Investigation of temperature sensing characteristics in selectively infiltrated photonic crystal fiber

Zhilin Xu; Junlong Lim; Dora Juan Juan Hu; Qizhen Sun; Rebecca Yen-Ni Wong; Kun Li; Meng Jiang; Perry Ping Shum

doi:10.1364/OE.24.001699

1. Introduction

Due to the flexibly tailorable air holes along the entire fiber length, photonic crystal fibers (PCFs) have attracted great interest from the fields of super-continuum generation source [1], spectral filtering [2], non-linear optics [3], optical sensing [4–13] and so on. Particularly, filling air holes of PCFs with high refractive index (RI) liquid has been demonstrated to be an effective way to form sensors. Owing to their proximity to the optical core, these liquid-filled channels have good overlap with the silica core modes of PCF, which is favorable to sensitively detecting the variation of ambient environment [4]. Among all of the liquid-infiltration patterns, selectively infiltrating only one air hole is a well accessible manner to achieve ultra-high sensitivity [6–9]. In this case, the liquid-infiltrated PCF functions as a directional coupler where light coupling from the silica core mode to the liquid core mode. For illustration, Darran K. C. Wu et al. proposed a microfluidic RI sensor based on a directional coupler architecture using PCF and achieved RI sensitivity as high as 30100nm/RIU [6]. Ying Wang et al. reported a temperature sensor with sensitivity of 54.3nm/°C by selectively filling liquid with RI of 1.46 into one of the air holes [7]. Besides, our previous works [8, 9] also adopted liquid crystal filled PCFs to form compact and temperature-sensitive directional couplers. In these structures, it is obvious that the distance between the silica core and the liquid core of the infiltrated PCF will affect the performance of the artificial directional PCF coupler and sensor. However, hardly any prior research has systematically studied the above issue, to the best of our knowledge.

In this paper, we theoretically and experimentally explore the impacts of separation between the silica core and the glycerin core of a selectively glycerin-infiltrated PCF on the mode characteristics and the temperature sensitivity. The investigation is conducted by comparing the simulation and experiment results of three single-void glycerin-infiltrated PCFs, with the glycerin core being one period, two periods and three periods away from the silica core, respectively. By using the finite element method, mode characteristics and temperature responses of the three glycerin-infiltrated PCFs are simulated and analyzed in detail. Moreover, the experimental results show good agreement with the simulation data.

2. Principle and simulation

The infiltrated PCF is formed by selectively filling glycerin into single void of a PCF. The glycerin is employed in this work because of its properties of easy accessibility, high RI, and high thermo-optic coefficient (TOC). The RI profiles of PCFs with non-infiltrated, the 1st void infiltrated, the 2nd void infiltrated and the 3rd void infiltrated are given in Figs. 1(a)-1(d) respectively. Due to the multi-mode nature of the infiltrated PCF, silica core modes and glycerin core modes are concurrently propagated and interfered, resulting in interference pattern with the intensity expressed as:

I = \sum_{p, q = 1}^{N} A_{p q} [I_{p} + I_{q} + 2 \sqrt{I_{p} I_{q}} \cos (\frac{2 π Δ n_{e f f}^{p, q} L}{λ})]

where

N

is the maximum mode number that is supported in the infiltrated PCF.

λ

and

L

denote the operating wavelength and the physical length of the infiltrated PCF respectively.

Δ n_{e f f}^{p, q} = n_{e f f}^{p} - n_{e f f}^{q}

is the effective index difference between the p-th mode (

n_{e f f}^{p}

) and the q-th mode (

n_{e f f}^{q}

).

I_{p}

and

I_{q}

are the intensities of p-th and q-th modes.

A_{p q}

is the intensity weighting of interference between p-th and q-th modes among the whole interference procedure. According to Eq. (1), the transmission spectrum of the infiltrated PCF results from superposition of many modal interference spectrum components. Among all of the interference components, the one with highest intensity dominates the interference spectrum [14–16]. For interference between p-th mode and q-th mode, the resonant wavelength can be described as:

λ_{d i p} = \frac{2 Δ n_{e f f}^{p, q} L}{2 m + 1}

λ_{p e a k} = \frac{Δ n_{e f f}^{p, q} L}{m}

where m is a positive integer representing the interferential order. When ambient temperature of the infiltrated PCF is changed by

