Abstract

We fabricated a magneto-optical (MO) isolator with a TE mode nonreciprocal phase shift. The isolator is based on a Mach–Zehnder interferometer composed of 3-dB directional couplers, a reciprocal phase shifter, and a nonreciprocal phase shifter. To realize TE mode operation in the optical isolator, we designed a novel waveguide structure composed of a hydrogenated amorphous silicon waveguide with an asymmetric MO garnet lateral clad on a garnet substrate. The isolator operation is successfully demonstrated in a fabricated device showing the different transmittances between forward and backward directions. The maximum isolation of the fabricated isolator is 17.9 dB at a wavelength of 1561 nm for the TE mode.

© 2017 Optical Society of America

1. Introduction

Stable operation of laser diodes and semiconductor optical amplifiers (SOAs) requires blocking back reflections from entering or leaving the optical active device. If back reflections are launched into a laser diode, the lasing mode becomes unstable, causing intensity variation, and phase noises can be generated in the laser output. In case of SOAs, amplified spontaneous emission (ASE) to backward propagation may cause instability of the system performance. Implementing countermeasures to back reflections is becoming more important because highly stable operation of optical active devices is required for the higher bit-rate transmission and increasing number of multiplexed wavelengths in wavelength division multiplexing systems.

To avoid these problems, optical isolators that allow one-way lightwave propagation are usually installed between the optical active device and other devices in the circuit or system. In optical fiber communication systems, bulk-type optical isolators are widely used. However, it is difficult to integrate these optical isolators with other optical devices. Converging lenses are needed for efficiently coupling lightwaves between isolators and other devices including optical fibers. This, in turn, requires highly accurate optical alignment.

Magneto-optical (MO) effects play an essential role in realizing the nonreciprocal function. Yttrium iron garnet Y3Fe5O12 (YIG) has a strong MO effect and a low optical absorption in the optical fiber communication wavelength range. Partially substituting yttrium with cerium can greatly enhance the MO effect [1]. Single-crystalline CeY2Fe5O12 (Ce:YIG) grown on a lattice-matched substituted gadolinium gallium garnet (SGGG) substrate has a saturation Faraday rotation of −4500 deg/cm at a wavelength of 1550 nm [2].

Nonreciprocal phase shift (NPS), brought about by the first-order MO effect, holds promise for realizing waveguide optical isolators [3–5]. Direction-dependent propagation constants are obtained in planar waveguides even with an MO material cladding layer. An optical isolator based on a Mach–Zehnder interferometer (MZI) with an NPS has been investigated. Single-crystalline MO garnet was directly bonded onto optical waveguides using a surface-activated direct bonding technique [6]. Using this method, single-crystalline MO garnet can be integrated onto various waveguide platforms with a relatively low temperature process (~200°C). MZI-based optical isolators were demonstrated with a 30-dB isolation, which was defined by the transmittance ratio of the forward to the backward direction. Also, an operation bandwidth of 8 nm for >20-dB isolation was demonstrated in the 1550-nm wavelength region [7]. A ring-resonator-based optical isolator was demonstrated in a silicon waveguide fabricated by plasma-assisted bonding of an MO garnet, where the electric current flowing along the ring resonator provides a magnetic field to align the magnetization of the MO garnet in the radial direction [8]. Polycrystalline Ce:YIG was formed on Si waveguides by a pulsed laser deposition technique followed by thermal annealing with an intermediate YIG seed layer [9]. The deposited polycrystalline Ce:YIG was reported to exhibit a Faraday rotation of −3000 deg/cm [10].

The NPS is brought about in the waveguide with an MO material placed asymmetrically with respect to the electric field of the lightwave. The NPS-based waveguide isolators mentioned above operate only for the transverse magnetic (TM) mode because MO garnets are placed as an upper cladding layer, as shown in Fig. 1(a). However, most semiconductor lasers emit transverse electric (TE) polarized light, so development of a waveguide optical isolator that can operate in the TE mode is needed. One approach to realize this is to integrate a waveguide TE–TM mode converter (polarization rotator) with the isolator operating in the TM mode [11–14]. However, sufficient TE–TM mode conversion efficiency is required for obtaining a high optical isolation and/or a low forward loss. Another approach is to devise an asymmetric waveguide structure in the horizontal direction, which coincides with the main electric field direction of the TE mode. Either the waveguide materials or the magnetization directions must be different in the left- and right-hand sides of the waveguide core [15]. If an MO garnet is formed only in one side of the waveguide core, NPS is available for the TE mode [16]. Owing to the complexity of the fabrication process, waveguide cores composed of asymmetric MO materials remain at the proposal stage [17].

