NIST Special Publication 260-133

2001 Edition

Standard Reference Materials

Acetylene 12C2H2 Absorption Reference

for 1510 nm to 1540 nm Wavelength

Calibration—SRM 2517a

Sarah L. Gilbert

William C. Swann

Optoelectronics Division

Electronics and Electrical Engineering Laboratory

Boulder, CO 80305-3328

Supersedes NIST Special Publication 260-133 (January 1998)

U.S. DEPARTMENT OF COMMERCE, Donald L. Evans, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Karen H. Brown, Acting Director

Issued February 2001
Certain commercial equipment, instruments, or materials are identified in this paper in

order to specify the experimental procedure adequately. Such identification is not intended

to imply recommendation or endorsement by the National Institute of Standards and

Technology, nor is it intended to imply that the materials or equipment identified are

necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 260-133 2001 ED

Natl. Inst. Stand. Technol. Spec. Publ. 260-133 2001 ED, 29 pages (Feb. 2001)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2001

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov Phone: (202) 512-1800 Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
1

NIST Special Publication 260-133 (2001 Edition)

Standard Reference Materials:

Acetylene 12C2H2 Absorption Reference for 1510 nm to 1540 nm Wavelength Calibration –

SRM 2517a

Sarah L. Gilbert and William C. Swann

Optoelectronics Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, CO 80305-3328

Abstract

Standard Reference Material (SRM) 2517a is an optical-fiber-coupled wavelength reference

based on the fundamental absorption lines of acetylene in the 1510 nm to 1540 nm region. The

main difference between SRM 2517a and its predecessor, SRM 2517, is the use of lower

pressure in the acetylene cell to produce narrower lines. Thus SRM 2517a extends the use to

higher resolution and higher accuracy applications. The center wavelengths of 56 lines of the

U1 + U3 rotational-vibrational band of acetylene 12C2H2 are certified for this SRM. Fifteen lines

are certified with an uncertainty of 0.1 pm, two lines are certified with an uncertainty of 0.6 pm,

and the remainder of the lines are certified with an uncertainty of 0.3 pm. This document

describes SRM 2517a and details the uncertainty analysis.

Keywords: absorption; acetylene; molecular spectroscopy; optical fiber communications; pressure

broadening; pressure shift; Standard Reference Material; wavelength calibration; wavelength

division multiplexing; wavelength reference; wavelength standards; WDM
2

1. Introduction

Wavelength references are important in the 1500 nm region to support wavelength division

multiplexed (WDM) optical fiber communication systems. In a WDM system, many wavelength

channels are sent down the same fiber, thereby increasing the bandwidth of the system by the

number of channels. If one channel’s wavelength were to shift, crosstalk could occur between it

and a neighboring channel. Wavelength references are needed to calibrate instruments that are

used to characterize components and monitor the wavelengths of the channels.

Fundamental atomic or molecular absorption lines provide wavelength references that are very

stable under changing environmental conditions, such as temperature and pressure variations or

the presence of electromagnetic fields. There are several good molecular transitions in the

1500 nm region. The acetylene 12C2H2 U1 + U3 rotational-vibrational combination band, shown in

Fig. 1, contains about 50 strong lines between 1510 nm and 1540 nm. The corresponding band

in 13C2H2 extends from about 1520 nm to 1550 nm. Hydrogen cyanide also has a good spectrum,

with lines between 1530 nm and 1565 nm for H13C

14N. NIST has developed wavelength

calibration Standard Reference Materials (SRM) based on acetylene (SRM 2517 [1]) and

hydrogen cyanide (SRM 2519 [2]).

We have developed a new wavelength calibration standard, SRM 2517a. The main difference

between SRM 2517a and its predecessor, SRM 2517, is the use of lower pressure in the

acetylene cell to produce narrower lines. Thus SRM 2517a can be used in higher resolution and

higher accuracy applications. This document describes SRM 2517a and summarizes the results

of our uncertainty analysis.

Standard Reference Material 2517a is intended for wavelength calibration in the spectral region

from 1510 nm to 1540 nm. It is a single-mode optical-fiber-coupled absorption cell containing

acetylene (12C2H2) gas at a pressure of 6.7 kPa (50 Torr). The absorption path length is 5 cm and

the absorption lines are about 7 pm wide. The cell is packaged in a small instrument box

(approximately 24 cm long × 12.5 cm wide × 9 cm high) with two FC/PC fiber connectors for

the input and output of a user-supplied light source. Acetylene has more than 50 accurately

measured absorption lines in the 1500 nm wavelength region. This SRM can be used for high

resolution applications, such as calibrating a narrowband tunable laser, or lower resolution

applications, such as calibrating an optical spectrum analyzer. The certificate for SRM 2517a is

presented in Appendix A. It includes the certified wavelength values, spectra, and instructions

for use.

The vacuum wavelengths of the acetylene U1 + U3 lines have been measured at very low pressure

(1 Pa to 4 Pa, or equivalently 10 mTorr to 30 mTorr) with an uncertainty of about 10-6 nm [3].

