-evolution-based devices have less wavelength sensitivity and better fabrication tolerance. However, the device length is longer in order to achieve adiabatic mode-evolution [26–29]. The current designs of the PRS mainly comprise combinations of mode-evolution parts and mode-coupling parts in the polarization splitter or rotator segments [21–27]. Realizing the PRS in silicon PICs is possible with more compact footprints because of the ultra-high waveguide birefringence and the high-index-contrast. The fabrication tolerances, however, are tens of nanometers [21–26] and thus very challenging. A review of the recent work on the high-performance silicon photonic PRS is given in [19,26]. In contrast, InP-based PICs require a larger footprint to realize PRS, because of waveguide geometries with low birefringence and index contrast. However, monolithic InP-based PICs offer high-performance components and easy semiconductor optical amplifier and laser integration. An alternative concept using InP platforms has been proposed in [31] by making use of the properties of multiple-quantum wells (MQWs) to detect TE and TM polarized light separately. Especially polarization diverse coherent optical receivers (PD-CRx) will benefit from this monolithic photodetector concept because neither polarization beam splitters nor rotators are needed, resulting by eliminating the polarization diversity network and one 90° hybrid in approximately 25% of the chip size of conventional PD-CRxs. However, this concept needs an extra selective-area regrowth, and the MQW carrier transit time limits the photodetector bandwidth [31]. Recently a new InP-based PRS for mid-infrared sensing application (λ> 6 µm) with a length of 10 mm has been demonstrated [32]. In this work, we demonstrate a mode-evolution-based PRS built on an InP substrate, combining adiabatic width tapers with an asymmetric Y-coupler. The PRS is a mode-evolution-based device in both parts of the rotator and the splitter, resulting in large bandwidth and fabrication tolerance. This paper is the first demonstration of such an InP-based PRS for telecom wavelengths since the concept was introduced in [27]. Furthermore, we simplified the fabrication process to only a single etch-step waveguide by proposing a new pre-converter. This paper is organized as follows. Section 2 explains the mode-evolution structure in the rotator segment. Section 3 provides the design and simulation of the proposed PRS. Section 4 describes the fabrication and measurement results of the device. Conclusions are given in section 5.

2. Polarization mode-converter based on mode-evolution principle

In contrast to symmetric waveguides like buried channel waveguides, hybrid super-modes can occur in rib waveguides for certain waveguide dimensions (see Fig. 1). The vertical asymmetry in the refractive index profile can be interpreted as a perturbation that leads to a coupling of the TM0 and TE1 modes within a waveguide for certain widths of the waveguide and therefore to a mode hybridization. Such hybrid modes can be understood as super-modes [28,33,34] of the undisturbed TM0 and TE1 modes. The hybrid super-modes S1 and S2 can be expressed as a combination of the two eigen-modes. Figure 1 shows the propagation constant (β) of the modes for a taper structure along the propagation direction (z) which corresponds to the rib-waveguide width variation. In order to evaluate the amount of mode hybridization in the super-modes, the mode polarization ratio γx is defined as [35]:

γx=s|Ex2|dxdys|Ex2|dxdy+s|Ey2|dxdy
where Ex and Ey are the x- and y-component of the electrical field for any eigen-mode considered. For typical TE modes, Ex is significantly larger than Ey and consequently, the ratio γx approaches 100%. In contrast, for pure TM modes, γx is 0%. The super-modes have γx between 0% and 100%. The hybrid super-modes are the uncoupled eigen-modes of the waveguide system. They arise from the coupling between the TM0 and TE1 modes.

 

Fig. 1 Dispersion curves in the rib taper-waveguide of the mode-evolution-based polarization rotator. β is the propagation constant, W the rib-width along the propagation direction (z). The ridge height h1 is 120 nm, the waveguide height h2 is 320 nm. Wavelength is 1550 nm. S1 and S2 correspond to the coupled waveguide super-modes; the coloring along the lines indicate the mode polarization ratio (γx), showing the conversion of TM0 to TE1.

