論文 / 著書情報
Article / Book Information
題目(和文)

非相反移相効果を用いた導波路型光アイソレータに関する研究

Title(English)

Study of waveguide magneto-optical isolator employing nonreciprocal
phase shift

著者(和文)

庄司雄哉

Author(English)

Yuya Shoji

出典(和文)

学位:博士（工学）,学位授与機関:東京工業大学,
報告番号:甲第7194号,
授与年月日:2008年3月26日,
学位の種別:課程博士,
審査員:水本 哲弥

Citation(English)

Degree:Doctor of Engineering,
Conferring organization: Tokyo Institute of Technology,
Report number:甲第7194号,
Conferred date:2008/3/26,
Degree Type:Course doctor,
Examiner:

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Tokyo Institute Research Repository)

Study of Waveguide Magneto-Optical Isolator
Employing Nonreciprocal Phase Shiftby
YUYA SHOJI

Department of Electrical and Electronic Engineering
Graduate School of Science and Engineering
Tokyo Institute of Technology

Doctorial Dissertation
Supervisor : Professor Tetsuya Mizumoto

February 2008

Tokyo Institute of Technology
2-12-1-S3-11 Ookayama, Meguro-ku, Tokyo 152-8550, JAPANi

Contents

Contents
Chapter 1:
Introduction
1.1
1.2
1.3

Introduction
Optical isolator
Waveguide isolators
1.3.1 Faraday rotation type
1.3.2 Nonreciprocal phase shift type
1.3.3 Nonreciprocal loss shift type
1.4 Integration technology
1.5 Objective of study and organization of dissertation
1.5.1 Objective
1.5.2 Organization of the dissertation
References

1
2
5
5
7
9
10
13
13
15
17

Chapter 2:
Nonreciprocal phase shift for magneto-optical isolator
2.1
2.2

Introduction
Theoretical analysis of nonreciprocal phase shift
2.2.1 Solving eigenvalue equation with 1-D waveguide model
2.2.2 Perturbation theory with 2-D waveguide model
2.2.3 Calculation results and comparison
2.3 Principle of isolator operation
2.4 Summary
References

21
21
23
28
30
39
41
42

Chapter 3:
Magneto-optical isolator with silicon waveguides fabricated bydirect bonding technique
3.1
3.2
3.3
3.4

Introduction
Device structure and design
Fabrication of Si waveguide
Direct bonding between Si and Ce:YIG
3.4.1 Surface activated bonding with oxygen plasma treatment
3.4.2 Experiment

43
44
51
58
58
59

Contents

ii

3.5

64
64
70
70
72
76
77

Characterization
3.5.1 Isolator operation
3.5.2 Insertion loss
3.5.3 Temperature dependence
3.6 Discussion
3.7 Summary
References

Chapter 4:
Wideband operation of a magneto-optical isolator using phaseadjustment in Mach-Zehnder interferometer
4.1
4.2
4.3

Introduction
Principle of wideband operation
Calculation results
4.3.1 Wideband design of three types of isolator
4.3.2 Fabrication tolerance
4.3.3 Ultra-wideband design
4.4 Fabrication of a wideband isolator
4.5 Characterization
4.6 Discussion
4.7 Summary
References

79
80
83
83
93
97
100
104
109
110
111

Chapter 5:
Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift
5.1
5.2
5.3
5.4
5.5

Introduction
Principle of polarization-independent operation
Device structure
Design of nonreciprocal phase shifter
Design of polarization converter
5.5.1 Principle of waveguide polarization converter
5.5.2 Calculation results
5.6 Discussion
5.7 Summary
References

113
114
116
118
126
126
128
136
137
138

iii Contents

Chapter 6:
Conclusions
140

Acknowledgement
143

Publication list
145

Chapter 1: Introduction

1

Chapter 1:
Introduction

1.1 Introduction
The spread of the Internet has led an explosive demand for communication-network systems.
New multimedia services such as database queries and updates, music distribution, video
streaming, and real-time voice telephone increase the data traffic. Several internet service
companies in Japan provide broadband access technologies with digital subscriber lines(DSL), cable television (CATV), and fiber to the home (FTTH). The number of the subscriber
is more than 23 million, and especially that of the FTTH is more than 5 million which isincreasing rapidly [1]. The optical fiber communication is promising technology forhigh-capacity network and international backbone systems.
The first breakthrough of optical fiber communication is the invention of the laser in 1960[2]. Lightwaves from the coherent source can carry enormously large amounts of informationcompared with radiowaves and microwaves. Also the transmission channel, namely the
optical fiber has been the dramatic improvement of low-loss transmission in 1970 by Corning
Glass Works in the United States [3]. Now typical loss of optical fibers is in the range of 0.2
dB/km at a wavelength of 1550 nm that is almost the lowest loss predicted theoretically in asilica fiber [4]. The transmission capacity upto 10 Gbit/s are widely installed and 40 Gbit/s
systems are ready to be installed in Japan. In the mid-1990s, a use of erbium-doped fiber
amplifier (EDFA) and wavelength-division multiplexing (WDM) offers a further boost infiber transmission capacity to higher levels and to increase the transmission distance. The
basis of WDM is to use multiple sources operating at slightly different wavelengths totransmit several independent data streams over the same fiber. This system has high flexibility
to provide new network architectures as well as high capacity [5].
Recently, the optical communication systems are attracted to not only a long-haul

2

Chapter 1: Introduction

transmission but short distance transmissions such as rack-to-rack, board-to-board, andchip-to-chip due to its high capacity. In such systems, integrated optics, which usually denotes
an optical waveguide device on transparent substrate such as glass, lithium niobate, or
semiconductor, is desired to reduce the cost and size by integrating them high-densely on asingle chip. The advance of the integrated optics pioneers a new field of optoelectronics that
integrate optical and electronic devices on the same semiconductor platform monolithically.

1.2 Optical isolators
When light travels through a fiber link, some optical power gets reflected at refractive-index
discontinuities such as in splices, couplers, and filters, or at air-glass interfaces in connectors.
The reflected signals can degrade both transmitter and receiver performance. In high-speed
systems, this reflected power causes optical feedback which can induce laser instabilities
caused by enhanced effect of carrier vibration [6], mode hopping phenomena among external
cavity modes [7], transition to a chaotic state [8], and effect of coherence collapse [9]. These
instabilities appear as either intensity noise (output power fluctuations), jitter (pulse
distortion), or phase noise in the laser, that can change its wavelength, linewidth, andthreshold current. Since they reduce the signal-to-noise ratio, these effects cause power
penalties in receiver sensitivities. Multiple reflection points set up an interferometric cavity
that feeds power back into the laser cavity, thereby converting phase noise into intensity noise.
And the multiple optical paths occurs the appearance of spurious signals arriving at thereceiver with variable delays. Unfortunately, these problems are signal-dependent, so that
increasing the transmitted or received optical power does not improve the bit-error-rate
performance. To eliminate reflections, optical isolators are essentially needed.
Figure 1.1 shows a schematic configuration of an optical transmission system. A
distributed-feedback laser diode (DFB-LD), capable of single-mode operation in high-speed
modulation owing to its high coherence, must be protected by an optical isolator within thetransmitter module [10]. In addition, optical amplifiers such as EDFA enables systemdesigners to remove the bottleneck in electronics in regenerated subsystems, where opticalisolators are connected the both sides of the EDF to prevent amplifying noise signals.

Chapter 1: Introduction

3

Consequently, optical isolators are indispensable to construct high-performance optical fiber
link systems.

Opticalfiber
Transmitter
data

Drive
circuits

LD

OpticalamplifierOpticalfiber
Receiver
PD

LD

Drive
circuits

data

EDF

Lens
Isolator

input

outputcoupler

fiber
Isolator

filterPump-LD

Fig. 1.1 Schematic configuration of optical transmission system.

An optical isolator using magneto-optic effect is so-called magneto-optical isolator. It is
typically composed of a magneto-optic garnet such as yttrium iron garnet (YIG) which has
magneto-optic effect with small optical absorption in the near-infrared region where opticalfiber communication is developed.
Figure 1.2 shows a schematic drawing of a bulk isolator. It is based on the Faraday
rotation in a magneto-optic material. A Faraday rotator is set between two polarizers whosetransmission polarization planes are angled by 45o to each other. The polarization plane offorward traveling wave passing through the left-hand polarizer is rotated by 45o in the
Faraday rotator and pass through the right-hand polarizer. Backward traveling wave whichhas 45o rotated polarization are selected by the right-hand polarizer. Since the Faraday rotator
rotated the polarization by 45o nonreciprocally, backward traveling wave is eliminated by theleft-hand polarizer.
Calcite crystals or birefringent materials are used as the polarizer. The Faraday rotation
angle is proportional to the Faraday rotation coefficient of the material that determines thetotal device size. Since a bulk YIG crystal has small Faraday rotation coefficient (~200
deg/cm) and requires large external magnetic field, miniaturization of magneto-optical

4

Chapter 1: Introduction

isolators has been an issue to be solved. Recently, a bismuth-substituted gadolinium irongarnet film such as (GdBi)3(FeGaAl)5O12 which is grown by liquid phase epitaxy (LPE) andhas large Faraday rotation coefficient (~1500 deg/cm) is usually used for bulk isolators [11].
Figure 1.3 shows a configuration of bulk isolator for polarization-independent operation.
Birefringent materials are used as polarization splitters, which combine the different
polarization waves into the output fiber in the forward direction, while distract them from the
input fiber in the backward direction.
These bulk isolators are realized with an extinction ratio between the forward andbackward direction, so-called an isolation ratio, more than 35 dB and an insertion loss lessthan 0.8 dB. In a high-speed transmission system, two isolators are typically cascaded toachieve a high isolation ratio more than 55 dB [12].
At present, commercially available isolators are only bulk types. Unfortunately, the bulk
isolators are not suitable for integration because of assembling process of the magneto-optic
garnet, polarizers, and lens for focusing the light. The absence of waveguide isolator is abottleneck for reducing the cost of light source modules and realizing integrated opticalcircuits. A waveguide isolator is highly desired.

Fig. 1.2 Bulk isolator.

Fig. 1.3 Polarization-independent bulk isolator.

Chapter 1: Introduction

5

1.3 Waveguide isolators
In this section, several kinds of waveguide isolator that many researchers have investigatedare overviewed. The principle of operation and the demonstrated performance are discussed.

1.3.1 Faraday rotation typeFigure 1.4 shows a waveguide isolator based on TE-TM mode conversion. The principle ofoperation is based on a Faraday rotation used in a bulk isolator. In a planar waveguide, lights
propagate as two orthogonal eigenmodes, transverse electric (TE) mode or transverse
magnetic (TM) mode. Since it is difficult to construct 45o-rotated polarizer on a planar
waveguide, additional 45o reciprocal polarization conversion is installed. Then the total
polarization rotation is 0o or 90o depending on the propagation direction. Ando et al.
demonstrated the waveguide isolator with Cotton-Mouton effect for the reciprocal
polarization conversion [13]. This effect is based on a magnetic linear birefringence in amagneto-optic material obtained when its magnetization vector turns to a direction tilted fromthe film normal in perpendicular to the light propagation as shown in Fig. 1.4. The laser
annealing with about 1200 Co at the spot can change the direction of the magnetization that
forms the Faraday and Cotton-Mouton regions in a same magneto-optic film plane. The
optical isolator was constructed by splitting the converted light with rutile prisms and theisolation ratio of 12.5 dB at λ= 1150 nm was reported.
There is a problem that the difference in phase velocity (phase mismatch) between TE andTM modes determines the upper limit of the polarization conversion. In Ref. [14], a conditionof phase matching is carefully analyzed and the fabrication tolerance in an isolator setting isturned out to be very strict.
Another type of the waveguide isolator using the Faraday rotation is a semi-leaky isolator
as shown in Fig. 1.5 [15-16]. The isolator is based on the coupling between TE guided andTM radiation modes in a thin-film magneto-optic waveguide and an anisotropic cladding layer.
Two kinds of mode coupling occur concurrently. One is a gyrotropic longitudinal mode
coupling by the Faraday rotation in the guiding layer, and the other is an anisotropic polar
coupling by the birefringence of the cladding layer. These couplings are set so as to be6

Chapter 1: Introduction

cancelled in the forward direction but added in the backward direction. Since the waveguidestructure is cut-off for the coupled TM modes, therefore called “semi-leaky,” an opticalisolation is obtained as the light propagation. Compared with the mode conversion isolator
described above, the coupling efficiency of the semi-leaky isolator is insensitive to the phasematching because the coupled radiation modes exist continuously.
This isolator was firstly proposed by Yamamoto et al. but it is required to realize acontinuous layered-structure of magneto-optic garnet and an anisotropic material without any
gap. Recently the isolator was fabricated and demonstrated with an isolation ratio of 20.2 dB
at λ= 1550 nm in our group [17]. A cerium-substituted yttrium iron garnet (Ce:YIG) as themagneto-optic layer and LiNbO3 as the anisotropic layer were bonded directly by the surface
activated bonding (this technique is described more in detail in Chapter. 3).

Fig. 1.4 TE-TM mode conversion isolator utilizing Faraday and Cotton-Mouton effect.

Fig. 1.5 Semi-leaky isolator.

Chapter 1: Introduction

7

1.3.2 Nonreciprocal phase shift type
Nonreciprocal phase shift is a direction-dependent change of the propagation constant which
occurs for one propagation mode propagating in a magneto-optic waveguide when an external
magnetic field is applied transversely to the light propagation direction [18]. Since phasematching is not required, this effect is insensitive to the fabrication errors and suitable for a
waveguide isolator.
Auracher et al. firstly proposed a Mach-Zehnder interferometer (MZI) configuration inwhich nonreciprocal and reciprocal phase differences between two interferometer arms are
induced [19] and many researchers have intensively investigated with this configuration[20-24]. Figure 1.6 shows the schematic diagram of the isolator. By applying external
magnetic fields to the two arms in anti-parallel direction, where the nonreciprocal phase shift
is yielded with different sign, the nonreciprocal phase difference of −π/2 or +π/2 is induced
depending on the propagation direction between two interferometer arms. A reciprocal phasedifference of +π/2 given by an optical path difference cancels it in the forward direction but isadded to it in the backward direction. Therefore the MZI isolator exhibits constructive anddestructive interferences in respective direction.
Fujita et al. fabricated this type of isolator with (Bi,Lu,Nd)3(Fe,Al)5O12 garnet film, anddemonstrated an isolation ration of 19 dB at λ= 1540 nm [23]. Yokoi et al. proposed an
improved design of the MZI configuration with different upper cladding layers in two arms tosimplify the magnetization, and demonstrated an isolation ratio of 9.9 dB at λ= 1550nm [24].
When the magnetization is aligned in the film plane, a nonreciprocal phase shift is induced in
TM mode. On the other hand, when the magnetization is aligned vertically to the film plane, it
is induced in TE mode. Two research groups have proposed a polarization-independent
isolator using TE and TM mode nonreciprocal phase shift in a MZI simultaneously.
Zhuromskyy et al. used horizontal and vertical domain walls in the magneto-optic guiding
layer [25] and Fujita et al. used different side cladding layer [26].
The author has also studied about the improvement of the magneto-optical isolator with
the MZI configuration in this dissertation. The objective is mentioned in the Section 1.5.

8Chapter 1: Introduction

Fig. 1.6 Mach-Zehnder interferometric isolator employing nonreciprocal phase shift.

Shintaku et al. proposed and demonstrated another configuration of a waveguide isolator
employing nonreciprocal phase shift in conjunction with nonreciprocal guided-radiation mode
conversion [27]. Figure 1.7 shows the device structure and the relationship of the propagation
constants required for the isolator operation. The directional-dependent propagation constants
for TM modes provided by the nonreciprocal phase shift are set to across the propagation
constant of the TE radiation mode. Then the TM mode with smaller propagation constant isconverted to the TE radiation mode. Applying the external magnetic field with a little
component of light propagation direction, the conversion efficiency is enhanced. An isolation
ratio of 27 dB at λ= 1535 nm was reported. A large amount of the nonreciprocal phase shift isrequired to achieve the design such that one mode is guided but the other is cut-off.
Many other configurations of a waveguide isolator employing nonreciprocal phase shift
were proposed by a research group of Osnabrück University. They proposed a nonreciprocal
directional coupler [28], a nonreciprocal multi-mode interference isolator [29], a cross strip
isolator utilize an nonreciprocal interference between fundamental mode and first-order mode[30], and also a nonreciprocal mode conversion using combination of Faraday rotation andnonreciprocal phase shift [31]. However, since the amount of the nonreciprocal phase shiftitself is small, the MZI configuration is the most superior in the device size, fabrication
tolerance, and operation bandwidth.

Chapter 1: Introduction

9Fig. 1.7 Nonreciprocal mode conversion isolator employing nonreciprocal phase shift. (a)Devise structure and (b) relationship of the propagation constants required for the isolator
operation.

1.3.3 Nonreciprocal loss shift type
A new concept of waveguide isolator using a magneto-optic effect in a ferromagnetic metal
contact was proposed by two research groups. Takenaka et al. used InGaAsP active layergrown on InP substrate and Ni or Fe ferromagnetic layer [32], and Zayets et al. used
GaAsP/AlGaAs-quantum well (QW) active layer grown on GaAs substrate and Co
ferromagnetic layer [33]. Figure 1.8 shows the layer structure and the diagram of the complex
effective refractive indices in the isolator operation. This waveguide is a semiconductor
optical amplifier (SOA) as well as a magneto-optical waveguide. By magnetizing theferromagnetic metal in a direction transversely to the propagation direction, the magneto-optic
Karr effect induces a nonreciprocal complex index change, that is, the direction-dependentchange in the optical absorption loss as well as phase shift. The loss in the forward direction iscompensated by the gain of SOA. Consequently, this isolator is transparent in the forward
direction and the remaining loss in the backward direction extinguishes the reflected lights.
The position of the ferromagnetic metal and the direction of its magnetization determine
the operating polarization. When they are arranged as shown in Fig. 1.8, the nonreciprocal
loss shift occurs in TM mode. Whereas, when the metal layer is located on the side of the10 Chapter 1: Introduction

waveguide and the magnetization is aligned transversely to the waveguide plane, thenonreciprocal loss shift occurs in TE mode. The isolator operations were demonstrated in TE
mode with the isolation ratio of 14.7 dB/mm [34] and in TM mode with that of 9.9 dB/mm[35].
The problem of this isolator is the ASE noise of SOA. Nonetheless, this waveguideisolator is one of the most suitable configurations for integration with a semiconductor laser
diode.

k

Neff*=n−jkferromagnetic metal
Backward

Nonreciprocal

cladding layer

loss shift
SOA gainguiding layer
ForwardNonreciprocal

active gain layer

Isolation

guiding layerncladding layeryphase shiftxzFig. 1.8 Nonreciprocal loss shift isolator. (a) Operation principle and (b) the device structure.

1.4 Integration technology
These waveguide isolators except the nonreciprocal loss shift type are basically composed ofa magneto-optic garnet thin-film waveguide grown on a lattice-matched garnet substrate, suchas Bi or Ce substituted rare-earth iron garnet film on a gadolinium gallium garnet (GGG)
substrate. It is impossible to deposit the film epitaxially on a semiconductor or a silica
substrate. This makes it difficult to integrate a waveguide isolator with other optical devices.
Optical hybrid integration is a promising way of producing a low cost and highly
functional optical component. Sugimoto et al. demonstrated a hybrid integrated waveguideisolator by assembling a magneto-optic waveguide, thin-film half-wave plate sheet, andthin-film polarizer sheets on a silica-based planar lightwave circuit (PLC) as shown in Fig. 1.9[36]. They realized a high isolation ratio of 25-34 dB at λ= 1550 nm, and also apolarization-independent operation by using a MZI configuration [37].

Chapter 1: Introduction

11

However, the insertion loss of 2.3-3.2 dB is mainly dominated by the reflection loss at theinterfaces of each component. In addition, high accuracy of the alignment position is required
to achieve the low insertion loss. Hence, it is preferable to configure the monolithicallyintegrated optical isolator.

Fig. 1.9 Configuration of hybrid integrated waveguide optical isolator [36].

Debnath et al. used a magnetic semiconductor Cd1-xMnxTe which can be grown on a GaAs
substrate for an integrated isolator [38]. The maximum mode conversion efficiency of
98%±2% at λ= 735nm was reported. The conversion length of about 1.6 mm, the appliedexternal magnetic field of 5.5 kG, and the optical loss of 0.2 dB/cm led a magneto-opticalfigure-of-merit of 1000 deg/dB/kG.
Guo et al. fabricated a magneto-optical semiconductor by doping Fe into InP or InGaAsP[39]. Magnetic dopants couple to the free carriers in a semiconductor to dramatically enhance
the Faraday rotation due to interband transitions. With an appropriate choice of magnetic
dopant, the free carrier concentration can be reduced along with free carrier absorption, and it
is possible to simultaneously enhance the magneto-optical activity and reduce the opticalabsorption of a semiconductor. A 45o Faraday rotation with a Verdet coefficient of 23.8
deg/cm/T and the insertion loss of 1.66 dB at λ= 1550 nm were reported.
Although these magnetic semiconductor waveguides are suitable for monolithic
integration with semiconductor optical active devices, the magneto-optic effects are still12 Chapter 1: Introduction

smaller than that of magneto-optic garnet. Integrating technology by adhesives such as an
epoxy and solder is reliable for hybrid integrated devices. However, they cannot be applied tomonolithic integration as an intermediate thin layer because of the difficulties in controlling
the thickness and its uniformity. A wafer direct bonding technique is one of the promisingsolutions to overcome this problem.
Wafer direct bonding is a phenomenon that two flat and clean wafers are directly bonded
without any adhesives. Yokoi et al. proposed a use of direct bonding technique to realize amagneto-optic waveguide with a semiconductor waveguide GaInAsP/InP and a magneto-optic
upper cladding layer as shown in Fig. 1.10 [40]. It enables one to realize a semiconductor
laser diode monolithically integrated with a magneto-optical isolator by using epitaxial
selective area growth technique of semiconductor waveguides [41]. Moreover, it was foundthat waveguide structure of Si based on a silicon-on-insulator (SOI) substrate with amagneto-optic upper cladding layer has large nonreciprocal phase shift [42,43]. Due to thestrong optical confinement in the Si waveguides, the total device size can be miniaturized
dramatically. In addition, the field of Si photonic device is the most attractive in the recent
years. It is mentioned more in detail in Chapter 3.

Fig. 1.10 Integrated isolator with semiconductor waveguide.

Chapter 1: Introduction

13

1.5 Objective of study and organization of dissertation
1.5.1 Objective
Table 1 summarizes the characteristics of the optical isolators mentioned above. The bulk
isolator composed of discrete components is not suitable for integration. The fabrication
tolerance is large because it is aligned in open space and there is no need of phase matching.
However, the fabrication accuracies are required in polishing bulk crystals and collimatingthem. The device size is about 1 – 2 mm and some lenses are required to collect the lights.
The operation bandwidth is about 30 – 40 nm which is dominated by the wavelength
dependence of the Faraday rotation of the magneto-optic material. The TE-TM mode
conversion types can be composed of either magneto-optic garnet or magnetic
semiconductors where strict phase matching condition is required for each case. Using a
waveguide polarizer can reduce the device size of the isolator. While semi-leaky isolator haslarge fabrication tolerance and large operation bandwidth, it is not suitable for integration withother devices because it is composed of a magneto-optic garnet waveguide with a birefringent
cladding layer. The isolation ratio increases as the propagation length, for example it is 2.2
mm to obtain an isolation ration of 30 dB [17]. Nonreciprocal loss shift type is much suitablefor integration with semiconductor laser diodes and is relatively easy to fabricate. However, it
is not recommended for passive use due to its ASE noise. The isolation ratio increases as thelength, e.g. 2.0 mm to obtain an isolation of 30 dB. Nonreciprocal phase shift type especiallybased on MZI configuration is less sensitive to the fabrication errors and can be integrated
with other components by a direct bonding technique. The Si waveguide makes the device
size smaller than any other optical isolator ever-reported.
The objectives of this study are the following three about the nonreciprocal phase shift
type magneto-optical isolator:
1) Fabrication and demonstration of the magneto-optical isolator with Si waveguides
As mentioned above, it has much impact to demonstrate the magneto-optical isolator with
Si waveguides for not only integrated optics in long transmission systems but also recent Si
photonics. The author investigates the fabrication of the isolator with Si waveguide by directbonding technique. In this study, a surface activated bonding is employed and examined for14 Chapter 1: Introduction

the first demonstration of the isolator operation.
2) Wideband operation of the magneto-optical isolator using phase adjustment
The operation bandwidth of the nonreciprocal phase shift type isolator is as mush as thatof bulk types. A wideband operation is attractive for WDM application in an optical circuit.
Moreover, it becomes the great advantage over bulk isolators. The author proposes a novel
design of the wideband isolator and demonstrates the operation. The proposed design isapplicable to any kind of structures for the nonreciprocal phase shift type isolator.
3) Polarization-independent magneto-optical isolator using TM-mode nonreciprocal phaseshift
The operating polarization is preferred in TE mode because most semiconductor laser
diodes operate in TE mode. However, the integrated structure realized by direct bonding has
the nonreciprocal phase shift only in TM mode. The author proposes a novel configuration of
the polarization-independent waveguide isolator using only TM mode nonreciprocal phaseshift and examines the design principle. The isolator is comprised of waveguide polarization
converters and nonreciprocal phase shifters. Since the configuration uses only TM mode
nonreciprocal phase shift, it is well matched with the integrated structure fabricated by directbonding.
If these developments are achieved, the magneto-optical isolator employing nonreciprocal
phase shift becomes the most promising waveguide isolator to be practically used.

