thesis optical chemical sensing sf6 in switch gear

8/14/2019 Thesis Optical Chemical Sensing SF6 in Switch Gear

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6.4. Electron microscope probe analysis

Electron microscope probe analysis (with X-rays) reveals that the deposit on

the fibre is sulphur. A piece of the 15 cm length of unclad PCS 600N PUV fibre, which was

placed in the glow discharge chamber for 7 hours, was used for probe analysis with the

electron microscope. The analysis requires the fibre to be coated with carbon. A piece of the

fibre close to the chamber wall, complete with sulphur deposit, was analysed in the electron

microscope. Figure 6.7 (b) shows the result of the analysis in which only sulphur, silicon,

oxygen and carbon were detected. Carbon comes from the coating, while silicon and oxygen

are components of silica (SiO 2). Figure 6.7 (a) was obtained for reference using an unused

piece of PCS fibre core.

D

C

C a r

b o n

S

i

l

i

c

o

n

C a r b o n

S

i

l

i

c

o

n

S u

l

p

h

u

r

O x y g e n

O

x y g e n

b)a)

Figure 6.7. Electron microscope probe data: (a) fibre core (silica) in absence of a discharge (b) fibre core (silica)following a 7-hour glow discharge. Quantitative comparisons of pulse amplitudes cannot be made because of thenature of the electron-probe technique.

A part of the unclad fibre that was between the electrodes also was examined.

Probe analysis shows that there are other materials in the coating of this sample, such as iron

and chromium. They are released from the electrodes. The coating is cracked and uneven due

to the high temperature, up to 1000 oC, in the discharge centre (Ogle and Woolsey, 1987).

Electron micrographs of the fibre placed near the discharge wall and in the discharge centre,

are shown in figures 6.8 (a) and (b), respectively.

From figure 6.8 (b) it can be seen that the thickness of deposited sulphur for a

fibre from the centre of the discharge varies widely, since the high temperature of the

Chapter 6: Sulphur deposition experiment 78


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discharge causes cracks and flaking of the sulphur deposits. This suggests that measurements

of sulphur deposition on a centrally positioned fibre are unlikely to be useful. The following

studies are concentrated therefore on measurements made using fibres positioned near the

wall of the chamber. Even in this region a few cracks do occur in the sulphur coating on the

fibre. These can be seen in figure 6.9 which has a magnification of 30 times that of figure

6.8 (a).

a) b)Figure 6.8. a) An SEM (scanning electron microscope) picture of the fibre placed near the wall of the glowdischarge chamber . The width of the picture is 880 m and the SEM accelerating voltage is 20 kV. b) An SEM

picture of the fibre in the centre of the glow discharge. The picture width is 880 m, and the accelerating voltageis 20 kV.



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Figure 6.9. An SEM picture of sulphur deposited on a fibre placed near the wall of the discharge chamber. The picturewidth is 33 m, and the SEM accelerating voltage is 20 kV.

The layer of sulphur deposited on the 600 m - diameter fibre is very thin, ascan be observed in figure 6.10 (a). In order to estimate the thickness of the deposition, a wall

fibre was exposed to four consecutive glow discharges, each of 7 hours duration and current

10 mA. Prior to each of these discharges, the chamber was evacuated and filled again with

fresh SF 6 . After 7 hours of glow discharge almost all sulphur-containing gases were

dissociated. The sulphur derived from the initial SF 6 remained as powder on the surfaces of

the chamber and the optical fibre. It seems reasonable to assume that after four discharges

with initially undissociated SF 6 , the thickness of deposited sulphur is around 4 times that

following a single discharge.

a) b)

Figure 6.10. The cross section of the fibre with deposited sulphur: a) after 7 hours of discharge (the picture widthis 880 m, SEM accelerating voltage 20 kV); (b) after exposure to four separate glow discharges, each of seven-hours duration (the picture width is 13.2 m, SEM accelerating voltage 20 kV)

An estimate of the thickness of sulphur coating on a fibre can be obtained from

a figure such as 6.10 (b). For this particular electron microscope picture an estimate of 2.4 m



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was made. This suggests that the sulphur deposition following one discharge is around

600 nm.

6.5. Experimental results and discussion

The curve shown in figure 6.11 was obtained when the He-Ne laser was used in

the transmission experiment. In this figure there is a distinctive step that occurs as a sulphur

layer builds up on the optical fibre. The intensity of the output light starts to fall after 75 C of

charge has been transferred through the glow discharge (point 1). The mass spectrometer

analysis shows that at that time there was approximately 25% of the initial concentration of

SF 6 remaining in the chamber. This leads to the conclusion that the sulphur deposited on the

chamber wall and fibre is produced from product gases rather than directly from SF 6. The

concentration of SF 6 left in the chamber following the transfer of 140 C (point 2) is around

10% of the initial concentration.

charge (Coulombs)

0 50 100 150 200 250 300

l i g

h t t r a n s m

i s s i o n

( a r b

i t r a r y u n i

t s )

0

1

2

3

4

5

6

1

2

Figure 6.11. The output from the optical fibre when sulphur was being deposited on it.

The curve of figure 6.11 was obtained each time the fibre was cleaned and a

further SF 6 discharge generated using a fresh filling of SF 6 . When a further discharge was run

without removing sulphur from the fibre there was no further change in the light transmission.



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Also, it was observed that light escapes along the length of the unclad fibre following

deposition of sulphur. This is the scattered light that is coupled into the sulphur layer by

refraction or via the evanescent field.

There are several mechanisms which may account for the observation of output

signal attenuation and emission along the length of the unclad fibre.

Sulphur is a biaxial material and its refractive indices along three axes are 1.95,

2.043 and 2.24 (Gray, 1972). These values are higher than the refractive index of the core of

the fibre and so total internal reflection should not occur. However, the refractive index of the

deposited sulphur layer may be lower than these measured values because the pressure in the

chamber is high (1 Torr) and the deposited sulphur has a sponge-like structure as shown in

figure 6.10. (b). If the refractive index of the sulphur layer is higher than the refractive index of

the core, the light will escape mainly by refraction and point 2 in figure 6.11 will be reached

when the exposed core becomes fully covered by sulphur.

There is also the possibility of the existence of a thin gap between the core and

the sulphur layer. In this case frustrated total reflection will occur and the light will propagate

in the same direction through the sulphur as it would in the absence of a gap, but with a lower

intensity.