For a wavelength reference, the stability of the wavelength of each absorption line is a critical

characteristic. The symmetric isotopic species of acetylene are particularly insensitive to

external perturbation because they have no permanent dipole moment. The largest potential

source of line shift is energy level shift caused by the interaction of the molecules during elastic

collisions [4]. Commonly called the pressure shift, this shift depends linearly on the collision

frequency. For wavelength calibration of instruments, it is often desirable to use a moderate or

high pressure sample in order to increase the absorption depth. This results in pressure

broadening and a slight pressure shift of the line centers. Our measurement of the pressure-
3

induced shift and broadening for 15 lines in the U1 + U3 rotational-vibrational band of acetylene

12C2H2 and evaluation of other shift mechanisms is described in Ref. 5 (Appendix B of this

document).

The dominant sources of uncertainty for SRM 2517a are the pressure shift uncertainty and the

line center measurement uncertainty. Section 2 gives the uncertainty analysis for the pressure

shift adjustment. Section 3 details the uncertainty analysis for the line center measurement. We

summarize the results in section 4.

2. Pressure Shift Adjustment

SRM 2517a uses acetylene 12C2H2 gas at a pressure of 6.7 ± 1.3 kPa (50 ± 10 Torr). We have

made accurate measurements of the pressure shift for 15 lines in the U1 + U3 rotational-vibrational

band of acetylene 12C2H2 [5]. For SRM 2517a, we derive the line centers by adding each line’s

pressure shift (at 6.7 kPa) to the low-pressure literature values [3]. Unless we specify otherwise,

the uncertainties quoted in this document are expanded uncertainties using a coverage factor

k = 2 (i.e., our quoted uncertainty is ±2σ).

Figure 2 shows the results of our pressure shift measurements. The pressure shift varies with line

number and is largest for lines far from the band center (transitions between states with high

rotational quantum number). In the R branch, the shift slope ranges from 0.008(2) pm/kPa for

line R1 to 0.043(2) pm/kPa for line R27. The P branch shows less variation, with most lines

having a slope near 0.017 pm/kPa. Table 1 summarizes our pressure shift slope measurements

and the pressure shift derived for the SRM pressure of 6.7 ± 1.3 kPa. Our uncertainty for the

pressure shift of the 15 measured lines is dominated by the SRM cell pressure uncertainty. For

the remainder of the lines in the band, we assign pressure shift values based on polynomial leastsquares fitting to the data for each branch. The results for a quadratic fit of the R branch and a

third-order polynomial fit for the P branch are:

( ) 0.10 0.0044 5.41 10 1.93 10 ,

( ) 0.04 0.113 7.8 10

4 2 5 3

5 2

Pshift pm n n n

Rshift pm n n

− −

−

= + − × + ×

= + − ×

 (1)

where n is the line number and the shift (in picometers) is for a pressure of 6.7 kPa. These

values are tabulated in Table 2. The uncertainty of the fitted pressure shift is obtained by

combining (in quadrature) the uncertainty of the fit and the uncertainty of the measured pressure

shift.

3. Line Center Measurement Uncertainty

Wings of nearby lines can skew the shape of the line being measured and shift its apparent

center. In addition to the strong lines of the U1 + U3 band, there are a number of weak lines

throughout the spectrum which are due to hot bands (transitions that are not out of the ground

vibrational state) [6]. These small hot band lines overlap some of the main (U1 + U3) lines and

have a significant potential to shift their apparent line center. The 15 lines measured in Ref. 5

were selected on the basis of their relative isolation from nearby lines. We determined that our

standard uncertainty (1σ) for the measurement of these selected line centers was 0.05 pm [5].
4

Other lines in the band, however, will be assigned higher uncertainties due to the effect of nearby

small lines. Our determination of this uncertainty is described below.

We first determined the approximate strengths of the nearby lines relative to the main lines of the

U1 + U3 band. Using high resolution spectra from Ref. 6 and our own scans using a tunable laser,

we found that the strengths of most of these smaller lines are less than 15 % of the main U1 + U3

lines. Lines R0, P1, and P18 are notable exceptions to this. Line R0 is weak, has significant hot

band lines in the vicinity, and can be difficult to identify. For these reasons, we do not certify

line R0. Lines P1 and P18 overlap hot band lines that have fractional strengths of about 20 % to

30 %; these two lines are certified with a higher uncertainty.

We modeled the effect of small nearby lines on the measurement of the main line centers by

generating Lorentzian lineshapes and calculating the fitted line center for a line when it was

summed with a second smaller nearby line. (The true lineshape is a Voigt profile [4], which is a

convolution of a Lorentzian and Gaussian lineshape. Use of a Lorentzian function simplifies the

modeling and yields a reasonable approximation of the effect.) We chose a Lorentzian full width

at half maximum (FWHM) linewidth of 5 pm, which is close to the Lorentzian component of the

linewidth at this pressure [5]. A second Lorentzian line with the same linewidth and a center

wavelength slightly offset from the main line was summed with the modeled main line. We then

used a least-squares fitting routine to determine the center of the main line. We restricted the

fitting range to within ±5 pm of the line center. This process was repeated using a variety of

strengths and offsets for the second line. Figure 3 shows the results of the modeling for the

conditions where the second line’s fractional strength is 5, 10, 15, and 20 % of the main line.