Chapter 1: Introduction

15

Table 1 Summary of the characteristics of the optical isolators.
Type

Material

Integration

Fabrication
tolerance

Devicesize

Operation
bandwidth

Polarization

Bulk

Bi:RIG*

×

○

△

△

TE/
independent

TE-TM mode
conversion

Bi:RIG[13]

△

×

○

△

TE

CdMnTe/GaAs[38]Fe:GaInAsP[39]

○

×

△

△

TE

Semi-leaky

LiNbO3/Ce:YIG[17]

×

○

△

○

TE

Nonreciprocal
loss shift

GaInAsP/InP[34,35]

○

○

△

○

TE/TM

Nonreciprocal
phase shift(MZI)

Bi:RIG[23]

△

○

△

△

TM

Ce:YIG/GaInAsP/InP[40]

○

○

×

△

TM

Ce:YIG/Si/SiO2[42]

○

○

○

△

TM

*RIG: rare-earth (Gd, Lu, Y) iron garnet

1.5.2 Organization of the dissertation
The organization of this dissertation is summarized in Fig. 1.11.
In Chapter 2, the magneto-optical isolator employing nonreciprocal phase shift is
described. The nonreciprocal phase shift is numerically examined by 1-dimentional and2-dimentional simulations. All of the calculations and designs in the following chapter are
based on this analysis. The operation principle of the magneto-optical isolator is explained.
In Chapter 3, a magneto-optical isolator with Si waveguides fabricated by a direct bonding
technique is described. First, the device is designed with Si waveguides. Second, Siwaveguides on a SOI substrate are fabricated and characterized. Third, a surface activateddirect bonding is investigated to realize a magneto-optic isolator with a Ce:YIG/Si/SiO2-layered structure. Finally, fabricated magneto-optical isolator with Si waveguides ischaracterized.
In Chapter 4, a wideband operation of the magneto-optical isolator is described. First, theprinciple of the proposed wideband operation is explained. Second, the numerical results of

16 Chapter 1: Introduction

the wideband design are presented and the fabrication tolerance is examined. Third, amagneto-optical isolator of the wideband design is fabricated with a Ce:YIG rib waveguide,
and then characterized.
In Chapter 5, a polarization-independent isolator using TM-mode nonreciprocal phaseshift is described. First, the principle of the proposed polarization-independent operation is
explained. Next, the numerical results of the polarization-independent design in thenonreciprocal phase shifter are presented. Finally, designs of the waveguide polarization
converter are investigated by a finite-element method and a full-vector beam propagation
method.
In Chapter 6, the results obtained from this study are summarized.

Chapter 1
Introduction

Chapter 2
Magneto-optical isolator employing
nonreciprocal phase shift

Chapter 3

Chapter 4

Chapter 5

Magneto-optical isolator

Wideband operation of a

Polarization-independent

with silicon waveguides

magneto-optical isolator

magneto-optical isolator

fabricated by direct bonding

using phase adjustment inusing TM-mode nonreciprocal

techniqueMach-Zehnder interferometer

phase shift

Chapter 6
Conclusion

Fig. 1.11 Organization of this dissertation.

Chapter 1: Introduction

17

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18 Chapter 1: Introduction

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[25] O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysisof polarization independent Mach-Zehnder-type integrated optical isolator,” J. Lightwave
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Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

21

Chapter 2:
Nonreciprocal Phase Shift for
Magneto-Optical Isolator
2.1 Introduction
Optical nonreciprocal devices are indispensable to eliminate unwanted reflected light in thefiber link and protect optical active devices. The optical nonreciprocity is obtained frommagneto-optic effect. A waveguide magneto-optical isolator employing nonreciprocal phaseshift is investigated in this study. The nonreciprocal phase shift provides direction-dependent
propagation constants due to the first-order magneto-optic effect with an external magnetic
field applied transversally to the light propagation direction. A Mach-Zehnder interferometer
configuration with the nonreciprocal phase shift realizes a magneto-optical isolator.
In this chapter, the nonreciprocal phase shift in a planar waveguide structure is analyzed
by numerical calculation. Two numerical approaches are presented. One is solving directly the
eigenvalue equation derived from the Maxwell equation with 1-dimensional (1-D) waveguidemodels. The other is a calculation using the perturbation theory with 2-dimensional (2-D)
waveguide models. Then the principle of isolator operation and its design of themagneto-optical isolator are presented.

2.2 Theoretical analysis of nonreciprocal phase shift
The magneto-optic effects are described by the off-diagonal components of the dielectric
permittivity tensor in a magneto-optic material [1]. The complex relative permittivity tensor
of dielectric materials is given by

⎡ε xx
⎢
~
ε = ⎢ε yx⎢ε zx⎣

ε xy ε xz ⎤⎥ε yy ε yz ⎥ .
ε zy ε zz ⎥⎦(2.1)

22 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

As we consider loss-free material, the diagonal elements are real. The real and imaginaryparts of the off-diagonal elements involve anisotropic and gyrotropic systems, respectively.
Anisotropic systems are generated by the crystal-axis rotation in birefringent materials or theelectro optic effect. Gyrotropic systems are generated by the magneto-optic effect. Since thecorresponding elements such as εxy and εyx are complex conjugate to each other, theanisotropic systems are reciprocal due to the real part, and the gyrotropic systems are
nonreciprocal due to the imaginary part. The imaginary off-diagonal elements are induced byan orthogonal magnetization. When the light propagates along the z-axis, the εxy induced byz-aligned magnetization is related to the Faraday rotation and the εxz or εyz induced by y- or
x-aligned magnetization are related to the nonreciprocal phase shift.

In this section, the nonreciprocal phase shift is theoretically analyzed. We assume aloss-free magneto-optic waveguide in which the magneto-optic film is located in the x-z plane.
The magnetization is aligned along the x-axis and lightwaves propagate along the z-axis. Here,a magneto-optic linear effect such as Cotton-Mouton effect is neglected. The relative
permittivity of a magneto-optic film is then given by⎡ε x~
ε = ⎢⎢ 0
⎢⎣ 0

0

εy
− jγ

0⎤
jγ ⎥⎥
ε z ⎥⎦(2.2)

where εx, εy, and εz are related to the isotropic refractive indices denoted as ε = n2 in the x, y,
and z direction, respectively. The off-diagonal elements γ are proportional to the specific
Faraday rotation coefficient ΘF by

γ =

2nΘ F
k0

(2.3)

where k0 is the wavenumber in vacuum.
The Maxwell equation is written as∇ × Ε = − jωμ 0 Η(2.4)∇ × Η = jωε~ε 0 Ε(2.5)∇⋅Η = 0(2.6)

∇ ⋅ (ε~Ε ) = 0(2.7)

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

23

where ω is the angular frequency, E and H are the electric and magnetic field vectors,
respectively, ε0 and μ0 are the permittivity and permeability of free space, respectively. From
(2.2), the Maxwell equation (2.4) and (2.5) are rewritten in component form as∂E z ∂E y−= − jωμ 0 H x ,
∂y
∂z

(2.8)

∂E x ∂E z−= − jωμ 0 H y ,
∂z
∂x

(2.9)

∂E y

∂E x
= − jωμ 0 H z ,∂y(2.10)∂H z ∂H y−= jωε 0ε x E x ,∂y∂z(2.11)∂H x ∂H z−= jωε 0 (ε y E y + jγE z ),∂z∂x(2.12)

−

∂x

∂H y
∂x

−

∂H x
= jωε 0 (ε z E z − jγE y ) .
∂y(2.13)

2.2.1 Solving eigenvalue equation with 1-D waveguide model
We consider a 1-dimensional waveguide model as shown in Fig. 2.1. The thickness of theguiding layer is defined d. Since all layers are uniform along the x- axis, ∂ ∂x = 0 .

y

d
0

z

Upper cladding layer

ε~1

Guiding layer

ε~2Lower cladding layer

ε~3xFig. 2.1 Geometry of the three-layered slab waveguide model.

24 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

First, TM mode propagating along the z-axis is examined. Then the propagating modes aredescribed byΕ = (0, E y , E z )exp{ j (ωt − β z )} ,(2.14)

Η = (H x , 0, 0 ) exp{ j (ωt − βz )}(2.15)

where β denotes the longitudinal propagation constants along the z-axis. From (2.12) and(2.13), Ey and Ez are expressed asEy =⎛ ∂H x∂H x ⎞⎜⎜ γ⎟,− jε z∂z ⎟⎠ωε 0 (ε y ε z − γ ) ⎝ ∂y(2.16)Ez =⎛ ∂H x∂H x ⎞⎜⎜ γ⎟.
+ jε y∂y ⎟⎠ωε 0 (ε y ε z − γ ) ⎝ ∂z

(2.17)

1

2

1

2

Substituting (2.16) and (2.17) into (2.8), we obtain the following wave equation for Hx⎛ ∂2H x
∂2H x ⎞ 2
1
⎟ + k0 H x = 0⎜εy+εzε y ε z − γ 2 ⎜⎝∂y 2
∂z 2 ⎟⎠(2.18)

where we use k 02 = ω 2ε 0 μ 0 . Using ∂ ∂z = − jβ , (2.18) is rewritten as⎞∂ 2 H x ⎛⎜ 2
2 εz ⎟
′
+
−
k
H =0
ε
β
0
ε y ⎟⎠ x∂y 2 ⎜⎝(2.19)withε′ =ε yε z − γ 2.
εy(2.20)For a guiding mode in the planar waveguide shown in Fig. 2.1, the effective refractive index
N (=β / k0) must beε y1 , ε y 3 < N 2 < ε y 2(2.21)and the wave vectors along y-axis are defined with2
ε zi 2 ⎧⎪− η ik ε '−β =⎨ 2 .
ε yi
⎪⎩k 2
2
0 i

(i = 1,3)(i = 2)(2.22)

One can solve the wave equation (2.19) for each layer by⎧ A1 exp{− η1 ( y − d )}exp(− jβz )⎪H x = ⎨( A2 cos k 2 y + B2 sin k 2 y ) exp(− jβ z )⎪ A exp(η y ) exp(− jβz )3⎩ 3(y ≥ d)(0 ≤ y < d )( y < 0)(2.23)

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

25

where A1, A2, B2, and A3 are the field amplitudes. Substituting (2.23) into (2.17), Ez for eachlayer is obtained as⎧ (γ 1 β + η1ε y1 ) A1
exp{− η1 ( y − d )}exp(− jβz )⎪⎪ jωε 0ε 1 ' ε y1
⎪ (γ β A − ε k B ) cos k y + (γ βB + ε k A ) sin k y⎪ 2 2
y2 2 2yy2 2 2222
Ez = ⎨exp(− jβ z ) .
jωε 0ε 2 ' ε y 2⎪⎪ (γ β − η ε ) A
3 y3
3
⎪ 3
exp(η 3 y ) exp(− jβ z )
j
ωε
ε
ε
'
⎪⎩
y3
0 3

(2.24)

Using the boundary condition that Hx and Ez are continuous across y=0 and y=d, we obtainthe following eigenvalue equation

tan k 2 d =γ β⎞ 1⎫γ 1β ⎞ 1 ⎛k 2 ⎧⎛⎟⎟ + ⎜⎜η 3 − 3 ⎟⎟ ⎬⎨⎜⎜η1 +
ε 2 ' ⎩⎝
ε1 ⎠ ε1 ' ⎝ε3 ⎠ ε 3 '⎭⎧⎛γ β⎞ 1γ β⎞ 1 ⎛γ β ⎞⎛γ β⎞ 1⎫ γ β ⎛ γ β ⎞k 22 ⎛− ⎜⎜η1 + 1 ⎟⎟⎜⎜η 3 − 3 ⎟⎟+ ⎨⎜⎜η 3 − 3 ⎟⎟ − ⎜⎜η1 + 1 ⎟⎟ ⎬ 2 + ⎜⎜ 2 ⎟⎟2
ε 1 ⎠⎝
ε 3 ⎠ ε 1 'ε 3 ' ⎩⎝ε3 ⎠ ε3' ⎝ε 1 ⎠ ε 1 ' ⎭ ε 2 'ε 2 ⎝ ε 2 'ε 2 ⎠ε2' ⎝(2.25)
where εyi is simplified as εi for each layer i= 1, 2, or 3. This equation can be solved by anumerical analysis. Because of the linear terms in β involving the off-diagonal elements γ,
there are nonreciprocal solutions for β as the propagation and magnetization directions. And
the nonreciprocal phase shift is given by
Δβ = β + − β − .

(2.26)

Notice that, when the slab structure is symmetric denoted as ε1=ε3 and γ1=γ3, the linear termsin β vanish and Δβ becomes zero. This means that the nonreciprocal phase shift is induced by
the asymmetry of the waveguide structure transversally to the magnetization direction. The
difference in the propagation constant means the difference in the distribution ofelectro-magnetic field depending on the propagation direction.
Next, TE mode propagating along the z-axis is examined. The propagating modes aredescribed byΕ = (E x , 0, 0 ) exp{ j (ωt − βz )},Η = (0, H y , H z )exp{ j (ωt − β z )} .

(2.27)(2.28)

2

26 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

Substituting (2.9) and (2.10) into (2.11), we obtain the following wave equation for Ex∂ 2 Ex+ k 02ε x − β 2 E x = 0 .
2
∂y

(

)

(2.29)

With the wave vectors along the y-axis⎧⎪− η i2k ε xi − β = ⎨ 2 ,
⎪⎩k 2
2
0

2

(i = 1,3)(i = 2)(2.30)

one can solve (2.29) for Ex and Hz. Using the boundary condition for Ex and Hz across y=0
and y=d, we obtain the following eigenvalue equation
tan k 2 d =k 2 (η1 + η 3 ).
k 22 − η1η 3(2.31)

Since there are no linear terms in β, nonreciprocal phase shift is not induced for TE mode
propagations with the magnetization along the x-axis.
In the same way, we consider a four-layered waveguide model shown in Fig. 2.2. Aninterlayer with the thickness of d2 is inserted above the guiding layer with the thickness of d3.
TM propagating modes are described as (2.14) and (2.15), and we obtain the same wave
equation as (2.19). The wave vectors along the y-axis are defined with⎧− η i2⎪ε
k 02ε i '− zi β 2 = ⎨± η 22 ,
ε yi
⎪ 2
⎩k 3

(i = 1,4)(i = 2)(2.32)(i = 3)where the sign of i=2 is positive when the interlayer works as a part of core layer as ε2 > N2
and negative when it works as a cladding layer as ε2 < N2. The solutions for Hx are given by⎧ A1 exp{− η1 ( y − d 2 − d 3 )}exp(− jβz )⎪[A exp{η ( y − d )} + B exp{− η ( y − d )}] exp(− jβz )
⎪ 2
2
3
2
2
3
.
Hx = ⎨⎪( A3 cos k 3 y + B3 sin k 3 y ) exp(− jβ z )⎪⎩ A4 exp(η 4 y ) exp(− jβz )( y ≥ d 2 + d3 )(d 3 ≤ y < d 2 + d 3 )(0 ≤ y < d 3 )( y < 0)(2.33)

Substituting (2.33) into (2.17), Ez for each layer is obtained. Using the boundary condition
that Hx and Ez are continuous across y=0, y=d2 and y=d2+d3, we obtain the following
eigenvalue equation

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator27⎛
γ β⎞ 1 γ β k⎜⎜η 4 − 4 ⎟⎟ + 3 − 3 C0 = 0ε 4 ⎠ ε 4′ ε 3′ε 3 ε 3′⎝(2.34)

where
⎡⎧⎛
⎤
k
γ β
γ β⎞ 1 ⎫ 1γ β⎞ 1 ⎛C0 = ⎢⎨⎜⎜η 2 − 2 ⎟⎟ − ⎜⎜η 2 + 2 ⎟⎟ C1 ⎬cos k3 d 3 + 3 cos k 3 d 3 + 3 sin k3 d 3 ⎥ε 2 ⎠ ε 2′ ⎭ 1 + C1ε 3′ε 3ε 3′ε 2 ⎠ ε 2′ ⎝
⎢⎣⎩⎝
⎥⎦
⎡⎧ ⎛
⎤
γ β
k
γ β⎞ 1 ⎫ 1γ β⎞ 1 ⎛sin k 3 d 3 − 3 sin k3 d 3 + 3 cos k 3 d 3 ⎥⎢⎨− ⎜⎜η 2 − 2 ⎟⎟ + ⎜⎜η 2 + 2 ⎟⎟ C1 ⎬ε 2 ⎠ ε 2′ ⎭ 1 + C1ε 3′ε 3ε 3′ε 2 ⎠ ε 2′ ⎝⎣⎢⎩ ⎝⎦⎥(2.35)
and⎧⎛⎧⎛γ β⎞ 1⎫γ β⎞1 ⎛γ β⎞ 1⎫γ β⎞1 ⎛
C1 = − ⎨⎜⎜η1 + 1 ⎟⎟ + ⎜⎜η 2 − 2 ⎟⎟ ⎬ exp(2η 2 d 2 ) ⎨⎜⎜η1 + 1 ⎟⎟ − ⎜⎜η 2 + 2 ⎟⎟ ⎬ε 2 ⎠ ε 2′ ⎭ε 1 ⎠ ε 1′ ⎝ε 2 ⎠ ε 2′ ⎭ε 1 ⎠ ε 1′ ⎝
⎩⎝
⎩⎝

.

(2.36)
This equation can be solved by a numerical analysis. The linear terms in β involving theoff-diagonal elements γ induce nonreciprocal solutions for β, and the nonreciprocal phaseshift Δβ is obtained.

yUpper cladding layer

ε~1

d2

Interlayer

ε~2

d3

Guiding layer

ε~3Lower cladding layer

ε~4

0

z

x

Fig. 2.2 Geometry of the four-layered slab waveguide model.

28 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

2.2.2 Perturbation theory with 2-D waveguide model
We consider a 2-dimensional waveguide model as shown in Fig. 2.3. In this case, the wave
equation for Hx derived from the Maxwell equation (2.4)-(2.7) has differential terms ∂x , ∂ywith respect to x and y. The 2-D Maxwell equation considering ∂ ∂x and ∂ ∂y with themagneto-optic effect is a complex system even though a directly solution by finite element
method is reported [2]. Easier way to obtain the nonreciprocal phase shift is using
perturbation theory [1,3,4]. When the off-diagonal elements γ of the permittivity tensor are
much smaller than the diagonal elements ε, the gyrotropic effect can be treated as aperturbation in an unperturbed system without magnetization. The nonreciprocal propagation
constants are given by

β± = β0 ±Δβ2(2.37)

where β0 is the propagation constant of the unperturbed system. In perturbation theory, thenonreciprocal characteristic is given by
Δβ =

2ωε 0
Ε∗ Δε~Εdxdy∫∫
P

normalized by the power flow in the z direction()

P = ∫∫ Ε × Η ∗ + Ε ∗ × Η dxdy .
z(2.38)(2.39)

E and H are the electric and magnetic fields of the unperturbed system and Δε~ is theperturbation induced by the magnetization.
Using the semi-vector approximation, TM modes propagating along the z-axis aredescribed byΕ = (0, E y , E z )exp{ j (ωt − β z )} ,(2.40)

Η = (H x , 0, 0 ) exp{ j (ωt − βz )}.

(2.41)

From (2.12) and (2.13), Ey and Ez of the unperturbed system are expressed as
Ey = −

Ez =

∂H x
,
ωε 0ε y ∂z

j

∂H x
.
ωε 0ε z ∂yj

(2.42)(2.43)

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

29

Then a magnetization along the x-axis yields the perturbation along the y-axis for TM modes,
and the nonreciprocal phase shift is given by
0
⎡0
⎢
0
E ⎢0
⎢⎣0 − jγ2ωε 0
0 E y∗
Δβ =
∫∫
P

[

∗
z

0 ⎤⎡ 0 ⎤jγ ⎥⎥ ⎢⎢ E y ⎥⎥ dxdy
0 ⎥⎦ ⎢⎣ E z ⎥⎦

]

=

2ωε 0
E y∗ ( jγ ) E z + E z∗ (− jγ ) E y dxdy
∫∫
P

=

2ωε 0
2 Re jγE y∗ E z dxdy
∫∫
P

=

∂H x
2
2γβ
dxdy ,Hx∫∫∂yP ωε 0ε y ε z

{

}

{

}

{

(2.44)}

P = ∫∫ E y H x∗ + H x∗ E y dxdy
= 2 Re ∫∫ E y∗ H x dxdy =2βHωε ε ∫∫

2x

dxdy .

(2.45)y0

The integral term of y in (2.44) exists only across the interfaces of the magneto-optic layer at

y=ym as⎡ γ⎤γ ∂H xγ⎢∫ ε yε z ∂y dy = ⎢ ε yε z H x − ε yε z H x ⎥⎥ .
y −0
y +0

(2.46)∑ ν ∫ γ (ε ε ) H ( y ) dx
Δβ =∫∫ ε H dxdy

(2.47)⎣

mm⎦

Finally, we obtain
−1

m

y

−1
y

2

z

x

m

2

x

where ν is +1 or −1 determined by the position of magneto-optic layer in (2.46).
The H x of the unperturbed system can be calculated by numerical simulation such as abeam propagation method (BPM) or a finite element method (FEM). The numerator of (2.47)
is obtained from the calculation of the integral of off-diagonal elements, permittivity tensors,and simulated magnetic fields along the magneto-optic interface. The denominator of (2.47) is
obtained from the integral of permittivity tensors and simulated fields all over the simulation
region.

30 Chapter 2: Nonreciprocal phase shift for magneto-optical isolatoryw

Upper cladding layer

ε~1

ε~4

Side cladding layer

h
d
0

z

Guiding layer

ε~2Lower cladding layer

ε~3xFig. 2.3 Geometry of the 2-D waveguide model.

2.2.3 Calculation results and comparison
In this study, a cerium-substituted yttrium iron garnet CeY2Fe5O12 (Ce:YIG) grown on a
(Ca,Mg,Zr)-doped GGG substrate (SGGG) is used as the magneto-optic garnet. The Faraday
rotation coefficient ΘF of Ce:YIG is –4500 deg/cm, which corresponds to the off-diagonal
permittivity γ of 0.008525, at λ=1.55 μm [5]. As described in Chapter 1, our group has
proposed the magneto-optical isolator employing nonreciprocal phase shift with somematerial systems. Here, we consider three kinds of waveguide structure as shown in Fig. 2.4,(a)SiO2/Ce:YIG/SGGG, (b)Ce:YIG/GaInAsP/InP, and (c)Ce:YIG/Si/SiO2 -layered structures,
respectively. Rib waveguides are formed on the guiding layer to confine lightwave laterally.
The latter two structures have side-cladding layer of air so that they are realized by a directbonding [6-8]. The refractive indices of the material at λ= 1.55 μm are shown in Table 2.1.

w

w

w

SiO2

Ce:YIG

Ce:YIG

airr
Ce:YIG
y

z

x

h

air

r
GaInAsP

h

r
Si

SGGG

InP

SiO2

(a)

(b)

(c)

Fig. 2.4 Waveguide structures for magneto-optical isolator.

hChapter 2: Nonreciprocal phase shift for magneto-optical isolator

31

Table 2.1 Refractive indices at λ= 1.55 μm.
Material

Refractive index

Ce:YIG

2.20

SGGG

1.94

GaInAsP (λg= 1.42 μm)

3.45

InP

3.17

Si

3.48

SiO2

1.44

Figure 2.5 shows calculation results of the nonreciprocal phase shift as a function of
waveguide height h. Dashed lines are calculated by solving eigenvalue equation with 1-D slab
waveguide model where the side cladding layer is neglected. Solid lines are calculated by the
perturbation theory with 2-D waveguide model where the unperturbed magnetic field issimulated by the mode solving via imaginary distance BPM [9,10]. In the semi-vector
simulation, the magnetic fields are derived from the electric fields. For all the structure, thewaveguide width w and rib height r are fixed at 2.0 μm and 0.1 μm, respectively. The
simulation grid sizes along x- and y-axis are Δx= 0.05 μm and Δy= 0.01 μm, respectively, andthe slice step along z-axis is Δz= 0.005 – 0.05 μm. There is little difference in the results
between two methods, solving eigenvalue equation and perturbation theory. It is observed thata large nonreciprocal phase shift is obtained from the waveguide structure with
Ce:YIG/Si/SiO2. This is because there is a large intensity of the magnetic field at the interface
between Ce:YIG and Si layer as can be seen in Fig. 2.6.
Figure 2.7 shows calculation results of the nonreciprocal phase shift for different
waveguide widths with 2-D structure. Here, we use the waveguide structure with
Ce:YIG/Si/SiO2 and the rib height is the same as the waveguide height, i.e., it is a channel
waveguide. The simulation grid sizes are Δx= 0.01 μm and Δy= 0.01 μm to model the narrow
waveguide width. As is the particular problem for the software, spin-off intensity peaks
sometime appear on the magnetic fields at the waveguide corners as shown in Fig. 2.8. The
semi-vector simulation derives the magnetic fields from the firstly calculated electric fields so

32 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

as to satisfy the Maxwell equation. They appear only when the simulation is carried withsmall grid size for a high-index-contrast waveguide. These must be eliminated when thenonreciprocal phase shift is calculated using the magnetic fields. As you can see in Fig. 2.7,
the maximum nonreciprocal phase shift becomes small for narrower width. This means thatthe magnetic field distribution is broaden in the vertical direction due to the lateral opticalconfinement as the waveguide width is narrow. Consequently, we should calculate thenonreciprocal phase shift with 2-D structure instead of 1-D structure if the lateral optical-1

Nonreciprocal phase shift (mm )confinement is strong in the waveguide structure.

8.0
SiO2/Ce:YIG/NOG
Ce:YIG/GaInAsP/InP
Ce:YIG/Si/SiO2

6.0
4.0
2.0
0

0.2

0.4
0.6
0.8
waveguide height (μm)

1

Fig.2.5 Calculated nonreciprocal phase shift for some waveguide structures. Dashed lines arecalculated by solving eigenvalue equation with 1-D structure and Solid lines are calculated byperturbation theory with 2-D structure, at λ= 1.55 μm.

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

33

(a)

(b)

(c)

Fig. 2.6 Mode profiles of magnetic field calculated by semi-vector BPM.
(a)SiO2/Ce:YIG/SGGG at h= 0.48μm, (b)Ce:YIG/GaInAsP/InP at h= 0.36μm, and(c)Ce:YIG/Si/SiO2 at h= 0.20μm. All the width and rib height are w= 2.0μm and r= 0.1μm,

Nonreciprocal phase shift (mm -1)

respectively.

Slab
BPM(W=2.0μm)
BPM(W=1.5μm)
BPM(W=1.0μm)
BPM(W=0.6μm)
BPM(W=0.4μm)

8
6
4
2
0

0.15

0.2 0.25 0.3 0.35
waveguide thickness (μm)

0.4

Fig.2.7 Calculated nonreciprocal phase shift for some waveguide width with the
Ce:YIG/Si/SiO2 structure, at λ= 1.55 μm.

34 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

Spin-off peakFig. 2.8 Mode profile of magnetic filed with the Ce:YIG/Si/SiO2 structure at w= 0.6μm andh= r= 0.20μm.

