Optics Communications 234 (2004) 435–441

www.elsevier.com/locate/optcom

Erratum

Investigation of erbium-doped fiber laserintra-cavity absorption sensor for gas detection q,qq

Y. Zhang a,b,*, M. Zhang b, W. Jin b, H.L. Ho b, M.S. Demokan b, X.H. Fang b,B. Culshaw c, G. Stewart c

a Department of Physics, Capital Normal University, Xisanhuan Beilu 105, Beijing, 100037, People�s Republic of Chinab Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong, People�s Republic of China

c Department of Electronic and Electrical Engineering, Strathclyde University, Glasgow G1 1XW, Scotland, UK

Received 15 July 2003; received in revised form 12 December 2003; accepted 18 February 2004

Abstract

Steady state theoretical analysis of an erbium-doped fiber laser intra-cavity absorption sensor shows that high

sensitivity can be achieved when the laser is working near threshold but is limited by the spontaneous emission. Ex-

periments are carried out using a linear cavity fiber laser. The general trends of experimental results agree with the

theoretical prediction. The use of the intra-cavity sensor for gas detection is demonstrated. A sensitivity of 91 times that

of a single-pass absorption sensor is achieved.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Fiber optics sensors; Laser sensors; Absorption spectroscopy

1. Introduction

Detection of pollutant gases such as methane,

acetylene, carbon monoxide, and carbon dioxide is

important in environmental and pollution moni-

toring [1]. Optical fiber sensors based on the ab-sorption of light within the low loss window (1–2

lm) of silica fiber allow for remote detection of

these gases with additional advantages such as

qPII of original article S0030-4018(04)00034-3.qqDOI of original article 10.1016/j.optcom.2004.01.013.

* Corresponding author. Tel.: +86-10-68902178; fax: 0086-10-

68902178.

E-mail address: yzhang@mail.cnu.edu.cn (Y. Zhang).

0030-4018/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.optcom.2004.02.046

immunity to electromagnetic interference, multi-

plexing capability, and low cost. The absorption-

based sensors that use narrowband lasers or

‘‘comb-filter’’ tuned to the characteristic absorp-

tion line or lines of the gas being detected have

been proved to offer excellent selectivity [1,2].Multi-point gas detection has been demonstrated

by networking a number of compact micro-optic

gas cells, allowing for wide area monitoring at

multiple locations and reducing the cost per sens-

ing point [3]. Wavelength modulation spectros-

copy and digital filtering techniques have also been

applied to improve the performance of the multi-

point sensor network, but the etalon effects in themicro-optic cells limit the detection resolution [4].

ed.

436 Y. Zhang et al. / Optics Communications 234 (2004) 435–441

An alternative technique for high sensitivity

absorption measurement is intra-cavity laser spec-

troscopy [5]. With an absorber directly placed

within the laser cavity, the very large number of

passes through the absorber can effectively trans-

form a short absorption cell into a highly efficientmulti-pass system, and thus improves the detection

sensitivity. The implementation of an intra-cavity

spectroscopic system in a fiber optic format would

allow a detection system with the high sensitivity of

the intra-cavity spectroscopy and the advantages of

fiber sensors. Furthermore, all fiber intra-cavity

systems can use the mature fiber components al-

ready developed for communication industry [6],allowing for the realization of cost-effective sys-

tems. The broad gain bandwidths of the fiber gain

mediums, such as erbium-doped fiber amplifier

(EDFA), cover the absorption lines of a number of

pollutant gases and thus permit multi-gas detection

without needing to use individual lasers with

wavelengths designed specifically for the absorp-

tion lines of different gases. Some promising resultson fiber intra-cavity sensor have already been re-

ported [6,7]. In our previous work, we have made

preliminary investigations on the sensitivity of an

erbium-doped fiber (EDF) laser intra-cavity ab-

sorption sensor [8,9]. The effect of spontaneous

emission was however not considered. We here

examine the sensitivity enhancement of an intra-

cavity fiber laser sensor when the effect of sponta-neous emission is considered. The use of the

intra-cavity sensor for acetylene gas detection is

also presented.