We found that the maximum shift of the main line always occurred when the second line was

offset by about 3 pm from the main line center (about 60 % of the linewidth). Figure 4 plots the

maximum shift of the main line versus the fractional strength of the second line. Since most of

these smaller lines have fractional strengths of less than 15 %, we determine our uncertainty

based on the maximum shift caused by a line with this fractional strength. As seen in Fig. 4, this

shift is 0.25 pm. Assuming a rectangular distribution with upper and lower limits of ±0.25 pm

about the line center, this corresponds to a standard uncertainty (1σ) of 0.14 pm (=0.25/√3) [7].

For lines P1 and P18, where there are nearby lines with fractional strengths of up to 30 % of the

main lines, we determine the uncertainty based on the maximum shift caused by a small line with

a fractional strength of 30 %. From the data shown in Fig. 4, this maximum shift is 0.54 pm.

Assuming a rectangular distribution with upper and lower limits of ±0.54 pm about the line

center, this corresponds to a standard uncertainty (1σ) of 0.31 pm.

4. Summary

Table 3 gives the SRM certified wavelengths for 56 lines of the U1 + U3 band of acetylene 12C2H2.

The uncertainties were obtained by combining the pressure shift uncertainty and the line center

measurement uncertainty in quadrature. The 15 NIST-measured lines are certified with

expanded uncertainties (2σ) ranging from 0.10 pm to 0.12 pm. The remaining lines are assigned

higher uncertainty, due primarily to the possible skewing of the lineshapes by small nearby lines.

Thirty-nine of these lines are certified with an expanded uncertainty of 0.3 pm, and two lines are

certified with an expanded uncertainty of 0.6 pm.
5

5. References

[1] SRM 2517 used an acetylene pressure of 27 KPa (200 Torr). SRM 2517a (6.7 kPa

pressure) replaces SRM 2517.

[2] Gilbert, S.L.; Swann, W.C.; Wang, C.M. Hydrogen cyanide H13C

14N absorption reference

for 1530–1560 nm wavelength calibration – SRM 2519. Natl. Inst. Stnd. Technol. Spec.

Publ. 260-137; 1998.

[3] Nakagawa, K.; Labachelerie, M.; Awaji, Y.; Kourogi, M. Accurate optical frequency atlas

of the 1.5-μm bands of acetylene. J. Opt. Soc. Am. B 13: 2708-2714; 1996.

[4] Demtröder, W. Laser Spectroscopy, second edition. Berlin, Heidelberg, New York:

Springer-Verlag; 1996. pp. 67-82.

[5] Swann, W.C.; Gilbert, S.L. Pressure-induced shift and broadening of 1510–1540-nm

acetylene wavelength calibration lines. J. Opt. Soc. Am. B 17: 1263-1270; 2000.

[Appendix B of this document].

[6] Baldacci, A.; Ghersetti, S.; Rao, K.N. Interpretation of the acetylene spectrum at 1.5 μm.

J. Mol. Spectrosc. 68: 183-194; 1977; Guelachvili, G.; Rao, K.N. Handbook of Infrared

Standards II. San Diego, CA: Academic Press, Inc.; 1993. pp. 564-571.

[7] Taylor, B.N.; Kuyatt, C.E. Guidelines for Evaluating and Expressing the Uncertainty of

NIST Measurement Results. Natl. Inst. Stand. Technol. Tech. Note 1297; 1994.
6

Table 1. Pressure Shift Measurement Results

Pressure shift results from Ref. 5 for the 15 measured lines of the U1 + U3 band of acetylene

12C2H2. The uncertainties in the last digits of the values are indicated in parentheses. The

uncertainties quoted are the expanded uncertainty using a coverage factor k = 2 (i.e., our quoted

uncertainty is ±2σ).

Line

Pressure shift slope

(pm/kPa)

Pressure shift,

P = 6.7 ± 1.3 kPa

(pm)

R27 + 0.043(2) 0.29(6)

R17 + 0.032(2) 0.21(4)

R11 + 0.023(2) 0.15(4)

R7 + 0.017(2) 0.11(2)

R1 + 0.008(2) 0.05(2)

P3 + 0.016(2) 0.11(2)

P4 + 0.017(2) 0.11(2)

P5 + 0.017(2) 0.11(2)

P6 + 0.016(3) 0.11(2)

P10 + 0.017(2) 0.11(2)

P13 + 0.016(2) 0.11(2)

P14 + 0.016(2) 0.11(2)

P23 + 0.023(2) 0.15(4)

P24 + 0.024(3) 0.16(4)

P25 + 0.026(2) 0.17(4)
7

Table 2. Pressure Shift Fit Results

Pressure shift values for a pressure of 6.7 kPa derived from polynomial fitting (Equation 1) of

the data in Table 1.