Next, we compare the simulation methods to calculate the magnetic field distribution with
2-D structure. The mode solving via semi-vector BPM, full-vector BPM, and full-vector FEM
are considered [9,11]. The full-vector simulations provide Hx and Hy fields which are
distinguished major or minor component as their distributions. Typically, major and minor
components are distributed at the center and the corner in the waveguide, respectively. The Hxof major component is called quasi-TM mode or TM-like mode.
Figures 2.9 and 2.10 show the calculation results for comparison of the semi-vector BPM
with the full-vector BPM and the full-vector FEM, respectively. The waveguide is composedof SiO2/Ce:YIG/SGGG and is a channel waveguide h=r. The magnetic fields are calculated
directly in the full-vector simulations where no spin-off peaks appear as shown in Fig. 2.11.
The semi-vector BPM shows larger maximum nonreciprocal phase shift than the full-vector
simulations for small dimension of the waveguide. At the same time, the semi-vector BPM
gives larger propagation constant than the full-vector simulations. This difference is thought
to be caused by the spin-off peaks at the waveguide corners as mentioned above. The peaks

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

35

seem to prevent the field distribution from broadening to upper region as can be seen in Fig.
2.11 (a). This results in large distribution of the magnetic field at the magneto-optic interface

Nonreciprocal phase shift (mm -1)

and enhances the nonreciprocal phase shift.

(W=2.0μm)(W=1.5μm)(W=1.0μm)(W=0.6μm)(W=0.4μm)

8
6
4
2
0

0.15

0.2 0.25 0.3 0.35
waveguide height (μm)

0.4

Fig. 2.9 Comparison between semi-vector BPM and full-vector BPM. The lines are calculatedNonreciprocal phase shift (mm -1)

by the semi-vector BPM, and the dots are calculated by the full-vector BPM.

(W=2.0μm)(W=1.5μm)(W=1.0μm)(W=0.6μm)(W=0.4μm)

8
6
4
2
0

0.15

0.2 0.25 0.3 0.35
waveguide thickness (μm)

0.4

Fig. 2.10 Comparison between semi-vector BPM and full-vector FEM. The lines arecalculated by the semi-vector BPM, and the dots are calculated by the full-vector FEM.

36 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

(a)

(b)

(c)

Fig. 2.11 Mode profiles of magnetic field with the SiO2/Ce:YIG/SGGG structure at w=
0.40μm and h= 0.24μm calculated by (a) semi-vector BPM, (b) full-vector BPM, and (c)full-vector FEM.

The discontinuity of the data for w= 1.0 μm in Fig. 2.10 is due to hybrid supermodes. To
understand the hybrid supermodes, effective refractive indices and nonreciprocal phase shift
are calculated at the fixed height of 0.28 μm as shown in Fig. 2.12 and Fig. 2.13. The mode-0
corresponds to the TE0 mode. On the other hand, as the width increase, the mode-1 changes
from TM0 mode into TE1 mode, and the mode-2 changes from TE1 mode into TM0 modeacross w ~ 1.0 μm. The nonreciprocal phase shift is calculated with Hx component consideredas TM0 mode. The magnetic field distributions around the cross point of mode-1 and mode-2
are shown in Table 2.2. At w= 1.0 μm, the Hx and Hy can not be distinguished as major orminor component, then they are considered as hybrid supermodes. This behavior of the modetransition affects the field distributions at w ~ 1.0 μm. For example, Hx1 at w= 0.95 μm andHx2 at w= 1.0 μm are slightly pushed up and down, respectively. Therefore, the nonreciprocal
phase shift calculated from the field distributions becomes discontinuous across w ~ 1.0 μm.

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

37

As a result, we should not design a waveguide with such parameter as hybrid supermodeappears because they induce mode transition between TM fundamental and TE higher-ordermodes. Such mode transition is observed during the full-vector BPM simulation when the
propagation constant of TM0 is close to that of TE1.

3

Neff

2.8
2.6

FEM (full-v)
mode0
mode1
mode2
mode3
BPM (semi-v)
TE0
TM0

2.4
2.2

0.5

1
1.5
width (μm)

2Fig. 2.12 Effective refractive indices simulated by semi-vector BPM and full-vector FEM

Nonreciprocal phase shift (mm -1 )with the Ce:YIG/Si/SiO2 structure at h= r= 0.28 μm.

54

BPM (semi-v)
BPM (full-v)(Neff tole:1e-8)(Neff tole:1e-7)
FEM (full-v)(mode-1)(mode-2)(mode-3)

3
0.5

1
1.5
width (μm)

2Fig. 2.13 Calculated nonreciprocal phase shift using the magnetic fields simulated bysemi-vector BPM and full-vector FEM.

38 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

Table 2.2 Mode profiles of magnetic field calculated by full-vector FEM with the
Ce:YIG/Si/SiO2 structure at h= r= 0.28 μm.
w

0.9 μm

0.95 μm

1.0 μm1.05 μm

Hx1

Hy1

Hx2

Hy2

2.3 Principle of isolator operation
In this section, the principle of a magneto-optical isolator operation employing nonreciprocal
phase shift is described. Figure 2.14 shows the basic configuration of the isolator which is a
Mach-Zehnder interferometer with nonreciprocal and reciprocal phase shifters. Hence weutilize the nonreciprocal phase shift for TM mode, the isolator operates for TM mode.
External magnetic fields are applied in anti-parallel direction to the two arms of thenonreciprocal phase shifter. These provide direction-dependent propagation constants for thelightwave traveling in each arm. The nonreciprocal phase differences θN between the twoarms are given byθ N ( forward ) = (β f 1 − β f 2 )L ,(2.48)

θ N (backward ) = (β b1 − β b 2 )L

(2.49)

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

39

where L is the propagation length of the nonreciprocal phase shifter. When the waveguidestructures of the two arms are symmetric, the θN has different sign depending on the
propagation direction

β 0 − Δβ 2 = β f 1 = β b 2 ,(2.50)

β 0 + Δβ 2 = β f 2 = β b1 .

(2.51)In the isolator operation, the θN are set at −π/2 and +π/2 in the forward and backward
directions, respectively. The reciprocal phase difference θR is set at +π/2 by an optical path
difference ΔL between the two arms given byθ R = β ⋅ ΔL

(2.52)

where β is the longitudinal propagation constant of the mode propagating in the waveguide ofreciprocal phase shifter.
A forward traveling wave from the input port is divided into two waves with identicalamplitudes and phases at the 3dB coupler. The nonreciprocal phase difference is cancelled by
the reciprocal one and the total phase difference is 0. So the two waves are coupled to the
output port by the constructive interference at the 3dB coupler. A backward traveling wave
from the output port is divided into identical two waves at the 3dB coupler. In this time, thenonreciprocal phase shift is added to the reciprocal one and the total phase difference is +π.
Then the two waves are not coupled to the input port and radiated at the 3dB coupler by thedestructive interference. Consequently, the MZI functions as a magneto-optical isolator. Table
2.3 shows designed length of the nonreciprocal and reciprocal phase shifters for somewaveguide structures. The refractive indices as shown in the Table 2.1 are used.
The output intensity of a MZI is given by [12]
Eout

2

−j
=
2
=

{

( a e + a e )E
jθ1

1

2

jθ 2

2

in

}

1
2
a1 + a2 + 2 a1a2 cos(θ 2 − θ1 ) Ein
4(2.53)

where Ein and Eout are the amplitudes of the electric field at the input and output ports and θ1,

θ2, a1, and a2 are the phase differences and attenuations of intensity in each arm. As the 3 dB
coupler divided a wave into two waves with identical phase and amplitude, and the waves

40 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

propagate without any attenuation in both arms, the (2.53) is rewritten as
Eout

2

=

1 + cos(θ 2 − θ1 )
2
Ein .
2

NPS
input

(2.54)

RPS
3dB
coupler

3dB
coupler

outputNPS

Forward

θN

θR

−π/2

+π/2

+π/2

+π/2

Backward

Fig. 2.14 Basic configuration of the magneto-optical isolator employing nonreciprocal phaseshift. NPS: Nonreciprocal phase shifter, RPS: Reciprocal phase shifter.

Table 2.3 Designed lengths of nonreciprocal and reciprocal phase shifters.
ΘF= −4500 deg/cm of Ce:YIG at λ= 1.55 μm.
Parameters

LNPS (mm)w / h / r (μm)

(a)

(b)

(a)

(b)

2.0 / 0.48 / 0.10

0.840

0.839

0.196

0.196

Ce:YIG/GaInAsP/InP 2.5 / 0.36 / 0.16

3.498

3.661

0.121

0.121

Ce:YIG/Si/SiO2

2.0 / 0.20 / 0.01

0.213

0.231

0.164

0.165

Ce:YIG/Si/SiO2

0.6 / 0.22 / 0.22

0.233

0.298

0.168

0.170

Structure

SiO2/Ce:YIG/SGGG

LRPS (μm)(a) semi-vector BPM, (b) full-vector FEM

Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

41

2.4 Summary
In this chapter, the nonreciprocal phase shift is analyzed by numerical calculation. Using 1-D
and 2-D waveguide models, the nonreciprocal phase shift is calculated. For narrower
waveguide, 2-D model should be used for taking the effect of the lateral optical confinement
into account. In the comparison among the several mode solving methods, reliable results are
obtained by using full-vector simulations than semi-vector BPM. However, the full-vector
simulations take much time to obtain the filed distributions and make it complex due to thehybrid supermode.

42 Chapter 2: Nonreciprocal phase shift for magneto-optical isolator

References[1] S. Yamamoto and T. Makimoto, “Circuit theory for a class of anisotropic and gyrotropic thin-film
optical waveguides and design of nonreciprocal devices for integrated optics,” J. Appl. Phys.,vol.45, pp.882-888 (1974).
[2] M. Koshiba and X-P. Zhuang, “An efficient finite-element analysis of magnetooptic channel
waveguides,” J. Lightwave Technol., vol.11, pp.1453-1458 (1993).
[3] M. Shamonin and P. Hertel, “Analysis of nonreciprocal mode propagation in magneto-optic
rib-waveguide structures with the spectral-index method,” Appl. Opt., vol.33, pp.6415-6421(1994).
[4] N. Bahlmann, V. Chandrasekhara, A. Erdmann, R. Gerhardt, P. Hertel. R. Lehmann, D. Salz, F-J.
Schröteler, M. Wallenhost, and H. Dötsch, “Improved design of magnetooptic rib waveguides for
optical isolators,” J. Lightwave Technol., vol.16, pp.818-823 (1998).
[5] T. Shintaku, “Integrated optical isolator based on efficient nonreciprocal radiation mode
conversion,” Appl. Phys. Lett., vol.73, pp.1946-1948 (1998).
[6] H. Yokoi and T. Mizumoto, “Proposed configuration of integrated optical isolator employing
wafer-direct bonding technique,” Electron. Lett., vol.33, pp.1787-1788 (1997).
[7] H. Yokoi, T. Mizumoto, and Y. Shoji, “Optical nonreciprocal devices with a silicon guiding layer
fabricated by wafer bonding,” Appl. Opt., vol.42, pp.6605-6612 (2003).
[8] R. L. Espinola, T. Izuhara, M.-C. Tsai, and R. M. Osgood, Jr., “Magneto-optical nonreciprocal
phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett., vol.29, pp.941-943 (2004).
[9] BeamPROP software from RSoft Design Group, (http://www.rsoftdesign.com/)[10] S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using theimaginary-distance beam-propagation methods for modal analysis,” J. Quantum Electron., vol.30,
pp.2098-2105 (1994).
[11] FemSIM software from RSoft Design Group, (http://www.rsoftdesign.com/)[12] T. Suhara, “Optical-wave Engineering (Kouha-kougaku),” (Corona publishing co., ltd., Tokyo,
1998), Chap.3, p.49. (in Japanese)Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

43

Chapter 3:
Magneto-Optical Isolator with
Silicon Waveguides Fabricated by
Direct Bonding Technique

3.1 Introduction
A silicon-on-insulator (SOI) material system is an efficient platform for both electronic andphotonic devices. The high refractive index contrast of a Si waveguide enables one to realize
ultracompact photonic devices and dense integrated optical circuits [1]. A high speed opticalmodulator based on a MOS capacitor has attracted much attention for advanced Si photonics[2]. In addition, combining III-V compound semiconductors that have direct bandgap andhigh mobility with Si-LSI provides new scope of optoelectronic integrated circuits (OEICs).
Because, Si offers several advantages that it is low-cost, mechanically strong, and transparent
at the emission and absorption wavelengths of III-V materials. A hybrid evanescent laser
integrating III-V active region with Si waveguide is an example of the high-potential
application [3]. Recently, Luxtera, Inc. released an optical transceiver using a Si photonics
technology based on monolithic optoelectronic devices manufactured in a low-cost CMOS
process [4]. An optical isolator or circulator is as yet unrealized in Si-based waveguide, while
it is required for high-speed transmission in optical fiber links to ensure the stable operationof active devices.
On the other hand, magneto-optical garnets such as yttrium iron garnet (YIG), that have alarge magneto-optic effect and are transparent in the near-infrared region, are grown
epitaxially on a garnet substrate. We have investigated a waveguide magneto-optical isolator
using a Mach-Zehnder interferometer (MZI) with a directly bonded magneto-optic garnet44 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

upper cladding layer [5,6]. As mentioned in Chapter 2, a use of a Si high-index-contrast
waveguide enhances nonreciprocal phase shift in a magneto-optic garnet / Si / SiO2 layered
structure, which enables an ultracompact optical isolator with Si waveguides. Figure 3.1
shows an application of Si-based optical transceiver integrated with a magneto-optical isolator.
Since a WDM scheme is promising technology for high capacity transmission, a wideband
operation of the magneto-optical isolator which is proposed in Chapter 4 is suitable for thisscheme. In other words, a high-performance optical transceiver can be realized on a Si
platform owing to the magneto-optical isolator.
CMOS driver
III-V hybrid laser [2]Si p-i-n modulator [3]WDM coupler
Magneto-optical isolator

SOI wafer

λ1, λ2, λ3…, λnFig. 3.1 Concept image of Si-based optical transceiver integrated with a magneto-opticalisolator.

3.2 Device structure and design
The schematic drawing of the device structure is shown in Fig. 3.2. The principle of theisolator operation composed of a MZI configuration has been mentioned in Section 2.3. The
nonreciprocal phase shifter is composed of a Ce:YIG / Si / SiO2 -layered structure. The 3×2
multi-mode interference (MMI) coupler is employed as 3dB coupler in which a lightwave

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

45

from the center port of the 3 branches are divided into two waves with identical amplitude andphase through the two ports of the other 2 branches. And the MMI coupler provides
interferences between the two waves from the 2 branches so that constructive and destructive
interferences lead the lightwave to the center port and the side ports of the 3 branches,
respectively.
In this section, all the designs are calculated with the refractive indices as shown in Table
3.1. First, the thickness of the Si guiding layer on a SOI wafer is determined. Figure 3.3
shows a nonreciprocal phase shift calculated by the perturbation theory with anelectromagnetic field distribution given by the full-vector FEM as a function of theSi-thickness. The waveguide width and rib height are fixed at 2.0μm and 0.01μm, respectively.
The nonreciprocal phase shift is maximized at the Si-thickness of ~0.20 μm and the required
propagation length is 213 μm to obtain ±π/2 phase differences by external magnetic fields inanti-parallel direction.

Fig. 3.2 Schematic drawing of the magneto-optical isolator with Si waveguide.

46 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Material

Refractive index

Si

3.48

SiO2

1.44

air

1.0

Ce:YIG

2.20

SGGG

1.94

HfO2

1.98

8.0

1
0.8

6.0

0.6
4.0
0.4
2.0
0
0.15

0.2
0.2
0.25
0.3
0.35
waveguide thickness (μm)

00.4

Propagation length for π/2 (mm)Nonreciprocal phase shift (mm -1)

Table 3.1 Refractive indices at λ= 1.55 μm.

Fig. 3.3 Calculated nonreciprocal phase shift and the propagation length required for π/2
phase difference of Ce:YIG/Si/SiO2 structure at w= 2.0μm, r= 0.01μm, and λ= 1.55μm.

However, there are some problems when the thickness is small. One is a leakage loss into
the Si substrate through the SiO2 lower cladding layer due to large evanescent fields in thislayer. For example, the thickness of the SiO2 layer required for loss-free guiding of TM
fundamental mode is more than 2.0 μm as the 0.20-μm-thick Si layer while 1.0 μm is
sufficient for the case of the 0.30-μm-thick Si layer. The other problems are a scattering loss

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique47

and a reflection at the boundary between the different upper cladding regions fabricated by adirect bonding technique. Figures 3.4 (a) and 3.5 (a) show the decrease in transmittance due tothe scattering at a boundary with different upper cladding regions on a Si waveguidecalculated by a bi-directional finite difference (FD) BPM in a 2-D (x-z) structure [7] and abi-directional optical propagation analysis based on eigenmode expansion method [8]. The
material of the upper cladding layers are assumed to be air, SiO2, and HfO2 against Ce:YIG
region. The decrease in transmittance is 2.6 dB for a 0.20-μm-thick Si guiding layer at aboundary between Ce:YIG and air cladding regions. Also, the reflection coming back to the
input is calculated by these methods as shown in Figs. 3.4 (b) and 3.5 (b). The reflection is−27 dB for a 0.20-μm-thick Si guiding layer. It is possible to prevent the reflections fromreturning into the input port by adjusting the phase difference between the reflections in twoarms to be antiphase. The scattering loss and reflection can be reduced as the thickness of Si
increases or the refractive index of the upper cladding layer is close to that of Ce:YIG.
However, the required length of the nonreciprocal phase shifter is long for a thicker Si layer
as shown in Fig. 3.3. Also, the waveguide dimensions become large for lower index contrast
between Si and the cladding layer. Consequently, the thickness of Si guiding layer is to be
determined taking into account the trade-off between the scattering loss and the device size.
Hence, we consider two designs of the isolator. One is a low-loss design for a test
fabrication with 2.0-μm-wide and 0.01-μm-height rib waveguide on 0.30-μm-thick Si layer.
The other is for an ultracompact design with 0.6-μm-wide channel waveguide on
0.22-μm-thick Si layer. The propagation lengths of the nonreciprocal phase shifter (LNPS) andreciprocal phase shifter (LRPS) are designed by mode solving based on FEM and a perturbation
theory as described in Section 2.3. The MMI coupler is designed by 3-D FD-BPM [7]. Figure
3.6 shows the configuration and its design parameters. Table 3.2 shows two designs of themagneto-optical isolator. A 1×2 MMI coupler is designed for the ultracompact design. The
total length of 364 μm is the world’s smallest among optical isolators ever-reported.

48 Chapter 3: Magneto-optical isolator with silicon waveguides

Scattering loss (dB)fabricated by direct bonding technique0-1
nc=1.0nc=1.44nc=1.98

-2
-3

0.2

0.3
0.4
Si thickness (μm)

0.5

(a)

Reflection (dB)0nc=1.0nc=1.44nc=1.98

-20
-40
-60
-80
0.2

0.3
0.4
Si thickness (μm)

0.5

(b)
Fig. 3.4 (a) Decrease in transmittance due to scattering and (b) reflection at a boundary
between different upper cladding layers on a Si waveguide calculated by a bi-directional BPM.
One side of the upper cladding layer is Ce:YIG with the refractive index of 2.20. Simulation
grid sizes are Δx = 0.01 μm and Δz = 0.02 μm and the Padé order is (2,2).

49

Scattering loss (dB)

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique0-1
nc=1.0nc=1.44nc=1.98

-2
-3

0.2

0.3
0.4
Si thickness (μm)

0.5

(a)

Reflection (dB)0nc=1.0nc=1.44nc=1.98

-20
-40
-60
-80
0.2

0.3
0.4
Si thickness (μm)

0.5

(b)
Fig. 3.5 (a) Decrease in transmittance due to scattering and (b) reflection at a boundary
between different upper cladding layers on a Si waveguide calculated by a bi-directional
optical propagation analysis based on eigenmode expansion method. One region has upperand side cladding layers of 2.20 and 1.0, respectively, and the other region has covered layerof modified index. The width of Si channel waveguide is set at 2.0 μm.

50 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniqueFig. 3.6 Design of a MMI coupler on SOI wafer.

Table 3.2 Two sets of design parameters of the magneto-optical isolator with Si waveguides.
(unit: μm)
Low-loss design

Ultracompact design

Cover material

Air

SiO2

Width (w)

2.0

0.60

Height (h)

0.30

0.22

Rib height (r)0.01(channel)

LNPS for ±π/2

401

298

LRPS for +π/2

0.152

0.170

MMI width (wmmi)

15.0

4.0

MMI length (lmmi)

210

22

Arm distance (d)

6.0

1.6

Bending (R, φ)~500, 60o

10, 90o

Total length

~3000

364

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique51

3.3 Fabrication of Si waveguide
Figure 3.7 shows a fabrication process of the Si waveguide. We use a Unibond SOI wafer
manufactured by wafer bonding and splitting techniques with a hydrogen-implantation called“Smart-Cut®” proposed by Bruel [9]. The SOI wafer is first cleaned with ethanol, acetone,
and isopropanol. The native oxide on Si surface is not removed by hydrofluoric acid in thisstage so as to protect the wafer surface until a direct bonding process. After coating
300-nm-thick electron-beam resist ZEP-520A on the sample surface by a spin coater with
6000 rpm for 60 sec, it is baked at 170 oC for 15 min. The waveguide patterns are exposed byelectron-beam lithography with accelerating voltage of 50 kV and are developed with amixture of methyl isobutyl ketone and isopropanol (1:1) for 2 min. The patterns aretransferred to an e-beam deposited Cr mask, which is then lifted off with dimethylformamide.
The rib or channel waveguide is formed on Si surface by reactive ion etching (RIE) in a
CHF3:O2 (15:1) plasma with a 50-W radio frequency (RF) power. The Cr mask is stripped off
with hydrochloric acid at ~120 oC. Finally, the ends of the Si waveguide are obtained bycleaving the sample at a notch formed by dicing-saw.
Figure 3.8 shows scanning electron microscope (SEM) images of the fabricated0.20-μm-thick and 0.60-μm-wide Si-wire waveguides. The roughness of the sidewall is about
10 nm. The bending radius and angle are 2.5 μm and 90 degree. The 2.0-μm-wide and3.0-μm-length MMI coupler is well fabricated.

52 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniqueFig. 3.7 Fabrication process of Si waveguide.

53

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

(a)

(b)

(c)

Fig. 3.8 Fabricated Si-wire waveguides. (a)Straight waveguide, (b)bending waveguide,and (c)MMI coupler.

Figure 3.9 shows measurement results of the propagation loss of 0.2-μm-thick Si channel
waveguides for TM mode propagation. The losses shown in (a) and (b) are measured for asample with the upper cladding of air and that after 0.8-μm-thick SiO2 deposition,
respectively. The transmitted power of the Si waveguides with several widths through fiber tofiber alignment is measured by optical power meter at λ=1.55 μm. The propagation loss
except the coupling loss between fiber/sample is estimated from the gradient as a function of
propagation length, which is known as a “cut-back” method. The propagation loss is about 3.7– 4.0 dB/mm independent of the waveguide width. The sidewall roughness ~10 nm of Si
waveguide dominates the propagation loss. The coupling loss decreases after covering SiO2
cladding layer.
In the same way, the propagation loss of 0.3-μm-thick and 2.0-μm-wide Si rib waveguides
with several rib heights are measured as shown in Fig. 3.10. The propagation loss is 0.63

54 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

dB/mm for the rib height of 10 nm.
Figure 3.11 shows the measured bend loss of curved section for 0.2-μm-thick and0.6-μm-wide Si-wire waveguide with several bending radii. The loss of 90-degree bend with
2.5-μm-radius is ~4.9 dB that is dominated by the sidewall roughness. It becomes negligible
small when the bending radius is more than 20 μm. Figure 3.12 shows the measured excess
loss of branching characteristic of the fabricated MMI coupler. 0.2-μm-thick and 0.6-μm-wide
Si-wire waveguides are connected to the 2.0-μm-wide multimode section. The divided powersof around −3 dB, almost identical to each port, are obtained at the coupler length of 3.2 μm.

70

Loss (dB)60

W=2.0μm
W=1.0μm
W=0.6μm

50
40
30

W
a
a

(a)

20
0

2
4
6
Propagation length (mm)870Loss (dB)60

W=2.0μm
W=1.0μm
W=0.6μm

50
40
30

W
a
a

(b)

20
0

2
4
6
Propagation length (mm)8Fig. 3.9 Propagation loss of 0.2-μm-thick Si channel waveguide with (a) air and (b) SiO2
upper cladding materials for TM mode, at λ= 1.55 μm.

55Propagation loss (dB/mm)

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

2.0

1.0

0
0

20

40
60
80
rib height (nm)100

Fig. 3.10 Propagation loss of 0.3-μm-thick and 2.0-μm-wide Si rib waveguides with several
rib heights for TM mode, at λ= 1.55 μm.

8
φ = 30deg
φ = 60deg
φ = 90deg

Loss (dB)

6
4
2
0
-2
0

5
10
15
Bending radius (μm)

20Fig. 3.11 Bend loss of 0.2-μm-thick and 0.6-μm-wide Si-wire waveguide for TM mode, at λ=1.55 μm.

56 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique0
Divided power (dB)TM mode

-1.5
-3.0
-4.5
calculated
Port 1
Port 2-6.0
2.6

2.8 3.0 3.2 3.4
Coupler length (μm)

3.6Fig. 3.12 Excess loss of branching characteristic of the fabricated MMI coupler for TM mode,
at λ= 1.55 μm. The solid line is calculated by 3-D BPM.

