




版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
第7章
光学微腔:原理集成光电子器件及设计2Outline
1.
Background
2.
Optical
Micro‐cavities:
2.1.
Standing‐wave
type:
F‐P
cavity;
2.2.
Traveling‐wave:
2.2.1.
Microring
resonator;
2.2.2.
Micro‐disk
resonator.
3Standing‐wave
&
Traveling‐wave
The
Fabry–Pérot
Cavity
~
Standing‐wave
λq
2LThe
Microring
Cavity
~
Traveling‐wave42.1.
Standing‐wave:
Fabry–Pérot
CavityL1L2hPG1
G2Charles
Fabry
(1867‐1945)Alfred
Perot(1863‐1925)F‐P
resonator
(1897)567Transmission:Reflection:Transmission
(dBm)8-30-40-10-20
FSR:
~
21
nm;
Q‐value:
~2600;
Extinction
ratio:
13dB;
1.52
1.545
1.57
1.595
1.62
Wavelength
(μm)FSR
could
be
as
large
as
200nm
by
reducing
the
cavity
length
to
about
1μm.
It
is
much
larger
than
the
MRR’s
FSR.
SOI‐nanowire
F‐P
micro‐cavity
0J.
Wang,
D.
Dai,
and
S.
He.
IPRA
conference
2010,
USA.
Bragg
gratingsQ=(6.3±0.8)x101092.2
Traveling‐wave
optical
cavity/?page_id=59silica
microtoroids10Microring
resonators&
micro‐racetrack
resonators⎪
(0)E1'
=
k2
(0
'1)
'E2
(0
'
)exp(−
jφ2
0'1')=
eE1k2
(0
'1)
'k12
(0')=
k12
(0')
+11Model
of
a
single
ring
resonator
with
one
waveguide
General
formula
11′Method
I
2
2′l4′1′l23′(0
(
(2'
('(
(0
(
(2
('⎧E20)
=
k12)E10)
+k1'0)E10)⎨E2'
=
k12')E10)
+k1'0)E10)⎪
(0)⎩('1'
(2'(2'
('1'
(0(('('1'
(2'('('1'
(2'(2
('1'
(0(0((E10)
(0)E20)E10)E20)E10)1−
k20)k1'0)
k1'0)k20)k12')
1−
k20)k1'0)=k1'0)k20)k12')1−
k20)k1'0)=
k12)
+0k0
0
k2′1′
0
αl2'1'2'1'
φ2'1'
=
βl2'1'0βl2'1'
=
mλResonance
wavelgnth⎪
(0)E1'
=
k2
(0
'1)
'E2
(0
'
)E1=
k12
(0)
+k2
(0
'1)
'k12
(0')=
k12
(0')
+=⎜
⎜∏k1'2'
⎟
⎟γ
tol
exp(−
jΦtol)=
E
⎜
⎜k1'2
∏k1'2'
⎟
⎟γ
n
exp(−
jΦn)⎝⎠(0
(
(2'
('(
(0
(
(2
('⎧E20)
=
k12)E10)
+k1'0)E10)⎨E2'
=
k12')E10)
+k1'0)E10)⎪
(0)⎩('1'
(2'(2'
('1'
(0(('('1'
(2'('('1'
(2'(2
('1'
(0((E20)E10)E10)
(0)E20)E10)=
k1'0)k20)k12')
1−k20)k1'0)1−k20)k1'0)
k1'0)k20)k12')
1−k20)k1'0)1′2′2′#N
1′1′
#1
1′
1
#0#n
2′
2
The
resonator’s
response
Ring
resonator
with
N
output
ports.
Through
port
2
1
Input
port
1
2output
port
#1
output
port
#N
2′
2
1output
port
#n
(0)2'1'k⎛
N
(n)⎞⎝
n=1
⎠Daoxin
Dai
and
Sailing
He.
Proposal
of
a
coupled‐microring‐based
wavelength‐selective
1×N
122'
(n)2E(0)⎛
(n)
n−1
(m)⎞
m=1=
k
=
−
jkk13121′2′#01′12′2#1121′2′#N1′21#n
2′Input
portThrough
portoutput
port
#1output
port
#noutput
port
#N(
(('1'
(0
(0
(2'
(2
(0
1
1′l4′1′
The
critical
coupling
condition
2No
power
outputs
from
the
thru
port,
i.e.,
2′
E20)
/
E10)
=
0
l23′
k20)
=
k12)
/[k12)k1'0)
−
k1'0)k12')]k2′1′(0
(2'(1)
For
coupler
#0,
one
has
(0)
(0)
1'2
12'('1'k20)
=
1−k
2
k12)
=
k1'0)
=
1−k
2Finally
the
critical
coupling
condition
becomes14
Special
case
I:
all
passed
filter
(n=1)
The
critical
coupling
condition
becomes0
(0)2'1'0kαl2'1'exp(−
jφ2'1')=
e
1
1′l4′1′
2
2′l23′k2′1′and2
(0)2'1'k=
1−kα<0α>0
λPowerFSR=⎜
⎜∏k1'2'
⎟
⎟γ
tol
exp(−
jΦtol)E1=
k12
+=
E
⎜
⎜k1'2
∏k1'2'
⎟
⎟γ
n
exp(−
jΦn)⎝⎠15Special
case
II:
add‐drop
filter
(n=2)
(0)2'1'k⎛
N
(n)⎞⎝
n=1
⎠2'E('1'
(2'(2
('1'
(0(0)(E20)
(0)k1'0)k20)k12')1−k20)k1'0)(0)⎛
(n)
n−1
(m)⎞
m=1
1
1′
l4′1′
(n)2
2
2′
l23′k2′1′16The
resonator’s
response
Key
features:
FSR
(free
spectral
response).