Another possible mechanism involves penetration of the evanescent field of the

light in the core into the sulphur layer. As shown below, the penetration depth is expected to

be around 100 nm. In order to estimate how deep the evanescent wave spreads around the

fibre, it is assumed that the refractive indices of the core (fused silica) and the cladding

(polymer) are 1.457 (Malitson, 1965) and 1.400 (Gowar, 1984, page 86), respectively. Because

the light is launched into the fibre at an angle, as described in section 6.3, in order to maximisethe evanescent field, and because the core is very thick (0.6 mm diameter), the propagation

can be treated as propagation in a planar waveguide. In that case the critical angle for the

glass/polymer boundary is 73 o 55'. In the unclad region the critical angle for the glass/vacuum

boundary is 43 o 20'. When the light reaches the unclad region only the rays between 73 o 55'

and 90 o are present. The other rays have been refracted into the cladding before they reach the



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( i ) choosing the position of the fibre within the high-voltage system,

( ii ) placing a shield in an appropriate position around the fibre,

( iii ) choosing the length of the unclad fibre section,

( iv ) choosing an appropriate fibre diameter,

( v ) launching the light in a particular way.

The ultimate test of the applicability of the optical fibre technique, including its

long-term reliability, is, of course, its performance in a practical SF 6 - insulated system.



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Chapter 7

Experiment on CO 2 laser light absorption

The measurement of SF 6 concentration, using CO 2 - laser absorption of the

evanescent wave in a silver halide optical fibre, is based on the 948 cm -1 absorption line of SF 6 .

The SF 6 absorption spectrum from 2 m to 25 m is shown in figure 7.1. It was recorded byLagemann and Jones (1951). As seen in figure 7.1, SF 6 has strong absorption peaks at around

10.7 m and 16.3 m. Chapados and Birnbaum (1988) measured the lower wavelength to beat 948 cm-1 (10.5485 m). An analysis with better resolution shows that the peak is closer to10.55 m ( Rabinowitz et al. , 1969). The wavelength of the peak varies for differentinvestigators. According to the most recent measurement (Messica et al ., 1994), it is

10.562 m. The value with highest precision comes from Bobin et al. (1987):947.9763358 cm -1 (10.548786528 m). In fact, the SF 6 line spectrum has over 1000 lines/cm -1

in the region of 10.6 m (Kildal and Deutsch 1976; Hinkley 1970). However, the 10.55 m lineis the strongest and is close to the CO 2 laser line P(16) at 10.5513950296 m (Maki et al .,1994). These features of CO 2 laser light and the SF 6 absorption spectrum have been employed

for measuring SF 6 concentrations using a grating CO 2 laser or a diode laser tuned to 10.55 m(Sun and Wittaker 1993; Shimizu 1969). But the absorption is so high that this method is

suitable only for low pressures. For example, no signal can be detected when light from a 2 W

CO 2 laser is passed through a 10 cm cell containing 2 Torr pressure of SF 6 at room

temperature. Increasing the power of the laser is not a solution because it may dissociate SF 6

molecules if raised too high; even a few watts of laser power can cause dissociation when

focussed inside the cell. This saturation is not a problem, however, when the CO 2 - laser

radiation is transmitted through an optical fibre and absorption occurs as a result of an

evanescent-field interaction with the SF 6.

85


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Figure 7.1. The SF 6 infrared absorption spectrum (from Lagemann and Jones, 1951)

As mentioned earlier, the evanescent-field absorption by SF 6 at the P(16) CO 2

laser line, using an optical fibre, is more appropriate for higher pressures. This is demonstrated

in recent work where a silver halide optical fibre and a tunable laser diode were used to

measure concentrations of SF 6 (Messica et al ., 1994). As shown in figure 7.2 the peak at

10.562 m is distinctive and is very close to the CO 2 laser P(16) line. Silica fibres, as used for communications, are not suitable because they are not transparent beyond 4 m. Nor arefluoride-containing fibres, for the same reason. For the mid-infrared region which includes

CO 2 laser light, silver halide fibres (Simhony et a l., 1986), thallium halide fibres (Grigorjeva et

al ., 1996) and chalcogenide glass fibres (Sanghera et al ., 1994) are suitable. Some metal

fluoride optical fibres are transparent at 10.6 m, but they are not as good as silver halidefibres because of their higher absorption at this wavelength. However, the possibility of using

these fibres for measuring SF 6 concentration should be investigated when they become

commercially available.

7.1. Experimental arrangement

The experimental arrangement for measuring the amount of SF 6 in the corona

discharge chamber is shown in figure 7.3. The laser used was a SYNRAD 48G-2-28w CO 2

Chapter 7: Experiment on CO 2 laser light absorption 86


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grating laser. A circular aperture of 1.5 mm diameter was placed in front of the laser output. A

ZnSe beam splitter divided the beam in the ratio 2:1, with two thirds of the power entering the

monochromator. One third was incident on the ZnSe biconvex lens, which collimated the

light, so that it was launched into the fibre at an angle of 45 o to the fibre axis. The fibre passed

through a 25 cm long cylinder connected to the glow discharge chamber as described in

chapter 3. The glow discharge chamber was connected to the corona chamber via a 1.5 m long

tube as described in chapter 3. A pyrodetector (Murata IRA-E600S0) detected the infrared

light at the output of the fibre. The signal from the pyrodetector was amplified, extracted with

the lock-in amplifier ORIEL model 70707, and recorded on a chart recorder. The reference

signal for the lock-in amplifier was supplied by the digital signal generator that modulates the

laser. The signal from a pyrodetector ORIEL model 70841 attached to the monochromator

was amplified with an ORIEL amplifier/readout model 70701, extracted with the lock-in

amplifier PAR model 124, and recorded on a chart recorder.

Figure 7.2. The SF 6 absorption spectrum around10.6 m (Messica et al ., 1994). The peak in the curveis at 10.562 m.

The signal from this pyrodetector is proportional to the power of the laser and

is used to compensate any fluctuation in the laser power. The pressure and temperature in the

corona chamber were monitored. These values are used to calculate the pressure of the same



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density at 25 oC and the percentage of SF 6 in the corona discharge chamber. During a corona

discharge the pressure rises as dissociation occurs, because more molecules are produced.

Dissociation of SF 6 molecules in the discharge environment can lead to several events. These

include sulphur deposition on the chamber wall, reactions which produce sulphur

oxyfluorides, and production of SiF 4 as a result of reaction between fluorine and glass

windows. The net effect of all such events is to produce a significant number of additional

molecules and a consequent rise in the total gas pressure in the corona chamber.

Carbon dioxide grating laser

micrometers

Pyroelectricdetector head

ORIEL

amplifier Lock-in

amplifier

Laser controller & modulator

Digitalsignal

generator

Monochromator 1/8 m

Z

n

S

e

s p l i t t e r

grating

Coronachamber

Silver halide opticalfibre

Pyrodetector Murata

(see Fig. 7.5)

Lock-in amplifier

Timer/Counter

Figure 7.3. Experimental arrangement for measuring evanescent-field absorption during an SF 6 corona discharge.