A spot-size converter in the Si waveguide is investigated to improve the coupling
efficiency between fiber and waveguide. The coupling loss is induced by the mismatch in thefield distribution between fiber and waveguide. The width and height of Si channel
waveguide are set at 0.60 μm and 0.20 μm, respectively. The waveguide is covered with
~1.0-μm-thick SiO2 cladding layer by sputter deposition. The 0.2-mm-long waveguide fromthe end facet is changed its width and is connected to the normal waveguide by a
0.3-mm-long tapered region. First, the coupling efficiency between a waveguide and a fiber
through air gap of 10 μm is calculated by 3-D BPM. The coupling loss is calculated bynormalizing the fiber mode power in a fiber with the launched power in a waveguide. Figure
3.13 (a) shows the doubled coupling loss assuming the two connections. Next, the spot-size
converter is fabricated on a 0.20-μm-thick SOI waveguide with several widths of waveguideend. Figure 3.13 (b) shows the measured coupling loss through two fiber/waveguideconnections that is obtained from transmitted power except the propagation loss. The
calculated and measured coupling losses show similar behavior though they have different
peaks. For the channel waveguide, the coupling loss is the smallest at the width of 0.20 μm in57

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniquethe measurement while it is the smallest at the width of 0.06 μm in the calculation. This is dueto that the fabricated waveguide has large scattering loss at the sidewall which increases the
propagation loss more than the improvement of coupling efficiency at the narrower width.
The coupling loss is reduced about 10 dB for 0.20-μm-width of the end waveguide comparedwith 0.60-μm-width of the waveguide without any taper. On the other hand, for a rib
waveguide, such a down tapered spot-size converter is not effective as the field distribution at
the narrower width is confined in the slab region of the Si layer.

coupling loss (dB)

0

10

20
(a)

coupling loss (dB)

30
0

1.0
2.0
3.0
width of the end waveguide (nm)

20

30

40
0

(b)
1.0
2.0
3.0
width of the end waveguide (nm)Fig. 3.13 (a) Calculation and (b) measurement results of coupling loss between an opticalfiber to Si channel waveguide. The simulation grid sizes are Δx = 0.05 μm, Δy = 0.02 μm, andΔz = 0.02 μm.

58 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

3.4 Direct bonding between Si and Ce:YIG
A wafer bonding is key technique to realize integrated optical devices since III-V compound
semiconductor, crystalline Si, and magneto-optic garnet can not be epitaxially grown on eachother due to the large lattice mismatch. Although indirect bonding technologies such as“adhesive bonding” and “eutectic bonding” are easy to use, the glue layer in the order ofmicron between the wafers is too thick to obtain an efficient magneto-optic effect. A
conventional wafer bonding technique is classified in “hydrophobic” or “hydrophilic”
bonding where hydrides or hydroxyl groups contribute to the bonding interface, respectively.
Covalent bondings are formed by desorption of these chemisorbed molecules inhigh-temperature annealing at 800 – 1000 oC. These bonding procedures between two arbitralmaterials A and B are expressed as
A−H + H−B → A−B + H2

(3.1)

for hydrophobic and
A−OH− + −HO−B → A−O−B + H2O or A=O2=B + H2

(3.2)

for hydrophilic treatments. Then, a difference in thermal expansion between dissimilarmaterials results in high mechanical stress at the interface. It can make the wafers crack andcompletely debond. Therefore, a number of effort and research in wafer bonding is focused on
developing low-temperature procedures [10-14]. Typically, bonding strength increases
proportional to the temperature of thermal treatment. In order to achieve strong bonding with
low-temperature annealing procedures, the surface treatment of bonded wafers is very
important.

3.4.1 Surface activated bonding with oxygen plasma treatment
In this study, a surface activated bonding with oxygen plasma treatment [15,16] is utilized forbonding between Si and CeY2Fe5O12 (Ce:YIG) grown on a (GdCa)3(GaMgZr)5O12 (SGGG)
substrate by a RF sputtering epitaxy. Two wafers activated by oxygen plasma treatment arebonded together and annealed at low temperature in situ the vacuum chamber.
The oxygen plasma is considered to affect a wafer surface physically and chemically at
the same time. Physical effect is removal of contaminants on a surface by oxygen ions

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique59

accelerated by self-bias voltage of the RF plasma. It is well known that oxygen plasma
treatment is very efficient in removing hydrocarbon and water related species. Chemical
effect is a formation of oxidized or ionized thin layer by the ion “bombardment” that isindicated by observing a hydrophilic surface after oxygen plasma exposure. In Ref. [15],ultrathin oxide layer (< 5 nm) is observed at the bonding interface between Si and InP where
SiO2 is formed rather than InP-oxide. In the case of bonding between Si and Ce:YIG, we
speculate that Si is oxidized by oxygen plasma to be O−−Si, while oxide atom terminating the
crystal lattice of Ce:YIG is sputtered or ionized by oxygen plasma to be CeY2Fe5O11− orCeY2Fe5O11–O−. It is plausible that a direct bonding is achieved as
CeY2Fe5O11− + O−−Si≡Si → CeY2Fe5O12−Si≡Si(3.3)

CeY2Fe5O11–O− + O−−Si≡Si → CeY2Fe5O11−SiO2−Si

(3.4)

or

by sharing the oxygen atoms in the intermediate oxide layer which is amorphous of Ce:YIG
rich or SiO2 rich in each case. We will discuss about the influence of the ultrathin interlayer
on isolator design in Section 3.5.
There are two advantages to bond wafers in situ vacuum chamber without exposing themto ambient air after oxygen plasma treatment. One is enhancement of bonding strength by
preventing dusts or molecules in air trapping at the activated surfaces which result in voids or
failure of bonding [14]. In addition, the low ambient pressure enhances the bonding speed by
efficient removal of gas molecules such as O2 generating or remaining at the interface [17].
Whereas, Suga et al. have showed that strong bonding is obtained when two wafers arecontacted in air after oxygen plasma activation owing to water molecules absorbed on theactivated surfaces [16]. The author presumes that the oxygen activation and hydrophilic
bonding contribute simultaneously in that case even though it is uncertain why the bonding
strength is enhanced.

3.4.2 Experiment
We prepare an experimental setup for surface activated bonding with oxygen plasma
treatment followed by in situ annealing and pressing as shown in Fig. 3.14. Si and Ce:YIG

60 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniquewafers are cleaned elaborately with organic solutions and RCA cleaning for Si [18] as theprocedures shown in Table 3.3, where the deionized (DI) water has the electrical resistivity of> 18.2 MΩ·cm refined by ultrapure water system. The surface roughness (RMS) of the two
wafers is below 1 nm. When single particles or protrusions are much higher than this value,
they will create voids and result in nonuniform bonding region. After placing wafers on thesample stage, the chamber is vacuumed to ~1 × 10-5 Pa. The plasma is generated with a RF
system of 13.56 MHz between a 3×4 cm2 electrode and the chamber. The wafers are exposedto oxygen plasma with 100-W RF power for 30-s in the chamber pressure of 4.0 Pa, because
moderate plasma treatment gives smooth surfaces and higher surface energy together withefficient removal of contaminants on the surfaces [15]. After that, the activated surfaces areattached to each other immediately by using a manipulator in situ the vacuum at ~10-5 Pa. The
samples loaded to the press position together with the sample stage are pressed with theapplied pressure of ~5 MPa. Temperature is then increased for annealing at 150 – 400 oC for
30 min and kept it for 1 hour with the pressure. To mitigate the stress induced by thedifference in thermal expansions, the temperature is decreased gradually at a rate of –50
oC/hour.

Fig. 3.14 Experimental setup for surface activated bonding with oxygen plasma treatment.

61

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Table 3.3 Cleaning procedure before surface activated bonding.
Si (SOI)

Ce:YIG

Solution

o

C

min

Solution

o

C

min

Ethanol120

5Ethanol

120

5(Ultrasonic 100kHz)

R.T.

3

(Ultrasonic 100kHz)

R.T.

3

Ethanol120

5Ethanol120

5Acetone100

5Acetone100

5(Ultrasonic 100kHz)

R.T.

3

(Ultrasonic 100kHz)

R.T.

3

Acetone100

5Acetone100

5

HF:H2O (1:19)

R.T.

40s

Ethanol120

5

DI water

R.T.

30s

(Ultrasonic 100kHz)

R.T.

3

NH4OH:H2O2:H2O (1:1:5)

90~10010Ethanol120

5

DI water

R.T.

1

Acetone100

5

HCl:H2O2:H2O (1:1:5)

90~10010

DI water

R.T.

1

HF:H2O (1:19)

R.T.

30s

DI water

R.T.

10s

Figure 3.15 shows photo images of the sample of Ce:YIG bonded onto Si and SOI flat
wafers with the annealing temperature at 400 oC. The bonded region and surrounding Newton
ring are observed since a thin Ce:YIG layer and an SGGG substrate are transparent at visible
light. Table 3.4 shows the experimental results of the bonding at several annealing
temperatures. Direct bonding is obtained at annealing temperature higher than 200 oC. The
wafers bonded at 300 oC are debonded as time goes by. Cracks are observed in the Ce:YIG
wafer with the annealing at 350 oC and higher, while the bonding remains in the cracked
regions. The bonding strength and the thermal stress increase as the annealing temperature
independently to each other. We notice that debond occurs when the thermal stress becomes
more than the bonding strength, and cracks occurs when both exceed the stiffness limit of the62 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Ce:YIG wafer since Si is mechanically a stronger material. The thermal shear stress τmax at theedge of the bonded interface can be estimated by the following equation [19]τ max =

ΔαΔT

λk

,

(3.5)

(
)

)(

)

⎡1 − ν 12 1 − ν 22
3(d1 + d 2 ) 1 − ν 12 1 − ν 22 ⎤
+
+
λ≡⎢
⎥,
E 2 d 2 E1 d 13 1 − ν 22 + E 2 d 23 1 − ν 12 ⎦⎣ E1 d 1

(

k≡

(

(3.6)

)

2d 1 (1 + ν 1 ) 2d 2 (1 + ν 2 )
+
,
3E1
3E 2

(3.7)

where Δα is the difference in thermal expansion coefficients between the two bonded
materials, ΔT is the temperature change, d1 and d2 are the wafer thickness, E1 and E2 are theYoung’s moduli, and ν1 and ν2 are the Poisson ratios. The τmax is calculated to be 2.44
kg/cm2/K or 3.37 kg/cm2/K for the interface between Si (α= 2.6 × 10-6/K, d= 0.6 mm, E= 1.30
× 1013 dyn/cm2, ν= 0.28) and Ce:YIG (α= 8.0 × 10-6/K, d= 0.5 mm, E= 2.0 × 1012 dyn/cm2,

ν= 0.29) or between Si and GGG (α= 9.18 × 10-6/K, d= 0.5 mm, E= 2.74 × 1012 dyn/cm2, ν=
0.281), respectively. This can be reduced by using small chip of bonded wafer as well as
annealing at low-temperature.
Figure 3.16 shows a SEM image of the bonding interface between Ce:YIG and Si rib
waveguide bonded with annealing at 400 oC.

Si

Ce:YIGSOI

Ce:YIG

9.5
mm

(a)

9.5 mm

9.5mm(b)

9.5 mmFig. 3.15 Photo images of bonded sample between (a)Si and Ce:YIG, (b)SOI and Ce:YIG withthe annealing temperature at 400 oC.

63

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Table 3.4 Experimental results of the surface activated bonding with Si and Ce:YIG
using oxygen plasma of 100-W RF power for 30s, pressed with ~5 MPa.
Temperature (oC)

Bonding

Crack

150

×

No

200

○

No

250

○

No

300

○

No −> debonded as time goes by

350

○

Yes

400

○

Yes

SGGG
Ce:YIG
Si rib waveguideFig. 3.16 SEM image of the bonding interface between Ce:YIG and Si rib waveguide.

64 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

3.5 Characterization
3.5.1 Isolator operation
A magneto-optical isolator with Si waveguides is fabricated. The MZI of the low-loss design
shown in Table 3.2 is fabricated with Si rib waveguides on a SOI wafer with a 0.3-μm-thick
Si top layer and a 1.0-μm-thick SiO2 layer. Ce:YIG film is grown on a garnet substrate(SGGG) with the thickness of 0.5 μm, which is sufficient to offer a nonreciprocal phase shift
without influence of the non-magnetooptic garnet substrate. Figure 3.17 shows thenonreciprocal phase shift as a function of the Ce:YIG thickness calculated by solving
eigenvalue equation with four-layered structure as described in Section 2.2.1.
Figure 3.18 shows the photo image of the fabricated sample bonded with Ce:YIG by thesurface activated bonding with oxygen plasma treatment and annealing at 250 oC for one hourwith a pressure of 5 MPa. Broad contact areas are formed on Si surface 50-μm away from therib waveguide to provide a sufficient bonding area. The total length of the waveguide is 4.0mm, which includes 4.0-μm-wide taper waveguides at input and output ends to increase thecoupling efficiency into connecting fibers. The length of the bonded garnet chip is 2.0 mm,
where the nonreciprocal phase shifter is composed by parallel waveguides with the
propagation length of 0.40 mm. The distance of the interferometer arms is to be 0.50 mm,

Nonreciprocal phase shift (mm -1 )sufficient to apply an external magnetic field in anti-parallel directions.

8.0
6.0
tSi= 0.2μm

4.0
2.0
0
0

tSi= 0.3μm

0.2
0.4
0.6
0.8
thickness of Ce:YIG (μm)

1Fig. 3.17 Calculated nonreciprocal phase shift in a SGGG/Ce:YIG/Si/SiO2 -layered structure
as a function of Ce:YIG thickness by solving eigenvalue equation.

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Ce:YIG

2.0 mm65

SOI

4.0 mmFig. 3.18 Photo image of the fabricated sample.

The optical setup for the measurement of isolator operation is shown in Fig. 3.19. An
amplified spontaneous-emission (ASE) diode having an optical gain in the wavelength rangeof 1.53 – 1.565 μm, is used as a light source. This light is polarized to TM mode and islaunched into the sample under test through a polarization maintaining fiber (PMF). An
optical switch determines the optical path along clockwise (CW) or counter-clockwise (CCW)
direction through the sample/fiber test setup. The output light transmitted through the sample
is coupled to another PMF to measure the transmittance with a spectrum analyzer. An external
magnetic field is applied to the interferometer arms in anti-parallel direction by using a pair ofsmall permanent magnets with three reversed poles. The external magnetic field required tosaturate the magnetization of Ce:YIG in-plane is 20 Oe.
The experimental characterizations of the isolator are shown in Fig. 3.20 and Fig. 3.21
that correspond to different isolators of fifth and fourth waveguides from the top on thesample shown in Fig. 3.18. The dashed lines show the wavelength dependence of the

66 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniquetransmission spectra for light propagating in CW and CCW directions without applying
external magnetic fields. In this case, the symmetry of the expected two optical paths in themeasurement setup is essentially confirmed. The small power difference in the transmittance
between CW and CCW directions is ascribed to a difference in the performance of MMI
couplers, since the left-hand and right-hand side MMI couples have different upper cladding
layer, as shown in Fig. 3.18. Next, a permanent magnet is placed on the top surface of thesample to apply external magnetic fields in anti-parallel directions to the two MZI arms. In
this case, it is observed that the transmission spectra differ significantly depending on the
propagation direction as shown by the solid lines in Fig. 3.20 (a) and Fig. 3.21 (a). When we
exchange the permanent magnet for another one with reversed poles, i.e., S-N-S for N-S-N,
the directions of phase shift are also reversed as shown in Fig. 3.20 (b) and Fig. 3.21 (b). Thatis the change in transmission spectra by reversing the magnetic field direction corresponds tothat given by reversing the propagation direction. It can be concluded that thedirection-dependent transmittance is due to the nonreciprocal phase shift. The difference inthe transmittance between CW and CCW directions corresponds to the isolation ratio of themagneto-optical isolator. The maximum isolation ratios of 21 dB at λ= 1559 nm and 17 dB at
λ= 1546 nm are obtained in the measured transmittance of Fig. 3.20 and Fig. 3.21,
respectively.

Permanent magnet

S

CW

Sample
CCW

N
S
ASE

PMF

PMF

OpticalPath Switch

Polarizer

Spectrum
Analyzer

TM modeFig. 3.19 Setup for the measurement of isolator operation.

67

transmittance (dB)

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

-40

CW

-50
-60

CCW
No-magnetization

-70
1530

1540
1550
1560
wavelength (nm)1570

transmittance (dB)

(a)

-40
-50
-60
-70
1530

1540
1550
1560
wavelength (nm)

1570

(b)
Fig. 3.20 Measured transmission spectra for different propagation directions. Light transmits
the sample from left to right at clockwise (CW) direction and from right to left atcounter-clockwise (CCW) direction. Sold lines show the transmission spectra measure withexternal magnetic fields applied to the interferometer arms in anti-parallel direction. Dashedlines show the transmission spectra measured without magnetic fields. The poles of thepermanent magnet are (a) S-N-S and (b) N-S-N.

68 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniquetransmittance (dB)

-40
CW

-50

No-magnetization

-60
-70
1530

CCW

1540
1550
1560
wavelength (nm)

1570

(a)

transmittance (dB)

-40
-50
-60
-70
1530

1540
1550
1560
wavelength (nm)

1570

(b)
Fig. 3.21 Measured transmission spectra for different propagation directions. The poles of thepermanent magnet are (a) N-S-N and (b) S-N-S.

69

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniqueFigure 3.22 shows the calculated transmission loss of the isolator design assuming that the
MMI couplers work ideally. The measured transmittance in Fig. 3.21 agrees well with thesolid lines in Fig. 3.22, while the lack of a deep isolation feature at ~1550 nm is limited by theexperimental noise floor at ~70 dB. Note that the bandwidth of the high isolation ratio
observed in Fig. 3.20 is narrower than the calculation and is shifted by ~10 nm. These
differences can be ascribed qualitatively to small dimensional errors in assembling the bonded
garnet chip. These errors cause deviation of the reciprocal phase difference from the designed
value of +π/2, since they make the interferometer arm asymmetry. The modified reciprocal
phase difference is then give by

θ R = (β 1 − β 2 )L asym + β 2 ΔL

(3.8)

where β1 and β2 are the longitudinal propagation constants with upper cladding layer of
Ce:YIG and air, respectively, ΔL is the designed optical path difference given by EB
lithography, and Lasym is the assumed dimensional error. As an example, the dashed lines inFig. 3.22 show the calculated transmission loss when there is a dimensional error of 111 μm
propagation distance where the two interferometer arms have different upper cladding regions,
i.e., Ce:YIG and air. In this case, the calculated transmission loss agrees with the measured

Transmission loss (dB)results in Fig. 3.20.

0
-10
-20

ForwardBackward

-30
-40
-50
1530

Lasym=0 μm
Lasym=111μm

1540
1550
1560
wavelength (nm)1570

Fig. 3.22 Calculated transmission of the designed isolator. Solid lines show the transmission
spectra without any dimensional error (Lasym= 0 μm), incurred during bonding. Dashed lines
show the transmission spectra with an assumed dimensional error of Lasym= 111 μm.

70 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique3.5.2 Insertion loss
The insertion loss of the fabricated isolator is also examined. The measured transmission loss
is dominated by a coupling loss of 37 dB between waveguide and fiber at the two
waveguide-end facets. The value for coupling loss is obtained by fabricating a sample
waveguide adjacent to the isolator, measuring the total insertion loss of this waveguide (41dB), and subtracting off the waveguide propagation loss. The insertion loss due to the isolator
itself is 8 dB at the transmission peak of 45 dB in Fig. 3.20. Of 8 dB loss, the excess loss of
the interferometer is ~4 dB, total propagation loss of the interferometer waveguide is ~2.5 dB
at a wavelength of 1550 nm based upon the 0.63 dB/mm transmission loss measured in Fig.
3.10 for 10-nm-height rib waveguide, and additional measured losses include ~0.2 dB after
the direct bonding process due to Ce:YIG absorption and ~1.3 dB scattering losses at thebonding interfaces calculated in Fig. 3.4 for 0.3-μm-thick waveguide.

3.5.3 Temperature dependence
Changing the temperature 20 – 60 oC with a temperature controller beneath the sample, thetransmission spectrum of the isolator operation is measured as shown in Fig. 3.23, where thepermanent magnet is fixed on the sample and the propagation direction is changed from (a)CW to (b) CCW direction in the measurement setup. The spectrum peak shifts about 3 nm as
the temperature changes by 5 oC while the distance of corresponding peaks between forward
and backward propagation directions is unchanged. This means that the temperaturedependence of the nonreciprocal phase shift is small and the spectrum shifts are incurred by
the temperature dependence of the refractive index of the composed materials. The phasedifference between two symmetric arms ought to be unchanged since the refractive indices are
simultaneously changed in both arms. The temperature dependences of refractive index Δn/ΔT
in Si, SiO2, and Ce:YIG are 1.8 × 10-4/ oC, 1.0 × 10-5/ oC, and 1.7 × 10-5/ oC (estimated fromthat of GGG [22]), respectively. On the other hand, there is no temperature dependence ofrefractive index in air. Thus, the measured spectrum shifts are mainly induced by theasymmetry in the MZI due to the assembly error as mentioned above. The difference intemperature dependence of the effective refractive index between the Ce:YIG and air cladding

71

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniqueregions along the estimated path length of 111 μm may give the spectrum shifts. The
difference in the effective refractive index neff is estimated at 0.001 from the spectrum shiftsof ~3 nm as the temperature changes by 5 oC, i.e., Δneff/ΔT ~2.0 × 10-4/ oC. However, thisorder is much larger than that of Δn/ΔT in Ce:YIG. Consequently, the Δneff/ΔT is caused by adifference in thermal diffusion at the waveguide surface between the Ce:YIG and air cladding
regions since the temperature is provided from the bottom of substrate in this measurement.
Anyway, the temperature dependence of the isolator operation can be restrained by antransmittance (dB)accurate fabrication ensuring the design.

-40
-50
-60
-70
1530

transmittance (dB)

20oC
25ooC
30oC
35 C
40ooC
45 C
50ooC
55oC
60 C

(a)

1540
1550
1560
wavelength (nm)

1570

-40

20oC
25ooC
30oC
35 C
40ooC
45 C
50ooC
55oC
60 C

-50
-60
-70
1530

(b)

1540
1550
1560
wavelength (nm)1570

Fig. 3.23 Temperature dependence of the fabricated isolator. Light transmits the sample at(a)CW and (b)CCW directions in the measurement setup.

72 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

3.6 Discussion
A magneto-optical isolator with Si waveguides has been successfully demonstrated. And weneed to discuss about the fabrication processes of Si waveguides and direct bonding techniqueprospecting for an ultracompact optical isolator.
The propagation loss and the bend loss can be reduced even for a Si-wire waveguide byusing e-beam resist mask and etching with inductively coupled plasma (ICP) or electron
cyclotron resonance (ECR). Yamada et al. realized a Si-wire waveguide with a propagation
loss of 2.4 dB/cm, a 90-degree bend loss of 0.15 dB for 2-μm-radius, and also the couplingloss from/into fiber of 0.5 dB through a spot-size converter of SiON second-core [1]. A MZIwaveguides of the 0.36-mm-length ultracompact design shown in Table 3.2 can be realizedwith the insertion loss of about 2.9 dB including the propagation loss of ~0.9 dB, the twobend losses of ~0.3 dB, the scattering losses of ~1.2 dB at the two bonding boundaries, andthe absorption loss of Ce:YIG of ~0.5 dB.
The direct bonding between Si and Ce:YIG is achieved by the surface activated bonding
with oxygen plasma treatment at 200 – 250 oC which is compatible to a CMOS process.
However, we have not examined the bonding strength yet. The annealing temperature should
be determined after thermal durability testing in the temperature range of practical use.
The oxygen plasma treatment may generate ultrathin oxidized interlayer. The amorphousinterlayer of Ce:YIG-rich without any magneto-optic effect or SiO2-rich may be formed as eq.
(3.3) and (3.4), respectively. Such interlayer makes the nonreciprocal phase shift smaller thanthe expected value, which results in longer propagation length to provide the designed
nonreciprocal phase difference. Figure 3.24 shows the propagation length as a function of theinterlayer thickness calculated by solving eigenvalue equation with four-layered structure. If
there is an interlayer of 5-nm-thick SiO2, which has been observed in the Si-to-Si bonding
with oxygen plasma bonding in Ref. [15], the required propagation length changes by ~20 %.
Therefore, we need to investigate the thickness and composition of the interlayer relating to
the bonding conditions by using a transmission electron microscopy (TEM) and a X-ray
photoelectron spectroscopy (XPS). Also, the amount of the nonreciprocal phase shift in the
Ce:YIG/Si/SiO2 waveguide should be examined by a measurement setup described in Ref

73

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Propagation length for π/2 (mm)[20] or [21].

0.6

ninter =1.44

0.5

n inter =2.20
Θ F=0 deg/cm

0.4
0

2
4
6
8
thickness of interlayer (nm)10Fig. 3.24 Propagation length to obtain ±π/2 nonreciprocal phase difference, where top layer is
Ce:YIG (n= 2.20) with ΘF= −4500 deg/cm, guiding layer is 0.3-μm-thick Si (n= 3.48), lower
cladding layer is SiO2 (n= 1.44), and the interlayer is located between top and guiding layers.

In order to obtain a high extinction in a MZI, it is important to balance the optical powerin two arms. As described in Chapter 2, the output intensity of a MZI is expressed as (2.53)

Eout

2

=

{

}

1
2
a1 + a2 + 2 a1a2 cos(θ 2 − θ1 ) Ein
4

where Ein and Eout are the amplitudes of the electric field at the input and output ports and θ1,

θ2, a1, and a2 are the phase differences and attenuations of power in each arm. Figure 3.25
shows the calculated output powers as a function of balance in two arms a2/a1 where thephase differences (θ2−θ1) are in-phase and antiphase for forward and backward operations,
respectively. The balance must be more than 0.9 to achieve an isolation ratio > 30 dB. The sub
Mach-Zehnder structures in the MZI arms have been proposed for achieving high extinction
ratio (~48 dB) [23]. The sub MZI is used as an attenuator to compensate the unbalance ofpowers in two arms. In the case of our isolator with Si waveguide, ultraviolet light irradiation
can adjust the phase difference in the sub MZIs by changing the refractive indices of Si and
SiO2 after fabrication of the isolator.

74 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding techniqueOutput power (dB)40
30

ForwardBackward
Isolation

20
10
0
0

0.2
0.4
0.6
0.8
Power balance (a2/a1)

1

Fig. 3.25 Output power of a MZI as a function of balance of the intensities in two arms.

In consideration of mass productivity, there is difficulty in integrating refractorymagneto-optic garnet crystals. It is impossible to cleave the Si gently with the garnet crystal.
Dicing is necessary to cut the Si substrate with the garnet crystal in order to separate one
device from the massively produced wafer. To separate the devices by means of cleaving,
crystal ion slicing technique [24] is useful. Fig. 3.26 shows a schematic drawing of thefabrication process of the magneto-optical isolator with photonic integrated circuits on a Si
substrate by using a crystal ion slicing technique. As shown in Fig. 3.1, laser diodes, opticalmodulators, their drive circuits, and optical waveguides for isolators without magnetic garnet
crystals are fabricated all over one wafer with Si-LSI process. Grooves are formed on thesurface of the garnet crystals coincident with a period of the device. Proper ions are implantedon the garnet crystals with a depth smaller than that of the grooves from the top surface. Then,the garnets are bonded onto the Si substrate by the direct bonding technique. By selective
etching or rapid thermal annealing, the garnet substrate is removed and thin garnet layers areleft on the Si substrate due to crystal ion slicing. Therefore, each device can be separated bycleaving the Si substrate. By preparing such grooved magneto-optic garnet crystals, a numberChapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

75

of photonic circuits integrated with a magneto-optical isolator can be fabricated in a single
direct bonding process.