3dB‐bandwidth,
Q
factor
=
λ/BW3dB.
Resonance
wavelengths.
17Model
of
a
single
ring
resonator
with
one
waveguide
Method
IIα
is
the
loss
coefficient
of
the
ring
(zero
loss:
α
=
1).
θ
=
ωL/c,
L
=
2πr,
c
=
c0/neff,
ω
=
kc0,
k
=
2π/λThe
transmission
power
Pt1
in
the
output
waveguide,The
circulating
power
Pi2
in
the
ring
is
given
bywhere
t
=
|t|
exp
(jϕt),
|t|
representing
the
coupling
losses
and
ϕtthe
phase
of
the
coupler.On
resonance,
(θ+ϕt)
=
2πm,
where
m
is
an
integer
critical
coupling:
α=|t|
1819The
spectral
response
of
an
all‐passed
filter20Model
of
a
basic
add–drop
single
ring
resonator
filterAt
resonance:Critical
coupling:21Spectral
response
of
an
add–drop
ring
resonator
filter22Some
important
parameters
FSR
(free
spectral
range):
neffL=mλn’effL=(m‐1)λ’
(neff+
Δλ
(∂neff/
∂
λ))L=(m‐1)(λ+Δλ)
ΔλFSR=
λ/[m
(ng/neff)]
Group
index233dB
bandwidth
(full‐width
at
half‐maximum)
|Et2|2=0.5Pt2_resonance_When
α=1,
t1=t2
(symmetrical),
one
has
Finess
Q
valueThe
intensity
enhancement
or
buildup
factor
B:
On‐resonanceLossless,
κ1=κ2
B=Qλ/(πneffL)
2425An
example
to
show
the
field
enhancement
in
the
resonator:B
~
105
Q
~1×108,
D
~
50μm,
Vm~
600
μm3Pin
=
1
mWExperimental
data1
mWPcav~
100
W,
Icav
~
2.5
GW/cm2,τ
~
100
ns,
#
of
round
trip
~
2×105.
>
100
W26Serially
Coupled
Double
Ring
Resonatorwhere
α1,2
represent
the
half
round
trip
loss
coefficients
of
ring
resonator
one
and
two
respectively.27Assuming
a
coupler
without
losses
and
symmetric
coupling
behavior,
setting
t
=
t∗
andκ=−κ∗,
one
hasIn
order
to
achieve
a
double
ring
resonator
filter
with
maximally
flat
response
for
the
drop
port,
one
should
make
28An
exampleR1=R2=5.08um,
n1=3.45,
n2=1.456,
k1=0.18,
k2=0.01~0.09.
k1=0.18,
k2=0.0164729Parallel
Coupled
Double
Ring
ResonatorSimplifiedRegular
model:30Finally31Parallel
Coupled
Double
Ring
Resonator
with
Coupling
Between
the
Two
Ring
ResonatorsThe
distance
Λ
between
the
rings
does
not
have
an
influence
on
the
transfer
characteristic.For
lossless
couplers
with
κ1=κ3=
κ:Chremmos
and
Uzunoglu.
PTL.
17(10):
2110‐2112
,
200532In
order
to
realize
a
maximally
flat
response
with
a
single
peak,
the
coupling
coefficients
have
to
obey
the
following
equation:The
corresponding
FWHM
is
given
by33Modeling
cascaded‐ring
resonators:
Method
IIIwhere34Numerical
simulation
for
microring
resonators:
FDTD
methodFDTD
simulation/en/fdtd/user_guide_cw_norm_ring.html/rsoft/application‐galle
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 制造业智能化转型的数字化双胞胎解决方案探讨
- 2025年针入度仪项目市场调查研究报告
- 2025年采样阀项目市场调查研究报告
- 基于数据驱动的商业决策分析数字孪生技术的应用研究
- 2025年过锡炉胶带项目市场调查研究报告
- 2025年电解铜产品项目市场调查研究报告
- 多学科协同工作以数智平台促进肿瘤诊疗模式的创新变革
- 2025年拉拔自润滑剂项目市场调查研究报告
- 教育APP的体验优化实践与案例分析
- 掌握Excel成就职场精英
- 低龄儿童龋的临床管理专家共识
- 2023年生药学应考试题库有答案
- 公共机构节能量保证型、能用费用托管型合同能源管理项目合同文本模板示例
- 普鲁士蓝类正极材料未来可期
- 智能吓数纸培训手册
- 未带有效居民身份证考生承诺书
- 原子分光光度法测定水中重金属镉的含量
- 学生实习安全及突发事件应急预案
- 新教材高一必修下册《游园》教案
- DIN1783厚度在0.35mm以上冷轧的铝及铝塑性合金带材和板材、尺寸
- 低风险FOF产品方案设计目标最大回撤3%以内的投资策略
评论
0/150
提交评论