光学微环谐振器同时测量折射率与温度方法
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"Simultaneous measurement of refractive index and temperature using a microring resonator"
本文提出了一种利用微环谐振器同时测量折射率和温度变化的方法，并进行了理论验证。微环谐振器在光学传感器领域具有广泛的应用，因为它们能够以高灵敏度探测物理或化学参数的变化。在该研究中，研究人员特别关注了液芯二氧化硅微环谐振器，这种谐振器的两个不同阶次的 Whispering Gallery 模式（WGMs）不仅对折射率有响应，而且对温度变化也有不同的敏感性。
Whispering Gallery 模式是光在微环谐振器内部沿表面传播时形成的模式，其名称来源于声学中的类似现象，即声音在圆柱体壁面上的低频共振。在这种光学系统中，光可以在微环内多次反射，形成高品质因数（Q因子）的谐振，使得微小的折射率或温度变化能引起显著的光强变化。
为了同时测定折射率和温度，研究者定义了一个二次传感矩阵。这个矩阵基于不同阶次的 WGMs 的响应，可以解耦折射率和温度的影响，从而实现两者的同时精确测量。通过这种方法，理论上可以达到亚ppm级别的折射率检测限（10^-7 RI单位）和毫开尔文级别的温度检测限（10^-3 K）。
微环谐振器的优势在于其紧凑的尺寸、高灵敏度和潜在的集成能力，使其成为监测环境变化、生物医学应用以及光通信等领域中理想的选择。例如，在化学和生物学实验中，它可以用来监测溶液的折射率变化，从而推断出溶质浓度或生物分子的存在。而在温度监测方面，它可能应用于热管理、环境监控或极端条件下的温度测量。
这项工作为同时测量折射率和温度提供了一种创新的解决方案，进一步推动了微环谐振器在精密传感领域的应用。通过优化谐振器设计和提高信号处理技术，未来可能会实现更高级别的性能和更高的测量精度。
COL 10(5), 052802(2012) CHINESE OPTICS LETTERS May 10, 2012
Simultaneous measurement of refractive index and
temperature using a microring resonator
Nai Lin ( GGG), Lan Jiang (ñññ >>>)
∗
, Sumei Wang (rrr), Lei Yuan ( XXX),
and Qianghua Chen (rrruuu)
Laser Micro/Nano Fabrication Laboratory, School of Mechanical Engineering,
Beijing Institute of Technology, Beijing 100081, China
∗
Corresp onding author: jianglan@bit.edu.cn
Received October 11, 2011; accepted December 12, 2011; posted online February 24, 2012
An approach to the simultaneous measurement of refractive-index (RI) and temperature changes using
optical ring resonators is proposed and theoretically demonstrated. With a liquid-core silica ring resonator
as an example, two different-order whispering gallery modes (WGMs) might differ in not only RI but also
temp erature sensitivities. Thus, a second-order sensing matrix should be defined based on these WGMs to
determine RI and temperature changes simultaneously. The analysis shows that the RI and temperature
detection limits can be achieved on the order of 10
−7
RI unit and 10
−3
K at a wavelength of approximately
780 nm.
OCIS codes: 280.4788, 280.6780, 140.4780.
doi: 10.3788/COL201210.052802.