7.1.1. The grating laser SYNRAD 48G-2-28w

The grating laser SYNRAD 48G-2-28w requires water cooling. Water flow needs to be

constant within +3% and at least 3.6 litres per minute. The recommended temperature of the

water is 20 oC and it should not vary by more than +0.1 oC, although +0.01 oC is preferred.



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These cooling conditions are provided by an attached cooler NESLAB RTL-211D. Two

micrometers on top of the laser are used to select the lasing line. The large one is used to

change the angle of the grating. It selects the laser spectral line. The smaller one is used to

adjust the length of the optical cavity. Using this micrometer it is also possible to change the

wavelength within a few tens of megahertz around the spectral line. This also happens if the

temperature of the cooling water is not constant. If the temperature is not constant the laser

stays within the defined line, but drifts a few megahertz on either side. At maximum output

optical power, the grating and cavity length are set for the required spectral line. TEM mode

changes were observed during laser warm-up prior to experimental run. During the

experiment, mode changes were not observed.

Figure 7.4 . The absorption coefficient of SF 6 around the CO 2 laser spectrallines (P12, P14, P16, P18 and P20). The width of the x-axis for one spectralline is estimated to be between 40 and 50 MHz (from Shimizu , 1969). Thearrows show the centres of the spectral lines. The centres of these lines are (Maki et al. , 1994):P12 - 10.5131216772 mP14 - 10.5320883339 mP16 - 10.5513950296 mP18 - 10.5710454539 mP20 - 10.5910434604 m

7.1.2. Source-fibre coupling



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The coupling of laser light into the fibre is not very efficient but this is not a

problem. Indeed, the power after the ZnSe lens must be maintained below 60 mW. The reason

for this is that, in the same way that the SF 6 absorbs light via the evanescent field, other

materials in contact with the fibre also absorb light. Torr-Seal , a two-component adhesive for

vacuum applications, is used to seal the fibre at ends of the cylinder, and where the Torr-Seal

contacts the fibre it absorbs CO 2 laser light and thus heats up. This heat is transferred to the

fibre and softens it at those points. At higher power the fibre melts at the point closer to the

input.

The limit of 60 mW was set for a launching angle of the beam into the optical

fibre of 19 o. When the launching angle increases this limit increases, because more power is

reflected from the input end of the fibre. Equation 7.1 can be used to show that the intensity of

the light reflected from the fibre input face increases (when the light is coupled into the fibre)

when the incident angle with respect to the fibre axis is increased. Also, it will be used to

estimate the power absorbed by the Torr-Seal . The reflection coefficient from a flat dielectric

surface, defined as the ratio of the reflected and incident electric field wave amplitudes, is

given by (Collin, 1991) :

(7.1) R = Z T Z I Z T + Z I

where

Z I is the wave impedance of the incident medium,

Z T is the wave impedance of the refracted medium,

, where is the magnetic permeability and for most optical components it is Z = = Z 0

n

equal to the magnetic permeability of vacuum (nonmagnetic substances), is the dielectricconstant, Z 0 is the impedance of vacuum and n is the refractive index. There are two sets of

equations for R, Z T and Z I . One is for s-polarisation and one for p-polarisation. However,

only s-polarisation will be considered here. In figure 7.3, the fibre lies in the plane of the page

and the laser beam is polarised in the direction normal to the page. Consequently, the laser



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beam enters the fibre as an s-polarised beam and propagates through the fibre as mainly TE

mode. This provides better sensitivity in an FEFA sensor than TM mode coupling (see the

calculation in section 5.2.3.1). For s-polarisation,

(7.2) Z S = E H cos

which finally provides an expression for the electric field reflection coefficient of the

s-polarised light

. (7.3) R S = n I cos I n T cos T n I cos I +n T cos T

This equation is one of Fresnel's equations (Lorrain and Corson, 1970).

gives the value of the reflected power. R S2

When the incident angle is 19 o the reflected power is 14% of the incident

power. When 60 mW of laser power is transmitted through the lens, 51.6 mW is coupled into

the fibre. When the pyrodetector was replaced with a power meter at the output, the power

recorded was 14 mW. Hence, 37.6 mW was absorbed by the two Torr-Seal joints.

Having recorded this limit to the power of the laser, the power was set at a

substantially lower level to ensure that no over-heating of the sealing points occurred. During

the absorption measurement the output power from the laser was 38 mW, and following the

1.5 mm aperture, the power was 6.3 mW. Two-thirds of this power was reflected from the

beamsplitter into the monochromator, and 2.1 mW was directed onto the ZnSe lens: this lens

has an antireflective coating, and focal length of 4.25" (107.95 mm). The lens was used to

launch the light into the fibre. The launching angle was 45 o and 22.4% of the input power was

reflected at the input face of the fibre. The remaining 1.63 mW was coupled into the fibre and

around 0.445 mW was detected at the output.

The laser power was maintained at a constant level using the following

procedure. The power of the laser is controlled by a modulator, with a duty cycle of 5 kHz

pulses. Initially a power meter was placed in front of the laser output. The average laser power



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of 38 mW was obtained using 5.8 s wide pulses. This width was measured with a digitalcounter (see figure 7.3). Then the power meter was removed and the pulse width, as

monitored by the digital counter, was maintained at around 5.8 s. For all measurements; atdifferent incident angles and during the corona discharge, no power meter was used. This

method of monitoring the laser power was preferred to the use of a beam splitter to direct

some fraction of the laser beam to a power meter, since the introduction of another optical

component adds noise to the system.

7.1.3. Pyrodetectors

D

47K Ohm

+ -

Output

2200nF, 35 V Tantalum capacitor

Pyroelectric Infrared Sensor Murata IRA-E600S0

9V

S

G

Figure 7.5. The electric circuit for the mid-infrared light detector used for the measuringthe light at the output of the fibre.

After adjustment of the laser power level, the power meter at the output of the

fibre was replaced by the Murata IRA-E600S0 pyrodetector which is used for all further

measurements of the output light from the fibre because the precision and the resolution of the

power meter is much lower than those of the pyrodetector. This detector incorporates a

piezoelectric crystal that generates electrical charge when pressure is applied to it. A

temperature change produces a similar effect. The power of the light from the fibre raises the

temperature of the crystal. A constant heat input to the detector does not generate a signal, for

which reason the light beam must be chopped. Here, the laser beam was modulated with a



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17 Hz, 50% duty cycle square-wave signal from a digital signal generator. The piezocrystal is

encapsulated in a transistor-like case together with a FET transistor. A silicon window in the

case transmits light from 1 m to 20 m. To obtain a signal from the detector, the circuitshown in figure 7.5 was assembled.