Δ T

, due to thermo-optic effect of glycerin and silica, the modes indices will be correspondingly varied by different degrees, enabling the interference spectrum to shift as:

Δ λ_{d i p} = \frac{λ_{d i p}}{Δ n_{e f f}^{p, q}} \cdot \frac{\partial Δ n_{e f f}^{p, q}}{\partial T} \cdot Δ T

Δ λ_{p e a k} = \frac{λ_{p e a k}}{Δ n_{e f f}^{p, q}} \cdot \frac{\partial Δ n_{e f f}^{p, q}}{\partial T} \cdot Δ T

where

\partial Δ n_{e f f}^{p, q} / \partial T

is the variation of the effective index difference induced by the temperature change, which is determined by fiber structure. It should be noted that the thermo-expansion coefficient is usually too small to be considered. The above equation indicates that the temperature sensitivity of interference between p-th mode and q-th mode can be derived by calculating

\partial Δ n_{e f f}^{p, q} / \partial T

.

Fig. 1 The RI profiles of (a) an unfilled PCF, and (b)-(d) PCFs with 1st void, 2nd void and 3rd void infiltrated, respectively.

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According to our previous analysis [8], the liquid core and the silica core in an infiltrated PCF can be taken as two parallelly coupled waveguides, with the coupling coefficient $k_{c}$ being dependent on their distance [17]:

\begin{array}{l} k_{c} = \frac{ω ε_{0}}{2} \int_{0}^{2 π} \int_{0}^{a} (n_{1}^{2} - n_{2}^{2}) C \frac{J_{0} (U)}{K_{0} (W)} J_{0} (\frac{U}{a} r) K_{0} (\frac{W}{a} R) r d r d θ \\ C = \frac{W^{2} \sqrt{μ_{0} / ε_{0}}}{π n_{1} a^{2} V^{2} J_{1}^{2} (U)} \\ R = {(D^{2} + r^{2} - 2 D r \cos θ)}^{1 / 2} \end{array}

where

μ_{0}

,

ε_{0}

,

n_{1}

,

n_{2}

,

a

,

D

are the magnetic permittivity, dielectric constant, RI of silica core, RI of effective cladding, radius of PCF silica core, and distance between the silica core and the liquid core, respectively.

ω = 2 π c / λ_{0}

is the angular frequency of the electromagnetic field, where the

λ_{0}

is the operation wavelength.

J

and

K

represent the Bessel function and modified Bessel function.

U

,

W

and

V

are the normalized transverse wave numbers and normalized frequency of silica core and can be expressed as:

\begin{array}{l} U = a \sqrt{k_{0}^{2} n_{1}^{2} - β^{2}} \\ W = a \sqrt{β^{2} - k_{0}^{2} n_{2}^{2}} \\ V = \sqrt{U^{2} + W^{2}} = k_{0}^{2} a \sqrt{n_{1}^{2} - n_{2}^{2}} \end{array}

where

β

and

k_{0}

are the propagation constant and wave number in the silica core of PCF. Equations (4) and (5) indicate that, when the PCF and the liquid are chosen, the coupling coefficient

k_{c}

is inversely related to the distance between the silica core and the glycerin core

D

. That is to say, the intensities of glycerin core modes will be decreased as the distance between the silica core and glycerin core gets larger.

To have a deeper insight into the infiltrated PCF, we use finite element method (FemSim, Rsoft) to analyze its modes properties, as well as the temperature response. The PCF used in this work is commercially available large area mode PCF (LMA-25, NKT Photonics) with air hole diameter of 8.4µm, pitch of 16.35 µm and outer diameter of 268 µm, as shown in Fig. 1(a). The RI and TOC of silica ( $ξ_{g}$ ) are 1.4446 (at 19 °C) and $ξ_{s} = 8.5 \times 10^{- 6} R I U / ° C$ , while the RI and TOC of glycerin ( $ξ_{s}$ ) are 1.4746 (at 19 °C) and $ξ_{g} = - 2.3 \times 10^{- 4} R I U / ° C$ [18].