Fig. 3.26 Integration process of magneto-optical isolator with Si photonic circuits using acrystal ion slicing technique in consideration of mass productivity.

76 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

3.7 Summary
In this chapter, a magneto-optical isolator with Si waveguide is demonstrated. First, Si
waveguide is fabricated on a SOI wafer and characterized. Second, a surface activated directbonding with oxygen plasma treatment is investigated. A direct bonding between Si and
Ce:YIG is successfully achieved with oxygen plasma treatment of 100-W RF power for 30-s
followed by annealing at 200 – 250 oC with an applied pressure of ~5 MPa. Then, amagneto-optical isolator composed of a 0.3-μm-thick Si rib waveguide for low-loss design isfabricated and characterized in terms of the nonreciprocal operation by reversing the
propagation direction. The maximum isolation of 21 dB is obtained at a wavelength of 1559
nm. The insertion loss of 8 dB and the temperature dependence of the isolator are also
examined.

Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

77

References[1] K. Yamada, T. Tsuchizawa, T. Watanabe, J. Takahashi, H. Fukuda, M. Takahashi, T. Shoji, S.
Uchiyama, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on siliconwire waveguiding system,” IEICE Trans. Electron., vol.E87-C, pp.351-357 (2004).
[2] A. Liu, L. Liao, D. Rubio, H. Nguyen, O. Cohen, R. Nicholaescu, and M. Paniccia, “High-speed
optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express, vol.15,
pp.660-668 (2007).
[3] A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped
hybrid AlGaInAs-silicon evanescent laser,” Opt. Express, vol.14, pp.9203-9210 (2006).
[4] Product information of Luxtera, Inc., (http://www.luxtera.com/)[5] H. Yokoi, T. Mizumoto, and Y. Shoji, “Optical nonreciprocal devices with a silicon guiding layer
fabricated by wafer bonding,” Appl. Opt., vol.42, pp.6605-6612 (2003).
[6] R. L. Espinola, T. Izuhara, M.-C. Tsai, and R. M. Osgood, Jr., “Magneto-optical nonreciprocal
phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett., vol.29, pp.941-943 (2004).
[7] BeamPROP software from RSoft Design Group, (http://www.rsoftdesign.com/)[8] FIMMPROP software from Opto Design Inc., (http://www.opto-design.com/)[9] M. Bruel, B. Aspar, B. Charlet, C. Maleville, T. Poumeyrol, A. Soubie, A. J. Auberton-Herve, J.
M. Lamure, T. Barge, F. Metral, and S. Trucchi, “®Smart cut : a promising new SOI material
technology,” Proc. of 1995 IEEE International SOI Conference, pp.178-179 (1995).
[10] J. Steinkirchner, T. Martini, M. Reiche, G. Kästner, and U. Gösele, “Silicon wafer bonding via
designed monolayers,” Adv. Mater., vol.7, pp.662-665 (1995).
[11] U. Gösele, H. Stenzel, T. Martini, J. Steinkirchner, D. Conrad, and K. Scheerschmidt,“Self-propagating room-temperature silicon wafer bonding in ultrahigh vacuum,” Appl. Phys.
Lett., vol.67, pp.3614-3616 (1995).
[12] H. Takagi, K. Kikuchi, R. Maeda, T. R. Chung, and T. Suga, “Surface activated bonding of siliconwafers at room temperature,” Appl. Phys. Lett., vol.68, pp.2222-2224 (1996).
[13] A. Berthold, B. Jakoby, and M. J. Vellekoop, “Wafer-to-wafer fusion bonding of oxidized silicon
to silicon at low temperatures,” Sens. Actuators, vol.A68, pp.410-413 (1998).
[14] Q.-Y. Tong, W. J. Kim, T.-H. Lee, and U. Gösele, “Low vacuum wafer bonding,” Electrochem.

78 Chapter 3: Magneto-optical isolator with silicon waveguides
fabricated by direct bonding technique

Solid State Lett., vol.1, pp.52-53 (1998).
[15] D. Pasquariello and K. Hjort, “Plasma-assisted InP-to-Si low temperature wafer bonding,” IEEE J.
Selected Topics in Quantum Electron., vol.8, pp.118-131 (2002).
[16] T. Suga, T. H. Kim, and M. M. R. Howlader, “Combined process for wafer direct bonding bymeans of the surface activation method,” Proc. of Electronic Components and Technology
Conference, pp.484-490 (2004).
[17] U. Gösele, S. Hopfe, S. Li, S. Mack, T. Martini, M. Reiche, E. Schmidt, H. Stenzel, and Q.-Y.
Tong, “What determines the lateral bonding speed in silicon wafer bonding?,” Appl. Phys. Lett.,vol.67, pp.863-865 (1995).
[18] R. Hull, “Properties of crystalline silicon,” (University of Verginia, Verginia, 1999), Chap.5,
pp.219-225.
[19] T. Izuhara, M. Levy, and R. M. Osgood, Jr., “Direct bonding and transfer of 10-μm-thickmagnetic garnet films onto semiconductor surfaces,” Appl. Phys. Lett., vol.76, pp.1261-1263(2000).
[20] Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation inmagnetooptic YIG rib waveguides,” J. Lightwave Technol., vol.LT-4, pp.711-714 (1986).
[21] J. Fujita, M. Levy, R. U. Ahmad, and R. M. Osgood, Jr., “Observation of optical isolation basedon nonreciprocal phase shift in a Mach-Zehnder interferometer,” Appl. Phys. Lett., vol.75,
pp.998-1000 (1999).
[22] D. L. Wood and K. Nassau, “Optical properties of gadolinium gallium garnet,” Appl. Opt., vol.29,
pp.3704-3707 (1990).
[23] A. Chiba, T. Kawanishi, T. Sakamoto, K. Higuma, and M. izutsu, “Low-crosstalk operation of
LiNbO3 optical switch having sub Mach-Zehnder structures,” Proc. of 2006 IEICE Society
Conference, p.178 (2006).
[24] M. Levy, R. M. Osgood, Jr., A. Kumar, and H. Bakhru, “Epitaxial liftoff of thin oxide layers:
Yttrium iron garnets onto GaAs,” Appl. Phys. Lett., vol.71, pp.2617-2619 (1997).

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

79

Chapter 4:
Wideband Operation of a Magneto-Optical
Isolator Using Phase Adjustment in
Mach-Zehnder Interferometer

4.1 Introduction
Optical nonreciprocal devices are important components in high speed optical communication
systems. At present, only bulk isolators are commercially available, which are not suitable for
integration. In addition, the operation bandwidth where the isolation >30 dB is obtained istypically ±30 nm around its center wavelength due to a large wavelength dependence of
Faraday rotation of magneto-optic materials. Ando et al. demonstrated a waveguide isolator
using TE-TM mode conversion with the isolation ratio of 12.5 dB [1]. Shintaku demonstrated
a waveguide isolator using nonreciprocal radiation mode conversion with the isolation of 27
dB [2]. However, they suffered small fabrication tolerance as well as the narrow operation
bandwidth.
A waveguide isolator employing nonreciprocal phase shift has been intensively investigatedin Mach-Zehnder interferometer (MZI) configuration [3-7]. It is less sensitive to a fabrication
error because there is no need of phase matching between orthogonally polarized modes.
Fujita et al. demonstrated it with the isolation ratio of around 19 dB at a wavelength range of
1.49 – 1.57 μm which is wider than the operation bandwidth of bulk isolators [7]. However,
the wavelength dependence of this isolator has not been fully investigated. In this chapter, theauthor proposes and demonstrates a wideband operation of the isolator using phaseadjustment in MZI. First, he explains the proposed principle of wideband operation. Next, thenumerical results of the wideband design are presented for several types of the isolator, and80 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometerthe influence on the fabrication tolerance is discussed in the wideband design. An
ultra-wideband design operating at a wavelength range in 1.31 – 1.55 μm is investigated. A
magnet-optical isolator is fabricated with the wideband design on a magneto-optic garnet
waveguide, and the successful wideband operation is demonstrated experimentally.

4.2 Principle of wideband operation
The magneto-optical isolator is based on a MZI composed of nonreciprocal phase shifter(NPS) and reciprocal phase shifter (RPS) as shown in Fig 4.1. External magnetic fields areapplied to the arms of NPS in anti-parallel directions to obtain a nonreciprocal phasedifference (θN) of ±π/2 in a push-pull manner. A reciprocal phase difference (θR) is provided
by an optical path difference between two arms. In the conventional design, θR is set to be+π/2 to cancel the θN or add to the θN, which results in constructive or destructive interferencein forward or backward direction, respectively. The phase differences are set at a center
wavelength (λ0) of the designed transmission bandwidth, e.g., λ= 1.55 μm. Figure 4.2 shows
the schematic wavelength dependence of θN, θR, and the total phase difference in two
directions. Typically, θN and θR decrease monotonically as the wavelength becomes longer.
The wavelength dependence of θN is dominated by the field distribution and the Faraday
rotation of the magneto-optic material. The wavelength dependence of θR is dominated by therefractive indices of the waveguide structure and the wavenumber k. Deviations of thenonreciprocal and reciprocal phase differences from respective designed values are cancelledin the forward direction, while added in the backward direction as shown in Fig. 4.2 (a) and(b). This behavior determines the wavelength dependence of the isolator operation, and large
backward loss is obtained only in a narrow wavelength range.
To obtain a large backward loss in a wide wavelength range, we change the phasedifferences as shown in the lower part of Fig. 4.1. The θR is set to be +3π/2, instead of +π/2,
and the sign of the θN is reversed, which is done just by reversing the direction of appliedmagnetic field, to satisfy the isolator operation. This makes the backward loss less sensitive towavelength change as shown in Fig. 4.2 (c) and (d). In addition, the wavelength dependenceof θR is adjusted by tailoring the waveguide parameters such as waveguide width and lengthChapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer81of the reciprocal phase shifter as shown in Fig 4.3. Then the θR is expressed as β2L2−β1L1 withthe longitudinal propagation constants β1, β2 and their modified lengths L1, L2. When thedeviation of θR cancels that of θN in a wide wavelength range, the wideband operation ofisolator is realized. On the other hand, wavelength dependence of the forward loss isdeteriorated compared with the conventional design as one can see in Fig. 4.2 (d). However,
the increase in the forward loss is acceptably small for a dramatic improvement of the
backward loss, which is shown by the calculation results mentioned in the next section.

input

NPS

RPS

C

C

output

NPS
θN

θR

−π/2

+π/2

+π/2

+π/2

+π/2

+3π/2

−π/2

+3π/2

Conventional design
ForwardBackward

Wideband design
ForwardBackward

Fig. 4.1 Schematic diagram of MZI configuration of magneto-optical isolator employing
nonreciprocal phase shift.

82 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

θ

θ

θR
θN

π/2
0
−π/2

λ0

Backward=θN+θRπλ0λλ0 Forward=−θN+θR

−θN

(a)

(b)

θ

θ
2π

θR

3π/2

Forward=θN+θR

π0−π/2

Backward=−θN+θR

θN

π/2
λ0

λ

0

λ0

−θN

(c)

λ

(d)

Fig. 4.2 Schematic illustration of wavelength dependence of nonreciprocal and reciprocal
phase differences and the total phase differences in the MZI isolator. (a), (b) correspond to theconventional design and (c), (d) correspond to the wideband design.

arm 2

β2

Reciprocal
phase shifter

L2
input

outputL1

β1
Nonreciprocal
phase shifterarm 1

Fig. 4.3 Tailoring waveguide width and length to adjust a wavelength dependence of thereciprocal phase difference.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer83

4.3 Calculation results
4.3.1 Wideband design of three types of isolator
Figure 4.4 shows three types of magneto-optical isolator employing nonreciprocal phase shift
we have investigated. These isolators are composed of a magneto-optic garnet rib waveguide(type-1), a GaInAsP/InP rib waveguide (type-2), and a Si-wire waveguide (type-3),
respectively. The latter two isolators have a magneto-optic garnet upper cladding layer that isbonded on the waveguide by use of a direct bonding technique [8-10]. The type-2 isolator is
attractive for monolithic integration with a laser diode of compound semiconductor. The
type-3 isolator is realized in ultracompact size as described in Chapter 3.
In the following design, a CeY2Fe5O12 (Ce:YIG) grown on a (111)-oriented (Ca, Mg, Zr)
doped GGG substrate (SGGG) is used as a magneto-optic garnet. We assume the 3 dB
couplers work ideally to clarify the validity of the idea. The cross sectional image of the
waveguide structures in the nonreciprocal phase shifter is shown in Fig. 4.5, where the lattertwo structures have side-cladding layer of air so that they are realized by a direct bonding. On
the other hand, in the reciprocal phase shifter, the upper and side cladding layers are air forthe type-2 structure and SiO2 for the type-3 structure. The refractive indices and the Faraday
rotation coefficient of the materials are expressed as shown in Table 4.1 approximating the
wavelength dependence with a quadratic polynomial. The approximations are based on thelisted references, except Si and SiO2 obtained from ellipsometry measurement for a SOI wafer.
The waveguide width, thickness, and rib height are set as shown in Table 4.2 so that the TM
propagation is single-mode. The propagation constant is calculated by mode solving offull-vector FEM [16].
First, the θN is designed with the propagation length of nonreciprocal phase shifter so as tobe ±π/2 at λ= 1.55 μm. The nonreciprocal phase shift is calculated by perturbation theory as
described in Chapter 2. The wavelength dependence of θN is determined by the nonreciprocal
phase shift for the fixed propagation length L designed at λ= 1.55 μm.

84 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

(a)

(b)

(c)
Fig. 4.4 Three types of magneto-optical isolator employing nonreciprocal phase shift.

w

w

SiO2

Ce:YIG
airr
Ce:YIG
y

z

x

h

w
Ce:YIGr

GaInAsP

h

air

Si

SGGG

InP

SiO2

(a)

(b)

(c)

air

Fig. 4.5 Waveguide structures of the nonreciprocal phase shifter.

hChapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer85

Table 4.1 Refractive indices approximated as a function of the wavelength λ (μm).
Material

Refractive index n(λ)

Ref.

Ce:YIG

2.2122709−0.0079167*λ[11-13]

SGGG

1.9661938−0.0270747*λ+0.00656483*λ2[13,14]GaInAsP (λg= 1.42 μm)

5.81338353−2.72352246*λ+0.772876982*λ2

[15]

InP

3.66193927−0.516531590*λ+0.128646194*λ2

[15]

Si

3.8152773−0.349117169*λ+0.085683376*λ2

-

SiO2

1.44716−0.00787891*λ+0.00210296*λ2-

Faraday rotation of Ce:YIG−20000+10000*λ (deg/cm)[11-13]

Next, the width of one arm in the reciprocal phase shifter is modified. In the case of
type-1 isolator, the modified width is set at w2= 2.4 μm against the waveguide width w1= 2.0
μm. Then the L1 and L2 are adjusted so that the θR is ~3π/2 at λ= 1.55 μm and the wavelength
dependence of θR is similar to that of θN. The section lengths of the reciprocal phase shifterare designed at L1= 10.0 μm and L2= 10.575 μm, and the wavelength dependences of θN andθR for type-1 isolator are calculated as shown in Fig. 4.6 (a). The total phase differences of the
MZI in both propagation directions are calculated as shown in Fig. 4.6 (b). One can see thatthe total phase difference of the backward direction in the wideband design is very flat as the
wavelength since the wavelength dependences of θN and θR are cancelled each other. Fig. 4.7
shows the forward and backward losses of the type-1 isolator calculated from the phasedifferences. The backward loss exhibits tremendous improvement in the wideband design.
The wavelength range with the isolation ratio of >30 dB is over 200 nm at λ= 1.45 – 1.65 μm
in the wideband design while that is 30 nm at λ= 1.535 – 1.565 μm in the conventional design.
On the other hand, the forward loss of the wideband design gets worst compared with theconventional design as predicted from Fig. 4.2 (d). However, the deterioration is <0.5 dB in
the calculated wavelength range, which is acceptably small against the dramatic improvementof the backward loss.
In the same way, wideband designs are investigated in the type-2 and type-3 isolators. In
the case of type-2 isolator, the modified widths are w2= 1.6 μm against w1= 1.5 μm and the86 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

section lengths are designed at L1= 6.0 μm and L2= 6.279 μm. The phase differences in the
MZI are calculated as shown in Fig. 4.8. The forward and backward losses are obtained fromthem as shown in Fig. 4.9. The wavelength range with the isolation ratio of >30 dB is over
200 nm at λ= 1.45 – 1.65 μm in the wideband design while that is 20 nm at λ= 1.54 – 1.56
μm in the conventional design. The deterioration of the forward loss is <1.0 dB in thecalculated wavelength range.
In the case of type-3 isolator, the modified widths are w2= 0.7 μm against w1= 0.6 μm andthe section lengths are designed at L1= 40.0 μm and L2= 39.68 μm. The phase differences in
the MZI are calculated as shown in Fig. 4.10. The forward and backward losses are obtained
from them as shown in Fig. 4.11. The wavelength range with the isolation ratio of >30 dB is~110 nm at λ= 1.485 – 1.595 μm in the wideband design while that is 20 nm at λ= 1.54 – 1.56
μm in the conventional design. The deterioration of the forward loss is <1.5 dB in thecalculated wavelength range. The type-3 isolator shows larger wavelength dependence of thereciprocal phase difference even in the wideband design. This is because Si has larger
wavelength dependence than any other materials. In addition, the high-index-contrast
waveguide is sensitive to the dimensional modification.
These designs are examples of the wideband design with a combination of modified
waveguide width. The design concept is applicable to the isolator with any other material,
structure, and dimension.

Table 4.2 Waveguide dimension of the wideband designs. (unit: μm)
Type-1

Type-2Type-3Height (h)

0.48

0.36

0.22

Rib height (r)

0.08

0.16

0.22

Width (w1)

2.0

1.5

0.6

Modified width (w2)

2.4

1.6

0.7

Conventional design (LRPS)

0.196

0.121

0.212

Wideband design (L1 / L2)

10.0 / 10.575

6.0 / 6.279

40.0 / 39.68

87

110

290

100

280

90

270

80
70
1.45

NPS
RPS (conventional)
RPS (wideband)

1.5
1.55
1.6
wavelength (μm)

260

Phase difference (deg)Phase difference (deg)Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

250
1.65

(a)

Phase difference (deg)

240
180
120
60

Conv. - Forward
Wide. - Forward (-360deg)
Conv. - Backward
Wide. - Backward

0
-60
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.6 (a) Phase differences in the nonreciprocal and reciprocal phase shifters, and (b) total
phase differences of the MZI in both propagation directions for type-1 isolator

88 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

Forward loss (dB)

0
0.2
0.4
conventional
wideband

0.6
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(a)

Backward loss (dB)0conventional
wideband

10
20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.7 Wavelength dependence of the (a) forward loss and (b) backward loss in conventional
and wideband designs for type-1 isolator.

89

120

300

110

290

100

280

90

270

80
70
60
1.45

260
NPS
RPS (conventional)
RPS (wideband)

1.5
1.55
1.6
wavelength (μm)

250

Phase difference (deg)Phase difference (deg)Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

240
1.65

(a)

Phase difference (deg)

240
180
120
60

Conv. - Forward
Wide. - Forward (-360deg)
Conv. - Backward
Wide. - Backward

0
-60
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.8 (a) Phase differences in the nonreciprocal and reciprocal phase shifters, and (b) total
phase differences of the MZI in both propagation directions for type-2 isolator

90 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

Forward loss (dB)00.5
conventional
wideband
1
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(a)

Backward loss (dB)0conventional
wideband

10
20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.9 Wavelength dependence of the (a) forward loss and (b) backward loss in conventional
and wideband designs for type-2 isolator.

91

120

300

110

290

100

280

90

270

80
70
60
1.45

260

NPS
RPS (conventional)
RPS (wideband)

1.5
1.55
1.6
wavelength (μm)

250

Phase difference (deg)Phase difference (deg)Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

240
1.65

(a)

Phase difference (deg)

240
180
120
60

Conv. - Forward
Wide. - Forward (-360deg)
Conv. - Backward
Wide. - Backward

0
-60
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.10 (a) Phase differences in the nonreciprocal and reciprocal phase shifters, and (b) total
phase differences of the MZI in both propagation directions for type-3 isolator

92 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

Forward loss (dB)

0

0.5

1
conventional
wideband
1.5
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(a)

Backward loss (dB)010conventional
wideband

20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.11 Wavelength dependence of the (a) forward loss and (b) backward loss inconventional and wideband designs for type-3 isolator.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer93

4.3.2 Fabrication tolerance
We examine the dependence of fabrication errors in the wideband design comparing with thecase of the conventional design. We assume three fabrication errors in waveguide width, ribheight, and optical path length for the type-1 isolator.
The waveguide width may have some errors caused in the fabrication process. Fig. 4.12
shows the wavelength dependence with errors in the waveguide widths w1 and w2, where
uniform errors are assumed along the whole waveguides. The θN is re-calculated for every w1.
A combination of narrow widths makes the θR large as the difference in propagation constants

β1 and β2 increase. Since the change of θR is larger than that of θN, the total phase differencein the backward direction slightly increases from the designed one for a combination of
narrow widths, and vice versa. Slightly concave wavelength dependence of the backward
direction as shown in Fig. 4.8 (b) determines the wavelength dependence of the backward loss.
That is, the extinction peaks appear when the total phase difference corresponds to π.
The rib height may also have some errors caused in the fabrication process. Fig. 4.13
shows the wavelength dependence with errors in the rib height of all waveguide of the isolator.
The θN is also re-calculated for every rib height. In this case, both the propagation constants

β1 and β2 increase for smaller rib height since the light field distributes less in the sidecladding layer. These increments are larger in β1 than β2, and the θR becomes small forsmaller rib height. On the other hand, the θN hardly changes as the rib height. Therefore, thetotal phase difference in the backward direction slightly decreases from the designed one for asmaller rib height, and vice versa. The backward loss is determined by the slightly concave
wavelength dependence of the total phase difference.
The optical path lengths of MZI arms are precisely determined by e-beam lithography. An
error induced in both arms with the same amount can be neglected since it provides no phasedifference between two arms. So, very small error in the length of one arm is considered. Fig.
4.14 shows the wavelength dependence with an error in the modified length L2 of thereciprocal phase shifter in the wideband design and in the path length of one arm in theconventional design. The difference in optical path length between two arms is very importantfor MZI to provide the phase difference. Even in the conventional design, the wavelength94 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

dependence shifts ~20 nm with the errors from –5.0 nm to +5.0 nm. This is a serious problem
because the wavelength range with >30 dB isolation ratio is just ~30 nm. Even though the
backward loss in the wideband design changes significantly, the isolation ratio remains high(>30 dB) in a wide wavelength range. One can see that the fabrication tolerance is improvedin the wideband design compared with that in the conventional design.

Forward loss (dB)

0
0.2
0.4
conventional design
wideband design

w1 / w2
1.6μm / 2.0μm
1.8μm / 2.2μm
2.0μm / 2.4μm
2.2μm / 2.6μm
2.4μm / 2.8μm

0.6
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(a)

Backward loss (dB)010conventional design
wideband design
w1 / w2
1.6μm / 2.0μm
1.8μm / 2.2μm
2.0μm / 2.4μm
2.2μm / 2.6μm
2.4μm / 2.8μm

20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.12 Wavelength dependence of the type-1 isolator with errors in waveguide width, for(a) forward loss and (b) backward loss. The other waveguide parameters are fixed at thedesigns shown in Table 4.2.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer95

Forward loss (dB)0
rib 60nm
rib 70nm
rib 80nm
rib 90nm
rib 100nm

0.2
0.4
conventional design
wideband design

0.6
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(a)

Backward loss (dB)010conventional design
wideband design
rib 60nm
rib 70nm
rib 80nm
rib 90nm
rib 100nm

20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.13 Wavelength dependence of the type-1 isolator with errors in rib height, for (a)forward loss and (b) backward loss. The other waveguide parameters are fixed at the designs
shown in Table 4.2.

96 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

Forward loss (dB)0
L2 -5.0nm
L2 -2.5nm
L2 0nmL2 +2.5nm
L2 +5.0nm

0.2
0.4
conventional design
wideband design

0.6
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(a)

Backward loss (dB)010conventional design
wideband design
L2 -5.0nm
L2 -2.5nm
L2 0nmL2 +2.5nm
L2 +5.0nm

20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

(b)
Fig. 4.14 Wavelength dependence of the type-1 isolator with errors in length of one arm, for(a) forward loss and (b) backward loss. The other waveguide parameters are fixed at thedesigns shown in Table 4.2.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer97

4.3.3 Ultra-wideband design
In this section, the author investigates further widening the operation bandwidth using the
proposed concept. The wideband design is based on a flat wavelength dependence of total
phase difference in the backward direction. However, it is not completely flat as θN and θR
have specific wavelength dependences. Typically, θN and θR are a convex and concave
function as the considering wavelength range, respectively, as can be seen in Fig. 4.6. In orderto realize further wideband operation, the wavelength dependence of θR is to be elaborately
adjusted to that of θN.
The waveguide parameters of reciprocal phase shifter affect its wavelength dependence asfollows. Wider waveguide has larger propagation constant at the shorter wavelength due tohighly optical confinement into the waveguide core. The wavelength dependence of the
propagation constant is as shown in Fig. 4.15 (a). The difference between β1 and β2 is large at
the shorter wavelength and is convex as shown in Fig. 4.15 (b). When the section lengths L1and L2 are equal, the phase difference between two sections exhibits the convex wavelength
dependence and its curve is multiplied by the length as shown in Fig. 4.15 (c). When thesection length L2 is increased for a fixed L1, w1, and w2, the wavelength dependence of thephase difference changes as shown in Fig. 4.15 (d). The reason is that the phase difference ofthe elongated section is affected only by β2, and has a concave wavelength dependence.

