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Title

Ultra-compact microring optical isolator using an aluminum-substituted
cobalt ferrite thin film

Authors

Kotaro Sato, Makoto Okano, Yuya Shoji

Citation

Optica, Vol. 11, No. 6, pp. 889-895

Pub. date

2024, 6

Copyright(c) 2024 Optica Publishing Group. Users may use, reuse, and build
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is maintained. All other rights are reserved.

DOI

http://dx.doi.org/10.1364/OPTICA.511956

Powered by T2R2 (Science Tokyo Research Repository)

Research Article

Vol. 11, No. 6 / June 2024 / Optica

889

Ultra-compact microring optical isolator using an
aluminum-substituted cobalt ferrite thin film
Kotaro Sato,1 Makoto Okano,2

1,3,

AND Yuya Shoji*1

Department of Electrical and Electronic Engineering, School of Engineering, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku,
Tokyo 152-8550, Japan
2
National Institute of Advanced Industrial Science and Technology (AIST), Ibaraki 305-8568, Japan
3
Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku,
Tokyo 152-8550, Japan*shoji@ee.e.titech.ac.jp
Received 9 November 2023; revised 5 June 2024; accepted 5 June 2024; published 20 June 2024

Yttrium iron garnets, which are typically used as magneto-optical isolators, are not suitable for monolithic integration with photonic circuits. We experimentally demonstrated an ultracompact microring optical isolator using an
aluminum-substituted cobalt ferrite (CAFO) thin film directly deposited on silicon waveguides. The device footprint
was only 43 × 71 µm2 . The isolator can operate without an external magnet owing to the strong remanent magnetization of the CAFO film and achieved a maximum isolation ratio of 24.7 dB at a wavelength of 1545.7 nm. Our study could
facilitate integration of nonreciprocal photonic devices on Si platforms. © 2024 Optica Publishing Group under the terms of
the Optica Open Access Publishing Agreement
https://doi.org/10.1364/OPTICA.511956

1. INTRODUCTION
Optical isolators are nonreciprocal devices that allow the propagation of light in only one direction while preventing light frompropagating in the opposite direction, which is indispensable forprotecting optically active elements from backward reflections andstabilizing their operation. A plethora of approaches to realize integrated optical isolators by breaking the Lorentz reciprocity [1] havebeen reported using nonlinear [2–6], electro-optical [7–11], andacousto-optical effects [12–16]. Some of them are based on a directionally dependent spatio-temporal modulation first proposed in[11] taking advantage of the easy-to-fabricate structure, whereas
they suffer from a long interaction length and need of power consumption. On the other hand, integrated optical isolators basedon magneto-optical (MO) effects [17–26] are the most promisingbecause of their simple structure and purely passive operation. The
main challenge is how to integrate the materials.
Magnetized MO materials exhibit first-order MO effects andnon-reciprocal light propagation. Garnet ferrites, such as bismuthsubstituted yttrium iron garnet (Bi:YIG) and cerium-substituted
yttrium iron garnet (Ce:YIG), have a large MO effect and low
optical absorption in the telecommunication wavelength region[27,28]. However, the growth of single-crystalline MO garnets
on semiconductors is extremely difficult because of the lattice andthermal expansion mismatch. In addition, these garnets require
an external magnetic field to maintain magnetization using apermanent magnet or electromagnet, which increases the device
size. There are two approaches to integrating Ce: YIG on a silicon photonics platform: bonding and deposition. Direct bonding
between an epitaxially grown Ce:YIG film on a gadolinium gallium
2334-2536/24/060889-07 Journal © 2024 Optica Publishing Groupgarnet (GGG) substrate and a silicon-on-insulator (SOI) wafer was
realized using a surface-activated direct bonding technique [24].
This method allows the use of good-quality Ce:YIG films, but
requires a large chip area, and a thick GGG substrate remains; thus,
the fabrication process after bonding is complicated. Using an
yttrium iron garnet (YIG) seed layer, a polycrystalline Ce:YIG film
was deposited on the SOI [29]. The polycrystalline Ce:YIG film
exhibits a lesser figure of merit than the single-crystalline Ce:YIG
film.
Cobalt ferrite (CoFe2 O4 : CFO), a spinel ferrite, has a Faraday
rotation coefficient under saturated magnetization five times
larger than that of Ce:YIG and enables a compact MO isolator.
Serrano-Núñez et al. developed a silicon optical isolator using
a monolithically integrated CFO film [18]. According to thereport, the polycrystalline CFO film deposited on Si showed a large
Faraday rotation coefficient (θ F ) of 25,600 deg/cm at 1550 nm
wavelength, while high material loss of 3.4 dB/µm was a challenge[30]. Therefore, the figure of merit between the MO effect and theloss was much lower than that of Ce:YIG. However, CFO possesses
a strong remanent magnetization and coercive force, which meansthat a more compact structure is possible without the need forexternal permanent magnets.
In this paper, we focus on aluminum-substituted cobalt ferrite,
which can reduce material loss by sacrificing a slight degradationof θ F . CoAl0.57 Fe1.43 O4 (CAFO) is expected to have the highest
advantages among reported compositions [31]. The sputtering
method was employed for the deposition of the CAFO. Using the
sputtering method, films of the same composition as the target
material are easily formed, the energy of the film particles is large,