R Branch Shift (pm) P Branch Shift (pm)

29 0.30 1 0.10

28 0.30 2 0.11

27 0.29 3 0.11

26 0.28 4 0.11

25 0.27 5 0.11

24 0.27 6 0.11

23 0.26 7 0.11

22 0.25 8 0.11

21 0.24 9 0.11

20 0.23 10 0.11

19 0.23 11 0.11

18 0.22 12 0.11

17 0.21 13 0.11

16 0.20 14 0.11

15 0.19 15 0.11

14 0.18 16 0.11

13 0.17 17 0.11

12 0.16 18 0.12

11 0.15 19 0.12

10 0.15 20 0.13

9 0.14 21 0.13

8 0.13 22 0.14

7 0.11 23 0.15

6 0.11 24 0.16

5 0.09 25 0.17

4 0.08 26 0.19

3 0.07 27 0.20

2 0.06 28 0.22

1 0.05

0 0.04
8

Table 3. Certified Wavelengths for SRM 2517a

Literature values from Ref. 3 adjusted for the pressure shift listed in Table 2 due to the 6.7 kPa

(50 Torr) cell pressure. These vacuum wavelengths of the U1 + U3 band 12C2H2 are certified with

the uncertainty indicated in parentheses for the last digits. The uncertainties quoted are the

expanded uncertainty using a coverage factor k = 2 (i.e., our quoted uncertainty is ±2σ). The

lines in bold were accurately characterized by NIST [5] and have the lowest uncertainty.

R Branch Wavelength (nm) P Branch Wavelength (nm)

29 1511.7304(3) 1 1525.7599(6)

28 1512.0884(3) 2 1526.3140(3)

27 1512.45273(12) 3 1526.87435(10)

26 1512.8232(3) 4 1527.44114(10)

25 1513.2000(3) 5 1528.01432(10)

24 1513.5832(3) 6 1528.59390(10)

23 1513.9726(3) 7 1529.1799(3)

22 1514.3683(3) 8 1529.7723(3)

21 1514.7703(3) 9 1530.3711(3)

20 1515.1786(3) 10 1530.97627(10)

19 1515.5932(3) 11 1531.5879(3)

18 1516.0141(3) 12 1532.2060(3)

17 1516.44130(11) 13 1532.83045(10)

16 1516.8747(3) 14 1533.46136(10)

15 1517.3145(3) 15 1534.0987(3)

14 1517.7606(3) 16 1534.7425(3)

13 1518.2131(3) 17 1535.3928(3)

12 1518.6718(3) 18 1536.0495(6)

11 1519.13686(11) 19 1536.7126(3)

10 1519.6083(3) 20 1537.3822(3)

9 1520.0860(3) 21 1538.0583(3)

8 1520.5700(3) 22 1538.7409(3)

7 1521.06040(10) 23 1539.42992(11)

6 1521.5572(3) 24 1540.12544(11)

5 1522.0603(3) 25 1540.82744(11)

4 1522.5697(3) 26 1541.5359(3)

3 1523.0855(3) 27 1542.2508(3)

2 1523.6077(3)

1 1524.13609(10)
9

Figure 1. Spectrum of the acetylene 12C2H2 U1 + U3 band obtained by scanning a tunable diode

laser and measuring the laser power transmitted through a 5 cm long absorption cell filled to a

pressure of 6.7 kPa (50 Torr).

1510 1515 1520 1525 1530 1535 1540 1545

0.0

0.2

0.4

0.6

0.8

1.0

29

28

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

R Branch P Branch

5

4

3

2

0

1

Normalized Transmittance

Wavelength (nm)
10

Figure 2. Plot of the pressure shift slope and pressure shift at the SRM pressure of 6.7 kPa

versus line number for the R and P branches of the 12C2H2 U1 + U3 band. Data are from Ref. 5.

R30 25 20 15 10 5 0 5 10 15 20 25 P30

0.00

0.01

0.02

0.03

0.04

0.05

R Branch P Branch

Pressure Shift Slope (pm/kPa)

Line Number

0.00

0.05

0.10

0.15

0.20

0.25

0.30

 Pressure Shift at 6.7 kPa (pm)
11

Figure 3. Modeling results to determine the effect of nearby lines on the apparent line center of

a measured (main) line for the conditions where the nearby (second) line’s strength is 5, 10, 15,

and 20 % of the main line. The lines were modeled as Lorentzian lines with 5 pm FWHM. The

points are the modeling results, and the dashed lines are spline fits to guide the eye.

Figure 4. Modeling results: plot of the maximum shift of the main line versus fractional strength

of the second line. The points are the modeling results. A quadratic fit (dashed line) yields:

shift (pm) = 1.492 x + 1.076 x2, where x is the fractional strength of the second line relative to

the main line.

0 1 2 3 4 5 6 7 8 9 10 11

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

 2nd line 20% of main line

 2nd line 15% of main line

 2nd line 10% of main line

 2nd line 5% of main line

Shift of Main Line (pm)

Offset of Second Line (pm)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Maximum Shift of Main Line (pm)

Fractional Strength of Second Line
Appendix A

SRM 2517a Certificate

Appendix B

Journal Article:

W.C. Swann and S.L. Gilbert, “Pressure-induced shift and broadening of 1510–1540-nm

acetylene wavelength calibration lines,” J. Opt. Soc. Am. B 17, 1263-1270 (2000).
SRM 2517a Page 1 of 6

National Institute of Standards & Technology

Certificate

Standard Reference Material® 2517a

High Resolution Wavelength Calibration Reference for 1510 nm – 1540 nm

Acetylene 12C2H2

Serial No.:

This Standard Reference Material (SRM) is intended for wavelength calibration in the spectral region from 1510 nm to 1540 nm. 