β2−β1

β
w : large

θR(β2−β1)Lw2-w1 : const.
L : large

w2-w1 : largew2>w1 L2>L1

w2>w1 L2=L1
λ
(a)

λ
(b)

λ
(c)

λ
(d)

Fig. 4.15 Wavelength dependence of (a) propagation constant as a parameter of waveguide
width, (b) the difference in propagation constant β2−β1, (c) the phase difference provided by(β2−β1)L as a parameter of the section length, and (d) variation of reciprocal phase differenceθR= β2L2−β1L1 as a parameter of the difference in section length.

98 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

Based on such a behavior, we design a magneto-optical isolator operating in an ultrawideband range from 1.31 μm to 1.55 μm. Two extinction peaks where the backward phasedifference corresponds to π are adjusted to 1.31 μm and 1.55 μm. The center wavelength is tobe chosen properly to minimize the forward loss at the band edges and to provide sufficient
backward loss in a desired wavelength range. In this design, we set the center wavelength at
1.43 μm.
A rib waveguide formed on a Ce:YIG film grown on a SGGG substrate and covered by
SiO2 upper layer is assumed. The waveguide and rib heights are 0.48 μm and 0.08 μm,
respectively, that is the same as type-1 isolator treated thus far. We set the waveguide width w1
at 2.0 μm and modify the width w2 from 2.4 μm to 3.0 μm. Fig. 4.16 shows the reciprocal
phase difference θR of w1= 2.0 μm and w2= 2.4 μm with a parameter of section lengths where
L2 is slightly modified from L1 so that the –θN+θR becomes +π at λ= 1.55 μm. Table 4.3
shows the optimized lengths L1 and L2 so as to have two extinction peaks at λ= 1.31 μm and1.55 μm. Fig. 4.17 shows the nonreciprocal and reciprocal phase differences for several
combinations of waveguide width. In this case, the combination of the waveguide widths withlarger difference shows similar wavelength dependence of θR to that of θN. This realizes
higher backward loss in a wide wavelength range as shown in Fig. 4.18. In the ultra-wideband
design with the waveguide widths of w1= 2.0 μm and w2= 3.0 μm, the forward loss of <1.0 dB
and the backward loss of >26 dB is obtained at the wavelength range of 1.25 – 1.60 μm.

Table 4.3 Optimized waveguide parameters of reciprocal phase shifter.
w1 (μm)w2 (μm)L1 (μm)L2 (μm)

2.0

2.4

1900

1898.453

2.0

2.6

880

879.178

2.0

2.8

510

509.548

2.0

3.0

360

359.714

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

99

330

θR (deg)

300
270
240 θ +180deg
N
210
180
1.25

L1 (~L2)
100μm
500μm
1000μm2000μm

1.35
1.45
1.55
wavelength (μm)

1.65

Fig. 4.16 Reciprocal phase difference for fixed waveguide width w1= 2.0 μm and w2= 2.4 μm
with a parameter of section lengths where L2 is slightly modified from L1 so that the –θN+θR
becomes +π at λ= 1.55 μm.

300

90

270

60
30
0
1.25

w1 / w2
2.0 / 2.4 μm
2.0 / 2.6 μm
2.0 / 2.8 μm
2.0 / 3.0 μm

1.35
1.45
1.55
wavelength (μm)

240

θR (deg)θN (deg)

120

210
180
1.65

Fig. 4.17 Phase differences in the ultra-wideband design with several combinations of the
waveguide width.

100 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

Loss (dB)010Backward

Forward

w1 / w2

2.0 / 2.4 μm
2.0 / 2.6 μm
2.0 / 2.8 μm
2.0 / 3.0 μm

20
30
40
1.25

1.35
1.45
1.55
wavelength (μm)

1.65

Fig. 4.18 Wavelength dependence of forward and backward losses in the ultra-wideband
designs.

4.4 Fabrication of a wideband isolator
We fabricate a wideband isolator with the type-1 structure described above. A 0.48-μm-thick
Ce:YIG film is grown on a (111)-oriented (GdCa)3(GaMgZr)5O12 (SGGG) substrate by aradio frequency (RF) sputtering epitaxy with the substrate temperature at 670 oC. Argon
containing oxygen at a volume ratio of 0.28% is used as the sputter gas. After the growth, thefilm is covered by ~300-nm-thick SiO2 which protects the film surface during the following
procedures. A post-annealing process at a temperature of 800 oC for 30 min is employed toreduce the propagation loss of the Ce:YIG film [12,13]. After coating 400-nm-thickelectron-beam resist OEBR-1000 on the sample surface by a spin coater with 4000 rpm for 40
sec, it is baked at 180 oC for 30 min. ~30-nm-thick Al is coated on it to increase theconductivity of electron-beam. The waveguide patterns are exposed by e-beam lithography
with accelerating voltage of 50 kV and are developed with a mixture of methyl isobutyl
ketone and isopropanol (1:1) for 1 min. The patterns are transferred to a Ti mask formed bye-beam deposition, which is lifted off with acetone. After reactive ion etching in a CHF3
plasma for SiO2 etching, the rib waveguide is formed on Ce:YIG surface by Ar sputter etchingwith a 100-W RF power. The Ti mask is removed by a mixture of sodium hydroxide andhydrogen peroxide (1:1) at ~100 oC. Then SiO2 is deposited on the whole surface of theChapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer101

fabricated waveguide. Finally, the ends of the waveguide are obtained by cleaving at a notch
formed by dicing-saw.
Here, we utilize a concept of ultra-wideband design to realize wider bandwidth. That is,the curve of the wavelength dependence is considered in the design although it is focused on
the performance improvement in the wavelength around 1.55 μm. In this case, it is designedwith the propagation constants β1, β2, and the nonreciprocal phase shift calculated by solving
an eigenvalue equation of four layered structure approximated from the 2-D waveguidestructure. The waveguide height is set at 0.48 μm to maximize the nonreciprocal phase shift
and the rib height is set at 0.08 μm. The designed lengths of the modified waveguide widths
w1= 2.0 μm and w2= 2.4 μm are L1= 900 μm and L2= 899.55 μm, respectively. Tapered
waveguides which connect the modified section are installed in both arms to avoid theimbalance between the two arms such as excess loss and phase shift associated with the taper.
The designed forward and backward losses are indicated by red lines in Fig. 4.19. We also
calculate these losses with the designed parameter by using a mode solver of FEM and theperturbation theory to obtain the nonreciprocal phase shift as shown in Fig. 4.20. There is adifference in the optimum design between the calculation methods especially when thesection lengths are large.
A 0.5-mm-long and 24-μm-wide multi-mode interference (MMI) coupler is designed forthe 3dB coupler. The two MZI arms are formed 300 μm away from each other, sufficient toapply an external magnetic field in anti-parallel directions, by 5-degree bending waveguides
of 3.0-mm-radius. The total length of the waveguide is ~6.0 mm, which includes
0.75-μm-wide down-taper waveguides at input and output ends to increase the coupling
efficiency into connecting fibers. In order to confirm the wideband operation, twomagneto-optical isolators with the conventional and wideband designs are fabricated using
these waveguide components on a sample.
Fig. 4.21 shows the photo image of the fabricated sample from the top view. Fig. 4.22
shows the SEM image of cross section of the fabricated waveguide facets which is the end of
the 0.75-μm-wide down-taper waveguide. The rib height of the fabricated waveguide isobserved to be 60 nm. The calculated operation spectra considering this error in rib height are102 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometershown by the blue lines in Figs. 4.19 and 4.20. The extinction peaks shift to the longer
wavelength.

0
Loss (dB)10

rib 80nm Conv.
rib 80nm Wide.
rib 60nm Wide.

20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

Fig. 4.19 Calculated operation spectra of magneto-optical isolator in the conventional andwideband designs by solving eigenvalue equation with approximated waveguide. Dashed andsolid lines are forward and backward losses, respectively.

0
Loss (dB)10

rib 80nm Conv.
rib 80nm Wide.
rib 60nm Wide.

20
30
40
50
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

Fig. 4.20 Calculated operation spectra of magneto-optical isolator in the conventional andwideband designs by a mode solving of FEM and the perturbation theory. Dashed and solidlines are forward and backward losses, respectively.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

6.0 mmFig. 4.21 Photo image of the fabricated sample on a Ce:YIG film.

SiO2

Ce:YIG
SGGG

Fig. 4.22 SEM image of cross section of the fabricated waveguide on a Ce:YIG film.

103

104 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

4.5 Characterization
Optical measurement setup is shown in Fig. 4.23. Polarized light from an amplified
spontaneous emission (ASE) diode having an optical gain in the wavelength range of 1.53 –1.565 μm is launched into the waveguide facet with TM mode. First, near field pattern of thetransmitted light is observed with infrared-camera. The light is propagating along clockwise(CW) direction. The sign of nonreciprocal phase difference is determined by a direction of theapplied magnetic field. A permanent magnet with three poles is set on the waveguide to apply
an external magnetic field in anti-parallel directions to obtain a nonreciprocal phase shift. Fig.
4.24 shows the observed near field patterns of the transmitted light which is interchanged
between the center and side ports depending on the phase difference in the MZI arms. Whenthe external magnetic field is applied to the MZI arms in parallel to the propagation direction,
no nonreciprocal phase difference is induced between two arms. Inverse push-pull operations
are observed in each design for respective poles of the permanent magnet. This behavior
agrees with the operation principle as shown in Fig. 4.1.

Permanent
magnetSampleTunable LD

lens
IR-camera

S
N

ASE

S

CW
PMF

CCW
PMF

TV
MonitorPolarizer
Optical Power Meter
TM modeSpectrum
Analyzer

Fig. 4.23 Optical measurement setup for a magnet-optical isolator.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer(a) magnet: S-N-S(b) magnet: parallel(c) magnet: N-S-N(d) magnet: S-N-S(e) magnet: parallel(f) magnet: N-S-N

105

Fig. 4.24 Near field patterns of transmitted light with an ASE light source having an optical
gain around λ= 1.55 μm. The isolators are fabricated with (a), (b), (c) conventional design and(d), (e), (f) wideband design on a sample. An external magnetic field is applied in parallel tothe light propagation in (b) and (e).

Next, fixing the permanent magnet, transmitted light from the center waveguide iscoupled into another fiber. A tunable laser diode which has an operating wavelength range in
1.51 – 1.64 μm is used as the light source. Fig. 4.25 shows the transmitted power of the two
isolators measured with an optical power monitor for light propagating in clockwise (CW)
and counter-clockwise (CCW) directions. The forward loss corresponds to the case wherelarger power is transmitted to the center port, while the backward loss corresponds to thereversed direction with the fixed magnet. The propagation direction is reversed byinterchanging the connection of the optical fiber. The transmission loss measured in a single
waveguide fabricated beside the isolator on the sample is monotonically decreased from 40
dB at λ= 1.51 μm to 31 dB at λ= 1.64 μm, which includes the waveguide propagation loss
mainly dominated by the optical absorption of Ce:YIG and coupling loss of ~30 dB at two
facets between fiber and waveguide. There is little difference in the transmitted power
between the single waveguide and the forward propagation of isolator in wideband design,106 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

which means that the excess loss of the fabricated MZI is small. Therefore, the insertion lossof the fabricated isolator except the coupling loss between fiber and waveguide is mainly
dominated by the propagation loss of the waveguide and is estimated to be 6 dB at λ= 1.55
μm. The degradation of the forward loss in the conventional design is not due to the design
but the accuracy of fabrication. That is, the coupling loss between the fiber and waveguide or
the propagation loss of the waveguide is accidentally larger in the conventional design thanthat in the wideband design.
Figure 4.26 shows the transmission loss normalized with the transmittance of the single
waveguide. The measured results agree with the calculated ones qualitatively though it is not
as much as the calculation results. Generally, the extinction of a MZI is limited by the power
imbalance as well as the deviation of phase difference between two arms. Also, the maximum
sensitivity of the measurement setup is ~70 dB. The scattered data of the backward loss
measured at the shorter wavelength region are due to the latter one. Therefore, the small
extinction peak at λ~ 1.54 μm in Fig. 4.26 (b) may not correspond to the calculated peaks at
λ~ 1.55 μm shown in Fig. 4.19. If so, the measured results agree rather well with thecalculation results in Fig. 4.20. The difference in transmission loss between the forward andbackward directions corresponds to the isolation ratio. Larger isolation ratio is obtained in a
wider wavelength range in the wideband design. High isolation ratio of 15 – 25 dB is obtainedin a wavelength range between 1.53 μm and 1.64 μm in the wideband isolator.

transmitted power (dB)

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

107

-30
-40
-50
single waveguide
MZI forward
MZI backward

-60
1500

1550
1600
wavelength (nm)1650

transmitted power (dB)

(a)

-30
single waveguide
MZI forward
MZI backward

-40
-50
-60
1500

1550
1600
wavelength (nm)

1650

(b)
Fig. 4.25 Measured transmission of the fabricated isolator with (a) conventional design and(b) wideband design.

108 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometerloss (dB)01020
forwardbackward

30
1500

1550
1600
wavelength (nm)

1650

(a)

loss (dB)

0
10
20
30
1500

forwardbackward

1550
1600
wavelength (nm)

1650

(b)
Fig. 4.26 Measured transmission of the fabricated isolator with (a) conventional design and(b) wideband design.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

109

4.6 Discussion
In Section 4.5, a magneto-optical isolator with wideband design around λ= 1.55 μm has been
demonstrated on a Ce:YIG waveguide. It is difficult to control the nonreciprocal phasedifference in the MZI composed of a magneto-optic waveguide because the external magnetic
field is unfortunately applied to the bending waveguides which separate the two arms to be
applied the magnetic fields in anti-parallel direction. In this measurement, we control thenonreciprocal phase difference by placing the permanent magnet with three poles properly.
This problem is solved by using the magneto-optic material only in the nonreciprocal phaseshifter such as type-2 or type-3 isolator.
We also design an ultra-wideband isolator operating in 1.31 μm and 1.55 μm on a Ce:YIG
waveguide. However, it can not be demonstrated since the optical absorption loss of theCe:YIG waveguide is large at the shorter wavelength. Fig. 4.27 shows the propagation loss ofa Ce:YIG waveguide after post-annealing process measured by a cut-back method. The
transmission losses through the several propagation lengths are measured with tunable laser
sources having an operating wavelength range of 1.26 – 1.36 μm and 1.34 – 1.44 μm or an
ASE source. The propagation loss is ~1 dB/mm at λ= 1.55 μm but is 6 – 8 dB/mm at λ= 1.31
μm that is a serious problem for the magneto-optical isolator of the Ce:YIG waveguide. Thiscan be circumvented by using the waveguide structure of type-2 or type-3 isolator. Since the
Ce:YIG is used as an upper cladding layer, the absorption loss of a propagating light is greatly
reduced. A magneto-optical isolator with the ultra-wideband design is to be demonstrated withsuch a waveguide structure.

110 Chapter 4: Wideband operation of a magneto-optical isolator using

Propagation loss (dB/mm)

phase adjustment in Mach-Zehnder interferometer

10

5

0
1250

1350
1450
wavelength (nm)1550

Fig. 4.27 Propagation loss of a Ce:YIG waveguide as a function of wavelength.

4.7 Summary
A wideband operation of a magneto-optical isolator employing nonreciprocal phase shift has
been proposed and demonstrated. The wideband operation is realized by phase adjustment in
the MZI to compensate the wavelength dependence of nonreciprocal phase shift for that ofreciprocal one. First, we demonstrate a dramatic improvement of the backward loss withacceptably small deterioration of the forward loss by numerical calculations. This designconcept is applicable to the isolator with any other material, structure, and dimension. Next,
we fabricated a wideband isolator with Ce:YIG waveguide and demonstrate the wideband
operation experimentally. High isolation ratio of 25 dB is successfully obtained at λ= 1.60 μm
owing to the wider operation spectrum.
Such wideband operation has never been reported in bulk isolators because it is difficult tocontrol the wavelength dependence of the bulk materials. On the other hand, a waveguidestructure has many controllable parameters as mention above.

Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

111

References[1] K. Ando, T. Okoshi, and N. Koshizuka, “Waveguide magneto-optic isolator fabricated by laser
annealing,” Appl. Phys. Lett., vol.53, pp.4-6 (1988).
[2] T. Shintaku, “Integrated optical isolator based on efficient nonreciprocal radiation mode
conversion,” Appl. Phys. Lett., vol.73, pp.1946-1948 (1998).
[3] F. Auracher and H. H. Witte, “A new design for an integrated optical isolator,” Opt. Commun.,vol.13, pp.435-438 (1975).
[4] T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE
Trans. on Microwave Theory and Technique, vol.MTT-30, pp.922-925 (1982).
[5] Y. Okamura, T. Negami, and S. Yamamoto, Integrated optical isolator and circulator using
nonreciprocal phase shifters: a proposal,” Appl. Opt., vol.23, pp.1886-1889 (1984).
[6] N. Bahlmann, M. Lohmeyer, H Dötsch, and P. Hertel, “Integrated magneto-optic Mach-Zehnderinterferometer isolator for TE modes,” Electron. Lett., vol.34, pp.2122-2123 (1998).
[7] J. Fujita, M. Levy, and R. M. Osgood, Jr., “Waveguide optical isolator based on Mach-Zehnderinterferometer,” Appl. Phys. Lett., vol.76, pp.2158-2160 (2000).
[8] H. Yokoi and T. Mizumoto, “Proposed configuration of integrated optical isolator employing
wafer-direct bonding technique,” Electron. Lett., vol.33, pp.1787-1788 (1997).
[9] H. Yokoi, T. Mizumoto, and Y. Shoji, “Optical nonreciprocal devices with a silicon guiding layer
fabricated by wafer bonding,” Appl. Opt., vol.42, pp.6605-6612 (2003).
[10] R. L. Espinola, T. Izuhara, M.-C. Tsai, and R. M. Osgood, Jr., “Magneto-optical nonreciprocal
phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett., vol.29, pp.941-943 (2004).
[11] M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly
Ce-substituted iron garnet films prepared by sputtering,” J. Appl. Phys., vol.70, pp.7065-7067(1991).
[12] T. Shintaku and T. Uno, “Preparation of Ce-substituted yttrium iron garnet films formagneto-optic waveguide devices,” Jpn. J. Appl. Phys. Vol.35, pp.4689-4691 (1996).
[13] S. Narikawa, “Semi-leaky isolator using a direct bonding of LiNbO3/Ce:YIG,” (Master thesis ofTokyo Institute of Technology, Tokyo, 2003), Chap.4, p.34. (in Japanese.)[14] S. H. Wemple and W. J. Tabor, “Refractive index behavior of garnets,” J. Appl. Phys., vol.44,

112 Chapter 4: Wideband operation of a magneto-optical isolator using
phase adjustment in Mach-Zehnder interferometer

pp.1395-1396 (1973).
[15] K. Iga, “Semiconductor laser,” (Japan Society of Applied Physics, Tokyo, 1994), Chap.2,
pp.32-44. (in Japanese.)[16] FemSIM software from RSoft Design Group, (http://www.rsoftdesign.com/)Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

113

Chapter 5:
Polarization-Independent Magneto-Optical
Isolator Using TM-Mode Nonreciprocal
Phase Shift

5.1 Introduction
In high-speed optical fiber communication systems, magneto-optical isolators areindispensable in protecting optical active devices from unwanted reflected lights. Especiallyin highly developed optical fiber amplification systems, polarization-independent opticalisolators are strongly desired. At present, the polarization-independent isolators are widelyused in commercial systems [1]. However, there is no waveguide isolator operating even for
one polarization in commercial systems.
The waveguide isolator investigated in this study is employing nonreciprocal phase shiftnormally induced in TM mode with a thin-film magneto-optic waveguide. The essence of thenonreciprocal phase shift is based on the asymmetry of waveguide-layer structure with respect
to the direction of the electromagnetic field of the guided mode. In order to obtain anonreciprocal phase shift for a TE mode, a waveguide must be configured so as to havehorizontal asymmetry; typically, this is an asymmetry structure that is more difficult to realize.
Polarization-independent waveguide isolators that employ a nonreciprocal phase shift havebeen proposed by two researchers. Zhuromskyy et al. [2] used horizontal and vertical domain
walls in the magneto-optic guiding layer, and Fujita et al. [3] used different side cladding
layer in order to simultaneously induce nonreciprocal phase shifts for the TE and TM modes.
Other configurations for a polarization-independent operation of a waveguide optical isolator
based on Faraday rotation have also been proposed [4,5].

114 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

In this chapter, the author proposes a polarization-independent isolator using
nonreciprocal phase shift only for the TM mode. This device is a Mach-Zehnderinterferometer (MZI) with polarization converters and nonreciprocal phase shifters. The
operation is realized not by a polarization-diversity scheme but by the phase differences
between reciprocal TE and nonreciprocal TM modes. This configuration not only obviates theneed for a nonreciprocal phase shift for both modes but also makes it possible to fabricate
using an integrated structure, such as a semiconductor guiding layer, which we haveinvestigated [6-8].

5.2 Principle of polarization-independent operation
Figure 5.1 shows a schematic configuration of the proposed optical isolator. The MZI haspolarization converters (PC), nonreciprocal phase shifters (NPS), and an additional π phaseshifter. All components are composed of planar waveguide structures; the nonreciprocal phaseshifters utilize a magneto-optic material with an applied external field. Here, the polarization
converters are assumed to give 100% polarization conversion between TE and TM modes,
after which the lightwaves propagate in the nonreciprocal phase shifter of each arm, where
each has a different polarization mode. The nonreciprocal phase shifters induce phasedifferences between the different modes as follows:(β TE − β TM + )L + π = 2mπ(5.1)(β TE − β TM − )L + π = (2n + 1)π(5.2)

where βTE, βTM+, and βTM− denote the longitudinal propagation constants of the TE and theforward- and backward-traveling TM modes, respectively, and m and n are integers. Note thatthe second term of +π in (5.1) and (5.2) is induced by a π phase shifter. As a result of theconditions in these two equations, the forward waves interfere constructively, and the
backward waves interfere destructively in 3dB couplers. Since both input modes follow these
relations, the MZI functions as a polarization-independent optical isolator.
Although the additional π phase shifter is not necessary for polarization-independent
isolator operation, it makes backward loss keep high despite the inefficiency of thepolarization converters. This property enables one to use a broader range of waveguide

115

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shiftpolarization converters for this isolator application, which have been proposed anddemonstrated [9-15] although it would be rather difficult to realize a truly ~100% mode
conversion device. The performance of the isolator is summarized in Table 5.1 for four
possible input combinations of forward/backward and TM/TE mode, where m = n = 0 are
assumed for simplicity in (5.1) and (5.2). The polarization conversion efficiency isrepresented by η. Two rows in each case denote the waves that are divided into two arms of
the interferometer, where the relative phase of each polarization component is indicated inbrackets. The forward waves that are converted to the other mode from the input one as isdesired, become in-phase and are transmitted to the output port. The unconverted components
become anti-phase due to the additional π phase shift, and interfere destructively, which
results in the insertion loss. The backward waves become antiphase whether any mode
conversion is induced or not. That is, the design ensures that any backward traveling waves
become antiphase despite an incomplete polarization conversion, which is favorable for theisolator performance.

External magnetic field
input

PC1

π

NPS

C

C
NPS

outputPC2
C : 3dB coupler
PC : Polarization converter
NPS : Nonreciprocal phase shifterπ : Additional phase shift

Fig. 5.1 Schematic diagram of the proposed polarization-independent optical isolator.

116 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

Table 5.1 Operation principle of polarization-independent optical isolator.
3dB

TM

TE

PC1
TM [0]−>

TM [0]−>

TE [0]−>

TE [0]−>

0<−(1-η)TM [3π/2]ηTE [π/2]<−(1-η)TM [π/2]ηTM [3π/2]0<−(1-η)TE [π/2]TM [0]
ηTM [0]−>−>TE [0]TEM [3π/2]<−ηTE [π/2]<−<−

TE [3π/2]ηTM [π/2](1-η)TE [π/2]ηTE [π/2]−>

TM [−π/2]ηTM [−π/2]

<−

−>

−>

TE [π/2]

TM [π]<−<−TE [π]
ηTM [0](1-η)TE [0]ηTE [−π/2]ηTM [−π/2]ηTM [π/2]3dB
ηTE [3π/2](1-η)TM [π/2]−>ηTE [−π/2]

−>

ηTE

−>

ηTM

<−

TM

<−

TE

(1-η)TM [−π/2]−>(1-η)TE [π/2]ηTM [π/2](1-η)TE [3π/2]−>(1-η)TE [π/2]ηTM [π/2](1-η)TE [π/2]TM [π]<−<−

TM [0]<−

TM [0]<−TE [π]<−

TE [0]<−

TE [0]<−

TE [0](1-η)TM [0]<−−>(1-η)TM [−π/2]−>ηTE [0]ηTE [π/2](1-η)TM [−π/2](1-η)TE [π/2]
−>

π

PC2

(1-η)TM [−π/2](1-η)TM [π/2](1-η)TE [3π/2]
ηTM [π/2]−>(1-η)TE [0]−><−ηTE [0](1-η)TM [0]−>ηTE [3π/2]

NPS

TM [0]

5.3 Device structure
The author shows two examples of the device structure that realize the proposed isolator
configuration as is shown in Fig. 5.1. For both devices, a magneto-optic garnet CeY2Fe5O12(Ce:YIG) that has a large Faraday rotation coefficient of –4500 deg/cm at 1.55 μm is grown
on a (Ca, Mg, Zr) doped GGG substrate [16]. The type-1 isolator that is shown in Fig. 5.2 hasa Ce:YIG guiding layer and a SiO2 cover layer. The type-2 isolator, which is shown in Fig. 5.3,
has a Si waveguide that is fabricated on a silicon-on-insulator (SOI) wafer and a Ce:YIG
upper cladding layer, which is realized with a direct bonding technique [6-8]. An external
magnetic field is transversely applied to the propagation direction and is parallel to the film
plane to obtain a nonreciprocal phase shift only for TM mode.
The polarization converters have an asymmetric waveguide structure that realizes apassive polarization conversion. The isolators of type-1 and type-2 are assumed to have aperiodic loaded waveguide [9] and an angled facet waveguide [10,11,15], respectively.
The additional reciprocal phase shift, which must be an odd multiple of π for both TE andTM modes, is realized by installing an optical path difference between two interferometerChapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

117

arms. Another alternative is to employ 2 × 2 couplers for the MZI and to use its
straight-through ports since they divide an input wave into antiphase waves.
In the following design, the operating wavelength is assumed to be ~1.55 μm.

Fig. 5.2 Device structure of a polarization-independent isolator composed of a magneto-optic
guiding layer (type-1).