 

Fig. 1 Waveguide cross section of (a) conventional and (b) proposed structures for providing NPS.

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Here, we employ hydrogenated amorphous silicon (a-Si:H) as a waveguide core material. a-Si:H has a high refractive index and low absorption loss within an optical communication wavelength region similar to that of single-crystalline silicon (c-Si) [18]. In addition, a-Si:H can be deposited on several platforms at low temperature (~300°C) by plasma-enhanced chemical vapor deposition (PCVD). Therefore, we can fabricate an a-Si:H waveguide on single-crystalline MO garnet epitaxially grown on an SGGG substrate, where a large NPS can be expected, similar to the MO/c-Si/SiO2 waveguide shown in Fig. 1(a). Single-crystalline Ce:YIG has a large saturation Faraday rotation coefficient, which, in turn, enables us to reduce the nonreciprocal phase shifter length. Also, a small bend radius can be used in curved sections because an a-Si:H waveguide has a strong field confinement similar to c-Si. These contribute to reduce the footprint of the optical isolator.

In this article, we propose and fabricate a novel waveguide structure to obtain NPS for the TE mode, as shown in Fig. 1(b), in which asymmetry is realized in the horizontal direction by placing an a-Si:H waveguide core attached to an MO garnet lateral wall. We demonstrate the TE mode operation of an MZI-based optical isolator without TE–TM mode converters. Also, we discuss the prospect for designing a polarization-independent waveguide optical isolator.

2. Operation principle and design

2.1 Operation principle

The MZI-based optical isolator is composed of 3-dB directional couplers and reciprocal and nonreciprocal phase shifters, as shown in Fig. 2. The 3-dB directional couplers split the lightwave power equally to the two interferometer waveguides. The reciprocal phase shifter imparts a phase difference between the two waveguides by an optical path length difference regardless of the propagation direction. In the nonreciprocal phase shifter, Ce:YIG is placed as the lateral clad of an a-Si:H waveguide with the magnetization aligned vertically, as shown in Fig. 1(b). Since the Ce:YIG lateral clad is located in opposite sides in the two interferometer waveguides, NPSs are brought about with different signs in the two waveguides. Therefore, the nonreciprocal phase shifters impart a phase difference between the two waveguides in a push–pull manner. The phase difference provided by the NPS changes its sign when the propagation direction is reversed.

 

Fig. 2 Schematic of a TE mode isolator.

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First, we consider the propagation from port 1 to port 2. The lightwave input at port 1 is equally split into two interferometer waveguides. The nonreciprocal and reciprocal phase shifters impart π/2 and π/2 phase differences, respectively, between the two interferometer waveguides. The total phase difference between the two waveguides becomes zero and the lightwave is output at port 2 as a result of interference in the right 3-dB directional coupler. The lightwave input at port 2 is equally split into two interferometer waveguides. The phase difference provided by the nonreciprocal phase shifter changes the sign. That is, a π/2 phase difference between two interferometer waveguides is imparted by the nonreciprocal phase shifter, whereas the reciprocal phase shifter still imparts a π/2 phase difference. Therefore, the total phase difference becomes π and the lightwave is output at port 3 after interfering in the left 3-dB directional coupler. Consequently, the lightwave is transmitted from port 1 to port 2, whereas it is not allowed to transmit in the reverse direction. This is an optical isolator operation.

2.2 Device design

The propagation constant of a mode propagating in a waveguide, β, is expressed as β=2neqπ/λ with a wavelength λ and the equivalent refractive index neq of the mode. The reciprocal phase differenceθRPS is expressed with an optical path difference LRPS by

θRPS=βLRPS=2neqπλLRPS.
LRPS is determined to provide a phase difference of π/2 + 2mπ (where m is an integer) by
LRPS=(m+0.25)λ neq.
In this study, we used a single-mode rectangular waveguide (450 nm wide and 240 nm thick) consisting of an a-Si:H core on a 10-nm-thick SiO2 interlayer and an SGGG substrate together with an SiO2 overcladding layer. The calculated neq of the fundamental TE mode was 2.58, and LRPSwas determined to be 36.2 μm for m=60 at λ = 1550 nm. The free spectral range (FSR) of the interferometer was set to be 15 nm to observe multiple extinction wavelengths in a measurable wavelength range. From a practical view point, a wider FSR is desirable to obtain a wide operation bandwidth in an MZI-based optical isolator [7].