SRM 2517a is a single-mode optical-fiber-coupled absorption cell containing acetylene (12C2H2) gas at a pressure of 6.7 kPa (50

Torr). The absorption path length is 5 cm and the absorption lines are about 7 pm wide. The cell is packaged in a small

instrument box (approximately 24 cm long x 12.5 cm wide x 9 cm high) with two FC/PC fiber connectors for the input and output

of a user-supplied light source. This SRM can be used for high resolution applications such as calibrating a narrowband tunable

laser, or lower resolution applications such as calibrating an optical spectrum analyzer. Acetylene has more than 50 accurately

measured absorption lines in the 1500 nm wavelength region.

Certified Wavelength Values: The vacuum wavelengths of absorption lines in the R and P branch of the ν1 + ν3 rotationalvibrational band of 12C2H2 have been measured previously to high accuracy [1]. These literature values for the vacuum

wavelengths were adjusted for the pressure shift due to the collisions between acetylene molecules at the 6.7 kPa (50 Torr)

pressure within the SRM cell to obtain the certified wavelength values for this SRM. Details of the measurement procedure and

data analysis for the determination of the pressure shift can be found in Reference [2], and the uncertainty analysis for the SRM is

documented in Reference [3]. A spectrum of the absorption band is shown in Figure 1 and certified wavelength values are given

in Table 1. Figure 2 shows an expanded scan near line P25. The center wavelengths of 15 lines listed in Table 1 are certified

with an uncertainty of 0.1 pm, 39 lines are certified with an uncertainty of 0.3 pm, and 2 lines are certified with an uncertainty of

0.6 pm. These uncertainties are the expanded uncertainties using a coverage factor k = 2 (i.e., the quoted uncertainty is ± 2σ).

Expiration of Certification: The certification of this SRM is indefinite within the measurement uncertainties specified, provided

the SRM is handled, stored, and used in accordance with the instructions given in this certificate. The gas is contained in a glass

cell with all-glass seals at the windows and the fill port.

Development of the SRM and supporting measurements were performed by S.L. Gilbert and W.C. Swann of the NIST

Optoelectronics Division.

Statistical consultation was provided by C.M. Wang of the NIST Statistical Engineering Division.

The support aspects involved in the preparation, certification, and issuance of this SRM were coordinated through the NIST

Standard Reference Materials Program by J.W.L. Thomas.

Gordon W. Day, Chief

Optoelectronics Division

Gaithersburg, MD 20899 Nancy M. Trahey, Chief

Certificate Issue Date: 11 December 2000 Standard Reference Materials Program
SRM 2517a Page 2 of 6

Table 1. Certified Wavelengths for SRM 2517a

Literature values from Reference [1] are adjusted for the pressure shift due to the 6.7 kPa (50 Torr) cell pressure. These vacuum

wavelengths of the ν1 + ν3 band 12C2H2 are certified with the uncertainty indicated in parenthesis for the last digits. The

uncertainties quoted are the expanded uncertainty using a coverage factor k = 2 (i.e., the quoted uncertainty is ± 2σ). The lines in

bold were accurately characterized by NIST [2] and have the lowest uncertainty.

R Branch Wavelength

(nm)

P Branch Wavelength

(nm)

29 1511.7304(3) 1 1525.7599(6)

28 1512.0884(3) 2 1526.3140(3)

27 1512.45273(12) 3 1526.87435(10)

26 1512.8232(3) 4 1527.44114(10)

25 1513.2000(3) 5 1528.01432(10)

24 1513.5832(3) 6 1528.59390(10)

23 1513.9726(3) 7 1529.1799(3)

22 1514.3683(3) 8 1529.7723(3)

21 1514.7703(3) 9 1530.3711(3)

20 1515.1786(3) 10 1530.97627(10)

19 1515.5932(3) 11 1531.5879(3)

18 1516.0141(3) 12 1532.2060(3)

17 1516.44130(11) 13 1532.83045(10)

16 1516.8747(3) 14 1533.46136(10)

15 1517.3145(3) 15 1534.0987(3)

14 1517.7606(3) 16 1534.7425(3)

13 1518.2131(3) 17 1535.3928(3)

12 1518.6718(3) 18 1536.0495(6)

11 1519.13686(10) 19 1536.7126(3)

10 1519.6083(3) 20 1537.3822(3)

9 1520.0860(3) 21 1538.0583(3)

8 1520.5700(3) 22 1538.7409(3)

7 1521.06040(10) 23 1539.42992(10)

6 1521.5572(3) 24 1540.12544(11)

5 1522.0603(3) 25 1540.82744(11)

4 1522.5697(3) 26 1541.5359(3)

3 1523.0855(3) 27 1542.2508(3)

2 1523.6077(3)

1 1524.13609(10)
SRM 2517a Page 3 of 6

Storage and Handling: The protective caps provided for the FC/PC fiber connectors should be replaced when the SRM is not

in use. This SRM is intended to be used in a laboratory environment near ambient room temperature (22 ± 5) °C. The user

should avoid exposing the unit to large temperature variations, temperature cycling, or mechanical shock, as these may cause the

optical alignment to degrade. Such optical misalignment affects the throughput of the SRM but will not shift the centers of the

absorption lines. A more serious but less likely problem is cell breakage or leakage. The unit should be replaced if the linewidths

or depths differ significantly from those shown in Figures 1 through 4 when measured using comparable resolution.