2. Theoretical analysis and simulation

When pumped by 1480 nm laser, a fiber laserusing EDF as gain medium can be considered as a

two-level system [10]. The temporal behavior of

the fiber laser can be described by rate equations as

[10,11]

dN2

dt¼ WpN1 �

N2

s2� gsSsc

½NlreN2 � NlraN1�; ð1Þ

N1 ¼ N0 � N2; ð2Þ

dNl

dt¼ gsla

sc½ð1þ NlÞreN2 � raNlN1� �

dscNl; ð3Þ

where N1 and N2 are the population densities of

ground level, upper laser level, respectively. N0 is

the moderate dopant concentration of the EDF, Nl

is the photon number in cavity, Wp ¼ ðgpPprapÞ=Shmp is the pump probability, Pp is the pump powerof the pump laser, hmp is the pump photon energy,

rap is the absorption cross-section at the pump

wavelength, S is the fiber core area, gs and gp are

the proportions of the signal and pump power

within the fiber core, re and ra are the emission

and absorption cross-sections of the mode, re-

spectively. s2 is the life time of the stable level, sc isthe cavity round time, la is the length of the EDF,and d is total intra-cavity loss including the basic

cavity loss and the effect of gas absorption. The

term ðgsla=scÞreN2 represents the change of photon

number in the cavity due to spontaneous emission.

It should be noted that Eqs. (1)–(3) are developed

for the case of single longitudinal mode operation.

However, for multi-longitudinal mode operation,

as long as the bandwidth of laser gain is smallerthan that of the gas absorption line, the single

mode intra-cavity spectroscopy model is still valid

[12]. On the other hand, if the width of the ab-

sorption line is smaller than the bandwidth of the

laser gain, the spectroscopy is regarded as multi-

mode intra-cavity laser spectroscopy, which has a

much higher sensitivity than the single-mode intra-

cavity spectroscopy.If the spontaneous emission is not considered,

the steady-state photon number (N̂l) in cavity can

be obtained by setting dNi=dt ¼ 0 (i ¼ 1; 2 and l)in Eqs. (1)–(3) and expressed the

N̂l ¼A� Bd

d; ð4aÞ

A ¼ SsclaN0ðWps2re � raÞs2½ra þ re�

; ð4bÞ

B ¼ Sscð1þ Wps2Þgss2½ra þ re�

: ð4cÞ

The output power that is proportional to N̂l canbe expressed as

4 5 6 7 8 90

100

200

300

400

500

Sens

itivi

ty E

nhan

cem

ent F

acto

r

Pump Power (mW)

Fig. 1. Theoretical sensitivity as a function of pump power.

With (solid line) and without (dash line) the consideration of

spontaneous emission.

Y. Zhang et al. / Optics Communications 234 (2004) 435–441 437

I / N̂l ¼A� Bd

d: ð5Þ

In absorption sensors, the absorption signal Kis defined as [12]

K ¼ lnI0I; ð6Þ

where I and I0 are, respectively, laser outputpowers with and without absorber in the cavity.

I ¼ I0 � DI , DI is the reduction of the output

power due to the absorption induced cavity loss

variation Dd. For a small absorption, i.e., DI � I0,Eq. (6) can be approximated as

K � DII0

: ð7Þ

The sensitivity enhancement factor that is defined

as the ratio of the intra-cavity absorption signal Kover the single pass loss Dd can be obtained, using

Eqs. (5) and (7), as

KDd

¼ DIIDd

/ AdðA� BdÞ : ð8Þ

It can be seen from Eq. (8) that the sensitivity of

the intra-cavity sensor is inversely proportional to

dðA� BdÞ and can therefore be enhanced by re-ducing the value of dðA� BdÞ. As the basic cavity

loss d cannot be made too small, high sensitivity

can only be achieved when laser is running close to

the threshold, i.e., A� Bd � 0.

When the spontaneous emission is considered,

the steady-state photon number N̂l in cavity will

be:

N̂l ¼�b�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

b2 � 4acp

2a; ð9aÞ

a ¼ �s2ðre þ raÞ1þ Wps2 � gsres2

Ssc

dscSla

; ð9bÞ

b ¼ WpN0s2ðre þ raÞ1þ Wps2 � gsres2

Ssc

� dscSla

s2re

1þ Wps2 � gsres2Ssc

� N0ra �d

gsla; ð9cÞ

c ¼ WpN0s2re

1þ Wps2 � gsres2Ssc

: ð9dÞ

It is difficult to obtain an analytical expression for

the sensitivity enhancement factor by using Eqs.

(9), (6) and (7). We instead evaluated numerically

the dependence of sensitivity enhancement factor

on the pump power for various intra-cavity losses.