The monochromator used in the experiment (see figure 7.3) was equipped with

an ORIEL pyrodetector model 70841 with a KBr window, which operates on the same

principle as the Murata unit.

7.1.4. The ORIEL 1/8 m monochromator

The 1/8 m monochromator from ORIEL with grating 77302 (75 lines/mm,

7 m blaze wavelength) has a resolution of 8 nm ( 20 GHz ) with a 0.05 mm slit. Thisresolution is good enough to indicate when the laser is on the defined spectral line, but it does

not show up any drift around the spectral line due to thermal instability, and this instability

can be as large as +100 MHz. SF 6 absorption as a function of frequency ( or wavelength )

around the spectral lines is shown in figure 7.4. The NESLAB cooler greatly reduces these

thermal fluctuations. The signal from the pyrodetector is amplified using an ORIEL

amplifier/readout model 70701, input to a lock-in amplifier. The reference signal for the lock-in

amplifier is supplied by a digital signal generator connected to the laser control modulator, as

shown in figure 7.3.

7.2. Experimental procedure

7.2.1. Calibration procedureCalibration measurements were made to determine the dependence of the light

transmitted through the fibre on the pressure of SF 6 . The CO 2 laser was adjusted and left for a

couple of hours to stabilise. The output from the monochromator was used as a power

monitor and its output recorded in order to determine when the laser was operating in a stable

mode. The cylinder containing the optical fibre was attached to the glow chamber; the valve

between the glow and corona chambers was closed, and SF 6 was bled through a needle valve



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into the previously evacuated glow chamber. The chamber was filled slowly, while the fibre

output signal, Sf , was recorded on a chart recorder. The signal from the monochromator for

monitoring power was recorded on another chart recorder, S p . Chamber pressure was

measured with the VAISALA PTB200 A digital barometer described in chapter 4. The

temperature of the chamber was measured with a temperature probe attached to the wall of

the chamber. Pressures were normalised to 25 oC. Values of Sf / S p were recorded as a

function of pressure, with Sf / S p equal to one for zero pressure. Data were obtained both

when SF 6 was slowly admitted to the chamber and when it was slowly pumped out of the

chamber. Measurements for different incident angles were made in order to check the validity

of equation 5.7.

During these experiments it was important that no leakage of SF 6 occurred into

the laboratory, as can happen from exhaust lines. If SF 6 is released into the laboratory, it can

remain for a long time, since the heavy SF 6 molecules replace the air at ground level. This

"atmosphere" of SF 6 absorbs CO 2 laser light and even a small number of randomly moving

SF 6 molecules in the path of the laser beam can cause fluctuations in the final detector signal.

The effect was observed in the present work, before careful sealing of the exhaust line was

completed.

7.2.2. SF 6 monitoring

A typical corona - monitoring experiment took nine days. The initial pressure

of SF 6 was set at 90 kPa and the distance between electrodes (point and plane) at 10 mm. The

current was maintained between 85 A and 102 A at a voltage of 35 kV . The current wasrecorded on a chart recorder. The total amount of charge transported during the nine-day

discharge period was 63 Coulombs.

During this long time period the room temperature fluctuates and so the laser

wavelength varies around the lasing line. This can lead to substantial errors as SF 6 absorption

varies significantly over a frequency range of a few megahertz (figure 7.4). From observation

of the chart recorder it is clear when the laser is unstable: large fluctuations in power occur.

Measurements obtained during laser instability were not used for data analysis.



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The partial pressure of SF 6 during the discharge was calculated in the following

manner. An interpolation formula was first established to fit a calibration plot of absorbance as

a function of SF 6 pressure (section 7.4.1). This formula has the form

(7.4) pressure SF 6 (kPa ) = A + B ln(signal ) +C ln 2(signal )

where signal is the normalised signal obtained from the fibre output and the coefficients A, B

and C are calculated for the pressure range between 50 kPa and 90.1248 kPa. This range was

chosen because the partial pressure of SF 6 during the discharge fell from 90 kPa to around 70kPa. Equation 7.4 with these coefficients was then used to calculate the partial pressure of SF 6

during the discharge from the measurements of fibre output.

The pressure and temperature in the chamber were monitored at all times

during the experiment because the total pressure in the chamber continuously rises because of

SF 6 dissociation. The pressure and temperature values were used to calculate the

concentrations (as ratios) of the SF 6 and discharge by-products in the chamber at 1 atm and

25o

C. The partial pressure of the by-products is determined by subtracting the normalised partial pressure of SF 6 from the normalised total pressure.

7.3. Experimental results

7.3.1. Calibration

Before using this method to monitor the amount of SF 6 in a corona discharge

the calibration was carried out. The calibration was performed as described in section 7.3.1.

Data for two incident angles (14o and 29 o) were obtained for the transmittedsignal T as a function of SF 6 pressure7.6. The absorbance -ln [T ( L, )] was plotted as a

function of pressure (figure 7.6.) and the curves are in agreement with the data obtained using

a laser diode source (Messica et al ., 1994), which is shown in figure 5.4.



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Pressure (kPa) at 25 oC

0 20 40 60 80 100 120 140

A b s o r

b a n c e

( a r b

i t r a r y u n

i t s )

0.00.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

launching angle = 29 o


Figure 7.6. Calibration curves: evanescent-wave absorbance of CO 2 laser P(16) line versus pressure of SF 6 at25 oC for silver halide optical fibre, at launching angles of 29 o and 14 o, with the lines of the best linear fit.

After these measurements were completed the incident angle was set to 45 o in

order to increase sensitivity further. For this setting it was necessary to slightly bend the fibre.

Unfortunately, this introduced a nonlinearity into the absorbance curve (figure 7.7). The

mechanical characteristics of a silver halide optical fibre are somewhat similar to those of

copper wire. The fibre is soft and has low elasticity, so that attempts to straighten the fibre

were unsuccessful. As a result, the measurements for 16 o and 30 o incident angles are also

non-linear. The three curves are shown in figure 7.7.

The bend introduces higher order modes. The effect is similar to that of

launching two laser beams into the fibre at different angles. In that case the absorption

coefficient becomes (see equation 5.7)

(7.5) N L = L 12 + 12 + L 2

2 + 22 The effect can be observed in figure 7.7, for the 45 o curve, where it appears that

the bend creates more than one additional mode.



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Pressure (kPa) at 25 oC

0 20 40 60 80 100 120 140

A b s o r

b a n c e

( a r b

i t r a r y u n

i t s )

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6


launching angle = 30 olaunching angle = 45 o

Figure 7.7 . Calibration curves: evanescent-wave absorbance of CO 2 laser P(16) line versus pressure of SF 6 at25 oC for silver halide optical fibre, at launching angles of 45 o, 30 o and 16 o, with the lines of the best linear fit.The red and green triangles were recorded at the same incident angle. The red correspond to gas filling thechamber, and the green to the gas being pumped out of the chamber.