Measurement Conditions and Procedure: The long term stability of acetylene and the use of fundamental molecular

absorption lines render the SRM insensitive to changes in environmental conditions. The purpose of the certification procedure is

to verify that the unit contains the correct pressure of 12C2H2 gas and has no significant contaminants that produce additional

absorption lines. Measurements are made using a tunable diode laser (∼1 MHz linewidth) and a calibrated wavelength meter. 

Spectra similar to that shown in Figure 2 are taken of each SRM unit and one or more lines are accurately fit to verify the line’s

center using the procedure described in Reference [2].

INSTRUCTIONS FOR USE

General Considerations: The SRM can be used to calibrate a laser or wavelength measuring instrument in the 1510 nm to

1540 nm region. The values in Table 1 are vacuum wavelengths; if the user requires the wavelength in air, the appropriate

correction for the index of refraction of air must be applied (see Reference [4]). Depending on what type of instrument is being

calibrated, a user-supplied broadband source or a tunable narrowband source may be used. Typical optical connections are

shown in Figure 5. The unit is bi-directional (has no preferred input/output port); connections to the unit should be made using

single-mode optical fibers terminated with clean FC/PC connectors.

Use With a Broadband Source: A broadband source in the 1500 nm region (such as a light emitting diode, white light, or

amplified spontaneous emission source) is useful when calibrating an instrument such as a diffraction grating-based optical

spectrum analyzer. A schematic for this type of calibration is shown in Figure 5(a). Light from the broadband source is coupled

into the SRM and the output (transmission through the SRM) is connected to the instrument that is being calibrated. The

absorption lines of acetylene appear as dips in the spectrum of the light source. In general, the dips will not be as deep as those

shown in Figure 1; most instruments of this type will have a resolution bandwidth that is significantly larger than the widths of the

SRM absorption lines. An example of this effect is shown in Figures 3 and 4, where the spectrum in the region of lines P8–10 is

observed using a tunable diode laser (Figure 3) or a broadband source and an optical spectrum analyzer set to 0.05 nm resolution

(Figure 4).

Use With a Tunable Source: The SRM can be used to calibrate the wavelength scale of a tunable source in this region (such as

a diode laser, a fiber laser, or a source filtered by a tunable filter). A schematic for this type of calibration is shown in Figure 5(b).

 The laser is tuned over one or more of the acetylene absorption lines. The transmission through the SRM is monitored by a

detector; the transmitted power passes through a minimum at the center of an absorption line. Alternatively, a tunable laser source

and the SRM can be used to check the calibration of a wavelength meter by measuring the wavelength of the laser (using the

wavelength meter) as the laser is tuned through an absorption line.

Suggested Procedure for Low-Accuracy Requirements; Calibration Uncertainty > 30 pm: If calibrating an instrument

using a broadband source, use an instrument resolution of ≤ 0.1 nm. If using a tunable source, use a data point density of at least

one point every 0.005 nm (5 pm). After identifying a particular absorption line by comparing to the spectrum in Figure 1, find the

center or minimum point of the line. Calibrate the instrument to the center wavelength of this line (from Table 1) using the

calibration procedure specified by the instrument manufacturer. The instrument’s linearity can be checked by repeating the

procedure for a different absorption line and comparing it to the value listed in Table 1.

Suggested Procedure for Moderate-Accuracy Requirements; Calibration Uncertainty in the Approximate Range of 3

pm to 30 pm: If the source power varies significantly with wavelength, divide the SRM transmission spectrum by the source

spectrum to obtain a normalized trace. After identifying a particular absorption line by comparing to the spectrum in Figure 1,

make a high resolution scan of the line. If calibrating an instrument using a broadband source, use an instrument resolution of ≤

0.05 nm. If using a tunable source, use a data point density of at least one point every 0.002 nm (2 pm). Find the wavelength

readings on both sides of the line where the absorption is 50 % of the maximum; the line center is half-way between these two

wavelength readings. For higher accuracy results, repeat this procedure five times and take the average of the measurements. 

Alternatively, the line center can be determined by fitting the central portion using a 4th order polynomial. Calibrate the instrument

to the center wavelength of this line (from Table 1) using the calibration procedure specified by the instrument manufacturer. The
SRM 2517a Page 4 of 6

instrument’s linearity can be checked by repeating the procedure for a different absorption line and comparing it to the value listed

in Table 1.