In the nonreciprocal phase shifter waveguide with vertically magnetized Ce:YIG, an NPS is provided to the TE mode. The NPS is calculated by using the following equation derived from perturbation theory [3]:

ΔβTE=2ωε0PRe(jγEx*Ez)dxdy.
The coordinates x, y, and z are defined in Fig. 1. P is defined by
P=12(E×H*+E*×H)zdxdy,
which corresponds to the power flow along the z direction. The MO coefficient γ corresponds to the off-diagonal element of the perturbation relative permittivity tensor
Δε˜=(00jγ000jγ00  ).
γ is related to the saturation Faraday rotation coefficient θF by
γ=nλθFπ,
where n indicates the refractive index of the MO material. In the following experiment, we use Ce:YIG as an MO material, which has n = 2.20 and θF = −4500 deg/cm at a wavelength of 1550 nm, which corresponds to γ = 0.0085. Equation (3) shows the nonreciprocal phase shift per unit propagation distance for the TE mode.

We calculated the NPS for the fundamental TE mode at a wavelength of 1550 nm using Eq. (3), as shown in Fig. 3. The thickness of a-Si:H was kept constant at 240 nm and the width of the a-Si:H waveguide core was changed. Also, the thickness of the SiO2 interlayer, located at the bottom and on the side of the a-Si:H core, was varied as a parameter in the calculation. The NPS decreases monotonically as the thickness of the SiO2 interlayer is increased. We experimentally confirmed that the propagation loss of the a-Si:H waveguide was reduced by introducing an SiO2 interlayer. It is presumed that the SiO2 interlayer prevents Fe incorporated in Ce:YIG from diffusing into a-Si:H. Although the relationship between the SiO2 interlayer thickness and the propagation loss of the waveguide has not been fully examined yet, a 10-nm-thick interlayer substantially suppresses the loss. Thus, in the following design, we set the thickness of the SiO2 interlayer to 10 nm. The length of the nonreciprocal phase shifter minimizes at the waveguide width where NPS takes a maximum in Fig. 3. When the width of the a-Si:H core is <260 nm, neq of the fundamental TE mode becomes lower than the refractive index of Ce:YIG (2.20) and the mode gets cutoff. We designed the width of the a-Si:H waveguide core to be 300 nm in consideration of the misalignment between the core and lateral wall in our fabrication. The nonreciprocal phase shifter length LNPS is determined to provide ±π/2 phase differences by the following equation:

LNPS=π2ΔβTE.
LNPS is calculated to be 720 μm for the designed waveguide dimensions.

 

Fig. 3 NPS calculation result.

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3. Experiment

3.1 Fabrication

A 250-nm-thick single-crystalline Ce:YIG layer was grown on a (111)-oriented SGGG substrate by a radio-frequency sputter epitaxial technique. A 200-nm-thick SiO2 layer was deposited on the Ce:YIG layer by plasma chemical vapor deposition (PCVD) with tetraethyl-orthosilicate (TEOS) gas. Then, a 250-nm-thick Cr mask pattern was formed for fabricating Ce:YIG lateral walls and alignment marks by electron beam (EB) lithography, EB evaporation, and lift-off processes. The Cr mask pattern was transferred into SiO2 using reactive ion etching (RIE) with CF4 gas. Ce:YIG lateral walls were formed by Ar etching. After removing the Cr mask and SiO2 layer, a 10-nm-thick SiO2 interlayer was deposited on Ce:YIG by PCVD with TEOS gas. Then, an a-Si:H layer was deposited by PCVD with SiH4 gas. The a-Si:H waveguide pattern was formed by EB lithography and RIE with CF4, O2, and SF6 gases. Finally, a 2-µm-thick SiO2 overclad was deposited by PCVD.

Figures 4(a) and 4(b) show the microscope image of the fabricated optical isolator. Since the width of the a-Si:H core was narrower in the nonreciprocal phase shifter (300 nm) than in other sections (450 nm), 50-µm-long tapered a-Si:H cores were introduced at the input and output ports of the nonreciprocal phase shifter, as shown in Fig. 4(c). Figure 5 shows the scanning electron microscope (SEM) image of the cross section of the fabricated nonreciprocal phase shifter waveguide. A small prong at the upper right of the a-Si:H core remained because of the anisotropy of RIE, whereas a-Si:H is isotropically deposited on the Ce:YIG lateral wall.

