Design and modeling of a photonic crystal fiber gas sensor
Summary (3 min read)
1. Introduction
- Photonic crystal fiber PCF or holey fiber that incorporates air holes within the silica cladding region opens new opportunities for exploiting the interaction of light with gases through the evanescent field in the holes.
- The sensitivity was, however, very low owing to the 0.2% mode power exposed to the sensing region.
- Monro et al.1 examined the use of a particular PCF for gas detection and theoretically predicted that by choosing appropriately the PCF parameters, high-sensitivity gas detection can be achieved without significantly compromising the mechanical properties of the optical fiber.
- A proof of concept demonstration of a PCF gas sensor was recently reported by the authors.
2. Relative Sensitivity of the Gas Sensor of the Photonic Crystal Fiber
- The authors consider here the index-guided PCF Refs.
- The effective index ne and the mode-field pattern Ex, Ey and Hx, Hy can be calculated by solving Maxwell’s equations by using a numerical technique the finiteelement method .7,8.
- The basis for doing so is that, for both types of fiber, most of the guided power, especially for the fundamental mode the authors are interested in here, is distributed within the central silica core and the innermost ring, and the light power in the outer rings is negligible.
- The authors also calculated the relative sensitivity of a modified fiber with the same structure as the Lucent fiber but with varying hole diameter and separation.
3. Response Time of the Sensor of the Photonic Crystal Fibers
- One concern in using PCF as evanescent field sensors may be the limited response time due to the time required for gas to diffuse into the holes.
- (6) It can be seen from Eq. 6 that the average gas concentration in the hole columns depends on interaction length l.
- If the Knudsen number is larger than one, the diffusion will be dominated by the wall effect.
- The authors may estimate the diffusion time under the worst plan by replacing DAB K in Eq. 7 with DBB K.
4. Experiments and Results
- Experiments were conducted to investigate the relative sensitivity and the diffusion dynamics of Crystal Fiber’s PCF for acetylene measurement.
- The other end of the PCF was spliced to a single-mode fiber connected to a photodetector.
- The chamber was then sealed after 30 s of loading of acetylene.
- The relativity sensitivity r was estimated by using the steady-state t 3 in Eq. 10 value of the normalized minimum transmittance as shown in Fig.
5. Sensor Design, Power Budget Analysis, and Performance Evaluation
- From the analysis in Section 4 the authors conclude that the response time of PCF is limited by the time taken for acetylene gas to diffuse into the holes.
- For a gassensing application that requires a response time of 1 min the length of the sensing PCF should be limited to less than 7 cm.
- This design allows for a long sensing fiber to be used to improve the sensitivity without comprising response time.
- Figure 9a shows an example of a sensor design based on Crystal Fiber’s 1.7- mdiameter silica core PCF where the sensing PCF with periodic openings is connected to single-mode transmission fibers at the two ends.
- A 1.53- m distributed feedback laser is used as the source and an InGaAs photodetector as the receiver.
A. Loss Introduced from the Opening
- The openings in the PCF modify the waveguide structure and thus change the transversal field distribution in the fiber cross section.
- The 2 ne ne c ne ne c in Eq. 11 is the Fresnel coefficient, and the second term is the overlap integral between the fundamental modes of the respective PCF sections.
- Results show that the difference in the effective indexes with and without an opening is very small, and the first term is approximately equal to 1.
B. Lengths of the Open Sections
- The lengths of the opened sections l* as shown in Fig. 9b should be long enough to ensure that time required for acetylene gas diffusion into the holes is not dominated by the wall effect of the open sections.
- Assuming that Kn 0.01, the length of the open section should be longer than 6.5 m.
- Because the depth of the open fiber section is less than the radius of the original PCF 65 m , the time required for the acetylene to diffuse into the open air holes is estimated to be less than 0.001 s.
- As mentioned in this subsection the variation in the mode-field distribution due to the opening is small.
- The loss coefficient in the open section is then expected to be similar to that of the unopen fiber sections.
C. Power Budget and Performance Analysis
- Considering as an example the sensor system shown in Fig. 9 with a required response time of 1 min, the fiber length between the two open windows can be chosen as l 7 cm.
- Consider that the detection resolution of 3.75 parts per million for an equivalent of 1 m ppm m of acetylene has been achieved with wavelength modulation spectroscopy and digital signal processing.
6. Summary
- The authors have proposed an all-fiber gas sensor based on periodically windowed PCF fiber.
- Preliminary experiments and simulation show that an acetylene sensor system with a response time of 1 min and sensitivity of better than 6 ppm can be realized.