At first, we calculate the modes indices in three infiltrated PCFs displayed in Figs. 1(b)-1(d) at temperatures 37°C and 38°C, respectively. By comparing the simulation results of different infiltrated PCFs, we find that the modes indices in the infiltrated PCF are independent of the position of glycerin core. That is to say, three PCFs with 1st void, 2nd void and 3rd void infiltrated have the same modes composition and indices, as described all in Figs. 2(a) and 2(b). Moreover, in the infiltrated PCFs, the silica core can support 3 modes including LP₀₁ mode (1st mode) and two degenerated LP₁₁ modes (2nd mode), while the glycerin core supports 6 modes including LP₀₂ mode (3rd mode), two degenerated LP₂₁ modes (4th mode), two degenerated LP₁₁ modes (5th mode) and LP₀₁ mode (6th mode). The six order modes in the infiltrated PCF are able to interfere with each other, forming 15 interference components. From Figs. 2(a) and 2(b), it is obvious that the increasing temperature will reduce the effective index difference between the p-th and q-th mode, hence making the interference spectrum blue-shift. In particular, by substituting the calculated $δ Δ n_{e f f}^{p, q}$ into Eq. (3), the theoretical temperature sensitivity of arbitrary modes interference can be obtained. For example, the sensitivities resulting from the interferences between 1st mode and 2nd mode, 3rd mode and 4th mode, 2nd mode and 3rd mode of the infiltrated PCF are calculated to be $- 1.65 n m / ° C$ , $- 30.05 n m / ° C$ , $- 76.15 n m / ° C$ respectively. Then the final temperature sensitivity of the infiltrated PCF should be the weightings of sensitivities of all the interference components.

Fig. 2 The calculated modes indices in three glycerin-infiltrated PCFs at temperature of (a) 37°C and (b) 38°C, where the index differences between adjacent modes at 1585nm are also shown. Only one group of results are shown because three glycerin-infiltrated PCFs have the same modes composition and indices. (c) The profiles of fundamental modes in the silica cores of the 1st, 2nd and 3rd void infiltrated PCFs, which suggest the differences of the electromagnetic filed strength between the silica core and the glycerin core.

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Although the infiltrating position does not affect the modes composition and indices, it can greatly influence the modes intensities. The profiles of fundamental modes in the silica cores of the 1st, 2nd and 3rd void infiltrated PCFs are illustrated in Fig. 2(c). It can be seen that from 1st void infiltrated PCF to 3rd void infiltrated PCF, less and less energy is coupled from silica core to the glycerin core. This further indicates that the larger distance between the silica core and the glycerin core will decrease their coupling strength, and thus lower the intensities of glycerin core modes, aligning with the above theoretical analysis. Consequently, the role of glycerin core modes on the interference procedure is reduced. Since $ξ_{g}$ is much higher than $ξ_{s}$ , lower weightings of glycerin core modes will decrease temperature sensitivity. Therefore, in order to achieve higher temperature sensitivity, the separation between the silica core and the glycerin core should be as small as possible.

3. Sample fabrication and experimental setup

The following method is used to selectively fill single void of PCF with pure glycerin. Firstly, a clean PCF is cleaved and the flat end is focused under a microscope. Secondly, a single mode fiber (SMF) taper dipping tiny droplets of UV glue (NOA81, Thorlabs Inc.) is placed under the microscope as well and moved to the top of the flat end of PCF. Then, the slowly declined SMF fiber taper quickly transfers the UV glue onto the air holes to block them, but avoiding the selected single air hole. After that, the blocked air holes are cured via exposure to UV light (Xenon RC-250B) for 45 seconds. Then, the cured end of the PCF is immersed into pure glycerin to infiltrate the single unblocked air hole through capillary force. Finally, after observing the other side of the infiltrated PCF under microscope to confirm that the entire unblocked air hole is filled with pure glycerin, the sensing PCF sample is completed.

For experimental demonstration, three sensing samples with glycerin infiltrated single-voids being one period, two periods and three periods away from the silica core of PCF are carefully prepared by the method elaborated above. The microscope images of fabricated samples are presented in Fig. 3(a), where the white circular spots in three samples show the infiltrated glycerin cores and the black circular spots show the un-infiltrated air holes. This indicates that the liquid-filled length is the same with the length of PCF sample. The lengths of PCFs in samples 1-3 are 8.7cm, 9.5cm and 10.5cm, respectively. The lengths of PCFs are not intentionally controlled to be identical in the experiment, because temperature sensitivity can be set to be irrelevant with the length of sensing PCF, by controlling the wavelength of indicating peaks/dips i.e. $λ_{p e a k}$ or $λ_{d i p}$ to be the same according to Eq. (3).