Fig. 5.3 Device structure of a polarization-independent isolator composed of a Si waveguidebased on SOI structure (type-2).

118 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

5.4 Design of nonreciprocal phase shifter
The cross-sectional images of the nonreciprocal phase shifter are shown in Fig. 5.2 (b) and
Fig. 5.3 (b). Here, the refractive indices of Ce:YIG, (Ca,Mg,Zr)-GGG, Si, SiO2, and air are set
at 2.20, 1.94, 3.48, 1.44, and 1.0 at a wavelength of 1.55 μm, respectively. The nonreciprocal
phase shift Δβ (= βTM+−βTM−) is calculated based on the perturbation theory together with amode solver of beam propagation method (BPM) [17] as described in Chapter 2. Fig. 5.4
shows the calculated nonreciprocal phase shift as a function of waveguide thickness. The
waveguide widths are assumed to be 2.0 μm and 1.0 μm for type-1 and type-2 structures,
respectively. The nonreciprocal phase shifts are maximized at small film thickness. A large
nonreciprocal phase shift means a small propagation length L in (5.1) and (5.2). In thefollowing discussion, the thickness of the waveguide core is fixed at 0.5 and 0.2 μm for the
type-1 and type-2 isolators, respectively.
The nonreciprocal phase shifter is designed as a function of the waveguide width. Figure
5.5 (a) shows the width-dependent effective refractive indices of the TE and TM modes thatare calculated by BPM for the type-1 isolator. The nonreciprocal propagation constants of the
TM mode are estimated by adding and subtracting Δβ/2 to the unperturbed propagation
constant. Upon subtracting (5.2) from (5.1), the minimum propagation length L can beobtained by setting m = n. Figure 5.5 (b) shows the nonreciprocal phase shifts for the TM
mode and the minimum required propagation lengths as a function of the waveguide width.
By using these parameters, the output powers of the MZI are calculated from the left-handside of (5.1) and (5.2) (see the dashed and solid lines in Fig. 5.5 (c), where the 3 dB couplers
and polarization converters are assumed to ideally function). When one term becomes 1 andthe other becomes 0 at a particular waveguide width, (5.1) and (5.2) are satisfied, and the MZIfunctions as a polarization-independent isolator. For example, the type-1 isolator is designed
for a guiding layer thickness of 0.5 μm at a width of 3.5, 2.6, 2.25 μm, and so on. On the other
hand, at a width of 2.98, 2.38, and 2.14 μm, an optical isolator operation is obtained byreversing the direction of the external magnetic field.

119Nonreciprocal phase shift (mm -1)

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

8.0
type-1 (W=2.0μm)
type-2 (W=1.0μm)

6.0
4.0
2.0
0

0.2
0.4
0.6
0.8
waveguide thickness (μm)

1

2.05
TE

2.00
TM

1.95
(a)

5.0
4.0

1.5

3.0
2.0

C

1.0
0.5

(b)

1.0
0

Required propagation
length (mm)2.0CNonreciprocal phaseshift (mm -1 )Effective refractive
index

Fig. 5.4 Calculated nonreciprocal phase shift as a function of the waveguide thickness.

output power

1
0.8
0.6

eq.(5.1)

0.4

eq.(5.2)

0.2
0
1.0

(c)

1.5

2.0

2.5

3.0

3.5

4.0

waveguide width ( μm)

Fig. 5.5 (a) Calculated effective refractive indices, (b) nonreciprocal phase shift and required
propagation length, and (c) output power of the MZI for type-1 isolator at a waveguide
thickness of 0.5 μm.

120 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

In the same way, the type-2 isolator is designed as shown in Fig. 5.6 (a) – (c). For a
guiding layer thickness of 0.2 μm, the designed widths are 2.05, 1.6, and 0.9 μm, or for thereverse propagation direction, they are at 2.4, 1.5 μm, and so on. It should be noted that the
fabrication tolerance for the width of the MZI is higher for wider waveguides in both material

3.00

TE

2.80
2.60
TM

2.40

(a)

8.0
7.0

0.8

C

0.6

6.0
5.0

0.4
(b)

4.0

0.2

Required propagation
length (mm)Nonreciprocal phaseshift (mm -1 )

2.20

C

Effective refractiveindex

systems.

output power

1
0.8
0.6

eq.(5.1)

0.4

eq.(5.2)

0.2
0
0.5

(c)

1.0

1.5

2.0

waveguide width ( μm)

Fig. 5.6 (a) calculated effective refractive indices, (b) nonreciprocal phase shift and required
propagation length, and (c) output power of the MZI for type-2 isolator at a waveguide
thickness of 0.2 μm.

121

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

The operation spectrum of this device is determined by the difference in the wavelength
dependences of the propagation constants for the two orthogonal modes βTE(λ) and βTM(λ);
that is, the phase difference is based on (βTE(λ) – βTM(λ)). The nonreciprocal phase shifter isdesigned for fixed waveguide thickness. The designed waveguides have different wavelength
dependences for βTE(λ) and βTM(λ).
Figure 5.7 shows the schematic image of the wavelength dependence of the calculated
quantity (βTE(λ) – βTM(λ)). Here, we calculated the wavelength dependences of propagation
constants considering the wavelength dispersion of the refractive indices using the same
assumption in Section 4.3.1. For a fixed thickness, the widest operation bandwidth around thecenter wavelength (λC) is found at a specific width in case of Fig. 5.7 (b). Figure 5.8 shows
the calculated wavelength dependence of the type-2 isolator for 0.25-μm-thick Si layer withseveral waveguide widths. In this case, (b) shows the widest operation bandwidth in awavelength range from 1.53 to 1.565 μm (C-band). So, the waveguide width is optimized at
0.86 μm for 0.25-μm-thick Si layer.

βΤΕ−βΤΜβΤΕ−βΤΜβΤΕ−βΤΜ

(a)

λC

(b)

λ

λC

(c)

λ

λC

λ

width
thickness

Fig. 5.7 Schematic wavelength dependence of the difference between βTE and βTM.

122 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

Loss (dB)

0
10
20
30
40 (a)

ForwardBackward

0
10
20
30
40 (b)0102030
40 (c)010203040 (d)
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

Fig. 5.8 Calculated wavelength dependence of the type-2 isolator. The height of Si waveguideis set at 0.25μm. The widths and the lengths of nonreciprocal phase shifter are (a) w = 0.80
μm and L = 551.6 μm, (b) w = 0.86 μm and L = 543.9 μm, (c) w = 1.0 μm and L = 538.1 μm,
and (d) w = 2.0 μm and L = 524.0 μm, respectively.

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

123

The combination of the guiding layer thickness and width at which the operation
bandwidth becomes the largest in C-band is plotted in Figs. 5.9 and 5.10 for type-1 and type-2
isolators, respectively. The similar operational bandwidths, from 1.53 to 1.565 μm, areobtained for these parameter combinations. All designs are calculated for the TE and TM
fundamental modes. However, higher order modes may be excited at the polarization
converters when the waveguide width and/or height are large. The boundaries of asingle-mode operation for the TE and TM modes are drawn by solid lines in the figures.
In actual fabrication, thickness can be controlled more precisely than width. The
performance is less sensitive to width error for a wider waveguide, as shown in Figs. 5.5 (c)and 5.6 (c). Consequently, the thicknesses and widths of the preferred design that provides
wide bandwidth and single-mode operation are 0.66 and 1.8 μm for a type-1 isolator and 0.26
and 0.72 μm for a type-2 isolator, respectively. The required propagation lengths are 2448.2
and 600.9 μm for type-1 and -2, respectively. Figures 5.11 and 5.12 show the calculated
spectral response of these designs, where any propagation and coupling losses at 3 dB
couplers are ignored. In addition, the wavelength dependences of the 3 dB couplers and thepolarization converters are ignored because they are much less wavelength-sensitive than thephase shifters [15]. The isolation ratios and the insertion losses in the C-band wavelength
range are >32 dB and <0.006 dB for the type-1 isolator and >21 dB and <0.034 dB for the
type-2 isolator, respectively.

124 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shiftwidth (μm)

3.02.5
TM1 cut-off

2.0
TE1 cut-off

1.5
0.55

0.6

0.65
0.7
thickness (μm)

0.75

Fig. 5.9 Designed waveguide thicknesses and widths to obtain wide operation bandwidth in
type-1 isolator.

1.5
width (μm)

TM1 cut-off

10.5

TE1 cut-off

0.22

0.24

0.26 0.28
thickness (μm)

0.3

0.32

Fig. 5.10 Designed waveguide thicknesses and widths to obtain wide operation bandwidth in
type-2 isolator.

125

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

loss (dB)010Forward loss

20
30
Backward loss

40
1.45

1.5
1.55
1.6
wavelength (μm)

1.65

Fig. 5.11 Calculated spectral response of type-1 isolator, where the waveguide thickness is
0.66 μm and the width is 1.8 μm.

loss (dB)010Forward loss

20
30
40
1.45

Backward loss

1.5
1.55
1.6
wavelength (μm)

1.65

Fig. 5.12 Calculated spectral response of type-2 isolator, where the waveguide thickness is0.26 μm and the width is 0.72 μm.

126 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

5.5 Design of polarization converter
5.5.1 Principle of waveguide polarization converter
A polarization rotation in a planar waveguide is achieved by perturbing the asymmetry ofwaveguide structure so as to rotate the optical axis from the original position. The behavior isvery similar to a light propagation in a birefringent material.
Generally, a lightwave propagating in a planar waveguide has two orthogonal eigenmodes,
so-called slow and fast modes with specific longitudinal propagation constants β0 and β1. We
assume the x- and y-directions are the horizontal and vertical to the waveguide plane,
respectively, and the light propagates along the z-direction. In full-vectorial consideration, theelectromagnetic fields are expressed in terms of a superposition of two components as [9]E0 = A0 ( xˆ cos φ − yˆ sin φ ) exp(− jβ 0 z ) ,(5.3)

E1 = A1 ( xˆ sin φ + yˆ cos φ ) exp(− jβ1 z )(5.4)

where A0 and A1 are the normalized amplitudes of the field and φ is the angle of optical axis.
The polarization rotation can be explained in terms of the eigenmodes. We suppose that xpolarized wave is launched at the input z = 0 of a waveguide with the optical axis rotated −φ.
The wave is represented by a mixture of the two modes as shown in Fig. 5.13 (a). As they
propagate independently with their respective propagation constants, interference occurs ineach field component with respect to a half-beat length given byLπ =π
β 0 − β1.

(5.5)

Fig. 5.13 (b) shows the field states at z = Lπ where the phase difference between E0 and E1 is π.
The total field is rotated by –2φ from the excited direction.

Fig. 5.13 Electric fields E(z) as a superposition of two eigenmodes at (a) z = 0 and (b) z = Lπ.

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

127

The angle of optical axis φ is estimated from the x- and y-amplitudes of the eigenmodes.
However, the eigenmodes are calculated in 2-D field distributions for x- and y-components
using a full-vectorial simulation. The optical axis cannot be solved directly. Here, a rotation
parameter R is introduced [10]∫∫ n ( x, y) E ( x, y) dxdyR=∫∫ n ( x, y) E ( x, y) dxdy
2

2

x

2

2

(5.6)

y

where n(x,y) is the refractive index distribution and |Ex(x,y)|2, |Ey(x,y)|2 are the electric fieldcomponents of each eigenmode. The integrals are taken over the area of the computational
window. When R >> 1, the corresponding eigenstate is principally x-polarized; when R = 1,
the optical axis is rotated by 45o with respect to x or y; and when R << 1, the corresponding
eigenstate is principally y-polarized. The rotation parameters for the two eigenmodes aredenoted as R0 and R1, respectively. Since the modes are orthogonal to each other, the angle of
optical axis with respect to the x-axis is estimated by [15]φ = cot −1 R0 = tan −1 R1 .

(5.7)

In symmetric planar waveguide systems extending primarily in the x-direction, the slow mode(E0) has primarily x-component with a small y-component and the fast mode (E1) has
primarily y-component with a small x-component. Therefore, the angle of optical axis is ~0oand there is no polarization rotation for x- or y-polarized wave. On the other hand, inasymmetric waveguide systems, the optical axis is rotated from the x- or y-axis so that x- or ypolarized incident wave exhibits polarization rotation with respect to the half-beat length. In
addition, if another asymmetric waveguide that has reversed optical axis are cascaded
periodically with the half-beat length, the polarization rotation is accumulated as shown in Fig.
5.14. The polarization rotation is linearly accumulated by 2φ as each propagation length of Lπ.
In this study, the proposed polarization-independent isolator requires 100% conversion
between TE and TM modes, i.e., 90o polarization rotation. The cross-sectional images of thepolarization converters are shown in Fig. 5.2 (c) and Fig. 5.3 (c). For type-1 isolator,
asymmetric loaded waveguide is assumed. Since the rotation of optical axis is small in one
section of mode converter, the reversed asymmetric structure is periodically cascaded toachieve the complete polarization conversion. For type-2 isolator, an angled-facet waveguide128 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

structure is assumed. The optical axis can be designed to be rotated at 45o so that complete
polarization conversion is achieved in one perturbed section which results in reduction of theinsertion loss due to scattering at the junction of the reversed waveguides.

Fig. 5.14 Electric fields E(z) as a superposition of two eigenmodes in cascaded asymmetricwaveguides with reversed optical axes; at (a) z= 0 and (b) z= Lπ in a waveguide with theoptical axis –φ ; at (c) z= Lπ and (d) z= 2Lπ in a waveguide with the optical axis φ.

5.5.2 Calculation results
First, polarization converters composed of the type-1 and type-2 structures are designed at awavelength of 1.55 μm by using a full-vector FEM analysis [17]. It calculates the propagation
constants of two eigenmodes as well as the electromagnetic fields in x- and y-components. In
this section, the refractive indices of composed materials are set at the same as Section 5.4
and that of HfO2 is set at 1.98 at a wavelength of 1.55 μm.
For the type-1 isolator, the width and height of Ce:YIG channel waveguide are set at 3.0
and 0.6 μm, respectively, which is compatible to the design of nonreciprocal phase shifterinvestigated in Section 5.4. The width of the loaded layer of HfO2 is set at the half of the
waveguide, i.e., 1.5 μm. Fig. 5.15 shows the calculated half-beat length with a parameter ofthickness of the loaded layer as a function of computational grid sizes of x and y. The
accuracy of calculation increases at small grid sizes because the simulation results depend on
the relative positions of the interface boundary with respect to the grid points near theinterface, i.e., the simulation results in large grid sizes are not consistent. Ideally, an infinite
small grid size as close to zero as possible should be used so that the simulated profile will be
converged to the real profile. However, considering the limit of memory usage and the129

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shiftcomputation time, only finite grid size can be used. One can estimate an ideal result by
extrapolating the grid size to zero in Fig. 5.15. Also, a nonuniform grid which defines
elaborate index profiles near the interface increases the accuracy of simulation result. Figure
5.16 shows the calculated half-beat length as a function of thickness of the loaded layer with anonuniform computation grid. The calculated half-beat lengths are 27.2 μm, 32.1 μm, and36.5 μm, and the calculated angles of optical axis are 0.127o, 0.150o, and 0.170o, for the
thickness of loaded layer of 0.1 μm, 0.2 μm, and 0.3 μm, respectively. The angles of opticalaxis seem to be too small for the asymmetries of assumed structure. We find that theestimation of the angle of optical axis using (5.7) from (5.6) is invalid for an asymmetricstructure with weak perturbation because the angles obtained from each rotation parameter is
not coincident each other, i.e., cot−1(R0) ≠ tan−1(R1). A complete polarization conversion istheoretically achieved by cascading a number of the reversed asymmetric structures so thatthe total polarization rotation becomes 90o. In this case, the propagation length required forthe complete conversion is estimated to be about 9.5 mm which is too long compared with theHalf-beat length, Lπ (μm)

calculation result by using a full-vector BPM investigated later.

40
load: 0.3 μm

35
load: 0.2 μm

30

25
0

load: 0.1 μm

0.02

0.04 0.06 0.08
grid size (μm)

0.1

Fig. 5.15 Half-beat length as a function of computational grid sizes in type-1 structure of w=
3.0 μm and h= 0.6 μm.

130 Chapter 5: Polarization-independent magneto-optical isolator using

37

0.18

35

0.17

33

0.16

31

0.15

29

0.14

27

0.13

0.1

Angle of optical axis, φ1 (deg)Half-beat length, Lπ (μm)

TM-mode nonreciprocal phase shift

0.15
0.2
0.25
0.3
thickness of loaded layer (μm)

Fig. 5.16 Half-beat length as a function of thickness of the loaded layer calculated with anonuniform grid. The grid sizes of Δx= 0.1 μm, Δy= 0.05 μm in bulk region and Δx= 0.01 μm,
Δy= 0.005 μm near the boundary are connected with moderately varied grids.

For type-2 isolator, the waveguide has an angled facet in one sidewall. The angle is simply
set at the 54.736o coincided with a (111) plane of Si crystal in a (100)-oriented SOI wafer. The
sidewall is completely etched to SiO2 under-cladding layer. Width at the bottom of angled
facet is defined as the section width of the polarization converter. The height of Si waveguideis set at 0.30 or 0.40 μm. The rotation parameter is then designed to be R = 1 by varying thesection width. Figures 5.17 and 5.18 show the calculated propagation constants normalized by
the wavenumber k, i.e., the effective refractive indices of two eigenmodes, and the rotation
parameters. The calculation accuracy increase for small gird sizes. Since a nonuniform grid is
not useful for the angled facet waveguide, uniform gird of Δx = Δy = 0.01 μm is used in thiscase. The designed section widths are 0.38 and 0.51 μm, and the half-beat lengths are 1.87
and 3.35 μm, for the waveguide height of 0.30 and 0.40 μm, respectively. Figure 5.19 shows
the calculated x- and y-components of electric field distribution in two eigenmodes for thecase that the section width and height are 0.51 and 0.40 μm, respectively. Ex and Ey
correspond to the first and second terms in (5.3) and (5.4). The field distributions havedifferent discontinuities at the interface that means the orthogonality of two modes.

131

Normalized propagation
constant, β / k

2.5

Rotation parameter, R

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

10

(a)

2.0
mode-0mode-11.5(b)mode-0mode-1

1

0.1
0.35

0.4
0.45
waveguide width (μm)

0.5

Fig.5.17 (a) Normalized propagation constants and (b) rotation parameters of two eigenmodes

Rotation parameter, R

Normalized propagation
constant, β / k

as a function of section width for type-2 structure at h= 0.30 μm.

3.0
(a)

2.5
2.0
mode-0mode-1

1.5
10 (b)

mode-0mode-1

1
0.1
0.4

0.5
0.6
waveguide width (μm)

0.7

Fig.5.18 (a) Normalized propagation constants and (b) rotation parameters of two eigenmodes
as a function of section width for type-2 structure at h= 0.40 μm.

132 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift(a) Ex0(b) Ey0(c) Ex1(d) Ey1

Fig. 5.19 x- and y-components of electric field distribution in two eigenmodes for type-2
structure at w= 0.51 μm and h= 0.40 μm.

Next, the polarization rotation is analyzed by using a full-vector 3-D finite difference (FD)BPM [17,18]. For type-1 structure, the scattering loss at the junction of reversed waveguidesections is inevitable. A light propagation in periodically loaded asymmetric waveguides iscalculated as shown in Fig. 5.20. The dimension of waveguide structure is the same as
investigated above. The monitored power of excited and converted lights is associated withthe x- and y-components of electric field. Therefore, the results can be considered as thepolarization conversions from TE (-like) to TM (-like) modes as long as the fields distributelike fundamental modes. The converted power is maximized when the section lengths are set
at 27.2, 31.7, and 35.0 μm for 0.1-, 0.2-, and 0.3-μm-thick loaded layers, respectively. The
results are similar to the half-beat lengths designed by FEM. However, the power is not fully
converted to the other mode while that of excited mode almost disappears at some
propagation length. This is due to the scattering loss at the junction of reversed asymmetricwaveguide sections. Although a large perturbation by a thick loaded layer enables thepolarization conversion in shorter propagation length and less number of section, the133

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shiftconverted power decreases due to the large scattering loss at each junction. In addition, for a
thick loaded layer, there is large difference in the propagation length between minimizing theexcited power and maximizing the converted power. Consequently, a preferable design of thepolarization converter of type-1 structure is 39 number of periodically asymmetric waveguidecomposed of a 0.1-μm-thick loaded layer and a 27.2-μm-long half-beat length, where theNormalized power

Normalized power

Normalized power

polarization conversion of ~70% is obtained at the propagation length of 1060.8 μm.

1

N=39

0.8

(a)

0.6
0.4
0.2
0
1
0.8

N=22

(b)

0.6
0.4
0.2
0
1
0.8

N=18

(c)

0.6
0.4
0.2
0

0

500
1000
Propagation length (μm)

1500

Fig. 5.20 A light propagation in periodically loaded asymmetric waveguides calculated by 3-D
full-vector BPM with the grid sizes of Δx = 0.1 and Δy = 0.03 μm. The converted powers (redlines) are maximized at the half-beat lengths of (a)27.2 μm for 0.1-μm-thick loaded layer,(b)31.7 μm, for 0.2-μm-thick loaded layer and (c)35.0 μm for 0.3-μm-thick loaded layer,
respectively. N denotes the number of cascaded asymmetric waveguide sections.

134 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

For type-2 structure, our full-vector 3-D BPM tends to be unstable due to the highly
hybrid nature of the vectorial modes given by high-index contrast interface and the angled
facets. At the interface between Si and air, the abrupt index change may cause the FD BPM tobe unstable in some cases. This instability is associated with an algorithm called thealternating direction implicit (ADI) method used for solving 3-D systems. To improve thestability, a procedure described in Ref. [11] is adopted that the grid points near the interface
are artificially averaged by the indices of the nearby surrounding grid points such that asmoothly changed, linearly averaged, index profile at the interface replaces the real step-index
boundary with a large index contrast. Fig. 5.21 shows the refractive index profile represented
by step-index boundary with the grid size of 0.002 μm, and the modified index profile
represented by the smoothed boundary averaged by those of the surrounding grids within 20
points along x and y directions including itself, (i.e., 41×41 points) and converted to the gridsize of 0.01 μm.
Even though the smoothing procedure makes the simulation stable, the simulated index
profile deviates from the original physical structure. Fig. 5.22 shows the calculated half-beatlength as a function of number of surrounding points N, where (2N+1)×(2N+1) points areused for smoothing procedure. Here, the scheme parameter [18] is set at 0.55 to make thesimulation stable while it slightly attenuates the power along the propagation length. The
result shows different tendencies for the number of smoothing between N < 10 and N > 10.
Since no simulation result is obtained at N < 5 due to the instability, the results of N > 10 are
more reliable than those of N < 10. Therefore the ideal half-beat length can be estimated to be
Lπ = 2.2 μm by extending the asymptotic curve to N = 0 and ignoring the results of N < 10 in
Fig. 5.22. This is different from the result Lπ = 1.87 μm calculated by full-vector FEM. In thisBPM simulation, the x-component of one eigenmode is excited at the asymmetric waveguide.
However, the x-component of the other eigenmode should be excited at the same time toassume the x-polarized launched light. Actually, it takes a propagation length of several
microns to obtain stable propagation in the simulation. Even when the smoothing procedure isadopted, the 3-D BPM may not be suitable for such a problem with abrupt change inpolarization state along the propagation direction, while it can solve a problem of weakChapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

135

perturbation such as type-1 structure.

(a)

(b)

Fig. 5.21 Color scales of (a) refractive index profile represented by step-index boundary withthe grid size of 0.002 μm, and (b) the modified index profile represented by smoothedboundary averaged by those of the surrounding grids within 20 points.

Half-beat length, Lπ (μm)

5.0
4.0
3.0
2.0
1.0
0

10
20
30
40
number of smoothing points, N

Fig. 5.22 Half-beat length calculated with a smoothed index profile as a function of number ofsmoothing grid points N.

136 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

5.6 Discussion
In order to realize the polarization-independent isolator, one has to demonstrate and confirm
the operation of each component; nonreciprocal phase shifter, polarization converter, and3-dB coupler.
In our design, the dimension of the waveguide in the nonreciprocal phase shifter must be
strictly controlled to satisfy the condition. The different operation between TE and TM modes
can be confirmed by using a measurement setup as shown in Fig. 5.23 [19]. TE and TM
modes are simultaneously and equally excited from a ~45o-rotated fiber to a magneto-optic
waveguide. An external magnetic field is transversely applied to the propagation direction andis parallel to the film plane to obtain a nonreciprocal phase shift only for the TM mode. Bothmodes propagate in the magneto-optic waveguide and have a different phase at the end of the
waveguide due to the different propagation constants. After launched to the free space, themodes have an identical propagation constant in air and construct a circularly, ellipsoidally, or
lineally polarized state depending on the phase difference between TE and TM modes in the
waveguide. Using a free-space polarizer, the polarization state is analyzed by the power
intensity at the photo detector. Then the direction of external magnetic field is reversed, thepolarization state changes due to the nonreciprocal phase shift only for the TM mode. Bymeasuring the magnet-optic waveguides formed with different width or propagation length,
the difference in phase shift between TE and TM modes, including the nonreciprocal phaseshift for TM mode, can be analyzed as a function of the waveguide parameter.

Fig. 5.23 Setup for a measurement in nonreciprocal operation between TE and TM modes.

137

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

The polarization converter for type-1 structure is realized by depositing and selectively
etching a loaded layer on the waveguide. The angled facet asymmetric waveguide for type-2
structure is fabricated by a combination of dry and wet etching processes. An asymmetricwaveguide with very narrow slot can be formed in one dry etching process utilizing aphenomenon called “RIE lag” where the etching depth is controlled by the slot width [12].
Also, several deep slots etched at 45o into a waveguide structure largely rotate the optical axis
and provide high birefringence that enables complete polarization conversion with the
propagation length of several microns [13].
The 3-dB coupler must operate for both TE and TM modes as well. A Y-branch coupler isless sensitive to the polarization but it needs longer propagation length for low-loss coupling.
A directional coupler becomes sensitive if there is a large difference in the field distribution
between the two modes. A multi-mode interference (MMI) coupler becomes sensitive to thepolarization if there is a large birefringence in the multimode section.