Fig. 1 shows the typical results of K=Dd as a

function of pump power. The solid and dash linesare respectively the results with and without the

consideration of spontaneous emission. The

parameters used in the calculation are given in

Table 1. The basic loss of the cavity was taken as

d ¼ 7:0 dB and the loss change is set as Dd ¼ 0:2dB. The pump power varies with a step of 0.05

mW. At the basic loss of d ¼ 7:0 dB, the threshold

pump power calculated using above parameters is6.20 mW. As shown in Fig. 1, the sensitivity tends

to infinity when the pump power is close to the

threshold value if the spontaneous emission is not

considered. The pump power where the dash line

appears to head for infinity is about 7.08 mW. This

value corresponds to the threshold value of fiber

laser with basic loss d ¼ 7:0þ 0:2 dB. If the loss

change in cavity is made smaller, the pump powerwhere the dash line appears to head for infinity will

be more close to the 6.20 mW. The inclusion of

spontaneous emission into the laser equations

(solid line) shows that the sensitivity saturates near

the threshold. At low pump levels, the sensitivity

increases with pump power and reaches a maxi-

Table 1

Parameters used in calculation

Symbol Description Value

N0 Dopant concentration 7:16� 1024 m�3

rap Absorption cross-section at pump wavelength 4:76� 10�25 m2

kp Pump source wavelength 1480 nm

ks Signal light wavelength 1528.9 nm

re Emission cross-section at signal wavelength 4:48� 10�25 m2

ra Absorption cross-section at signal wavelength 4:48� 10�25 m2

S Fiber core area 2:2� 10�11 m2

gs Proportion of the signal power within the fiber core 0.78

gp Proportion of the pump power within the fiber core 0.85

s2 Life time of the stable level 10 ms

la Length of EDF 1.5 m

sc Cavity round time 100 ns

438 Y. Zhang et al. / Optics Communications 234 (2004) 435–441

mum value when the pump power is 6.60 mW, and

then decreases with further increase in pump

power.

3. Experiments and results

Experiments were carried out using a fiber la-ser shown in Fig. 2. The laser cavity includes an

EDFA pumped by a 1480 nm diode laser, a gas

cell made from a pair of collimated graded index

lenses [2,3], a variable attenuator (#1), a fiber

loop mirror, and a tunable optical filter made

from a fiber Bragg grating (FBG). The FBG was

bought from Bragg Photonics in Canada and has

a specified bandwidth of 0.05 nm and reflectivityof 50%, The dopant concentration of 1.5 m long

EDF is �400 ppm. The FBG is used to select

working wavelength to be 1528.9 nm, corre-

OSA

Fiber Loop Mirror

Pump Laser

Attenuator #2

WDM

EDF

Attenuator #1FBG

a

Power Meter

Gas Cell

Fig. 2. Experiment setup. WDM: 1550/1480 WDM coupler;

OSA: optical spectrum analyzer; and EDF: Er-doped fiber.

sponding to one of absorption lines of acetylene(C2H2) gas. The emission spectral width of the

laser is measured to be less than 0.08 nm, limited

by the spectral resolution of the optical spectral

analyzer (OSA). The actual spectral width should

be smaller than this value. This spectral width is

comparable to or smaller than the absorption

lines of acetylene gas around 1530 nm (under

atmospheric pressure). The variable attenuator#1 was used to introduce additional loss to the

cavity. The loss introduced by attenuator #1 is

relatively broadband, but may be used to simu-

late the absorption of gas induced loss because

the laser spectral width is smaller than that of the

gas absorption line. As already mentioned in

Section 2, the case studied here is belong to single

mode intra-cavity laser spectroscopy category.Although it is less sensitive as compared with the

multi-mode intra-cavity spectroscopy [13,14], the

single mode intra-cavity spectroscopy does not

need a very high resolution spectrometer and is

more suited for real time and low-cost gas de-

tection applications. In our present experiment,

an OSA was used to measure the output power

spectrum of the intra-cavity laser. However, anarrow band filter such as a fibre Bragg grating

with its pass band aligned to the gas absorption

line can, in principle, be used to measure directly

the laser output power. The OSA has a sensitivity

of )90 dBm and was set to a minimum resolution

of 0.08 nm to reduce the out-of-band spontane-

ous emission of the EDFA. Another attenuator

(#2) was used to adjust the pump power level.