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Normally, the super-mode theory is used to describe coupling processes in a system of waveguides, e.g., for two parallel waveguides in a directional coupler [33,34]. In our case, we only consider a single waveguide, but here the original TM0 and TE1 modes couple due to the vertical dielectric perturbation. The normalized super-modes (AS1 and AS2) can be expressed as column vectors with their components denoting the amplitudes of the two individual uncoupled TM0 and TE1 modes in the waveguide [34]:

AS1(z)=12((1-2δ/Δβ)(1+2δ/Δβ))e-jβS1z
AS2(z)=12((1+2δ/Δβ)(1-2δ/Δβ))e-jβS2z
Where δ=(βTM0-βTE1)/2is the mismatch of the propagation constants of the undisturbed TM0 and TE1 modes, Δβ=2δ2+κ2=βS1-βS2is the difference of propagation constants of the S1 and S2, and 𝜅 is the coupling strength between the two undisturbed modes. Therefore, Δβ is a measure for the strength of hybridization of the super-modes. According to Fig. 1, for the hybrid mode S1, three cases are of special interest: In the first case at zi, 𝛿 > 0 and 𝛿 ≫ 𝜅. One can notice the mode is substantially represented by the TM0 mode and therefore no hybrid mode is formed. For 𝛿 = 0 at z0, the two modes are phase matched. As a result, the amplitudes of the modes are equally divided between the TM0 and TE1 modes, here the strongest case for hybridization is occurring. Because of the phase-match of the undisturbed modes, 𝜅 can be determined as κ=(βS1-βS2)/2. The last case is at zf with 𝛿 < 0 and 𝛿 ≫ 𝜅, here the hybrid mode S1 is substantially represented by the TE1 and no hybridization occurs. Moreover, due to the coupling, the original TM0 mode has been converted to the TE1 mode.

3. Design and simulation

A rib waveguide as shown in Fig. 1 is considered for the proposed structure with a vertical asymmetry. The quaternary compound semiconductor material InGaAsP (Q1.35), lattice- matched to the InP substrate with a height of h1 + h2 is used as waveguide material. The waveguide rib has a height h1 and a width w. The cladding of the waveguide is air so that a maximum of vertical asymmetry for the waveguide is given, improving coupling strength 𝜅. Higher coupling strength between two super-modes increases the polarization conversion efficiency and reduces the adiabatic conversion-length according to the adiabatic criterion [30,34]. A commercial software (FIMMPROP, Photon Design) was used to simulate the structure [36]. h1 and h2 are varied. For each h1 and h2 pair, the propagation constants for different waveguide widths of the first three guided modes of the waveguide structure including the polarization ratios are obtained at 𝜆 = 1550 nm. The difference in propagation constants Δβ at the waveguide width of the strongest hybridization (γx = 50%) of the first and second super-modes is depicted in Fig. 2(a). For γx = 50%, Δβ = 2 𝜅 holds.

 

Fig. 2 (a) The difference in propagation constants at the waveguide width of highest hybridization of the first and second super-modes with 50% polarization ratio γx as a function of the InGaAsP thickness at the wavelength of 1550 nm; (b) calculated electric field profiles for two hybrid super-modes S1 and S2 with an equal 50% polarization ratio (γx) using h1 = 120 nm, h2 = 320 nm, at the wavelength of 1550 nm.

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To obtain a robust design for the mode-evolution taper, geometrical parameters of the waveguide are chosen to achieve a high coupling strength (𝜅) and therefore a high difference of propagation constants (Δβ). The waveguide geometry with h1 = 120 nm and h2 = 320 nm shows the largest Δβ (Fig. 2(a)), leading to shorter mode-converter designs and higher conversion efficiencies. Calculated electric field profiles of Ex and Ey for two hybrid super-modes S1 and S2 with an equal polarization ratio (γx) are shown in Fig. 2(b) using the optimum waveguide geometry and the wavelength of 1550 nm. However, a strong hybridization of the waveguide structure leads to slight mode hybridization of the input port further away from the main hybridization regime. Thus, an additional mode-adapter is needed to decrease the asymmetry of the input waveguide and to increase the conversion efficiency [27]. The proposed device in Fig. 3 is composed of three segments, a mode adapter, a mode-converter and an asymmetric Y-coupler while using the waveguide structure optimized for a high difference of propagation constants obtained from Fig. 2(a).

 

Fig. 3 The schematic layout of the mode-evolution-based polarization rotator-splitter and geometries after optimization.