Suggested Procedure for High-Accuracy Requirements; Calibration Uncertainty < 3 pm: Connect a narrowband tunable

light source (source bandwidth £ 1 pm) to one of the fiber connectors on the SRM unit. After identifying a particular absorption

line by comparing to the spectrum in Figure 1, make a high resolution scan of the line. Use a data point density of at least one

point every 1 pm and divide the SRM transmission spectrum by the source spectrum to obtain a normalized trace. Using a fitting

technique such as the least squares, fit the absorption data to a Lorentzian or Voigt lineshape. Details of a line fitting procedure

and potential errors sources can be found in Reference [2], which is also included as an appendix in Reference [3]. Calibrate the

instrument to the center wavelength of this line (from Table 1) using the calibration procedure specified by the instrument

manufacturer. The instrument’s linearity can be checked by repeating the procedure for a different absorption line and comparing

it to the value listed in Table 1. NOTE: Highly reproducible relative wavelength measurements can be made using the

procedure described for moderate-accuracy requirements. However, due to the presence of nearby lines, the procedure

described in this paragraph is recommended to achieve high-accuracy absolute wavelength calibration.

Figure 1. Normalized spectrum of SRM 2517a obtained by scanning a tunable diode laser and measuring the laser power

transmitted through a SRM unit. The SRM contains a 5 cm long absorption cell filled with acetylene 12C2H2 to a pressure of

6.7 kPa (50 Torr). A file containing these data can be downloaded from NIST at http://ois.nist.gov/srmcatalog/datafiles/.

1510 1515 1520 1525 1530 1535 1540 1545

0.0

0.2

0.4

0.6

0.8

1.0

29

28

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

R Branch P Branch

5

4

3

2

0

1

Normalized Transmittance

Wavelength (nm)
SRM 2517a Page 5 of 6

1540.80 1540.82 1540.84 1540.86

0.5

0.6

0.7

0.8

0.9

1.0

P25

Normalized Transmittance

Wavelength (nm)

Figure 2. Spectrum of line P25 from Figure 1 obtained by scanning a tunable diode laser

1529.5 1530.0 1530.5 1531.0

0.0

0.2

0.4

0.6

0.8

1.0

P10

P9

P8

Normalized Transmittance

Wavelength (nm)

Figure 3. Spectrum of the P8, P9, and P10 lines from Figure 1 obtained by scanning a tunable diode laser

1529.5 1530.0 1530.5 1531.0

0.0

0.2

0.4

0.6

0.8

1.0

P10

P9

P8

Wavelength (nm)

Normalized Transmittance

Resolution BW 0.05 nm

Figure 4. Spectrum of the P8, P9, and P10 lines obtained using a broadband source and an optical spectrum analyzer set

to 0.05 nm resolution
SRM 2517a Page 6 of 6

Figure 5. (a) Schematic of technique when using the SRM and a broadband source to calibrate an optical spectrum analyzer. (b)

Schematic of technique when using the SRM to calibrate a tunable source. A wavelength meter can be calibrated by using a

tunable laser in the configuration shown in (b) and measuring its wavelength using the wavelength meter.

REFERENCES

[1] Nakagawa, K., Labachelerie, M., Awaji, Y., and Kourogi, M., “Accurate Optical Frequency Atlas of the 1.5 μm Bands of

Acetylene,” J. Opt. Soc. Am. B 13, pp. 2708-2714, (1996).

[2] Swann, W.C. and Gilbert, S.L., “Pressure-Induced Shift and Broadening of 1510 to 1540 nm Acetylene Wavelength

Calibration Lines,” J. Opt. Soc. Am. B, 17, pp. 1263-1270, (2000).

[3] Gilbert, S.L. and Swann, W.C., “Acetylene 12C2H2 Absorption Reference for 1510 to 1540 nm Wavelength Calibration –

SRM 2517a,” NIST Special Publication 260-133 (revised 2000), In Press.

[4] Edlen, B., “The Refractive Index of Air,” Metrologia, 2, p. 12, (1966); and CRC Handbook of Chemistry and Physics, 77th

Ed., pp. 10-266, (1996).

Users of this SRM should ensure that the certificate in their possession is current. This can be accomplished by

contacting the SRM Program at: telephone (30l) 975-6776; fax (301) 926-4751; e-mail srminfo@nist.gov; or via the

Internet http://www.nist.gov/srm.

Broadband

Source

Tunable

Source

SRM

Unit

SRM

Unit

Optical

Spectrum

Analyzer

(a)

(b)

Detector
Pressure-induced shift and broadening

of 1510–1540-nm acetylene

wavelength calibration lines

W. C. Swann and S. L. Gilbert

Division of Optoelectronics, Electronics and Electrical Engineering Laboratory, National Institute of Standards

and Technology, Boulder, Colorado 80303

Received November 1, 1999; revised manuscript received January 24, 2000

We have measured the pressure-induced shift for 15 lines of the n 1 1 n 3 rotational–vibrational band of acetylene 12C2H2. These lines are useful as wavelength references in the 1510–1540-nm region. We find that the

pressure shift varies from 10.008(2) pm/kPa for line R1 to 10.043(2) pm/kPa for line R27, with many of the

lines exhibiting a shift near 10.017 pm/kPa (or, equivalently, 12.3 3 1023 pm/Torr or 20.29 MHz/Torr). In

addition, we have measured the pressure broadening of these lines and find that it also varies with line number and is typically ;0.7 pm/kPa (;12 MHz/Torr). We also evaluate the line sensitivity to temperature

changes and electromagnetic fields. [S0740-3224(00)01007-9]

OCIS codes: 020.3690, 060.2330, 120.3940, 120.4800, 300.6260, 300.6390, 300.0300.