Research Article
adhesion is strong, the film thickness can be controlled with highaccuracy only by time, and a uniform film can be formed even ona large surface area, while the deposition speed is slow. The characteristics of the CAFO film depend on the sputtering conditions
and the buffer layer. We investigated the use of two buffer layers,magnesium oxide (MgO) and zinc oxide (ZnO), to fabricate highlyoriented CAFO films. The low optical absorption and refractive
index of 1.71 of MgO in communication bands make it suitablefor integration in optical waveguides [32,33]. ZnO has a hexagonal
wurtzite crystalline structure and is a promising material for buffer
layers in the selective growth of CAFO films. (0001)-oriented
ZnO can be deposited on Si (100), and (111)-oriented CFO canbe deposited on ZnO (0001) [34,35]. The (111) single-oriented
CFO film may exhibit a magnetic easy axis in the in-plane direction
with a large remanent magnetization, which is potentially usefulfor TM-mode optical isolators using a CAFO film [36]. Finally, wefabricated a microring resonator (MRR)-based MO isolator witha compact device footprint. The CAFO/MgO was deposited on
the Si waveguide, where the over cladding was partially opened.
Efficient resonant wavelength shifts due to the MO effect and ahigh isolation ratio (IR) were successfully obtained.
2. PREPARATION OF ALUMINUM-SUBSTITUTEDCOBALT FERRITECAFO, MgO, and ZnO were deposited on a 1.5 × 1.5 cm2 Si(100) substrate using multi-target radio frequency (RF) magnetron sputtering equipment. The Si (100) substrate was dipped
in diluted hydrogen fluoride (DHF) for 30 s to remove the nativeoxide layer and cleaned with acetone using ultrasonication for
5 min. The MgO buffer layer was deposited using a MgO target
at a substrate temperature of 600◦ C, chamber pressure of 3 Pa, RF
power of 80 W, and argon (Ar) gas flow of 20 sccm. Under these
conditions, highly oriented MgO (100) layers with a thickness of
20 nm were formed on the Si (100) substrate [30]. The ZnO buffer
layer was deposited using a ZnO target at a substrate temperatureof 600◦ C, chamber pressure of 3 Pa, RF power of 80 W, and Ar gas
flow of 20 sccm. Under these conditions, a highly oriented ZnO(0001) layer with a thickness of 78 nm was formed on a Si (100)substrate. The CAFO films were deposited on these buffer layers
using a CAFO target under the following conditions: the CAFO