 

Fig. 4 Microscopic images of (a) a fabricated isolator and (b) a nonreciprocal phase shifter; (c) schematic of connecting taper waveguides.

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Fig. 5 Cross section of the nonreciprocal phase shifter.

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3.2 Characterization

The transmission characteristics of the fabricated device were measured using the setup shown in Fig. 6. Polarizer-incorporated focusing lens modules were aligned at the input and output waveguide ends. The TE mode polarized lightwave from an ASE source was launched into the device. The lightwave transmitted through the device was coupled to the lens module, which passed only the TE mode through the incorporated polarizer. The fiber-to-fiber transmittance was measured by a spectrum analyzer. The propagation direction through the device was reversed by switching the input and output polarization while maintaining fiber connections as shown in Fig. 6. An external magnetic field was applied vertically to Ce:YIG with a permanent magnet located above the device. The external magnetic field near the edge of the permanent magnet was measured to be ∼4 kOe, which was sufficiently strong to saturate the magnetization of Ce:YIG (2–3 kOe) in the vertical direction. The direction of the external magnetic field was maintained in the following measurement.

 

Fig. 6 Measurement setup.

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Figure 7 shows the measured transmittance between ports 1 and 2. In the measured transmittance, the coupling losses between the input and output lens modules and the device are included. The red line shows the transmittance from port 1 to 2 with the external magnetic field applied; the blue line shows the transmittance from port 2 to 1. When the external magnetic field is not applied, the transmittance shown by the broken line is identical, regardless of the propagation direction. However, when the external magnetic field is applied, different transmittances are observed depending on the propagation direction. The transmittance spectrum shifts to the longer wavelength side for the propagation from port 1 to 2 compared with the case of no external magnetic field applied. However, it shifts to the shorter wavelength side by reversing the propagation direction. This indicates that the lightwave traveling in the device experiences NPS. The maximum isolation defined by the transmittance ratio of the forward to backward direction is measured to be 17.9 dB at a wavelength of 1561.7 nm, where the forward direction corresponds to the propagation from port 2 to port 1. The transmittance of a straight waveguide fabricated adjacent to the MZI device was about −30 dB which is mainly due to the coupling loss between the fiber and waveguide. The maximum transmittance of −40 dB of the isolator includes about 10 dB excess loss at the 3-dB couplers, bending waveguides, and nonreciprocal phase shifter. In order to reduce the insertion loss of the device, we should clarify the loss breakdown and improve waveguide designs in future study.

 

Fig. 7 Measured transmittance of the fabricated isolator.

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The NPS obtained in the fabricated device is examined in the following. The nonreciprocal phase difference θNPS can be estimated from the measured transmittance spectra by using the following equation:

θNPS=2πΔλFSR.
In Eq. (8), FSR is the free spectral range of interference and Δλ is the wavelength shift brought about by applying the external magnetic field. θNPS of the fabricated device was calculated to be ~0.35π from a measured FSR of 9.1 nm and Δλ of 1.6 nm. θNPS calculated from the measured result is 70% of the designed value. The discrepancy can be attributed to the deviation of the fabricated waveguide structure from the designed one. In the fabricated nonreciprocal phase shifter waveguide, a small prong of the a-Si:H core is observed, as shown in Fig. 5. Also, the Ce:YIG lateral wall is inclined. Figure 8 shows the electric field distributions along the x direction of the TE modes simulated by using a finite element method. The θNPS value of the TE mode is calculated to be 0.37π, which is close to the measured θNPS value. According to the simulation, the optical axis of the mode is inclined with respect to the substrate surface. The waveguides connected to the nonreciprocal phase shifter do not have Ce:YIG lateral walls. At the connecting point to the nonreciprocal phase shifter, there exists the 50-µm-long tapered a-Si:H waveguide, as shown in Fig. 4(c). The tapered waveguide might gradually excite the inclined TE mode in the nonreciprocal phase shifter.

 

Fig. 8 Electric field distribution along the x direction of the TE mode.