From both figures 7.6. and 7.7 it can be seen that the highest sensitivity was

reached when the CO 2 laser beam was coupled to the fibre with an incident angle of 45o. This

is in agreement with theory and equation 5.7. Further increase in the incident angle increases

the sensitivity, but because of mechanical constraints it was not possible to go above 45 o.

7.3.2. SF 6 in the corona dischargeFollowing the procedure described in section 7.3.2 the partial pressure and

concentration of SF 6 was measured during the corona discharge and the results are presented

in figure 7.8. As expected, there is a steady fall in the concentration of SF 6 molecules during a

corona discharge.



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Charge transported (Coulombs)

0 10 20 30 40 50 60 70

C o n c e n t r a

t i o n o f

S F 6 ( m o l m

- 3 )

24

28

32

36

40

P a r

t i a l p r e s s u r e o f

S F 6 ( k P a )

50

60

70

80

90

100

Figure 7.8. The amount of SF 6 during a corona discharge. The solid line is the best linear fit. The corona currentwas between 85 A and 102 A. The distance between point-plane electrodes was 10 mm. The applied voltagewas around 35 kV. The initial pressure of SF 6 was 90.1248 kPa at 25

o

C.

Because SF 6 dissociation results in production of by-products, the

concentration of by-products builds up during the corona discharge. Figure 7.9 shows the

increase in by-products concentration as a function of charge transport: for comparison, the

SF 6 concentration is displayed. These results are in a good agreement with measurements

made by Mortensen et al. (1994) using mass spectrographic analysis, and these are shown in

figure 7.10.

The plot in figure 7.11 shows the concentration of SF 6 as a function of the input

energy. This energy was obtained as a product of current and voltage between the electrodes.

This energy is the sum of the heat that raises the temperatures of the gas and the electrodes,

and the energy dissipated in chemical reactions, dissociation and radiation.



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Charge transport (Coulombs)

0 10 20 30 40 50 60 70

C o n c e n t r a

t i o n

( % )

0

10

20

30

40

50

60

70

80

90

100

Energy (kJ)

0 500 1000 1500 2000

SF6

Discharge by-products

Figure 7.9 . Concentration of SF 6 and discharge by-products in a corona chamber. The solid lines are the bestlinear fits. Same corona conditions as figure 7.8.

7.4. Discussion and conclusion

This work shows that an FEFA sensor can be used to monitor the degradation

of SF 6 in a discharge. The fluctuations of the experimental points in figures 7.8 and 7.9 are

probably due mainly to variations in the equilibrium of the laser. The experimental data on

each of figures 7.8, 7.9 and 7.10 depict an overall linear trend and lines of best fit have been

drawn to illustrate this. On the other hand, a plateau region on each curve may possibly exist

in the range 20 C to 40 C. The fact that this trend is observed in both the present work and that

of Mortensen et al. may be a coincidence but it is something that warrants further study. It

should be possible to reduce laser fluctuations using a more stable CO 2 laser, and this might



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help determine whether or not a plateau region does in fact exist. Furthermore, it may be that

a lower power laser is more appropriate for these long-term measurements, since the output

power of such lasers is easier to control and the power dissipation is lower.

Figure 7.10. Concentration curves in a corona discharge obtained by using a massspectrometer. Initial pressure of SF 6 is 100 kPa and the average discharge current is75 A (Mortensen et al ., 1994).

As mentioned in section 5.3.2, there is a significant ageing effect of silver halide

optical fibres which can be compensated for by using a reference fibre. Another option is to

replace the silver halide optical fibre with a different type of optical fibre that will transmit light

of wavelength 10.6 m, for example, a chalcogenide optical fibre. Recently there has been asignificant improvement in the manufacturing of chalcogenide fibres (Busse et al ., 1996). The

Naval Research Laboratory (NRL) has started production of sulphur-based (As 40S60-xSe x)

fibres, for the 1 to 6 m region and telluride-based (Ge aAS bSe cTed) fibres for the 1 to 11 mregion. NRL has been able to reduce the transmission losses in chalcogenide fibres to an

extent that the losses are now only slightly higher than those for silver halide optical fibres.



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The chalcogenide fibres have the advantage of showing no ageing effect. Also, their durability

is better.

Another disadvantage of the FEFA sensor for SF 6 monitoring is the high cost

of CO 2 lasers. However, in an electrical plant containing several high-voltage insulating

devices, sensing fibres could be placed in each, and the CO 2 laser radiation delivered from a

single laser.

Since a CO 2 laser is much more powerful than a laser diode, pyrodetectors can

be used rather than the more sensitive, but expensive, cryogenic antimonide or HgCdTe

detectors.

The problem of wavelength drift can be solved in several different ways. For

example, the small micrometer that is used to tune the resonant cavity length of the laser

described in section 7.2.1 could be replaced with a piezocrystal that would vary the cavity

length and lock onto the lasing line P(16). Otherwise the piezocrystal could be used to scan the

frequencies around the lasing line, and measure the output signal from the fibre only when the

laser goes through the maximum point corresponding to the lasing line P(16). Such a device

was used in the experiments of Shimizu (1969).



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Chapter 8

Summary and conclusions

In the electrical power industry, there is a need for a simple and reliable method

of measuring the degradation of SF 6 in switchgear and other SF 6-filled high voltage devices.Such information can be useful for determining service-times for switchgear, and when the

SF6 should be replaced. At the moment there appears to be no sensor appropriate for such an

application. Samples can be taken from the switchgear and analysed with laboratory

instruments such as FTIR, but this is not cost effective, particularly when examining power

systems in remote areas.

In the present work three methods have been devised for monitoring SF 6

degradation, and each has the potential to be made simple and compact enough to be builtinto switchgear systems. The three methods involve measurements of SF 6 refractivity, sulphur

deposition, and evanescent-field absorption of SF 6 at 10.6 m.

The last two methods, based on optical fibre sensing, may be closer than the

first one to implementation as a final product for field measurement. Both can be used in high

voltage devices. A sensor based on sulphur deposition can be made extremely simple, in that

it requires only a source such as a red laser diode, a length of PCS optical fibre with a declad

section and a detector. In order to avoid interference from the high voltage device, the source

and detector can be placed remote from the device and the light can be delivered to and from it

with optical fibres. This sensor is irreversible but this should not be a problem, since it needs

to be replaced only when the SF 6 is replaced, and at that time maintenance involving

dismantling of the device is likely to take place. The interferometer described in chapter 4 for

refractivity measurement is neither simple nor compact and is not appropriate for field

monitoring. However, the data obtained with the interferometer have shown that refractivity

102


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measurement of the gas inside a high voltage device can provide useful information about the

insulating condition of SF 6.