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The proposed mode-converter consists of a two-step linear taper, as shown in Fig. 3. It is designed to transform the TM0 mode to the TE1 mode without changing the TE0 mode. The waveguide structure of the width taper is designed by etching through the InGaAsP layer, as shown in Fig. 3. The propagation constant (β) of the modes are shown in Fig. 1, simulated in the mode-rotator segment using the parameters illustrated in Fig. 3. At the input of the taper with a width of 1.7 μm, the propagation constant of the TM0 mode is larger than that of TE1 and the propagation constant difference is large. As the waveguide width increases up to 2.3 μm, the propagation constant between the TE1 and the TM0 becomes smaller. Due to the structure asymmetry in the vertical direction, these two modes do not cross each other and form two super-modes, which are neither pure TE nor TM polarization as it was discussed in the previous section. With further increase of the waveguide width beyond 2.7 μm, the propagation constant difference starts to increase, and two hybrid modes evolve back into TE1 and TM0 modes respectively. It should be noted that for the output taper wider than 2.7 μm, the super-mode S1 which was TM0 mode at the input of the taper converts to a TE1 mode. However, the TE0 mode propagates unchanged over both linear tapered waveguides. To avoid mode hybridization at narrower waveguides at the input before reaching the mode-converter, a novel mode adapter by using a single-layer silicon nitride (Si3N4) is proposed to decrease the asymmetry of the waveguide which leads to smaller hybridization effects and the modes adapt to be more TE- or TM-like. A 150 µm long adiabatic Si3N4 taper with a thickness of 150 nm is used to connect another waveguide with a pure TM0 mode to the input of width taper (w1 = 1.7 µm) and to convert the remaining hybrid polarization. The novel and low loss pre-converter is formed by pattering the same Si3N4 which was initially used during the waveguide etching. Thus, the Si3N4 sidewalls and the waveguide sidewalls are self-aligned. An extra low-resolution lithography, which is also less sensitive to a lateral misalignment, can be used to pattern the single side taper shown in Fig. 3. This can be realized by designing the mask to etch the Si3N4 in an area much wider than the rib waveguide itself, resulting in relaxed lateral alignment tolerance. Moreover, an ultra-small taper tip for Si3N4 can be formed by overlaying line-edge patterning with widths adequately larger than the diffractive resolution limit.

As shown in Fig. 3, an asymmetric Y-coupler [27] is designed to evolve the TE1 and TE0 from the output of the width taper into the TE0 in the narrower branch and the TE0 in the wider branch of Y-coupler, respectively. To realize a mode separation, the waveguide widths in the branches of the Y-coupler are chosen so that the propagation constant of TE0 in the narrow branch of the Y-coupler is matched to that of TE1 at the output of the converter section, and the propagation constant of TE0 in the wider branch is equal to that of TE0 at the output of the converter section. Therefore, both the fundamental mode TE0 and the first odd mode TE1 couple into the fundamental mode of their respective branches. This at the same time induces a spatial separation of the TE0 and TE1 modes as well as a mode conversion for TE1 transforming to TE0 modes at each port. The angle of the branching θ and the dimensions of the branches for a given width of the stem of the Y-coupler is designed to achieve very low insertion loss with high splitting ratio, contributing to an improved polarization extinction ratio (PER) of the PRS. The branching angle θ, gap, and branch widths are assumed to be 0.3°, 120 nm, 1.4 μm, and 1.5 μm respectively in the simulation for Y-coupler. Figure 4 shows the light propagation in the PRS for different input modes at 1550 nm wavelength. The input TM0 mode is predominantly converted into the TE0 mode at the narrow port (Port1), while the input TE0 mode is not converted in the taper and finally exits at the wider port (Port2).

 

Fig. 4 Simulated light propagation in the designed PRS when the TM0 and TE0 modes are launched at 1550nm.

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The performance of the PRS can be evaluated by the PER. The PER is defined as:

PERPort1=|10log(PTE0,Port1PTM0,Port1)|
PERPort2=|10log(PTE0,Port2PTM0,Port2)|
Where PTE0,Port1,2and PTM0,Port1,2are the power at the Port1 and Port2 of the asymmetric Y-coupler with a TE0 or TM0 input light respectively. Figure 5 shows the simulated PER spectra for both output ports of the Y-coupler as a function of the waveguide width deviation from the design value in the whole structure, including the Y-coupler. The simulation shows that a 200 nm gap in the Y-coupler is sufficient to achieve a high-performance device. For both TE0 and TM0 input modes, the device has a PER above 18 dB for the width variations of +/− 200 nm over the entire C- and L-band.

 

Fig. 5 Simulated PERport1,2 spectra when the TM0 and TE0 modes are launched at the input of the PRS for the width variation up to +/− 200 nm.

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4. Fabrication and characterizations

The InGaAsP layer was grown by MOVPE on semi-insulating 3-inch InP substrate. A 150 nm Si3N4 is deposited serving as a hard mask for the semiconductor etching and as a mode adapter for the PRSs. The waveguide structures are directly written using electron-beam lithography. This allows producing feature sizes down to hundred nanometers. Reactive-ion etching (RIE) is used to pattern the Si3N4 hard-mask as well as waveguide etching. Another contact lithography is used to pattern the Si3N4 tapers for the mode adapter and at the same time removing the hard mask on top of the mode-converter. This increases the vertical asymmetry and allows the Si3N4 to remain on top of the rest of the waveguides. Further, the optical facets of the chips are anti-reflection (AR) coated to reduce coupling loss. Figure 6 shows the microscope image of the fabricated PRS.