Fig. 3 (a) Three infiltrated PCF samples: for sample 1, 2 and 3, the glycerin infiltrated voids are 1 period, 2 periods and 3 periods away from the silica core, respectively; (b) The experimental setup for temperature sensing, BBS: broadband source, OSA: optical spectrum analyzer.

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The experimental setup displayed in Fig. 3(b) is built to investigate the mode characteristic and the temperature response of three infiltrated PCF samples one by one. For each sample, both sides of the PCF are cleaved and spliced to SMFs using a fusion arc splicer with customer settings. There are a few points that need to be noticed to get good splice for the glycerin-filled PCF to SMF [9]: (1) PCF should have a good cleaved facet. (2) In order to prevent bubble formation from airgap/glycerin in the voids and to minimize the damage of glycerin near the splice position due to heat, we shift the SMF-PCF splice joint from the center with 80μm offset to reduce the heat received at the PCF side. (3) Because of the huge outer diameter difference between PCF and SMF, a fully collapsed region is necessary to form a mechanically strong splice between two fibers. Therefore, we re-arc a few times to ensure that the air holes are completely collapsed at the PCF side near the splice interface. Nevertheless, the glycerin-filled channel is not collapsed. If the aforementioned considerations are addressed appropriately, we are able to fabricate the splice between SMF and glycerin-filled PCF, and avoid the bubble during splicing process. Then the SMF ends are connected to an amplified spontaneous emission broadband source (BBS, 1530–1600 nm) and optical spectrum analyze, respectively. For temperature sensing demonstration, the infiltrated PCF samples are placed in an oven with temperature controlling from 37°C to 39°C and accuracy of 0.1°C. The relatively small temperature range is chosen considering that this work is focused on comparing the temperature sensitives of the three infiltrated PCFs. Indeed, the dynamic range may be limited by the complex mode distribution. But by tracking $λ_{p e a k}$ or $λ_{d i p}$ in real time through the fringe-tracking method [19, 20], the highest temperature can theoretically be 177°C considering the point of flammability of the glycerin.

4. Result and discussion

To investigate the effect of distance between the silica core and the glycerin core on the mode characteristics, the transmission spectra of sample 1, sample 2 and sample3 at the same temperature 38.0°C are compared, as shown in Fig. 4(a). It is observed that as distance increases, the transmission loss decreases from 30dB to 12dB, which mainly derives from the unmatched RIs between SMF and the infiltrated PCFs, as well as propagation loss incurred in the glycerin core guided modes. The lowest transmission loss occurs in sample 3 due to minimal power transferred to the glycerin core. Besides, the visibilities of three infiltrated PCFs samples are 4.5dB, 11dB and 3dB respectively. This irregular visibility of three samples may be attributed to the irregular exciting of modes in three infiltrated PCFs, which is related to the splicing process between the PCF and the SMF. Since when the two interference modes have the equal intensity, the coefficient of finesse of interference and visibility of interference will be the best. Therefore, to get higher visibility, we can offset the SMF core between the silica core and liquid core of the infiltrated PCF to excite the silica core modes and glycerin core modes equally. Additionally, the envelope of interference spectrum gets clearer as the distance increases. The reason is that the increased distance between the silica core and the glycerin core reduces the intensities of glycerin core modes according to the theoretical analysis, which is equivalent to reduce the number of modes participating in the interference procedure, and then result in clearer interference envelope.

Fig. 4 Comparison of (a) transmission spectra and (b) frequency spectra of samples 1-3 at 38°C.

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For better analyzing the variations of propagating modes contributing to the interference procedure, the transmission spectra in Fig. 4(a) are fast Fourier transformed (FFT) into frequency spectra presented in Fig. 4(b). The frequency spectra of both sample 1 and sample 2 have three main peaks located around spatial frequencies of 0.033nm⁻¹, 0.0707nm⁻¹ and 0.14nm⁻¹, corresponding to the effective indices difference of interfering modes being $9.53 \times 10^{- 4}$ , $2.04 \times 10^{- 3}$ , $4.04 \times 10^{- 3}$ at wavelength of 1585nm. The locations of three peaks in three frequency spectra are slightly different due to different lengths of three sensing PCFs. Note that the three peaks in frequency spectrum of sample 2 are much stronger than that of the samples 1 and 3. The reason may be that the intensities of modes in sample 2 are distributed more evenly than in the other two samples. Corresponding to the theoretical calculation, the peaks in the frequency spectra are the interfering results between 1st mode and 2nd mode, 3rd mode and 4th mode, 2nd mode and 3rd mode of the infiltrated PCF, respectively. Moreover, from sample 1 to sample 3, the intensity of the third frequency peaks get smaller, further demonstrating that as the glycerin core far away from the silica core, the weighting of the glycerin core modes will decrease.