SF6 monitoring is important in other devices that use SF 6 insulation. For

example, when the amount of SF 6 by-products reaches 0.1 ppm in the ANU 14UD accelerator

at the Australian National University in Canberra, ACT, the SF 6 has to be purified (Ophel et

al ., 1983). The sampling method used for measuring this concentration of by-products is not

practical for switchgear because a few litres of SF 6 are released during each measurement.

According to Ophel the concentration of by-products in a circuit breaker should be detected

with at least 100 ppm accuracy. This value is likely to vary for different switchgear systems:

circuit breakers are known to operate efficiently with contaminant levels up to 0.2%, such as

the one shown in figure 2.2 (Yamauchi et al ., 1985).

The sulphur deposition method is the most sensitive of the three techniques.

The experiment described in chapter 6 was carried out at a pressure of 0.96 Torr of SF 6 , and

changes in deposition were readily detected. Indeed, in a high pressure device the deposition

sensor could be too sensitive, with saturation occurring soon after the first fall in optical

transmission (figure 6.11). However, the distribution of sulphur through the system is not

uniform, and by choosing the right position in the chamber or by placing a shield around the

fibre it should be possible to tune the sensor for appropriate SF 6 pressure and sensitivity.

The sensor based on evanescent-field absorption by SF 6 at 10.6 m is less

sensitive than the refractivity sensor. From the 45 o calibration curve of figure 7.7 it can be seen

that the SF 6 absorption sensor detects SF 6 pressure changes down to 0.67 kPa (~5 Torr), at

filling pressures of around 100 kPa, this limit being set by the sensitivity of the lock-in

amplifier. Increasing the incident angle of the CO 2 laser light into the fibre can increase thesensitivity further. Increasing the length of the fibre and choosing a more sensitive detector,

such as an indium antimonide or HgCdTe photoconductive detector operating at 77 K,

increases the sensitivity. In the long-term measurements on the corona discharge, the expected

sensitivity of 0.67 kPa was not achieved because the CO 2 laser did not remain stable over long

periods of time. With a more appropriate laser or laser diode it would be possible to achieve

the expected value of sensitivity.

Chapter 8: Summary and conclusions 103


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The refractive index measurement can detect changes of SF 6 concentration

equal to 623 Pa (partial pressure at 25 oC) when the initial pressure of SF 6 is 1 atm. For a

pressure of 10 atm (8 atm is the usual pressure in a single-pressure circuit breaker) this value is

658 Pa, which makes the precision of this method equal to 6.5 x 10 -4. This value is estimated

using equations 4.4 and 4.21 and assuming that the only product of the discharge is SOF 2 . The

precision of the measurement of refractive index described in chapter 4 is 5 x 10 -7. The

precision of the interferometer itself is higher than the precision of the pressure and

temperature measurements, and so the overall precision of the method is limited by the

accuracy of the pressure and temperature measurements. Temperature was measured with

0.1 oC accuracy and pressure with 0.02% (20 Pa) accuracy. The precision of the method would

be significantly improved if the precision of temperature measurement were 0.01 oC and the

precision of pressure measurement, 0.001%. Instruments with this precision are available but

the cost is high, over US$5000 each. Even with this accuracy they are less accurate than the

interferometer.

A practical field sensor does not need the high precision of the Lee-Woolsey

polarisation interferometer used in this work. Bulk-optic devices using white light or

low-coherence radiation can be designed to be small. They do not require initialisation at each

measurement, so that measurements can be made continuously. There are many different

types of low-coherence interferometers, including those using a multimode laser diode as

source (Wang et al ., 1995B); an arc lamp (Sinz C. et al ., 1994); a laser diode that works just

below threshold (Wang et al ., 1995A); 2 lasers (Wang et al ., 1995B); a white light source and

interference filters (Ludman et al. , 1995); an LED source (Wang et al ., 1995A); with PDA

(linear photodetector array) detector (Schnell et al ., 1996); a CCD (charge coupled device)array; and a single photodiode with electronics and positioner for fringe locking (Ludman et

al ., 1995). The accuracy of 1 part in 10 6 achieved by the latter is sufficient for detecting

changes in the refractive index of the gas mixture inside the SF 6-filled device. However,

pressure and temperature also must be measured so that the refractive index at 1 atm and

25 oC can be obtained.



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In a circuit breaker changes in refractive index are larger than those experienced

in the present work, because of the higher pressures used in the former. This means that a

refractometer based on surface plasmon resonance could be considered as a simple solution

(Jorgenson and Yee, 1994). Its sensitivity of 5 x 10 -5 may be enough for monitoring high

pressure systems. For low pressures, a bulk-optic device based on surface plasma resonance

has a resolution of 4 x 10-6 (Kunz et al ., 1996). One of these refractometers together with a

precise pressure meter and thermometer would be able to reach the sensitivity of 10 -4 required

for circuit-breaker monitoring. The arrangement chosen needs to be resistant to the high

electric and magnetic fields and the electromagnetic radiation that exist in switchgear under

usual working conditions.

Evanescent-field absorption at 10.6 m is a direct method and it does give

information about the remaining SF 6 , which is the information required. The refractive index

measurement and sulphur deposition methods require separate calibration for each

high-voltage device and if there is some defect in the device, such as a high level of water

vapour in the fill of SF 6 , a wrong measurement can result. Because of this, precautions must

be taken and sensors for other parameters may have to be included. The SF6

absorption sensor

is almost immune to such problems, because it provides information about the SF 6 wherever it

is placed. However, at the moment it would be the most expensive option, mainly due to the

high cost of the 10.6 m radiation source. Furthermore, a CO 2 laser is bulky, a lead salt

infrared laser diode requires a cryogenic cooler, and the life time of a high power tungsten

filament halogen light bulb or Nernst glower is short. The cost of a lead salt laser diode for

10.6 m is around US$4000, but it needs a cryogenic cooler which costs a further US$15 000.

Liquid nitrogen can be used to cool some of these diodes. Another solution could be aninfrared light-emitting diode, operating at room temperature. Work on mid-infrared LEDs at

room temperatures is still in the experimental stage and the maximum peak output power

achieved so far is 10 W (Tang et al. , 1995B). These are currently under development in a few

laboratories.

The work presented here has demonstrated the feasibility of the three optical

sensors. The sulphur deposition method has enough sensitivity to be employed for SF 6



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monitoring in switchgear, while the other two are close to the targeted sensitivity of 10 -4, but

more work is needed to produce a practical sensor. Indeed, more work is required to improve

all three techniques.