 

Fig. 6 Microscopic pictures of the fabricated PRS.

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The schematic setup for the measurement of the PRS chip is shown in Fig. 7. A laser source is connected via a fiber to a polarization synthesizer unit. A 90:10 power splitter divides the light into two fractions. The smaller fraction of the light is going to an optical power meter taken as a reference, and the larger amount is coupled to the PRS chip using a lensed fiber. After passing the chip, it is coupled out to an objective and a photodetector. The current is detected by a source measure unit (SMU). For calibration, the focused light travels to a free space polarizer that allows the blocking of either TE or TM components of the incident light before receiving by the photodetector.

 

Fig. 7 Schematic measurement setup, solid black lines denote fiber connections, broken black lines denote free space propagation of the light, and the solid blue line denote electrical connection to a source measure unit (SMU).

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The measured PER spectrums at Port1 and Port2 of the Y-coupler for PRS devices with a width variation of +/− 200 nm are represented at Fig. 8. For both input polarization states, the lowest PER was measured with respect to the tolerance width of −200 nm. This can be explained because of an extra 100 nm shrinkage of the actual width in the fabricated device compared to the designed value set on the mask. The undesired shrinkage of the waveguide width was verified with a scanning electron microscope (SEM). In future work, the lithography parameters will be calibrated to avoid this. That means the tolerance of the −200 nm on the mask is corresponding to the −300 nm deviation on the fabricated device. This causes the lower value of PER for the −200 nm deviation design. The same effect explains why the highest measured PER in Fig. 8 is related to + 100 nm deviation being in good agreement with simulated values in Fig. 5. For that reason, Fig. 8 shows a measured PER above 17 dB over the entire C- and L-band for both TE and TM input light from −200 nm to + 100 nm from the actual design value. The maximum measured the insertion loss of the TE0 and TM0 input modes were 1 ± 0.5 dB, 1.8 ± 0.5 dB respectively for the waveguide width deviation of +/− 200 nm from the design value.

 

Fig. 8 Measured PERport1,2 spectrum when the TM0 and TE0 modes are launched at the input of the PRS for the width variation up to +/− 200 nm.

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5. Conclusion

In this paper, a highly efficient PRS is proposed by combining a mode-evolution-based polarization mode-converter and an adiabatic asymmetric Y-coupler. The mode-converter consists of a simplified pre-converter structure and a two-step width taper. The pre-converter is made using Si3N4 as a hard etching mask for the waveguides, and a single etch-step waveguide is proposed for the width taper as well as for an asymmetric Y-coupler. The fabricated device has a total length of 2000 µm, and a polarization extinction ratio over 19 dB for TE and TM polarization states. Besides the simplified fabrication process with only a single-shallow-etch step process, this device has a large fabrication tolerance. The polarization extinction ratio remains over 17 dB for width variations of +/− 200 nm over the entire C- and L-band. The fabricated device shows interesting features for monolithic InP-integration, offering fully integrated polarization diversity for high-speed optical communication networks and sensing applications. The presented PRS is a candidate for InP based, fully integrated high-speed polarization diversity coherent receivers and modulators. The development of a spot-size converter for optimized fiber-chip coupling together with the integration of high-speed photodetectors is the next step towards a fully integrated dual-polarization coherent receiver.

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  5. W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
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  13. D. Pérez-Galacho, R. Zhang, A. Ortega-Monux, R. Halir, C. Alonso-Ramos, P. Runge, K. Janiak, G. Zhou, H.-G. Bach, A. G. Steffan, and I. Molina-Fernandez, “Integrated polarization beam splitter for 100/400 GE polarization multiplexed coherent optical communications,” J. Lightwave Technol. 32(3), 361–368 (2014).
    [Crossref]
  14. M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
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  18. H. Xu, D. Dai, and Y. Shi, “Ultra-broadband and ultra-compact on-chip silicon polarization beam splitter by using hetero-anisotropic metamaterials,” Laser Photonics Rev. 13(4), 1800349 (2019).
    [Crossref]
  19. D. Dai, “Advanced passive silicon photonic devices with asymmetric waveguide structures,” Proc. IEEE 106(12), 2117–2143 (2018).
    [Crossref]
  20. Y. Tian, J. Qiu, C. Liu, S. Tian, Z. Huang, and J. Wu, “Compact polarization beam splitter with a high extinction ratio over S + C + L band,” Opt. Express 27(2), 999–1009 (2019).
    [Crossref] [PubMed]
  21. D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19(11), 10940–10949 (2011).
    [Crossref] [PubMed]
  22. W. D. Sacher, T. Barwicz, B. J. Taylor, and J. K. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
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  23. J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014).
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  32. C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
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2019 (3)