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890

on the MgO buffer layer was deposited at a substrate temperatureof 750◦ C, chamber pressure of 1 Pa, RF power of 200 W, andAr gas flow of 20 sccm. The CAFO on the ZnO buffer layer was
deposited at a substrate temperature of 750◦ C, chamber pressure of
1 Pa, RF power of 180 W, and Ar gas flow of 20 sccm. In addition,
CAFO was directly deposited onto Si without any buffer layer at
a substrate temperature of 750◦ C, chamber pressure of 1 Pa, RF
power of 180 W, and Ar gas flow of 20 sccm.
The CAFO properties were evaluated using the following
equipment. The crystallinity of the deposited CAFO film wascharacterized by the θ -2θ scans of standard Cu-Kα X-ray diffraction (XRD). The film thicknesses were measured using scanningelectron microscopy (SEM).
The MO effects were measured using Faraday rotation (FR)characterization with light penetrating the film vertically underan out-of-plane external magnetic field at room temperature.
Magnetic hysteresis loops were measured using a vibrating sample
magnetometer (VSM) at room temperature. The material loss
was evaluated from the transmittances of the Si waveguides withdifferent CAFO cladding lengths along the light propagation
direction.
Figure 1(a) shows the XRD patterns of the CAFO/MgO/Si,
CAFO/ZnO/Si, and CAFO/Si films. The XRD pattern of thedeposited CAFO/MgO/Si film shows a peak of 2θ around 43.6◦ ,corresponding to a (400) miller index of CAFO and (200) miller
index of MgO. Almost all the single crystals of CAFO (100) wereobtained using the MgO buffer layer. The XRD pattern of thedeposited CAFO/ZnO/Si film shows peaks of 2θ around 18.6◦ ,34.6◦ , 37.5◦ , and 57.8◦ , corresponding to (111), (222), and (333)
miller indices of CAFO and (0002) miller index of ZnO. Almost
all the single crystals of CAFO (111) were obtained using the ZnO
buffer layer. The XRD pattern of the deposited CAFO/Si filmshows a small peak of intensity of 2θ around 35.9◦ , corresponding
to a (311) miller index of CAFO. A CAFO film with poor orientation was confirmed without using a buffer layer. Single-crystal
orientation of MO materials is important in photonic integrated
circuits (PICs) to avoid absorption loss and optical scattering
arising from the grain boundaries of multiplane structures. Using
buffer layers, highly oriented CAFO films can be deposited,making them suitable for low-loss MO materials.

Fig. 1.
(a) XRD patterns of CAFO/MgO/Si, CAFO/ZnO/Si, and CAFO/Si. (b) Room temperature Faraday rotation hysteresis loops of
CAFO/MgO/Si, CAFO/ZnO/Si, and CAFO/Si.

Research Article
The measured FR coefficients θ F of hysteresis loops of CAFO
films at a wavelength of 1550 nm are plotted in Fig. 1(b). Theθ F of the Si substrate, the MgO buffer layer, and the ZnO buffer
layer were subtracted from the original data. The thickness ofeach film was measured using SEM, and the rotation angle wasdivided by the film thickness. The θ F of the CAFO/Si film reached−22,000 deg/cm at the saturation, which was the largest FR
measured. The θ F of the CAFO/MgO/Si and the CAFO/ZnO/Si
films reached −15,000 deg/cm and −9,000 deg/cm, respectively. The maximum θ F of CAFO film was slightly smaller than25,600 deg/cm with CFO in our previous work [30]. The reason
for this is the substitution of Al. The negative loops are consistent with those reported by Suzuki et al. and do not affect theperformance of the optical isolator [31].
Next, we evaluated the magnetic anisotropy. Figures 2(a)–2(c) show the magnetic hysteresis loops of the CAFO/MgO/Si
film, both in-plane and out-of-plane, obtained using VSM atroom temperature. Here, we define the squareness ratio of theremanence magnetization Mr and saturation magnetization Ms .
In-plane squareness ratios of CAFO/MgO/Si, CAFO/ZnO/Si,
and CAFO/Si films are 29%, 49%, and 60%, respectively. The
CAFO/MgO/Si film exhibited an out-of-plane-oriented easy
axis, whereas the CAFO/ZnO/Si and CAFO/Si films exhibitedan in-plane-oriented easy axis. The in-plane easy axis, that is, alarge in-plane squareness ratio, is suitable for the MO effect in the
TM mode when the material is placed in the upper cladding layer.
Similarly, the out-of-plane easy axis is suitable for the MO effectin the TE mode when the material is placed in the side cladding
layer. However, the CAFO/MgO/Si film may have an in-planeoriented easy axis when deposited at a low substrate temperaturefor sputtering [30].
To evaluate material loss, CAFO/MgO, CAFO/ZnO, andCAFO films were deposited on Si waveguides with different window lengths. Figures 2(d)–2(f ) show the plots of the transmittancesof the CAFO/MgO/Si, CAFO/ZnO/Si, and CAFO/Si waveguides
at a wavelength of 1550 nm as a function of the window length.