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4. Discussion

Let us discuss the design of a polarization-independent optical isolator. As mentioned in the introduction, NPS depends on the polarization of the propagating lightwave and the geometry of the MO material in the waveguide. When the waveguide is asymmetric in the vertical direction and the magnetization of the MO material is aligned in the horizontal direction, TM modes experience NPS. In contrast, when the waveguide is asymmetric in the horizontal direction and the magnetization is aligned in the vertical direction, TE modes experience NPS. Therefore, when the waveguide is asymmetric in both vertical and horizontal directions and an MO material is properly magnetized, NPS can be provided for both TE and TM modes. To obtain NPS for both TE and TM modes, we propose the waveguide structure shown in Fig. 9. The magnetization of an MO garnet is inclined by 45 deg with respect to the substrate surface.

 

Fig. 9 Proposed waveguide structure for a polarization-independent optical isolator.

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NPS is calculated by using the following equations derived from perturbation theory for TE and TM modes:

ΔβTE=2ωε0PRe(jγEx*Ez/2)dxdy,
ΔβTM=2ωε0PRe(jγEy*Ez/2)dxdy,
where coordinates x, y, and z are defined in Fig. 9. Equations (9) and (10) give the NPS per unit propagation distance for the TE and TM modes, respectively.P is defined by Eq. (4) and corresponds to the power flow along the z direction. It should be noted that the perturbation relative permittivity tensor is given by
Δε˜=(00jγ/200jγ/2jγ/2jγ/20  ),
with the same MO coefficient γ defined by Eq. (6), because the magnetization is inclined by 45 deg with respect to the substrate surface.

The NPS values for the fundamental TE and TM modes are calculated at a wavelength of 1550 nm as shown in Fig. 10 by assuming a saturation Faraday rotation coefficient of θF = −4500 deg/cm for Ce:YIG. The height of a-Si:H waveguides, 240 nm, is kept constant. The thickness of an SiO2 interlayer between Ce:YIG and a-Si:H is varied as a parameter. The same amount of NPS is obtainable for the TE and TM modes at the waveguides widths indicated by arrows in the figure. That is, using these waveguides in the nonreciprocal phase shifter achieves polarization-independent operation of the MZI isolator, when other components such as directional couplers and a reciprocal phase shifter work equally for the TE and TM modes. The nonreciprocal phase shifter length required for obtaining an NPS of ± is 536 μm when the height and width of the a-Si:H waveguide are 240 and 260 nm, respectively.

 

Fig. 10 Calculated nonreciprocal phase shift for the fundamental TE and TM modes.

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5. Conclusion

We demonstrated an MZI magneto-optical isolator with a TE mode nonreciprocal phase shift. An a-Si:H waveguide was formed along an MO garnet lateral wall to obtain the nonreciprocal phase shift for the TE mode. The maximum isolation of the fabricated MZI isolator was 17.9 dB at a wavelength of 1561.7 nm for the TE mode. Higher isolation with wider bandwidth is expected by tailoring the MZI design [6,7]. In a bulk isolator, high isolation up to 50 dB has been obtained by cascading two isolators. In order to achieve this, reduction of forward loss is important. We also presented a nonreciprocal phase shifter waveguide with an MO garnet lateral wall that can be extended to realize a polarization-independent MZI optical isolator.

Funding

Japan Society for the Promotion of Science (JSPS) KAKENHI (26249047 and 16K06295); JST Core Research for Evolutional Science and Technology (CREST).

References and links

1. M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991). [CrossRef]  

2. T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997). [CrossRef]  

3. S. Yamamoto and T. Makimono, “Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys. 45(2), 882–888 (1974). [CrossRef]  

4. F. Auracher and H. H. Witte, “A mew design for an integrated optical isolator,” Opt. Commun. 13(4), 435–438 (1975). [CrossRef]  

5. T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw. Theory Tech. MTT-30(6), 922–925 (1982). [CrossRef]  

6. Y. Shoji and T. Mizumoto, “Magneto-optical non-reciprocal devices in silicon photonics,” Sci. Technol. Adv. Mater. 15(1), 014602 (2014). [CrossRef]   [PubMed]  

7. Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014). [CrossRef]  

8. D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2. [CrossRef]  

9. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011). [CrossRef]  

10. T. Goto, M. C. Onbasli, D. H. Kim, V. Singh, M. Inoue, L. C. Kimerling, and C. A. Ross, “A nonreciprocal racetrack resonator based on vacuum-annealed magnetooptical cerium-substituted yttrium iron garnet,” Opt. Express 22(16), 19047–19054 (2014). [CrossRef]   [PubMed]  

11. N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999). [CrossRef]  

12. Y. Shoji, I.-W. Hsieh, R. M. Osgood Jr, and T. Mizumoto, “Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007). [CrossRef]  