H. Xu, D. Dai, and Y. Shi, “Ultra-broadband and ultra-compact on-chip silicon polarization beam splitter by using hetero-anisotropic metamaterials,” Laser Photonics Rev. 13(4), 1800349 (2019).
[Crossref]

Y. Tian, J. Qiu, C. Liu, S. Tian, Z. Huang, and J. Wu, “Compact polarization beam splitter with a high extinction ratio over S + C + L band,” Opt. Express 27(2), 999–1009 (2019).
[Crossref] [PubMed]

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
[Crossref]

2018 (3)

D. Guo and T. Chu, “Broadband and low-crosstalk polarization splitter-rotator with optimized tapers,” OSA Continuum 1(3), 841–850 (2018).
[Crossref]

D. Dai, “Advanced passive silicon photonic devices with asymmetric waveguide structures,” Proc. IEEE 106(12), 2117–2143 (2018).
[Crossref]

F. Dell’Olio, D. Conteduca, G. Brunetti, M. N. Armenise, and C. Ciminelli, “Novel CMOS-compatible athermal and polarization-insensitive ring resonator as photonic notch filter,” IEEE Photonics J. 10(6), 1–11 (2018).
[Crossref]

2017 (1)

2016 (1)

2015 (2)

2014 (3)

2013 (1)

2012 (1)

2011 (3)

2010 (1)

2009 (1)

2008 (1)

2007 (2)

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

L. M. Augustin, J. J. G. M. van der Tol, R. Hanfoug, W. J. M. de Laat, M. J. E. van de Moosdijk, P. W. L. van Dijk, Y.-S. Oei, and M. K. Smit, “A single etch-step fabrication-tolerant polarization splitter,” J. Lightwave Technol. 25(3), 740–746 (2007).
[Crossref]

2004 (1)

W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
[Crossref]

1996 (2)

R. Kaiser, D. Trommer, H. Heidrich, F. Fidorra, and M. Hamacher, “Heterodyne receiver PICs as the first monolithically integrated tunable receivers for OFDM system applications,” Opt. Quantum Electron. 28(5), 565–573 (1996).
[Crossref]

K. Mertens, M. Sennewald, and H. J. Schmitt, “Polarization conversion by hybrid modes: Theory and applications,” Radio Sci. 31(6), 1773–1779 (1996).
[Crossref]

1995 (1)

K. Mertens, B. Scholl, and H. J. Schmitt, “New highly efficient polarization converters based on hybrid supermodes,” J. Lightwave Technol. 13(10), 2087–2092 (1995).
[Crossref]

1991 (1)

Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic devices on silicon,” IEEE J. Quantum Electron. 27(3), 556–566 (1991).
[Crossref]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]

Abadía, N.

Alonso-Ramos, C.

Armenise, M. N.

F. Dell’Olio, D. Conteduca, G. Brunetti, M. N. Armenise, and C. Ciminelli, “Novel CMOS-compatible athermal and polarization-insensitive ring resonator as photonic notch filter,” IEEE Photonics J. 10(6), 1–11 (2018).
[Crossref]

Augustin, L. M.

Bach, H. G.

Bach, H.-G.

D. Pérez-Galacho, R. Zhang, A. Ortega-Monux, R. Halir, C. Alonso-Ramos, P. Runge, K. Janiak, G. Zhou, H.-G. Bach, A. G. Steffan, and I. Molina-Fernandez, “Integrated polarization beam splitter for 100/400 GE polarization multiplexed coherent optical communications,” J. Lightwave Technol. 32(3), 361–368 (2014).
[Crossref]

R. Zhang, P. Runge, G. Zhou, R. Klötzer, D. Pech, H.-G. Bach, D. Pérez-Galacho, A. Ortega-Murnox, R. Halir, and I. Molina-Fernández, “56Gbaud DP-QPSK receiver module with a monolithic integrated PBS and 90° hybrid InP chip,” in 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.

Baier, M. F.

M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
[Crossref]

Barwicz, T.

W. D. Sacher, T. Barwicz, B. J. Taylor, and J. K. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
[Crossref] [PubMed]

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Bowers, J. E.

Brunetti, G.