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The propagation losses were determined to be 0.40 dB/µm,
0.36 dB/µm, and 3.48 dB/µm for the CAFO/MgO/Si,
CAFO/ZnO/Si, and CAFO/Si waveguides from the slope calculated by linear approximation, respectively. The material lossof the CAFO (αCAFO ) can be inferred from its confinement
factor (0CAFO ) in the waveguide. Based on the cross-sectional
dimensions of the waveguide by SEM, 0CAFO on MgO = 45.3%,
0CAFO on ZnO = 39.6%, and 0CAFO on Si = 57.8% were calculatedwith a mode solver based on the finite element method (Cybernet
RSoft FemSIM). Therefore, αCAFO on MgO , αCAFO on ZnO , andαCAFO on Si were determined to be 0.83 dB/µm, 0.92 dB/µm, and6.02 dB/µm, respectively. αCAFO on MgO and αCAFO on ZnO are lower
than that of CFO [31]. However, αCAFO on Si was higher, probably
because of its low crystal orientation.
The figure of merit (FoM) is used as an indicator to compare theperformance of the MO materials. Because optical isolator operation without applying an external magnetic field is assumed in thisstudy, the remanent FoM (◦ /dB) is defined as
FoMr =

θ F Mr,α Ms(1)where Mr /Ms is the in-plane square ratio of the CAFO film.
Table 1 shows the characteristics of the CAFO films deposited
with and without buffer layers as well as CFO and Ce:YIG in
previous works. The CAFO/MgO/Si film exhibits the highest
remanent FoM. The FoM of CAFO is much lower than that of
Ce:YIG. However, FoM is independent from propagation lengthand its large Faraday rotation has an impact on the device size. In
addition, Ce:YIG requires an external magnetic field integrating apermanent magnet.
3. DEVICE STRUCTURE AND FABRICATION
A schematic diagram of the device structure is shown in Fig. 3(a).
An MRR of 440-nm-wide and 220-nm-thick Si (n = 3.48)

Fig. 2. In-plane and out-of-plane room temperature magnetization hysteresis loops of (a) CAFO/MgO/Si, (b) CAFO/ZnO/Si, and (c) CAFO/Si. The
transmission loss of (d) CAFO/MgO/Si, (e) CAFO/ZnO/Si, and (f ) CAFO/Si waveguide as a function of its length.

Research Article

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Table 1. Optical and Magnetic Properties of CAFO, CFO, Ce:YIG Films Deposited on Each Buffer Layer at aaWavelength of 1550 nm
Material

CFO [30]

Ce:YIG [24]Buffer layer

MgO

ZnO

None

MgO

None

θ F (deg/cm)
α (dB/µm)−15,000
0.83
0.29
1.8
0.52

−9,000
0.92
0.49
0.98
0.42

−2,2000
6.02
0.6
0.37
0.22

25,600
3.4
0.54
0.75
0.40

−4,500
0.006
∼0
75
-

Mr
Ms

FoM (deg/dB)
FoMr (deg/dB)

CAFO

a

FoM and FoMr are at the saturated and remanent magnetizations, respectively.