Optical microresonators of various shapes, such as
microdisks
[1]
, microtoroids
[2,3]
, microspheres
[4,5]
, and
microrings
[6−10]
, have been widely studied. In these
resonators, light propagates in the form of whisper-
ing gallery modes (WGMs) because of its total inter-
nal reflection along the curved boundary between high
and low refractive-index (RI) materials. Microresonators
with WGMs are widely used as RI sensors for biolog-
ical material detection
[4,9]
and chemical-concentration-
change measurements
[5−8]
, among others, because of the
high Q factors and, thus, long light-material interaction
paths. However, WGMs are also sensitive to thermal
fluctuations induced by environmental temperature vari-
ations or probe-induced energy absorptions. In partic-
ular, for RI sensors with high Q factors, the resonance
instability due to temperature-induced fluctuations sig-
nificantly impairs sensor performance
[11]
. In such cases,
temperature control devices, such as thermoelectric cool-
ing units, are usually implemented to ensure small tem-
perature fluctuations
[12]
. Another way of reducing reso-
nance thermal drift is the introduction of some materi-
als with negative thermal-optic coefficients in the cavity
mode volume to compensate the positive thermal-optic
coefficient of the ring resonator material
[13−15]
. How-
ever, this method requires precise control of the coat-
ing layer thickness
[13,14]
or resonator size
[15]
. In practice,
achieving such precision, where the thermal drift can be
eliminated, is difficult. Moreover, some nonuniformity
of the coating layer or resonator further increases resid-
ual thermal drift. Meanwhile, the ultrasensitive shift of
the WGM resonance to the ambient temperature can be
used to design highly sensitive thermal sensors
[16−18]
, for
which the bulk RI should be kept unchanged.
This letter theoretically analyzes the use of optical ring
resonators for the simultaneous measurement of RI and
temperature changes. Both the RI and temperature sen-
sitivities of the WGMs in a ring resonator are studied as
a function of the ring wall thickness and WGM order.
The results show that a ring resonator of any wall thick-
ness has two WGMs of different orders with different RI
and temperature sensitivities. By monitoring the reso-
nant wavelength shifts of the WGMs of these two orders,
a second-order sensing matrix can be defined to deter-
mine the RI and temperature changes simultaneously. A
prism coupler
[8]
or a fused-tapered fiber tip
[19]
can be
used to excite WGMs of several different orders selec-
tively and efficiently within the same wavelength range,
providing the basis for the implementation of the pro-
posed approach. The most important contribution of the
proposed scheme is its ability to eliminate the thermal
noise induced by the environment temperature fluctua-
tion or the probe-light-induced cavity temp erature vari-
ation, considering that it detects both temperature and
RI changes.
For a ring resonator, the WGM can be characterized by
a set of integers, namely, m and v, which represent the
angular and radial (also known as the WGM order) mode
numbers, respectively. In addition, the WGM has two
polarizations, namely, the transverse electric (TE) and
magnetic (TM) modes, with the magnetic and electric
fields along the cylinder longitudinal direction, respec-
tively. The two polarizations can be selectively excited
by controlling the polarization of the coupling light, and
the WGM responses to the RI and temperature changes
are slightly varied with the mode polarizations
[20]
. For
simplicity and without losing the generality of the dis-
cussion, this study considers TM modes only. Taking a
ring resonator with inner and outer radii (R
1
and R
2
,
respectively) as an example (shown in the inset of Fig.
1), the characteristic equation for specifying the resonant
wavelength λ
R
of the TM modes can be expressed as
[21]
n
3
n
2
H
0(1)
m
(
−→
k
0
n
3
R
2
)
H
(1)
m
(
−→
k
0
n
3
R
2
)
=
B
m
J
0
m
(
−→
k
0
n
2
R
2
) + H
0(1)
m
(
−→
k
0
n
2
R
2
)
B
m
J
m
(
−→
k
0
n
2
R
2
) + H
(1)
m
(
−→
k
0
n
2
R
2
)
,
(1)
B
m
=
n
2
J
m
(
−→
k
0
n
1
R
1
)H
0(1)
m
(
−→
k
0
n
2
R
1
) − n
1
J
0
m
(
−→
k
0
n
1
R
1
)H
(1)
m
(
−→
k
0
n
2
R
1
)
n
1
J
0
m
(
−→
k
0
n
1
R
1
)J
m
(
−→
k
0
n
2
R
1
) − n
2
J
m
(
−→
k
0
n
1
R
1
)J
0
m
(
−→
k
0
n
2
R
1
)
, (2)
1671-7694/2012/052802(4) 052802-1
c
° 2012 Chinese Optics Letters
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