F. Dell’Olio, D. Conteduca, G. Brunetti, M. N. Armenise, and C. Ciminelli, “Novel CMOS-compatible athermal and polarization-insensitive ring resonator as photonic notch filter,” IEEE Photonics J. 10(6), 1–11 (2018).
[Crossref]

Buhl, L. L.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
[Crossref]

Butrie, T.

Chakravarty, S.

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
[Crossref]

Chandrasekhar, S.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
[Crossref]

C. R. Doerr, P. J. Winzer, S. Chandrasekhar, M. Rasras, M. P. Earnshaw, J. S. Weiner, D. M. Gill, and Y.-K. Chen, “Monolithic silicon coherent receiver,” J. Lightwave Technol. 28(4), 520–528 (2010).
[Crossref]

Chen, R. T.

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
[Crossref]

Chen, W.

Chen, Y. K.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
[Crossref]

Chen, Y.-K.

Chu, T.

Chung, C.-J.

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
[Crossref]

Ciminelli, C.

F. Dell’Olio, D. Conteduca, G. Brunetti, M. N. Armenise, and C. Ciminelli, “Novel CMOS-compatible athermal and polarization-insensitive ring resonator as photonic notch filter,” IEEE Photonics J. 10(6), 1–11 (2018).
[Crossref]

Conteduca, D.

F. Dell’Olio, D. Conteduca, G. Brunetti, M. N. Armenise, and C. Ciminelli, “Novel CMOS-compatible athermal and polarization-insensitive ring resonator as photonic notch filter,” IEEE Photonics J. 10(6), 1–11 (2018).
[Crossref]

Dai, D.

Dai, X.

de Laat, W. J. M.

Dell’Olio, F.

F. Dell’Olio, D. Conteduca, G. Brunetti, M. N. Armenise, and C. Ciminelli, “Novel CMOS-compatible athermal and polarization-insensitive ring resonator as photonic notch filter,” IEEE Photonics J. 10(6), 1–11 (2018).
[Crossref]

Dentai, A.

Doerr, C. R.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
[Crossref]

C. R. Doerr, P. J. Winzer, S. Chandrasekhar, M. Rasras, M. P. Earnshaw, J. S. Weiner, D. M. Gill, and Y.-K. Chen, “Monolithic silicon coherent receiver,” J. Lightwave Technol. 28(4), 520–528 (2010).
[Crossref]

Dominic, V.

Donegan, J. F.

Earnshaw, M. P.

Fidorra, F.

R. Kaiser, D. Trommer, H. Heidrich, F. Fidorra, and M. Hamacher, “Heterodyne receiver PICs as the first monolithically integrated tunable receivers for OFDM system applications,” Opt. Quantum Electron. 28(5), 565–573 (1996).
[Crossref]

Fukuda, H.

Gaertner, T.

M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
[Crossref]

Gan, F.

Gill, D. M.

Goldfarb, G.

Grote, N.

M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
[Crossref]

Guo, D.

Guo, J.

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
[Crossref]

Guo, W. H.

Halir, R.

Hamacher, M.

R. Kaiser, D. Trommer, H. Heidrich, F. Fidorra, and M. Hamacher, “Heterodyne receiver PICs as the first monolithically integrated tunable receivers for OFDM system applications,” Opt. Quantum Electron. 28(5), 565–573 (1996).
[Crossref]

Hanfoug, R.

Headley, W. R.

W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
[Crossref]

Heidrich, H.

R. Kaiser, D. Trommer, H. Heidrich, F. Fidorra, and M. Hamacher, “Heterodyne receiver PICs as the first monolithically integrated tunable receivers for OFDM system applications,” Opt. Quantum Electron. 28(5), 565–573 (1996).
[Crossref]

Henry, C. H.

Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic devices on silicon,” IEEE J. Quantum Electron. 27(3), 556–566 (1991).
[Crossref]

Houtsma, V.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
[Crossref]

Howe, S.

W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
[Crossref]

Hu, T.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
[Crossref]

Huang, Z.

Ippen, E. P.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Itabashi, S.

Janiak, K.

Kaiser, R.

R. Kaiser, D. Trommer, H. Heidrich, F. Fidorra, and M. Hamacher, “Heterodyne receiver PICs as the first monolithically integrated tunable receivers for OFDM system applications,” Opt. Quantum Electron. 28(5), 565–573 (1996).
[Crossref]

Kartner, F. X.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Kato, M.

Kazarinov, R. F.

Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic devices on silicon,” IEEE J. Quantum Electron. 27(3), 556–566 (1991).
[Crossref]

Kish, F.

Kistler, R. C.

Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic devices on silicon,” IEEE J. Quantum Electron. 27(3), 556–566 (1991).
[Crossref]

Klötzer, R.

R. Zhang, P. Runge, G. Zhou, R. Klötzer, D. Pech, H.-G. Bach, D. Pérez-Galacho, A. Ortega-Murnox, R. Halir, and I. Molina-Fernández, “56Gbaud DP-QPSK receiver module with a monolithic integrated PBS and 90° hybrid InP chip,” in 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.

Koike-Akino, T.

Kojima, K.

Kuntz, M.

Lal, V.

Lambert, D.

Li, W.

Little, B.

Liu, A.

W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
[Crossref]

Liu, C.

Liu, H. C.

Lu, Q.

Malendevich, R.

Mertens, K.

K. Mertens, M. Sennewald, and H. J. Schmitt, “Polarization conversion by hybrid modes: Theory and applications,” Radio Sci. 31(6), 1773–1779 (1996).
[Crossref]

K. Mertens, B. Scholl, and H. J. Schmitt, “New highly efficient polarization converters based on hybrid supermodes,” J. Lightwave Technol. 13(10), 2087–2092 (1995).
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Midkiff, J.

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
[Crossref]

Moehrle, M.

M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
[Crossref]

Molina-Fernandez, I.

Molina-Fernández, I.

R. Zhang, P. Runge, G. Zhou, R. Klötzer, D. Pech, H.-G. Bach, D. Pérez-Galacho, A. Ortega-Murnox, R. Halir, and I. Molina-Fernández, “56Gbaud DP-QPSK receiver module with a monolithic integrated PBS and 90° hybrid InP chip,” in 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.

Molina-Fernández, Í.

Nagarajan, R.

Neilson, D. T.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
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Nishikawa, S.

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Oei, Y.-S.

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[Crossref]

Ortega-Monux, A.

Ortega-Moñux, A.

Ortega-Murnox, A.

R. Zhang, P. Runge, G. Zhou, R. Klötzer, D. Pech, H.-G. Bach, D. Pérez-Galacho, A. Ortega-Murnox, R. Halir, and I. Molina-Fernández, “56Gbaud DP-QPSK receiver module with a monolithic integrated PBS and 90° hybrid InP chip,” in 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.

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W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
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Parsons, K.

Passenberg, W.

M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
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Pech, D.

R. Zhang, P. Runge, G. Zhou, R. Klötzer, D. Pech, H.-G. Bach, D. Pérez-Galacho, A. Ortega-Murnox, R. Halir, and I. Molina-Fernández, “56Gbaud DP-QPSK receiver module with a monolithic integrated PBS and 90° hybrid InP chip,” in 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.

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W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
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Sacher, W. D.

Sauer, N. J.

C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
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K. Mertens, M. Sennewald, and H. J. Schmitt, “Polarization conversion by hybrid modes: Theory and applications,” Radio Sci. 31(6), 1773–1779 (1996).
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K. Mertens, B. Scholl, and H. J. Schmitt, “New highly efficient polarization converters based on hybrid supermodes,” J. Lightwave Technol. 13(10), 2087–2092 (1995).
[Crossref]

Scholl, B.

K. Mertens, B. Scholl, and H. J. Schmitt, “New highly efficient polarization converters based on hybrid supermodes,” J. Lightwave Technol. 13(10), 2087–2092 (1995).
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Sennewald, M.

K. Mertens, M. Sennewald, and H. J. Schmitt, “Polarization conversion by hybrid modes: Theory and applications,” Radio Sci. 31(6), 1773–1779 (1996).
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Shi, Y.

H. Xu, D. Dai, and Y. Shi, “Ultra-broadband and ultra-compact on-chip silicon polarization beam splitter by using hetero-anisotropic metamaterials,” Laser Photonics Rev. 13(4), 1800349 (2019).
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Smit, M. K.

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M. F. Baier, F. M. Soares, W. Passenberg, T. Gaertner, M. Moehrle, and N. Grote, “Polarization beam splitter building block for InP based generic photonic integrated circuits,” 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.
[Crossref]