Fig. 3. (a) Schematic of the MRR isolator. (b) Cross-sectional SEM image of CAFO/MgO/Si waveguide. (c) Simulated E y field distribution of the fundamental TM mode.

waveguides was patterned on a 3-µm-thick SiO2 (n = 1.444)
substrate. The bending radius was 20 µm, the length of the straightsection in MRR was 30 µm, and the gap between the bus-line
waveguide and the ring resonator was 200 nm. A silica layer of
2-µm thickness was deposited as upper cladding, where a window
region was opened in one straight section. CAFO (250 nm)/MgO(20 nm) was deposited on Si at the window region to form a MO
waveguide with an interaction length (L MO ) of 25 µm. The ringradius, gap between the bus-line waveguide and ring resonator, and
L MO were designed to satisfy the critical coupling conditions forthe total internal loss, as described below. Owing to the thick silica
layer, the waveguide optical mode interacted with the CAFO film
only in the window region. When the CAFO film was magnetizedin-plane and perpendicular to the direction of propagating light,
the CAFO remnant magnetization induced nonreciprocal phaseshift effects (NRPS) of the TM mode by the MO effect. Figure 3(b)shows a cross-sectional view of the window region of the fabricateddevice as observed in SEM. Figure 3(c) shows the simulated modal
profile for the actual dimensions. The NRPS of the TM mode canbe calculated as
ZZ

2ωε0
NRPSTM =Re j γ E y∗ E z dx dy ,(2)
P
where ω is the angular frequency, ε0 is the vacuum dielectric constant, P is the power flux along the z-axis, γ is the off-diagonalcomponents of the permittivity tensor of the MO material,
and E y , E z are the electric field components along the y and z
directions. Considering in-plane remanent θ F of CAFO film(−4,350 deg/cm) the simulated NRPS is 6.1 rad/mm.
The intensity transmission factor of the ring resonator can begiven byT=

a 2 − 2ta cos β L + t 2,
1 − 2ta cos β L + (ta )2(3)

where a is the round-trip transmittance, which depends mainly on
the MO material loss and the bending loss of the waveguide. t is thepower transmission in the coupling region, which can be adjusted
by varying the gap between the bus-line and ring waveguides.
When the power loss inside the ring is equal to the coupled power,that is, a = t, T decreases to zero at the resonant phase. This is
known as the critical coupling condition of the resonator, in which
all resonant light is eventually dissipated inside the ring. To obtaina large isolation rate (IR), a design satisfying the critical coupling
condition is required to obtain a large IR value. The bending loss is
negligibly small at a ring radius r ≥ 20 µm, so the ring radius was
set at 20 µm. For L MO of 25 µm and ring and waveguide gap of
200 nm, the critical coupling condition (a ≈ t) would be satisfied.
Figure 4 shows the fabrication process flow of the device.
The ring resonator and bus-line waveguide were fabricated on

Research Article

Fig. 4.

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893

Fabrication process of MRR optical isolator.

Fig. 5. Optical microscopic picture of the fabricated device before
CAFO deposition.

silicon-on-insulator (SOI) wafers by using a CMOS-compatible
process [37]. It had a 2-µm-thick SiO2 over cladding layer on topof the Si waveguide. The window region is opened in a straightsection of the ring resonator. The window region was patternedby photolithography with AZ 5218 photoresist. The SiO2 in thewindow region was removed using reactive ion etching (RIE) in
CF4 plasma, and the top surface of Si was completely exposedby wet etching with DHF. Finally, the CAFO/MgO films were
deposited by sputtering under the optimized conditions describedin Section 2. A optical microscopic picture of the fabricated device
before CAFO deposition is shown in Fig. 5.
4. DEVICE CHARACTERIZATION
A fiber-device-fiber setup [38] was used to characterize the isolation performance of this device at telecom wavelengths bycoupling TM-polarized light through a bus-line waveguide. Prior
to the measurements, the CAFO film was magnetized in-planeand perpendicular to the direction of light propagation using anelectromagnetic coil at 15 kOe for 5 min. As shown in Fig. 2(a), theapplied magnetic field was sufficient to saturate the CAFO film.
Once the magnetization is saturated, the CAFO provides the MO
effect owing to the remnant magnetization in the absence of an
external magnet.
The transmission spectra were measured in the clockwise (CW)
and counterclockwise (CCW) directions along the ring resonatorFig. 6. Transmission spectra of the reference waveguide and the isolator
in forward and backward transmission.