5.7 SummaryA

polarization-independent

magneto-opticalwaveguide

isolator

using

TM

mode

nonreciprocal phase shift is proposed. The operation is not realized by a polarization diversity
scheme, but rather by the phase difference between the reciprocal TE mode and nonreciprocal
TM mode. Since the nonreciprocal phase shift is used only for the TM mode, it can be easily
realized with integrated structures. The author shows the proposed principle of operation andthe design rules that are needed for wide operational bandwidth and single-mode operation.
Two different isolator designs that assume two specific material systems are demonstrated.
Polarization converters for the use of the isolator are investigated. Some asymmetricwaveguide systems are compatible to the isolator configuration and they realize a passive andreciprocal polarization conversion. Two polarization converters with specific structures aredesigned by full-vectorial simulations of FEM and 3-D BPM.

138 Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

References[1] Products catalog of TDK Corporation (http://www.tdk.co.jp/)[2] O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dötsch, P. Hertel, and A. F. Popkov, “Analysisof polarization independent Mach-Zehnder-type integrated optical isolator,” J. Lightwave
Technol., vol.17, pp.1200-1205 (1999).
[3] J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, “Polarization-independent
waveguide optical isolator based on nonreciprocal phase shift,” IEEE Photon. Technol. Lett.,vol.12, pp.1510-1512 (2000).
[4] N. Sugimoto, T. Shintaku, A. Tate, H. Terui, M. Shimokozono, E. Kubota, M. Ishii, and Y. Inoue,“Waveguide polarization-independent optical circulator,” IEEE Photon. Technol. Lett., vol.11,
pp.355-357 (1999).
[5] T. R. Zaman, X. Guo, and R. J. Ram, “Proposal for a polarization-independent integrated opticalcirculator,” IEEE Photon. Technol. Lett., vol.18, pp.1359-1368 (2006).
[6] H. Yokoi and T. Mizumoto, “Proposed configuration of integrated optical isolator employing
wafer-direct bonding technique,” Electron. Lett., vol.33, pp.1787-1788 (1997).
[7] H. Yokoi, T. Mizumoto, and Y. Shoji, “Optical nonreciprocal devices with a silicon guiding layer
fabricated by wafer bonding,” Appl. Opt., vol.42, pp.6605-6612 (2003).
[8] R. L. Espinola, T. Izuhara, M.-C. Tsai, and R. M. Osgood, Jr., “Magneto-optical nonreciprocal
phase shift in garnet/silicon-on-insulator waveguides,” Opt. Lett., vol.29, pp.941-943 (2004).
[9] W. Huang and Z. M. Mao, “Polarization rotation in periodic loaded rib waveguides,” J.
Lightwave Technol., vol.10, pp.1825-1831 (1992).
[10] V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic
structure,” Opt. Commun., vol.127, pp.7-13 (1996).
[11] J. Z. Huang, R. Scarmozzino, G. Nagy, M. J. Steel and R. M. Osgood, Jr., “Realization of acompact and single-mode optical passive polarization converter,” IEEE Photon. Technol Lett.,vol.12, pp.317-319 (2000).
[12] B. M. Holmes and D. C. Hutchings, “Realization of novel low-loss monolithically integrated
passive waveguide mode converters,” IEEE Photon. Technol. Lett., vol.18, pp.43-45 (2006).
[13] M. V. Kotlyar, L. Bolla, M. Midrio, L. O’Faolain, and T. F. Krauss, “Compact polarization

Chapter 5: Polarization-independent magneto-optical isolator using
TM-mode nonreciprocal phase shift

139

converter in InP-based material,” Opt. Express, vol.13, pp.5040-5045 (2005).
[14] A. M. Radojevic, R. M. Osgood, Jr., M. Levy, A. Kumar, and H. Bakhru, “Zeroth-order half-wave
plates of LiNbO3 for integrated optic application at 1.55 μm,” IEEE Photon. Technol. Lett.,vol.12, pp.1653-1655 (2000).
[15] H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization
rotators,” J. Lightwave Technol., vol.23, pp.432-445 (2005).
[16] M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly
Ce-substituted iron garnet films prepared by sputtering,” J. Appl. Phys., vol.70, pp.7065-7067(1991).
[17] BeamPROP/FemSIM software from RSoft Design Group, (http://www.rsoftdesign.com/)[18] W. P. Huang and C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector
beam propagation method,” IEEE J. Quantum. Electron., vol.29, pp.2639-2648 (1993).
[19] Y. Okamura, H. Inuzuka, T. Kikuchi, and S. Yamamoto, “Nonreciprocal propagation inmagnetooptic YIG rib waveguides,” J. Lightwave Technol, vol.LT-4, pp.711-714 (1986).

140 Chapter 6: Conclusions

Chapter 6:
Conclusions

Magneto-optical isolators are indispensable in high-speed optical fiber communication
systems and are used to protect optical active devices from unwanted reflected lights.
However, the absence of practical waveguide isolator is a bottleneck for reducing the cost oflight source modules and realizing integrated optical circuits. Several types of waveguideisolator are investigated and developed by some researchers. The author studies the
waveguide magneto-optical isolator employing nonreciprocal phase shift. Integration,
miniaturization, wideband operation, and polarization-independent operation must be
accomplished for waveguide isolators to become a reality and replace bulk isolators. The
results obtained throughout this study are summarized as follows:
In Chapter 2, the nonreciprocal phase shift is theoretically and numerically analyzed.
Using 1-D and 2-D waveguide models, the nonreciprocal phase shift is calculated by directly
solving the eigenvalue equation and by perturbation theory using beam propagation method(BPM) as well as finite element method (FEM). For narrower waveguide, 2-D model should
be used for taking the effect of the lateral optical confinement into account. In the comparison
among the several mode solving methods, reliable calculation results are obtained by using
full-vector simulations than semi-vector ones. Then magneto-optical isolators based on a
Mach-Zehnder interferometer (MZI) employing nonreciprocal phase shift are designed forspecific material systems.
In Chapter 3, a magneto-optical isolator with Si waveguide is demonstrated. First, Si
waveguide is fabricated on a silicon-on-insulator (SOI) wafer and characterized. Second, asurface activated direct bonding with oxygen plasma treatment is investigated. A directbonding between Si and CeY2Fe5O12 (Ce:YIG) is successfully achieved with oxygen plasmaof 100-W radio frequency power for 30-s followed by annealing at 200 – 250 oC with aChapter 6: Conclusions

141

pressure of ~5 MPa. Then, a magneto-optical isolator composed of a 0.3-μm-thick Si rib
waveguide with low-loss propagation characteristics is characterized in terms of thenonreciprocal operation by reversing the propagation direction. The maximum isolation of 21
dB is obtained at a wavelength of 1559 nm. The insertion loss of 8 dB and the temperaturedependence of the isolator are also examined.
In Chapter 4, a wideband design of a magneto-optical isolator employing nonreciprocal
phase shift is proposed and its performance is demonstrated. The wideband operation isrealized by phase adjustment in the MZI to compensate the wavelength dependence ofnonreciprocal phase shift for that of reciprocal one. First, the author demonstrated a dramatic
improvement of the backward loss with acceptably little deterioration of the forward loss by
numerical calculations. This design concept is applicable to the isolator with any othermaterial, structure, and dimension. Next, the author fabricated a wideband isolator with
Ce:YIG waveguide to demonstrate the wideband operation experimentally. Compared withthe conventional design, higher isolation ratio up to 25 dB is successfully obtained at around
λ= 1.60 μm.
In Chapter 5, a polarization-independent magneto-optical waveguide isolator using TM
mode nonreciprocal phase shift is proposed. The operation is not realized by polarization
diversity, but rather by the phase difference between the reciprocal TE mode andnonreciprocal TM mode. Since the nonreciprocal phase shift is used only for the TM mode, it
can be easily realized with integrated device structures. The author shows the proposed
principle of operation and the design rules that are needed for wide operational bandwidth andsingle-mode operation. Two isolator designs that assume different material systems aredemonstrated. In addition, polarization converters for the use of the isolator are investigated.
Some asymmetric waveguide structures compatible to the isolator configuration areinvestigated to realize a passive and reciprocal polarization conversion. Two polarization
converters with different structures are designed by full-vectorial simulations of FEM and 3-D
BPM.
The author believes that the achievement shown in this thesis contributes largely to push
the waveguide isolator into a reality. Further studies to be done are as follows:142 Chapter 6: Conclusions

1) Magneto-optical isolator with Si waveguide
In order to integrate the magneto-optical isolator with Si photonic circuit, it is important tominiaturize the isolator with low-loss Si-wire waveguides. Next, the condition of directbonding should be optimized with respect to a thermal durability testing in the temperature
range of practical applications. Also, the bonding interface must be investigated about theinterlayer and the influence on the nonreciprocal phase shift.
2) Wideband operation of a magneto-optical isolator
The principle of the wideband operation is applicable to the magneto-optical isolator
based on Mach-Zehnder interferometer with any structures such as GaInAsP/InP and Si/SiO2
based waveguides. Even though an ultra-wideband operation is not achieved in a fabricatedisolator with Ce:YIG waveguide due to a large absorption at shorter wavelength region, it is
to be demonstrated by using semiconductor waveguides.
3) Polarization-independent magneto-optical isolator
In order to realize the polarization-independent isolator, one has to demonstrate andconfirm the operation of each component; nonreciprocal phase shifter, polarization converter,and 3-dB coupler. After that, a polarization-independent isolator compatibly designed withthese components will be demonstrated.

Acknowledgement

143

Acknowledgements
The author would like to express the most gratitude to Professor Tetsuya Mizumoto ofTokyo Institute of Technology for his teaching, encouragement, and fruitful discussions
throughout his whole study.
The author would like to appreciate Professor Kohroh Kobayashi, Professor Fumio
Koyama, Professor Shigehisa Arai, Associate Professor Nobuhiko Nishiyama of Tokyo
Institute of Technology, and Dr. Koji Ando of National Institute of Advanced Industrial
Science and Technology for their useful discussions and advices on this study.

A part of this study is supported by Research Fellowship of the Japan Society for the
Promotion of Science for Young Scientists.

The author would like to express sincere gratitude to Associate Professor Hideki Yokoi of
Shibaura Institute of Technology for his helpful guidance, discussion, and advice.
The author would like to appreciate Professor Richard M. Osgood, Jr., Mr. I-Wei Hsieh,
and Mr. Mitsuhide Takekoshi of Columbia University for their fruitful discussions andcontinuous supports since he has visited the university.
The author would like to acknowledge Associate Professor Katsumi Nakatsuhara(Kanagawa Institute of Technology), Dr. Seok-Hwan Jeong (Fujitsu), Dr. Jeong-Su Yang
(Yonsei University), and Dr. Takeo Maruyama (Tokyo Institute of Technology) for theirhelpful comments and discussions on meetings and conferences.
The author would like to thank senior and present members in the doctoral course; Dr.
Naoto Kitahara (Tokyo Polytechnic University), Dr. Itsuro Morita (KDDI), Dr. Shingo Kawai(NTT), Dr. Koichi Maru (Hitachi Cable), Mr. Akira Naka (NTT), Mr. Shin-ichi Wakabayashi(Panasonic), Mr. Kazumasa Sakurai, Dr. Jae-kuk Seo (BOSCH), Mr. Minoru Taya, Mr.
Shinichi Sakamoto, Mr. San-Hun Kim, and Mr. Ryohei Takei for their advices and inspiring
discussions.

144 Acknowledgement

The author wishes to thank all the members of Mizumoto Laboratory; Mr. Takashi Sakai,
Mr. Satoshi Narikawa, Mr. Jalil Mohammad Abdul, Mr. Ryotaro Takaki, Mr. Hiroaki Iwasaki,
Mr. Masahiro Kobayashi, Mr. Takayuki Ishii, Mr. Masaki Ono, Mr. Tomohiro Morita, Mr.
Atsushi Saito, Mr. Hideki Saito, Ms. Etsu Shin, Mr. Nguyen Anh Hong, Mr. Kazuhiko Tamura,
Mr. Yoichi Akano, Mr. Nobumasa Tanaka, Ms. Nguyen Thi Ngoc Nhi, Mr. Yoshihiro Yazaki,
Mr. Masashi Hashimoto, Mr. Ryohei Kouga, Mr. Kenji Abe, Mr. Masaki Yoshimura, Mr. Koji
Kubota, Ms. Yukie Inoue, Mr. Tetsuya Hagiwara, Mr. Tomohiro Takanashi and Mr. Etsuji
Hayakawa for their valuable cooperation in experiment and pleasant days in the laboratory.

Finally, the author deeply thanks his family and his lover, Manami for theirunderstandings, supports, and encouragements.

Publication list

145

Publication list

Journal Papers[1] Y. Shoji, H. Yokoi, and T. Mizumoto, “Enhancement of magneto optic effect in optical isolator
with GaInAsP guiding layer by selective oxidation of AlInAs,” Jpn. J. Appl. Phys., vol.43,
pp.590-593 (2004).
[2] Y. Shoji and T. Mizumoto, “Wideband design of nonreciprocal phase shift magneto-opticalisolators using phase adjustment in Mach-Zehnder interferometers,” Appl. Opt., vol.45,
pp.7144-7150 (2006).
[3] Y. Shoji and T. Mizumoto, “Ultra-wideband design of waveguide magneto-optical isolator
operating in 1.31μm and 1.55μm band,” Opt. Express, vol.15, pp.639-645 (2007).
[4] Y. Shoji and T. Mizumoto, “Wideband operation of Mach-Zehnder interferometricmagneto-optical isolator using phase adjustment,” Opt. Express, vol.15, pp.13446-13450 (2007).
[5] Y. Shoji, I-W. Hsieh, R. M. Osgood, Jr., and T. Mizumoto, “Polarization-independent
magneto-optical isolator using TM-mode nonreciprocal phase shift,” J. Lightwave Technol.,vol.25, pp.3108-3113 (2007).
[6] Y. Shoji, H. Yokoi, I-W. Hsieh, R. M. Osgood, Jr., and T. Mizumoto, “Magneto-optical isolator
with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett., vol.92, p.071117 (2008).
[7] H. Yokoi, T. Mizumoto, and Y. Shoji, “Optical nonreciprocal devices with a silicon guiding layer
fabricated by wafer bonding,” Appl. Opt., vol.42, pp.6605-6612 (2003).
[8] H. Yokoi, Y. Shoji, and T. Mizumoto “Calculation of nonreciprocal phase shift in magnetooptic
waveguide with silicon guiding,” Jpn. J. Appl. Phys., vol.43, pp.5871-5874 (2004).
[9] H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, “Interferometric optical isolator employing anonreciprocal phase shift operated in a unidirectional magnetic field,” Appl. Opt., vol.43,
pp.4745-4752 (2004).
[10] J-S. Yang, Y. Shoji, H. Yokoi, M. Ono, and T. Mizumoto, “Investigation of nonreciprocal
characteristics and design of interferometric optical isolator with multimode interference coupler
operating with a unidirectional magnetic field,” Jpn. J. Appl. Phys., vol.43, pp.7045-7049 (2004).

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[11] H. Yokoi, Y. Shoji, T. Suzuki, N. Nishimura, and T. Mizumoto, “Coupling characteristics of threeguide tapered coupler for optical isolator with Si guiding layer,” Jpn. J. Appl. Phys., vol.45,
pp.6323-6325 (2006).
[12] Y. Yazaki, Y. Shoji, and T. Mizumoto, “Demonstration of interferometric waveguide isolator witha unidirectional magnetic field,” Jpn. J. Appl. Phys., vol.46, pp.5460-5464 (2007).

International Conferences[13] Y. Shoji, H. Yokoi, and T. Mizumoto, “Enhancement of magneto-optic effect in magneto-optic
waveguide with low refractive index undercladding layer,” 2003 International Conference on
Solid State Devices and Materials (SSDM 2003), A-5-5, Tokyo, Japan, September 16-18 (2003).
[14] Y. Shoji, H. Yokoi, and T. Mizumoto, “Ultracompact optical isolator with a silicon high index
contrast waveguide,” Conference on Lasers and Electro Optics / International Quantum
Electronics Conference (CLEO/IQEC 2004), CThT7, San Francisco, California, May 16-21(2004).
[15] Y. Shoji, H. Yokoi, and T. Mizumoto, “Fabrication of ultracompact optical isolator with
Si-photonic wire waveguides,” International Quantum Electronics Conference 2005 and The
Pacific Rim Conference on Lasers and Electro Optics 2005 (IQEC/CLEO-PR 2005), CTuK1-2,
Tokyo, Japan, July 11-15 (2005).
[16] Y. Shoji, H. Yokoi, and T. Mizumoto, “Mach-Zehnder interferometer with Si wire waveguides forultracompact optical isolator,” The 11th Microoptics Conference (MOC’05), D1, Tokyo, Japan,
October 30- November 2 (2005).
[17] Y. Shoji and T. Mizumoto, “Novel design of nonreciprocal phase shift optical isolators for
wideband operation,” The 11th OptoElectronics and Communication Conference (OECC 2006),
5B4-5, Kaohsiung, Taiwan, July 3-7 (2006).
[18] Y. Shoji and T. Mizumoto, “Novel polarization-independent waveguide optical isolator employing
nonreciprocal phase shift,” The 12th Microoptics Conference (MOC’06), D-5, Seoul, Korea,
September 10-14 (2006).
[19] Y. Shoji and T. Mizumoto, “Wideband operation of magneto-optical isolator with phase adjusted

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Mach-Zehnder interferometer,” The 19th Annual Meeting of the IEEE Laser & Electro-Optics
Society (LEOS 2006), ThV2, Montreal, Canada, October 29- November 2 (2006).
[20] Y. Shoji and T. Mizumoto, “Ultra-wideband design of a magneto-optical isolator operating in
1.31μm and 1.55μm,” The 20th Annual Meeting of the IEEE Laser & Electro-Optics Society(LEOS 2007), TuC4, Lake Buena Vista, Florida, October 21-25 (2007).
[21] Y. Shoji, H. Yokoi, I-W. Hsieh, R. M. Osgood, Jr., and T. Mizumoto, “Magneto-optical isolator
with SOI waveguide,” The Optical Fiber Conference and Exposition and The National Fiber
Optic Engineers Conference (OFC/NFOEC 2008), OTuC8, San Diego, California, February
24-28 (2008).
[22] H. Yokoi, Y. Shoji, and T. Mizumoto, “Selective oxidation and successive wet etching forfreestanding structure of magneto-optical waveguide,” IEEE/LEOS International Conference on
Optical MEMS, TuP12, pp.75-76, Waikoloa, Hawaii, August (2003).
[23] T. Sakai, Y. Shoji, H. Yokoi, and T. Mizumoto, “Enhancement of magneto-optic effect in opticalisolator with semiconductor guiding layer by selective oxidation of AlInAs,” The 8th
Optoelectronics and Communication Conference (OECC 2003), Shanghai, China, 15E4-3, vol.1,
pp.179-180, October 13-16 (2003).
[24] H. Yokoi, Y. Shoji, and T. Mizumoto, “Optical isolator with Si guiding layer fabricated by wafer
bonding,” The 9th Microoptics Conference (MOC’03), H37, Tokyo, Japan, October 29-31 (2003).
[25] H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, “Interferometric optical isolator with distinct layer
structures employing nonreciprocal phase shift,” 7th International Symposium on Contemporary
Photonics Technology (CPT2004), P-11, pp.87-88, Tokyo, Japan, January 14-16 (2004).
[26] H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, “Demonstration of optical isolator employing
nonreciprocal phase shift operated under unidirectional magnetic field,” 9th OptoElectronics andCommunications Conference / 3rd International Conference on Optical Internet (OECC/COIN
2004), 13P-126, Kanagawa, Japan, July 12-16 (2004).
[27] H. Yokoi, Y. Shoji, and T. Mizumoto, “Feasibility of optical isolator with Si guiding layer
employing nonreciprocal phse shift,” The 10th Microoptics Conference (MOC’04), L-17, p.94,
Jena, Germany, September (2004).
[28] M. Taya, Y. Shoji, and T. Mizumoto, “TE-cut polarizer based on silicon wire waveguide,” The148 Publication list

11th Microoptics Conference (MOC’05), H10, pp.136-137, Tokyo, Japan, October 30-November 2(2005).
[29] T. Mizumoto, K. Sakurai, Y. Shoji, and H. Saito, “(Invited) Waveguide optical isolator
integratable to photonic devices,” Integrated Photonics Research and Applications Topicalmeeting (IPRA 2006), ITuG1, Uncasville, Connecticut, April 24-26 (2006).
[30] T. Mizumoto, H. Saito, and Y. Shoji, “Semi-leaky optical isolator fabricated by surface activation
wafer bonding,” The 11th Optoelectronics and Communications Conference (OECC 2006), 5B4-1,
Kaohsiung, Taiwan, July 3-7 (2006).
[31] T. Mizumoto, K. Sakurai, Y. Shoji, and H. Saito, “(Invited) Integration of optical isolators andsemiconductor lasers by wafer bonding,” Asia Pacific Optical Communications (APOC 2006),
6352-90, Gwangju, Korea, September 7 (2006).
[32] Y. Yazaki, Y. Shoji, and T. Mizumoto, “Demonstration of interferometric waveguide opticalisolator with a unidirectional magnetic field,” The 12th Microoptics Conference (MOC’06), C-5,
pp.66-67, Seoul, Korea, September 10-14 (2006).
[33] T. Mizumoto and Y. Shoji, “(Invited) Integrated waveguide optical isolators: principle andhistory,” 2008 Conference on Lasers and Electro-Optics (CLEO 2008), San Jose, California, May
4-9 (2008). (to be presented.)

Technical Reports[34] Y. Shoji, H. Yokoi, and T. Mizumoto, “Enhancement of magneto-optic effect in optical isolator
with semiconductor guiding layer by selective oxidation of AlInAs (非相反移相効果増大のための AlInAs 選 択 酸 化 に よ る 低 屈 折 率 ク ラ ッ ド 層 の 形 成 ),” Technical Report of IEICE,EMD2003-41, Aug. (2003). (in Japanese.)[35] Y. Shoji and T. Mizumoto, “Broad-band operation of asymmetric Mach-Zehnder interferometer
optical isolator using nonreciprocal phase shift (非対称マッハツェンダー干渉計を用いた非相反移相型光アイソレータの広帯域化)” Technical Report of IEICE, PN2005-66, Jan. (2006).
(in Japanese.)[36] Y. Shoji and T. Mizumoto, “Proposal of polarization-independent optical isolator using TM

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nonreciprocal phase shift and waveguide mode converter (TMモード非相反移相効果と導波路型モード変換器を用いた偏波無依存型光アイソレータの提案)” Technical Report of IEICE,
OPE2006-12, May (2006). (in Japanese.)[37] H. Yokoi, Y. Shoji, and T. Mizumoto, “Optical nonreciprocal devices with Si guiding layer (Si導波層を有する光非相反素子),” Technical Report of IEICE, OPE2003-273, Feb. (2004). (inJapanese.)[38] H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, “Demonstration of interferometric optical isolator
operated in unidirectional external magnetic field (一方向外部磁界で動作する干渉計光アイ
ソレータの動作実証),” Technical Report of IEICE, OCS2004-103, Nov. (2004). (in Japanese.)

Domestic Conferences[39] Y. Shoji, H. Yokoi, and T. Mizumoto, “Selective oxidation of AlInAs foe enhancement ofmagneto-optic effect in optical isolator (AlInAs選択酸化を用いた低屈折率クラッド層の形成
による非相反移相効果の増大),” Extended Abstracts (The 64th Autumn Meeting, 2003); The
Japan Society of Applied Physics, 30a-YH-8, Fukuoka, Japan, Aug. 30 (2003). (in Japanese.)[40] H. Yokoi, Y. Shoji, E. Shin, and T. Mizumoto, “Optical isolator employing nonreciprocal phaseshift operated under unidirectional magnetic field (一方向外部磁界で動作する非相反移相形
光アイソレータ),” Proc. of 2004 IEICE General Conference, C-3-107, Tokyo, Mar. (2004). (inJapanese.)[41] Y. Shoji, H. Yokoi, and T. Mizumoto, “Mach-Zehnder interferometer for an ultracompact opticalisolator with Si waveguides by use of surface activated direct bonding (Si細線導波路を用いた
超小型光アイソレータのためのマッハ･ツェンダー干渉計の製作と表面活性化処理接合の検討),” Proc. of 2005 IEICE Society Conference, CS-8-9, Hokkaido, Sept. (2005). (inJapanese.)[42] Y. Shoji and T. Mizumoto, “Proposal of polarization independent optical isolator employing TM
nonreciprocal phase shift (TMモード非相反移相効果を用いた偏波無依存型光アイソレータの提案),” Extended Abstracts (The 53rd Spring Meeting, 2006); The Japan Society of Applied
Physics and Related Societies, 25p-W-1, Tokyo, Mar. (2006). (in Japanese.)150 Publication list

[43] Y. Shoji and T. Mizumoto, “Wideband operation of Mach-Zehnder interferometric optical isolator
using phase adjustment (位相調整によるマッハツェンダー干渉型光アイソレータの広帯域化),” Extended Abstracts (The 67th Autumn Meeting, 2006); The Japan Society of Applied
Physics, 29a-ZX-4, Shiga, Aug. (2006). (in Japanese.)[44] Y. Shoji and T. Mizumoto, “Demonstration of wideband operation of nonreciprocal phase shift
optical isolator (非相反移相型光アイソレータの広帯域化の動作実証),” Proc. of 2006 IEICE
Society Conference, C-3-85, Ishikawa, Sept. (2006). (in Japanese.)[45] Y. Shoji and T. Mizumoto, “Design of an ultra-wideband optical isolator operating in
1.31–1.55μm band (1.31–1.55μm 帯 で 動 作 す る 超 広 帯 域 型 光 ア イ ソ レ ー タ の 設 計 ),”Extended Abstracts (The 68th Autumn Meeting, 2007); The Japan Society of Applied Physics,
4p-P3-23, Hokkaido, Sept. (2007). (in Japanese.)[46] Y. Shoji and T. Mizumoto, “Ultra-wideband design of nonreciprocal phase shift waveguideisolator (非相反移相型光アイソレータの超広帯域設計),” Proc. of 2007 IEICE Society
Conference, C-3-70, Tottori, Sept. (2007). (in Japanese.)

Patents[47] 水本 哲弥, 庄司 雄哉 “導波路型広帯域光アイソレータ,” 特願 2006-011234 (2006 年 1 月
19 日出願); 国際特許出願番号PCT/JP2006/320521 (2006 年 10 月 10 日出願)
[48] 水本 哲弥, 庄司 雄哉 “偏波無依存光アイソレータ,” 特願 2006-075854 (2006 年 3 月 20 日出願); 国際特許出願番号PCT/JP2007/056114 (2007 年 3 月 16 日出願)