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Appendix 1

The estimation of SOF 4 and SO 2F 2 refractive indices

For this calculation the equation for molar refractivity A (or atomic refractivity

in the case of monatomic substances) will be used. It is defined as (Born & Wolf, 1980):

(A1.1) A = 43

N m = RT pn 2 1n 2 +2

where:

N m = 6.022045 x 1023 mol-1 is the Avogadro number

is the mean polarisability,

R is the molar gas constant,

T is the temperature,

p is the pressure.

In equation (A1.1), the compressibility of the gases and the nonlinearity of the index of

refraction have been neglected; that is, it is assumed that coefficient B(T) (equation 4.4) is

equal to zero. This assumption matches reality for pressures below 1 atm at room

temperatures. When a molecule is made up of N 1 atoms with molar refractivity of A1 , and N 2 atoms of molar refractivity A2 , then the molar refractivity of the molecule is (Born & Wolf,

1980)

(A1.2)= A 1 N 1 + A 2 N 2

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Suppose that, in order to calculate the refractive index of SOF 4 , we assume that

it is the combination of one SOF 2 molecule and one F 2 molecule. The index of refraction of F 2

is 1.000214 at 101325 Pa and 0 oC measured at 589.4 nm (Landolt - Brnstein, 1962). As molar

refractivity is constant for a particular gas and does not depend on temperature and pressure,

equation (A1.1) can be used to calculate the index of refraction at 25 oC when it is known at

0o C. This gives the refractive index of 1.000196 at 25 oC and 101325 Pa. Also, 589.4 nm is

close to 632.99 nm and it can be assumed that the index of refraction is the same at both

wavelengths. The index of refraction of SOF 2 is 1.00062166 at 101325 Pa and 25oC (this

work, chapter 4). Using these values and equations (A1.1) and (A1.2), the value of 1.000818 is

obtained for the refractive index of SOF 4 .

A similar approach is used to calculate the refractive index of SO 2F2 ; as the

combination of a molecule of SO 2 and a molecule of F 2 . The refractive index of SO 2 is

1.000628 at 101325 Pa and 25 oC, calculated from 1.000686 at 101325 Pa and 0 oC at 589.6 nm

(Gray, 1972). This gives 1.000877 for the refractive index of SO 2F2 at 101325 Pa and 25oC.

In the determination of the refractive indices of SOF 4 and SO 2F2 , it has been

assumed that the gases are linear. Any non-linear contributions to the refractive indices are

likely to be small: for example, in the case of SF 6 the contribution of B(T) is only 8x10 -6 ,

although SF 6 is a very non-linear gas in terms of refractive index and compressibility in

comparison to other gases. Therefore, although the values of 1.000877 and 1.000817 for the

refractive indices of SO 2F2 and SOF 4 , respectively, may not be exact, the conclusion that their

refractive indices are higher than the refractive index of SF 6 , which is 1.00070296 at 1 atm and

25 oC at 632.99 nm, should be valid.

Appendix 1: The estimation of the SOF 4 and SO 2F 2 refractive indices 108


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Appendix 2

Data acquisition programs for the refractive indexmeasurement

Programs, "fill_in" and "pump_out", were written for the acquisition of data

during the refractive index measurement when the gas is bled in and out of the invar tube.

These programs control the A/D converter, receive data from the A/D converter, store the data

and receive data from the VAISALA barometer via a serial port. The A/D converter is in a

CONTEC ADC-10 card. It is a 12-bit A/D converter with a maximum speed of 30 ksamples/s.

With this program the sampling speed is 15 ksamples/s on an IBM PC compatible computer

with INTEL 386SX-16 processor, math cooprocessor and 4 MB memory. This speed is

sufficient, because the amplified signal from the photodiode which is a part of the polarisation

interferometer (see figure 4.1) is around 1 Hz. The programs were compiled with Borland

Turbo C++ ver. 3.0 for DOS. The VAISALA PTB 200A digital barometer sends ASCII string

data via the serial port. An interrupt 0x14 from BIOS was used to receive this string.

The photodiode signal I from the interferometer is given by (Born & Wolf,

1980):

(A2.1) I = A cos 2 2

where A is a constant that depends on beam intensities and the sensitivities of the

photodiode, is the phase difference between the two beams of the interferometer, and changes with time as the pressure in the invar tube changes. The programs monitor the

maxima and minima of this function. When the signal passes through a quadrature point the

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computer acquires the pressure information from the VAISALA barometer. If the pressure is

not recorded at the quadrature point the program makes the required correction. The fringe

number and pressure are stored on the hard disk.

A2.1. FILL_IN program

The flow chart in figure A2.1 represents the program for fringe counting and

pressure. The fringe-intensity signal is the signal from the photodiode (see figure 4.1)measured with a 12-bit analog/digital converter CONTEC in the computer. The program for

controlling this converter is part of the FILL_IN program. It also displays the signal and the

pressures. When the measuring system is evacuated, the program is started and the valve is

opened.

A driver for the A/D converter was not available for Turbo C++, so a driver was

written and is shown in the listing A2.1.

// driver for A/D converter on the CONTEC board ADC-10int get_val(){unsigned datal, datah;int val;

val=outp(port,0x87);for(;;){datal = inp (port);datah = datal & 0x80;

if(datah != 0x80)break;}datah= inp(port);datal= inp(port-1);datah=datah & 0xF;

val = (datah*256+datal);return(val);

}

Listing A2.1. The driver in TURBO C++ for the A/D converter channel 7 in the CONTEC ADC-10 card.

110


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store the values for the fringe shiftand the pressure on the hard disk

open the valve

monitor the signal

the bottom of the sinusoidal curveassign as a new minimum value

the top of the sinusoidal curveassign as a new maximum value

measure the signal for 5 seconds anddetermine the maximum and minimum values

the bottom of the sinusoidal curveis assigned as a new minimum value

the most recent value of the top of the sinusoidalcurve is assigned as the new maximum value

pressure > 56 Kpa

pressure > 111 Kpa pressure = < 111 kPa

calculate the exact value for fringeshift at the moment of pressure reading

pressure = < 56 kPa

close the valve

end

monitor the signal

measure the pressure when thesignal crosses the quadrature point

measure the pressure when thesignal crosses the quadrature point

Figure A2.1. The flow chart of the program for refractivity data acquisition.

Appendix 2: Data acquisition programs for the refractive index measurement 111


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The pressure from the VAISALA PTB-200A barometer via the serial interface

is read using a BIOS interrupt 0x14. The subroutines for retrieving data from this port are

shown in listing A2.2. The data from the barometer are sent as ASCII data. These are taken

from the computer at a time determined by the main program ( FILL_IN). The subroutine

takes 40 successive characters and the actual pressure is extracted in the main

program.

char receivech(char chs){

ou.h.ah=2;ou.x.dx=COMport;int86(0x14, &ou, &out);chs=out.h.al;return (chs);

}

void receive_line(char line[]){

char receivech(char ch);char ch='z';

int i=0;for(i=0; i < 40; i++){

ch=receivech(ch);if((ch == '\r')) ch='?';

if(ch=='\x0') ch='?';line[i]=ch;}line[i]='\x0';ch=receivech(ch);ch=receivech(ch);

}

Listing A2.2. The subroutines for receiving a character from the serial interface and for receiving 40 successivecharacters from the same port.