13. S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013). [CrossRef]  

14. A. Fujie, Y. Shoji, and T. Mizumoto, “Silicon waveguide optical isolator integrated with TE-TM mode converter,” in Optical Fiber Communication Conference, Los Angeles, 2015, W2A.7. [CrossRef]  

15. O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, and T. Popkov, “Analysis of polarization independent Mach-Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17(7), 1200–1205 (1999). [CrossRef]  

16. P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express 21(4), 5041–5052 (2013). [CrossRef]   [PubMed]  

17. J. Fujita, M. Levy, R. M. Osgood Jr, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000). [CrossRef]  

18. J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011). [CrossRef]  

References

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  1. M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991).
    [Crossref]
  2. T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997).
    [Crossref]
  3. S. Yamamoto and T. Makimono, “Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys. 45(2), 882–888 (1974).
    [Crossref]
  4. F. Auracher and H. H. Witte, “A mew design for an integrated optical isolator,” Opt. Commun. 13(4), 435–438 (1975).
    [Crossref]
  5. T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw. Theory Tech. MTT-30(6), 922–925 (1982).
    [Crossref]
  6. Y. Shoji and T. Mizumoto, “Magneto-optical non-reciprocal devices in silicon photonics,” Sci. Technol. Adv. Mater. 15(1), 014602 (2014).
    [Crossref] [PubMed]
  7. Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
    [Crossref]
  8. D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
    [Crossref]
  9. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
    [Crossref]
  10. T. Goto, M. C. Onbasli, D. H. Kim, V. Singh, M. Inoue, L. C. Kimerling, and C. A. Ross, “A nonreciprocal racetrack resonator based on vacuum-annealed magnetooptical cerium-substituted yttrium iron garnet,” Opt. Express 22(16), 19047–19054 (2014).
    [Crossref] [PubMed]
  11. N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
    [Crossref]
  12. Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, “Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007).
    [Crossref]
  13. S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
    [Crossref]
  14. A. Fujie, Y. Shoji, and T. Mizumoto, “Silicon waveguide optical isolator integrated with TE-TM mode converter,” in Optical Fiber Communication Conference, Los Angeles, 2015, W2A.7.
    [Crossref]
  15. O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, and T. Popkov, “Analysis of polarization independent Mach-Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17(7), 1200–1205 (1999).
    [Crossref]
  16. P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express 21(4), 5041–5052 (2013).
    [Crossref] [PubMed]
  17. J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
    [Crossref]
  18. J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
    [Crossref]

2014 (3)

Y. Shoji and T. Mizumoto, “Magneto-optical non-reciprocal devices in silicon photonics,” Sci. Technol. Adv. Mater. 15(1), 014602 (2014).
[Crossref] [PubMed]

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

T. Goto, M. C. Onbasli, D. H. Kim, V. Singh, M. Inoue, L. C. Kimerling, and C. A. Ross, “A nonreciprocal racetrack resonator based on vacuum-annealed magnetooptical cerium-substituted yttrium iron garnet,” Opt. Express 22(16), 19047–19054 (2014).
[Crossref] [PubMed]

2013 (2)

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express 21(4), 5041–5052 (2013).
[Crossref] [PubMed]

2011 (2)

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

2007 (1)

2000 (1)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

1999 (2)

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, and T. Popkov, “Analysis of polarization independent Mach-Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17(7), 1200–1205 (1999).
[Crossref]

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

1997 (1)

T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997).
[Crossref]

1991 (1)

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991).
[Crossref]

1982 (1)

T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw. Theory Tech. MTT-30(6), 922–925 (1982).
[Crossref]

1975 (1)

F. Auracher and H. H. Witte, “A mew design for an integrated optical isolator,” Opt. Commun. 13(4), 435–438 (1975).
[Crossref]

1974 (1)

S. Yamamoto and T. Makimono, “Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys. 45(2), 882–888 (1974).
[Crossref]

Abe, M.

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991).
[Crossref]

Amemiya, T.

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Arai, S.

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Atsumi, Y.

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Auracher, F.

F. Auracher and H. H. Witte, “A mew design for an integrated optical isolator,” Opt. Commun. 13(4), 435–438 (1975).
[Crossref]

Baets, R.

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

Bahlmann, N.

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Bowers, J. E.

P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express 21(4), 5041–5052 (2013).
[Crossref] [PubMed]

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

Di Pasquale, F.