for TM-polarized light, as shown in Fig. 6. The green curve represents the straight waveguide used as a reference adjacent to thedevice. It can be observed that IR of 24.7 dB and insertion loss (IL)of 16.1 dB at a wavelength of 1549.5 nm were obtained between
the two propagation directions under the self-biased CAFO film.
The nonreciprocal resonant wavelength splitting (1λ) can be
written as
1λ =FSR · L MO · NRPSTM
,
2π

(4)

where the FSR is the free spectral range of the resonant peaks.
The FSR and 1λ in this device were 3.6 nm and 0.5 nm, respectively. Using Eq. (4), the experimental NRPS is 16.8 rad/mm,
more than twice the theoretical NRPS of 6.1 rad/mm obtainedusing Eq. (2). The theoretical NRPS was based on the Faraday
rotation coefficient of −4,350 deg/cm under in-plane remanent
magnetization of as-deposited film, which was much less thanthat of −15,000 deg/cm under saturation magnetization. The
CAFO/MgO film showed strong remanence for out-of-planemagnetization, as shown in Fig. 2(a); however, it could have strong
remanence in the patterned CAFO film owing to shape anisotropy[39]. We presume the remanent Faraday rotation coefficient would
be as much as −12,000 deg/cm. Regardless, this is an underestimation. The operation wavelength for the isolation peak can beResearch Article
Table 2.

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894

Comparison of Device Performance at 1550 nm for Si-Based Isolator

Bias Magnet

Isolator TypeMO Material

Isolation Ratio(dB)

Insertion Loss(dB)

Footprint(µm × µm)

NeededNeededMZIMZI (TM/TE)

Ce:YIG
Ce:YIG/YIG

27
30

13
59

Needed (electrical)
NeededNeeded
Free
Free

Ring
Ring
Faraday rotator
Faraday rotator
Ring

Ce:YIG
Ce:YIG/YIG
Ce:TbIG
BiIG
CAFO

32
19.5
30
29
24.7

10
18.8
7
1.5
16.1

500 × 500
940 × 330
870 × 340
70 × 702907350 × 0.5
480 × 1243 × 71

tuned by integrating a thermo-optic phase shifter with a structureof low-power consumption [40].
Table 2 compares the device performance and footprint ofSi-based optical isolators on silicon. Our device has a remarkably
small footprint. The IR is sufficiently large for optical-isolator performance; however, a high IL remains an important issue. The loss
breakdown included an absorption loss of ∼10 dB in the CAFO
region, a scattering loss of ∼1 dB at the boundary of the CAFO
region, and an insufficient resonant shift of ∼5 dB. The absorption
and scattering losses can be reduced slightly by increasing the
thickness of the MgO buffer layer to reduce light confinement in
the CAFO film. However, it should be noted that the NRPS is also
reduced. If the absorption loss is half and the Faraday rotation coefficient under remanent magnetization is twice that of the current
CAFO film, the IL of the isolator can be improved to less than 5 dB.
5. CONCLUSION
In summary, we experimentally demonstrated an ultra-compact
TM mode optical isolator (43 × 71 µm2 ) using deposited CAFO
film as MO material, achieving the IR of 24.7 dB at a wavelengthof 1549.5 nm. To the best of our knowledge, this is the smallest
optical isolator reported thus far. The device was self-biased by
the strong remanent magnetization of the CAFO film and did
not require an external magnet. The high IL of 16.1 dB remainsa challenge, but it can be solved by a little more improvement onlower absorption loss and larger θ F of CAFO film. In other words,
depositing a CAFO film with a larger FoM, including magnetic
anisotropy, is key to improving the optical isolator properties.
Then, CAFO supersedes conventional YIGs to realize compact
and integrated optical isolators.
Funding. Japan Society for the Promotion of Science (22K18805,
23H04802); Core Research for Evolutional Science and Technology(JPMJCR18T4); New Energy and Industrial Technology Development
Organization (JPNP16007, JPNP20004); Advanced Research Infrastructure
for Materials and Nanotechnology in Japan (ARIM) (JPMXP1223IT0018,
JPMXP1223IT0019).
Acknowledgment. This work was conducted at Nanofab, Tokyo Tech.
Disclosures. The authors declare no conflicts of interest.
Data availability. The data underlying the results presented in this paper are
not publicly available at this time but may be obtained from the authors upon reasonable request.