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L. Socci, V. Sorianello, and M. Romagnoli, “300 nm bandwidth adiabatic SOI polarization splitter-rotators exploiting continuous symmetry breaking,” Opt. Express 23(15), 19261–19271 (2015).
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T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
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C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
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C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
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C. R. Doerr, L. Zhang, P. J. Winzer, N. Weimann, V. Houtsma, T. Hu, N. J. Sauer, L. L. Buhl, D. T. Neilson, S. Chandrasekhar, and Y. K. Chen, “Monolithic InP dual-polarization and dual-quadrature coherent receiver,” IEEE Photonics Technol. Lett. 23(11), 694–696 (2011).
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D. Pérez-Galacho, R. Zhang, A. Ortega-Monux, R. Halir, C. Alonso-Ramos, P. Runge, K. Janiak, G. Zhou, H.-G. Bach, A. G. Steffan, and I. Molina-Fernandez, “Integrated polarization beam splitter for 100/400 GE polarization multiplexed coherent optical communications,” J. Lightwave Technol. 32(3), 361–368 (2014).
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R. Zhang, P. Runge, G. Zhou, R. Klötzer, D. Pech, H.-G. Bach, D. Pérez-Galacho, A. Ortega-Murnox, R. Halir, and I. Molina-Fernández, “56Gbaud DP-QPSK receiver module with a monolithic integrated PBS and 90° hybrid InP chip,” in 26th International Conference on Indium Phosphide and Related Materials (IPRM) (IEEE, 2014), pp. 1–2.

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AIP Adv. (1)

C.-J. Chung, J. Midkiff, K. M. Yoo, A. Rostamian, J. Guo, R. T. Chen, and S. Chakravarty, “InP-based polarization rotator-splitter for mid-infrared photonic integration circuits,” AIP Adv. 9(1), 015303 (2019).
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W. R. Headley, G. T. Reed, S. Howe, A. Liu, and M. Paniccia, “Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator,” Appl. Phys. Lett. 85(23), 5523–5525 (2004).
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Nat. Photonics (1)

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
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S. Keyvaninia, T. Beckerwerth, G. Zhou, M. Gruner, F. Ganzer, W. Ebert, S. Mutschall, A. Seeger, P. Runge, and M. Schell, “Novel photodetector chip for polarization diverse detection,” J. Lightw. Technol., doi: 10.1109/JLT.2019.2908247 .

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T. Richter, M. Kroh, J. Wang, A. Theurer, C. Zawadzki, Z. Zhang, N. Keil, A. Steffan, and C. Schubert, “Integrated polarization-diversity coherent receiver on polymer PLC for QPSK and QAM signals,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW3G.1.
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Figures (8)

Fig. 1
Fig. 1 Dispersion curves in the rib taper-waveguide of the mode-evolution-based polarization rotator. β is the propagation constant, W the rib-width along the propagation direction (z). The ridge height h1 is 120 nm, the waveguide height h2 is 320 nm. Wavelength is 1550 nm. S1 and S2 correspond to the coupled waveguide super-modes; the coloring along the lines indicate the mode polarization ratio ( γ x ), showing the conversion of TM0 to TE1.
Fig. 2
Fig. 2 (a) The difference in propagation constants at the waveguide width of highest hybridization of the first and second super-modes with 50% polarization ratio γ x as a function of the InGaAsP thickness at the wavelength of 1550 nm; (b) calculated electric field profiles for two hybrid super-modes S1 and S2 with an equal 50% polarization ratio ( γ x ) using h1 = 120 nm, h2 = 320 nm, at the wavelength of 1550 nm.
Fig. 3
Fig. 3 The schematic layout of the mode-evolution-based polarization rotator-splitter and geometries after optimization.
Fig. 4
Fig. 4 Simulated light propagation in the designed PRS when the TM0 and TE0 modes are launched at 1550nm.
Fig. 5
Fig. 5 Simulated PERport1,2 spectra when the TM0 and TE0 modes are launched at the input of the PRS for the width variation up to +/− 200 nm.
Fig. 6
Fig. 6 Microscopic pictures of the fabricated PRS.
Fig. 7
Fig. 7 Schematic measurement setup, solid black lines denote fiber connections, broken black lines denote free space propagation of the light, and the solid blue line denote electrical connection to a source measure unit (SMU).
Fig. 8
Fig. 8 Measured PERport1,2 spectrum when the TM0 and TE0 modes are launched at the input of the PRS for the width variation up to +/− 200 nm.

Equations (5)

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

γ x = s | E x 2 | dx dy s | E x 2 | dx dy+ s | E y 2 | dx dy
A S1 ( z )= 1 2 ( ( 1-2δ/Δβ ) ( 1+2δ/Δβ ) ) e -j β S1 z
A S2 ( z )= 1 2 ( ( 1+2δ/Δβ ) ( 1-2δ/Δβ ) ) e -j β S2 z
PER Port1 =| 10log( P TE0,Port1 P TM0,Port1 ) |
PER Port2 =| 10log( P TE0,Port2 P TM0,Port2 ) |

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