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Dotsch, H.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, and T. Popkov, “Analysis of polarization independent Mach-Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17(7), 1200–1205 (1999).
[Crossref]

Fujie, A.

A. Fujie, Y. Shoji, and T. Mizumoto, “Silicon waveguide optical isolator integrated with TE-TM mode converter,” in Optical Fiber Communication Conference, Los Angeles, 2015, W2A.7.
[Crossref]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

Furuyama, H.

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991).
[Crossref]

Ghosh, S.

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

Gomi, M.

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991).
[Crossref]

Goto, T.

Hertel, P.

Hsieh, I.-W.

Hu, J.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Huang, D.

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

Inoue, M.

Inoue, Y.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

Ishii, M.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

Jiang, P.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Kang, J.

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Keyvaninia, S.

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

Kim, D. H.

T. Goto, M. C. Onbasli, D. H. Kim, V. Singh, M. Inoue, L. C. Kimerling, and C. A. Ross, “A nonreciprocal racetrack resonator based on vacuum-annealed magnetooptical cerium-substituted yttrium iron garnet,” Opt. Express 22(16), 19047–19054 (2014).
[Crossref] [PubMed]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Kimerling, L. C.

T. Goto, M. C. Onbasli, D. H. Kim, V. Singh, M. Inoue, L. C. Kimerling, and C. A. Ross, “A nonreciprocal racetrack resonator based on vacuum-annealed magnetooptical cerium-substituted yttrium iron garnet,” Opt. Express 22(16), 19047–19054 (2014).
[Crossref] [PubMed]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Kubota, E.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

Lohmeyer, M.

Makimono, T.

S. Yamamoto and T. Makimono, “Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys. 45(2), 882–888 (1974).
[Crossref]

Mino, S.

T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997).
[Crossref]

Mizumoto, T.

Y. Shoji and T. Mizumoto, “Magneto-optical non-reciprocal devices in silicon photonics,” Sci. Technol. Adv. Mater. 15(1), 014602 (2014).
[Crossref] [PubMed]

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, “Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007).
[Crossref]

T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw. Theory Tech. MTT-30(6), 922–925 (1982).
[Crossref]

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

A. Fujie, Y. Shoji, and T. Mizumoto, “Silicon waveguide optical isolator integrated with TE-TM mode converter,” in Optical Fiber Communication Conference, Los Angeles, 2015, W2A.7.
[Crossref]

Naito, Y.

T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw. Theory Tech. MTT-30(6), 922–925 (1982).
[Crossref]

Nishiyama, N.

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Oda, M.

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Onbasli, M. C.

Osgood, R. M.

Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, “Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007).
[Crossref]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

Pintus, P.

P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform,” Opt. Express 21(4), 5041–5052 (2013).
[Crossref] [PubMed]

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

Popkov, T.

Roelkens, G.

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

Ross, C. A.

T. Goto, M. C. Onbasli, D. H. Kim, V. Singh, M. Inoue, L. C. Kimerling, and C. A. Ross, “A nonreciprocal racetrack resonator based on vacuum-annealed magnetooptical cerium-substituted yttrium iron garnet,” Opt. Express 22(16), 19047–19054 (2014).
[Crossref] [PubMed]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Shimokozono, M.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

Shintaku, T.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997).
[Crossref]

Shirato, Y.

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

Shoji, Y.

Y. Shoji and T. Mizumoto, “Magneto-optical non-reciprocal devices in silicon photonics,” Sci. Technol. Adv. Mater. 15(1), 014602 (2014).
[Crossref] [PubMed]

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, “Polarization-independent magneto-optical waveguide isolator using TM-mode nonreciprocal phase shift,” J. Lightwave Technol. 25(10), 3108–3113 (2007).
[Crossref]

A. Fujie, Y. Shoji, and T. Mizumoto, “Silicon waveguide optical isolator integrated with TE-TM mode converter,” in Optical Fiber Communication Conference, Los Angeles, 2015, W2A.7.
[Crossref]

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

Singh, V.

Sugimoto, N.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

Tate, A.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997).
[Crossref]

Terui, H.

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

Wilkens, L.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

Witte, H. H.

F. Auracher and H. H. Witte, “A mew design for an integrated optical isolator,” Opt. Commun. 13(4), 435–438 (1975).
[Crossref]

Yamamoto, S.

S. Yamamoto and T. Makimono, “Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys. 45(2), 882–888 (1974).
[Crossref]

Zhang, C.