- The PCF sensor can also be used to detect other gases such as methane with a similar expected performance.
- The response time may be tailored with a certain range by selecting the distance between the two windowed sections.
- These include the low-loss connection between the single-mode transmission fibers and the PCF sensing fiber, fabrication of the window openings along the PCF, and packaging of the open section with gas permeable films that allow gas to diffuse in or out but prevent dirt to enter the open sections.
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Frequently Asked Questions (18)
Q2. What is the effect of the wall on the PCF?
Because the size of the holes in the PCF is small, the wall effect between the molecules and the wall of the hole column may also need to be taken into account.
Q3. How much blow rate was used to blow the acetylene gas into the chamber?
Acetylene gas with a concentration approaching C0 100% was blown into the chamber along a direction orthogonal to the PCF with a blow rate of 100 cm3 s.
Q4. What is the knudsen number for the wall effect?
The Knudsen number Kn m d is usually used to represent the wall effect of a capillary diffusion system,11 where m is the mean free path of the gas molecules and d is the diameter of the capillary tube the hole diameter here .
Q5. What is the spatial coordinate of the acetylene distribution along the length of the air?
At time t the distribution of acetylene concentration along the length of the air hole columns may be written as9C x, t C0(1 4 j 1,3,5 1 j sin j x l exp j l 2Dt ), (4)where D is the binary diffusion coefficient between the air and acetylene and can be found in the reference book10 and x is the spatial coordinate along the longitudinal direction of the PCF.
Q6. What is the effect of the openings in the PCF?
The openings in the PCF modify the waveguide structure and thus change the transversal field distribution in the fiber cross section.
Q7. What is the cross-sectional area of the outlet valve?
The cross-sectional area of the outlet valve is 2 cm2 and is 4 times bigger than that of inlet in order to prevent additional pressure that may affect the diffusion process when the C2H2 was loaded into the chamber.
Q8. How long should the sensing fiber be?
For a gassensing application that requires a response time of 1 min the length of the sensing PCF should be limited to less than 7 cm.
Q9. How many ppm of acetylene can be detected?
Preliminary experiments and simulation show that an acetylene sensor system with a response time of 1 min and sensitivity of better than 6 ppm can be realized.
Q10. How long does it take for the CA to reach 90% C0?
If the authors take the time for CA t to reach 90% C0 as the response time of the fiber, the response times for 3-, 5-, and 7-cm lengths of fiber with both ends open for diffusion are found to be 11.7, 32.5, and 62.7 s, respectively.
Q11. What is the evanescent field of power in the air holes?
4 and 5 where most of the guided light power is confined within the solid-core region with a fraction evanescent field of power extended into the holey region.
Q12. How many ppm of acetylene is detected?
Consider that the detection resolution of 3.75 parts per million for an equivalent of 1 m ppm m of acetylene has been achieved with wavelength modulation spectroscopy and digital signal processing.
Q13. What is the diffusion coefficient of B acetylene in the continuum state?
The corrected binary diffusion coefficient DABC of B acetylene in A air may be shown as12DAB C DABDBB K DAB DABK , (7)where DAB is the diffusion coefficient of air and acetylene in the continuum state, DABK is the combined Knudsen diffusion coefficient and can be written as12DAB K DAAKXB DBBKXA, (8)where XA and XB are the molar fractions of species A and B and DAA K and DBB K are the Knudsen diffusion coefficients of species A and B, which may be written as12D K 1 3 dV , (9)where V is the average molecular speed of species A or B .
Q14. What is the way to achieve a higher sensitivity with a reasonable response time?
To achieve a higher sensitivity with a reasonable response time, the authors propose introducing periodic openings along the sensing fiber.
Q15. What is the diffusion coefficient of acetylene in the continuum state?
The diffusion coefficient of acetylene in air in the continuum state is 0.17774 cm2 s 1,10 and the corrected diffusion coefficient in the innermost air-hole column Fig. 1b is 0.163 cm2 s 1 8.3% decreasing .
Q16. What is the effect of the openings on the response time of the PCF?
From the analysis in Section 4 the authors conclude that the response time of PCF is limited by the time taken for acetylene gas to diffuse into the holes.
Q17. What is the sensitivity of a sensing PCF?
Figure 9a shows an example of a sensor design based on Crystal Fiber’s 1.7- mdiameter silica core PCF where the sensing PCF with periodic openings is connected to single-mode transmission fibers at the two ends.
Q18. What is the relative sensitivity of the Lucent PCF?
The relative sensitivity of Lucent’s PCF with 1.4- m-diameter d air holes and 1.55- m holes of separation as a function of wavelength is shown in Fig.