REFERENCES
1. D. Jalas, A. Petrov, M. Eich, et al., “What is—and what is not—an opticalisolator,” Nat. Photonics 7, 579–582 (2013).

Reference
[24]
[21]
[23]
[25]
[22]
[20]
This work

2. A. D. White, G. H. Ahn, K. V. Gasse, et al., “Integrated passive nonlinear
optical isolators,” Nat. Photonics 17, 143–149 (2023).
3. K. Y. Yang, J. Skarda, M. Cotrufo, et al., “Inverse-designed nonreciprocal pulse router for chip-based LiDAR,” Nat. Photonics 14,
369–374 (2020).
4. K. Abdelsalam, T. Li, J. B. Khurgin, et al., “Linear isolators using wavelength conversion,” Optica 7, 209–213 (2020).
5. L. Del Bino, J. M. Silver, M. T. M. Woodley, et al., “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the Kerr
effect,” Optica 5, 279–282 (2018).
6. M. Krause, H. Renner, and E. Brinkmeyer, “Optical isolation in silicon
waveguides based on nonreciprocal Raman amplification,” Electron.
Lett. 44, 691–693 (2008).
7. M. Yu, R. Cheng, C. Reimer, et al., “Integrated electro-optic isolator on
thin-film lithium niobate,” Nat. Photonics 17, 666–671 (2023).
8. J. F. Herrmann, V. Ansari, J. Wang, et al., “Mirror symmetric on-chip frequency circulation of light,” Nat. Photonics 16, 603–608 (2022).
9. N. Dostart, H. Gevorgyan, D. Onural, et al., “Optical isolation using
microring modulators,” Opt. Lett. 46, 460–463 (2021).
10. C. R. Doerr, L. Chen, and D. Vermeulen, “Silicon photonics broadband
modulation-based isolator,” Opt. Express 22, 4493–4498 (2014).
11. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
12. D. B. Sohn, O. E. Örsel, and G. Bahl, “Electrically driven optical isolation through phonon-mediated photonic Autler–Townes splitting,” Nat.
Photonics 15, 822–827 (2021).
13. C. J. Sarabalis, R. Van Laer, R. N. Patel, et al., “Acousto-optic modulation of a wavelength-scale waveguide,” Optica 8, 477–483 (2021).
14. D. B. Sohn and G. Bahl, “Direction reconfigurable nonreciprocal
acousto-optic modulator on chip,” APL Photonics 4, 126103 (2019).
15. A. Yu. Petrov, “Non-reciprocal modulation via acousto-optics,” Nat.
Photonics 12, 570–571 (2018).
16. R. Fleury, D. L. Sounas, and A. Alù, “Non-reciprocal optical mirrors
based on spatio-temporal acousto-optic modulation,” J. Opt. 20,
034007 (2018).
17. S. Liu, D. Minemura, and Y. Shoji, “Silicon-based integrated polarizationindependent magneto-optical isolator,” Optica 10, 373–378 (2023).
18. M. A. Serrano-Núñez, Y. Shoji, and T. Mizumoto, “Small magnetless
integrated optical isolator using a magnetized cobalt ferrite film,” IEICEElectron. Express 19, 20210500 (2022).
19. W. Yan, Y. Yang, S. Liu, et al., “Waveguide-integrated high-performancemagneto-optical isolators and circulators on silicon nitride platforms,”
Optica 7, 1555–1562 (2020).
20. D. Karki, V. Stenger, A. Pollick, et al., “Broadband bias-magnet-free onchip optical isolators with integrated thin film polarizers,” J. Lightwave
Technol. 38, 827–833 (2020).
21. Y. Zhang, Q. Du, C. Wang, et al., “Monolithic integration of broadband
optical isolators for polarization-diverse silicon photonics,” Optica 6,473–478 (2019).
22. K. Srinivasan, C. Zhang, P. Dulal, et al., “High-gyrotropy seedlayerfree Ce:TbIG for monolithic laser-matched SOI optical isolators,” ACS
Photonics 6, 2455–2461 (2019).
23. P. Pintus, D. Huang, C. Zhang, et al., “Microring-based optical isolator
and circulator with integrated electromagnet for silicon photonics,” J.
Lightwave Technol. 35, 1429–1437 (2017).