Y. Zhang et al. / Optics Communications 234 (2004) 435–441 439

An1:99 coupler was used to tap a small amount

of the pump power for the purpose of pump

power monitoring. When the attenuator #1 was

set to a minimum loss of 1.61 dB, the threshold

pump power for fiber laser system was measured

to be 6.24 mW. The dependence of sensitivityenhancement factor on pump power was mea-

sured and shown in Fig. 3. The sensitivity en-

hancement factor was obtained by the following

procedure: when variable attenuator #1 was set

to 1.61 dB, and the laser output power was

measured when the pump power was varied from

5.6 to 7.0 mW at a step of 0.1 mW; the mea-

surement was repeated when the variable atten-uator was set to 1.71 dB, corresponding to a

round-trip loss variation of 2� ð1:71� 1:61ÞdB ¼ 0:2 dB. The difference between the two

measurements was then taken and divided by the

round-trip loss change Dd ¼ 0:2 dB. As expected,

the sensitivity increases when the pump power is

reduced to close to threshold value, and reaches a

maximum value of �110 when pump power was�6.5 mW. It should be pointed out that above

sensitivity enhancement factor was calculated by

using the nominal reading from the variable at-

tenuator. As specified by the manufacture, the

accuracy of the applied single pass attenuation is

�0.03 dB for the attenuator (EXPO FVA-3100)

we used. This would give a round-trip loss change

of Dd ¼ 0:2� 0:06 dB. The sensitivity enhance-ment factor could then be in the range from 85 to

157. The measurements were also limited by the

5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.20

20

40

60

80

100

120

Sens

itivi

ty E

nhan

cem

ent F

acto

r

Pump Power (mW)

Fig. 3. Measured sensitivity versus pump power.

stability and the tuning accuracy of the pump

power (�0.1 mW), and the spectral resolution of

the OSA.

The intra-cavity system was used to measure the

concentration of acetylene gas. The wavelength of

the FBG was firstly fine tuned (by applying strain)to an absorption peak of acetylene around 1528.9

nm. The pump power was set to �6.5 mW, cor-

responding to the maximum sensitivity point in

Fig. 3. Fig. 4(a) shows the spectra of laser output

when the gas cell (1cm long) was filled with 0%,

1%, 2%, 5%, 10% and 20% of acetylene under at-

mospheric pressure. As plotted in Fig. 4(b), the

laser peak output power varies approximatelylinearly with gas concentration inside the gas cell

and drops from )19.54 to )51.50 dBm when the

Fig. 4. (a) Fiber laser output spectra when the gas cell is filled

with different acetylene concentration: 0%, 1%, 2%, 5%, 10%

and 20%. (b) Light absorption as a function of acetylene con-

centration.

Fig. 5. Laser output when the gas cell is periodically filled with

air and 20% acetylene.

440 Y. Zhang et al. / Optics Communications 234 (2004) 435–441

acetylene concentration within the gas cell wasvaried from 0% to 20%. The single pass direct

absorption loss of the same cell was also measured

by filling the cell with same concentration of

acetylene and found to be �0.35 dB. This gives a

sensitivity enhancement factor of 91 times that

of the conventional single pass absorption

measurement.

Measurements were also conducted by fillingthe gas cell periodically with air and 20%

acetylene at atmospheric pressure. Fig. 5 shows

the results for two air/acetylene filling cycles.

The samples (the horizontal axis of Fig. 5) were

taken every 2 s. The fluctuation of laser output

power was measured to be 0.36 dB (root mean

square value), corresponding to a measurement

error in terms of minimum detectable acetyleneconcentration of 2253 ppm. The measurements

were found quite reversible with repeatability of

0.37 dB over five measurement cycles. This va-

lue of repeatability would cause a measurement

error similar to that of the minimum detectable

gas concentration and may be due to the in-

stability of the pump laser, polarization effect,

thermal effect, and various environmental effects.Further work is needed to minimize these effects

and optimize the system performance.

4. Summary

In summary, we have investigated theoretically

and experimentally the relationship between the

sensitivity and the pump power level of an erbi-

um-doped fiber laser intra-cavity absorption

sensor when spontaneous emission is considered.

It was found that the sensitivity of the intra-

cavity fiber laser sensor could be improved sig-

nificantly when the laser is working close to thethreshold, but limited by the spontaneous emis-

sion noise. However, as the sensitivity varies

significantly around the threshold even with a

slight variation in the pump power, the stability

of pump source is therefore crucial to ensure

high stability and sensitive absorption measure-

ments. The power level around the threshold is

also low, meaning that highly sensitive photo-receiver, preferably with matched wavelength fil-

ter to minimize the spontaneous emission noise

of the EDFA, is also required. Our experiments

have achieved a measurement sensitivity of 91

times higher than that of the single pass ab-

sorption measurement and a minimum detectable

(acetylene) gas concentration of 2253 ppm.

Acknowledgements

This work was supported by the Hong Kong

SAR government through a CERG Grant

PolyU5116/01E.

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