Then, the temperature responses of sample 1, sample 2 and sample 3 are investigated. Transmission spectra of sample 1, 2, and 3 varying as the increasing temperature are presented in Figs. 5(a)-5(c) respectively. The ambient temperatures of sample 1 and sample 2 are changed from 37.5°C to 38.4°C, while temperature of sample 3 ranges from 37.0°C to 38.9°C. It is observed that as the temperature increasing, the shapes of spectra keep unchanged, suggesting that the interference conditions hardly change in the measuring process. The dips or peaks around 1585nm are chosen to monitor the dependences of wavelengths on the temperature, as labeled in Figs. 5(a)-5(c). The detailed views of labeled areas are presented in Figs. 5(d)-5(f) which exhibit that the spectra shift to short wavelengths as temperature increasing, aligning the theory analysis.

Fig. 5 The spectra of (a) sample 1, (b) sample 2 and (c) sample 3 vary as the temperature; (d)-(f) the local views of positions labeled in (a)-(c) respectively.

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The dependences of wavelength shifts of sample 1, sample 2, and sample 3 on the temperature are presented in Fig. 6. Within the measurement range, the temperature responses of three samples are linear. The temperature sensitivities of sample 1, sample 2 and sample 3 are as high as −3.06nm/°C, −2.12nm/°C and −0.11nm/°C respectively, which indicates that the infiltrated PCF has the great potential for highly sensitive temperature measurement. However, the experimental sensitivities of three samples are smaller than the theoretical values. The reason may be that in the experiment, the pure glycerin is diluted by the water vapor in the air. Since the thermo-optical coefficient of water is only $- 9.5 \times 10^{- 5} R I U / ° C$ [21], much lower than that of glycerin, the experimental sensitivities are thus smaller than the theoretical values. Figure 6 also verifies that the temperature sensitivity is inversely proportional to the distance between the silica core and the glycerin core. Consequently, when designing the liquid-infiltrated PCF for sensing applications, the temperature sensitivity can be tuned by changing the liquid-infiltrating position in accordance with the practical requirements. Particularly, to obtain higher temperature sensitivity, the void nearest to the silica core of the PCF should be intentionally infiltrated.

Fig. 6 The dependences of wavelengths of samples 1-3 on the temperature.

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5. Conclusion

In conclusion, the influences of distance between the silica core and the glycerin core of a selectively glycerin-infiltrated PCF on the mode characteristics and the temperature sensitivity are deeply investigated. All the theoretical analysis, simulation calculation and experimental results reveal that for the single void glycerin-infiltrated PCF, the smaller distance between the silica core and the glycerin core does not affect the mode indices, but increases intensities of modes in the glycerin core and hence increases the temperature sensitivity. Moreover, the temperature testing results indicate that the infiltrated PCF is highly temperature-sensitive. The temperature sensitivities of three infiltrated PCFs with the glycerin core being one period, two periods and three periods away from the silica core are −3.06nm/°C, −2.12nm/°C and −0.11nm/°C, respectively. This work is expected to provide insights into designing and optimizing liquid-infiltrated PCF for sensing applications.

Acknowledgments

This work is supported in part by the Agency for Science, Technology and Research (A*STAR), Singapore, and in part by the Postgraduate Internship from Nanyang Technological University, Singapore. Zhilin Xu acknowledges funding from the sub-Project of the Major Program of the National Natural Science Foundation of China (No. 61290315), the National Natural Science Foundation of China (No. 61275004), the Natural Science Foundation of Hubei Province for Distinguished Young Scholars (No. 2014CFA036), the Innovation Foundation of Graduate Innovation and Entrepreneurship Base of Huazhong University of Science and Technology (No. 2015650011).

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Investigation of temperature sensing characteristics in selectively infiltrated photonic crystal fiber

Abstract

1. Introduction

2. Principle and simulation

3. Sample fabrication and experimental setup

4. Result and discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (7)

Optics Express