Research Article
24. 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, 022202 (2014).
25. L. Bi, J. Hu, P. Jiang, et al., “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5,
758–762 (2011).
26. Y. Shoji, T. Mizumoto, H. Yokoi, et al., “Magneto-optical isolator withsilicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92,
071117 (2008).
27. Y. Kim, D. J. Bang, Y. Kim, et al., “Magneto-optic property measurement of bismuth substituted yttrium iron garnet films prepared bymetal-organic-decomposition method at the 1310-nm and 1550-nm
wavelengths,” J. Magn. Magn. Mater. 492, 165673 (2019).
28. T. Shintaku, T. Uno, and M. Kobayashi, “Magneto-optic channel waveguides in Ce-substituted yttrium iron garnet,” J. Magn. Magn. Mater. 74,
4877–4881 (1993).
29. X. Y. Sun, Q. Du, T. Goto, et al., “Single-step deposition of ceriumsubstituted yttrium iron garnet for monolithic on-chip optical isolation,”
ACS Photonics 2, 856–863 (2015).
30. M. A. Serrano-Núñez, Y. Shoji, and T. Mizumoto, “Giant Faraday rotation of cobalt ferrite thin films deposited on silicon substrates for silicon
photonic nonreciprocal device applications,” Appl. Phys. Express 13,
062002 (2020).
31. K. Suzuki, T. Namikawa, and Y. Yamazaki, “Preparation of zinc- andaluminum-substituted cobalt-ferrite thin films and their Faraday
rotation,” Jpn. J. Appl. Phys. 27, 361 (1988).

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32. M. Ning, J. Li, C. K. Ong, et al., “High perpendicular coercive field of(100)-oriented CoFe2 O4 thin films on Si (100) with MgO buffer layer,” J.
Appl. Phys. 103, 013911 (2008).
33. N. A. Basit, H. K. Kim, and J. Blachere, “Growth of highly oriented Pb(Zr,Ti)O3 films on MgO-buffered oxidized Si substrates and its application
to ferroelectric nonvolatile memory field-effect transistors,” Appl. Phys.
Lett. 73, 3941–3943 (1998).
34. Ü. Özgür, Y. I. Alivov, C. Liu, et al., “A comprehensive review of ZnOmaterials and devices,” J. Appl. Phys. 98, 041301 (2005).
35. Y. Jiang, X. Li, X. Zhang, et al., “Absence of auxeticity in CoFe2 O4 epitaxial films,” Jpn. J. Appl. Phys. 61, 070901 (2022).
36. S. E. Shirsath, X. Liu, Y. Yasukawa, et al., “Switching of magnetic
easy-axis using crystal orientation for large perpendicular coercivity
in CoFe2 O4 thin film,” Sci. Rep. 6, 30074 (2016).
37. K. Ashida, M. Okano, M. Ohtsuka, et al., “Ultrahigh-Q photonic crystal
nanocavities fabricated by CMOS process technologies,” Opt. Express
25, 18165–18174 (2017).
38. E. Ishida, K. Miura, Y. Shoji, et al., “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,”
Opt. Express 25, 452–462 (2017).
39. H. Onoda, H. Sukegawa, and H. Yanagihara, “Study of induced magnetic anisotropy by lattice distortion in cobalt ferrite thin film grown on(Mg,Sn)3 O4 buffer layers,” IEEE Trans. Magn. 56, 1–4 (2020).
40. P. Sun and R. M. Reano, “Submilliwatt thermo-optic switches using freestanding silicon-on-insulator strip waveguides,” Opt. Express 18, 8406–
8411 (2010).