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A2.2. PUMP_OUT program

This program collects data when gas is pumped out of the measuring cylinder

of the interferometer. The program is similar to the program FILL_IN except that it runs in the

opposite direction: it starts at 115 kPa and stops at 57 kPa.



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Appendix 3

Equations for light propagation in an optical fibre

An optical fibre is a cylindrical dielectric waveguide. If the dielectric constants

of the core and cladding are 1 and 2 respectively, then 1 > 2 . The radius of the fibre is and it can be assumed that the radius of the cladding is infinite and both regions are perfect

insulators. If a cylindrical coordinate system is chosen with the z - axis lying along the axis of

the fibre, then the solutions for the electric and magnetic components of the electromagnetic

wave travelling in the fibre are (Snitzer, 1961):

(A3.1) E zcore = A m J m(h 1 r ) cos(m + m) exp [i ( z t )](A3.2) H zcore = B m J m(h 1 r ) cos(m + m) exp [i ( z t )](A3.3) E zclad =C m K m(h 2 r ) cos(m + m) exp [i ( z t )](A3.4) H zclad = D m K m(h 2 r ) cos(m + m) exp [i ( z t )]

where is the angular frequency; = 2 / g is the propagation constant along the axis of the fibre and g is the wavelength along the fibre (see figure A3.1); m and m are phasefactors; , m and m are determined by the boundary conditions. At the boundary r =,the tangential components of the field are the same on both sides of the boundary. J

m(h

1r )

and K m(h2r ) are the Bessel function and the modified Hankel function of the first kind,

respectively. The propagation constants k 1 and k 2 , and h1 and h2 are defined by ( k 1 and k 2 are

constants for a fibre, but h1 and h2 have different values for each mode)

(A3.5)k 2 = 2(A3.6)h 1

2 =k 12 2

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(A3.7)h 22 = 2 k 22

where is free-space magnetic permeability.

/n 1

Claddingn

Coren 1

2

g z - axis

Figure A3.1 . Considering geometrical optics propagation, the wavelength g along a fibre (z - axis) of a certainmode is ; is the free-space wavelength.

n 1sin

The transverse components of the fields E r , E , H r and H can be expressedin terms of E z and H z (Stratton, 1941 Chapter V). After taking the boundary conditions

(4 equations) into account, expressions for the field components in the core are obtained:

(A3.8) E z = J m(h 1r )F c

(A3.9) E r = i h 1 J m P m J mh 1 r

F c

(A3.10) E = i h 1P J m m J mh 1r

F s

(A3.11) H z = PJ mF s

Appendix 3 : Equations for light propagation in an optical fibre 115


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(A3.12) H r = i k 12

h 1 P2k 1

2 J m m J mh 1r

F s

(A3.13) H = i k 12

h 1 J m Ph 2

k 12

m J mh 1r

F s

where

P =

Bmcos(m + m)

Am sin(m + m)

(A3.14)=m 1(h 1)2

+ 1(h 2)2

J m(h 1)h 1 J m(h 1)+

K m(h 2)2K m(h 2)

1

(A3.15)F c = A m cos(m + m) exp [i ( z t )]

(A3.16)F s = A m sin(m + m) exp [i ( z t )]

and is the first derivative of the Bessel function with respect to its argument. For a J m

multimode fibre there are many values for (propagation constant along the fibre axis) that

satisfy these equations. Each of them represents a propagation mode. For every cross-section

geometry and refractive-index profile it may be stated that (Snyder and Love, 1983):

(A3.17)n cl 2

< n co 2

where n cl and n co are the refractive indices of the cladding and the core, respectively. The

lower limit for , namely , is called the modal cutoff (Snyder and Love, 1983). At then cl 2cutoff, h2 = 0, and equations A3.6 and A3.7 become

(A3.18) =k 2



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126/140


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(A3.24) N

22

k 1

2

k

2

2 =

2

2

nco

2

n

cl

2

If incoherent light is launched into a multimode fibre, all modes will be excited

and will carry equal amounts of power. In this case the power that travels in the cladding is

given by (Gloge, 1971)

. (A3.25)P clad = 431

N

P tot



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we get:

(A4.3) E 2 = E 0exp i20 x n 1sin 1 z 1

n 1n 2

2

sin2

1

Since for total reflection the term in the square root is negative, equation A4.3 needs to be

written as

(A4.4) E 2 = E 0exp i 20 x n 1sin 1 iz

n 1n 2

2

sin 21 1

or

(A4.5) E 2 = E 0exp i x 20 n 1sin 1 exp z 20

n 1n 2

2

sin 21 1

The solution with negative sign in the second exponential term is the real

solution. It shows that the electric field decays exponentially in the z direction; that is, the

direction perpendicular to the interface. This field is called the evanescent field. The first

exponential term shows that this field travels along the x-axis in the same direction and with

the same phase as the wavefront in the waveguide. The depth of the evanescent-field

penetration is defined as the distance over which the amplitude of the field falls to 1/e of its

value at the interface, and is given by

. (A4.6)d p = 0

2sin 1sin c

2

1

Appendix 4: Evanescent field of totally reflected light at a flat interface 121


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References:

Anderson G. P., Golden J. P. and Ligler F. S. "An Evanescent Wave Biosensor - Part I:Fluorescent Signal Acquisition from Step-Etched Fiber Optic Probes" IEEE Transactions on Biomedical Engineering vol. 41 (1994) pp. 578-584

Belmadani B., Casanovas J. and Casanovas A. M. "SF 6 Decomposition under Power Arcs -Chemical Aspects" IEEE Transactions on Electrical Insulation vol. 26 (1991A) pp. 1177-1182

Belmadani B., Casanovas J., Casanovas A. M., Grob R. and Mathieu J. "SF 6 Decompositionunder Power Arcs - Physical Aspects" IEEE Transactions on Electrical

Insulation vol. 26 (1991B) pp. 1163-1176

Bobin B., Bord C. J., Bord J. and Brant C. "Vibration-rotation molecular constants for theground and ( 3=1) states of

32SF 6 from saturated absorption spectroscopy" Journal of Molecular Spectroscopy vol. 121 (1987) pp. 91-127

Born Max and Wolf Emil Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light sixth edition, Pergamon Press 1980

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