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

Zhuromskyy, O.

Appl. Phys. Lett. (1)

T. Shintaku, A. Tate, and S. Mino, “Ce-substituted yttrium iron garnet films prepared on Gd3Sc2Ga3O12 garnet substrates by sputter epitaxy,” Appl. Phys. Lett. 71(12), 1640–1642 (1997).
[Crossref]

IEEE Photonics J. (1)

S. Ghosh, S. Keyvaninia, Y. Shirato, T. Mizumoto, G. Roelkens, and R. Baets, “Optical isolator for TE polarized light realized by adhesive bonding of Ce:YIG on silicon-on-insulator waveguide circuits,” IEEE Photonics J. 5(3), 6601108 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (2)

N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue, “Waveguide polarization-independent optical circulator,” IEEE Photonics Technol. Lett. 11(3), 355–357 (1999).
[Crossref]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Polarization-independent waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photonics Technol. Lett. 12(11), 1510–1512 (2000).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw. Theory Tech. MTT-30(6), 922–925 (1982).
[Crossref]

J. Appl. Phys. (1)

S. Yamamoto and T. Makimono, “Circuit theory for a class of anisotropic and gyrotropic thin-film optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys. 45(2), 882–888 (1974).
[Crossref]

J. Lightwave Technol. (2)

Jpn. J. Appl. Phys. (3)

J. Kang, Y. Atsumi, M. Oda, T. Amemiya, N. Nishiyama, and S. Arai, “Low-loss amorphous silicon multilayer waveguides vertically stacked on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 50(12R), 120208 (2011).
[Crossref]

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” Jpn. J. Appl. Phys. 70(11), 7065–7067 (1991).
[Crossref]

Nat. Photonics (1)

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Opt. Commun. (1)

F. Auracher and H. H. Witte, “A mew design for an integrated optical isolator,” Opt. Commun. 13(4), 435–438 (1975).
[Crossref]

Opt. Express (2)

Sci. Technol. Adv. Mater. (1)

Y. Shoji and T. Mizumoto, “Magneto-optical non-reciprocal devices in silicon photonics,” Sci. Technol. Adv. Mater. 15(1), 014602 (2014).
[Crossref] [PubMed]

Other (2)

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Silicon microring isolator with large optical isolation and low loss,” in Optical Fiber Communication Conference, Anaheim, 2016, Th1K.2.
[Crossref]

A. Fujie, Y. Shoji, and T. Mizumoto, “Silicon waveguide optical isolator integrated with TE-TM mode converter,” in Optical Fiber Communication Conference, Los Angeles, 2015, W2A.7.
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Waveguide cross section of (a) conventional and (b) proposed structures for providing NPS.
Fig. 2
Fig. 2 Schematic of a TE mode isolator.
Fig. 3
Fig. 3 NPS calculation result.
Fig. 4
Fig. 4 Microscopic images of (a) a fabricated isolator and (b) a nonreciprocal phase shifter; (c) schematic of connecting taper waveguides.
Fig. 5
Fig. 5 Cross section of the nonreciprocal phase shifter.
Fig. 6
Fig. 6 Measurement setup.
Fig. 7
Fig. 7 Measured transmittance of the fabricated isolator.
Fig. 8
Fig. 8 Electric field distribution along the x direction of the TE mode.
Fig. 9
Fig. 9 Proposed waveguide structure for a polarization-independent optical isolator.
Fig. 10
Fig. 10 Calculated nonreciprocal phase shift for the fundamental TE and TM modes.

Equations (11)

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θ RPS =β L RPS = 2 n eq π λ L RPS .
L RPS = ( m+0.25 )λ  n eq .
Δ β TE = 2ω ε 0 P Re( jγ E x * E z )dxdy.
P= 1 2 ( E× H * + E * ×H ) z dxdy,
Δ ε ˜ =( 0 0 jγ 0 0 0 jγ 0 0    ).
γ= nλ θ F π ,
L NPS = π 2 Δ β TE .
θ NPS = 2πΔλ FSR .
Δ β TE = 2ω ε 0 P Re( jγ E x * E z / 2 )dxdy,
Δ β TM = 2ω ε 0 P Re( jγ E y * E z / 2 )dxdy,
Δ ε ˜ =( 0 0 jγ/ 2 0 0 jγ/ 2 jγ/ 2 jγ/ 2 0    ),

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