1. INTRODUCTION

Wavelength references are important in the 1500-nm region to support wavelength-division-multiplexed optical

fiber communication systems. In a wavelength-divisionmultiplexed system many wavelength channels are sent

down the same fiber, thereby increasing the bandwidth of

the system by the number of channels. If one channel’s

wavelength were to shift, cross talk could occur between

that channel and a neighboring channel. To calibrate instruments that are used to characterize components and

monitor the wavelengths of the channels, wavelength references are needed.

Fundamental atomic or molecular absorptions provide

wavelength references that are stable under changing environmental conditions such as temperature and pressure

variations or the presence of electromagnetic fields.

There are several good molecular transitions in the

1500-nm region. The acetylene 12C2H2 n 1 1 n 3

rotational–vibrational combination band, shown in Fig. 1,

contains ;50 strong lines between 1510 and 1540 nm.

The corresponding band in 13C2H2 extends from ;1520 to

;1550 nm. Hydrogen cyanide also has a good spectrum,

with lines between 1530 and 1565 nm for H13C14N. The

National Institute of Standards and Technology (NIST)

has developed wavelength calibration transfer standards

based on acetylene and hydrogen cyanide.1,2

The vacuum wavelengths of the acetylene n 1 1 n 3 lines

have been measured at low pressure with an uncertainty

of ;1026 nm.3 For a wavelength reference, the stability

of the wavelength of each absorption line is a critical

characteristic. The symmetric isotopic species of acetylene are particularly insensitive to external perturbation

because they have no permanent dipole moment. The

largest potential source of line shift is energy-level shift

caused by the interaction of the molecules during elastic

collisions.4 Commonly called the pressure shift, this

shift depends linearly on the collision frequency. An upper limit for the pressure shift of 200 kHz/Torr (1.5 kHz/

Pa) has been reported for one acetylene line at low

pressure.5 For wavelength calibration of instruments,

however, it is often desirable to use an intermediate- or

high-pressure sample to match the reference bandwidth

to the instrument resolution. This results in the strongest signals for a given resolution bandwidth.

We have measured the pressure-induced shift and

broadening for 15 lines in the n 1 1 n 3 rotational–

vibrational band of acetylene 12C2H2. We describe our

measurement procedure in Section 2 and summarize the

results in Section 3. In Section 4 we estimate the line

center sensitivity to temperature changes and electromagnetic fields. Conclusions are given in Section 5.

2. MEASUREMENT DESCRIPTION AND

DATA ANALYSIS

A schematic diagram of our pressure shift measurement

apparatus is shown in Fig. 2. Light from a tunable diode

laser is sent through two absorption cells simultaneously,

and the transmission through each cell is monitored by

detectors. One cell contains acetylene gas at low pressure, and the other contains either intermediate or high

pressure, as specified below. A third detector monitors

the laser power, and a wavelength meter measures the laser’s wavelength with an uncertainty of 1 part in 107

(0.15 pm at 1500 nm). A computer controls the laser

wavelength scan and records the readings of the three detectors and wavelength meter.

Three absorption cells were filled with acetylene 12C2H2

at low pressure (6.7 6 0.1 kPa, ;50 Torr), intermediate

pressure (29.7 6 0.5 kPa, ;225 Torr), and high pressure

(66 6 1 kPa, ;500 Torr). The pressure uncertainty

quoted here is the expanded uncertainty obtained with a

W. C. Swann and S. L. Gilbert Vol. 17, No. 7/July 2000/J. Opt. Soc. Am. B 1263

0740-3224/00/071263-08$15.00
coverage factor k 5 2 (i.e., our quoted uncertainty is

62s).6 The fused-silica absorption cells are 5 cm long,

with windows fused to the cells by a glass frit method.

To prevent interference fringes in the transmitted signal

the windows are mounted at an angle of 11° and are also

wedged by ;2°. The cells were first evacuated and leak

checked and were then filled with isotopically pure gas

(99.96% 12C2H2). During the fill process the pressure in

the fill manifold (and hence the cell) was monitored with a

capacitance manometer and a strain gauge pressure sensor. Once filled, the cells were closed off with a glass

valve with o-ring seals.

Figure 3 shows spectra of line P4 obtained with the

low- and the high-pressure cells. The pressure broadening in the high-pressure spectrum is obvious. We are primarily interested in the shift of the high-pressure line

relative to the low-pressure line. Fifteen lines were

scanned by this technique, and 13 of these lines were also

scanned by use of the low- and the intermediate-pressure

cells. The measured quantity, the transmitted power IT ,

is related to the absorption coefficient a and the absorption path length L by

IT 5 I0 exp~2aL!, (1)

where I0 is the incident power. We first divided the cell

transmission curves by the laser power monitor signal to

remove common-mode intensity variations and normalized the data. We then took the natural logarithm to obtain the absorbance aL.

Individual lines were then fitted to Voigt profiles4 by

use of an orthogonal distance regression algorithm.7 The

orthogonal distance regression, called either error-invariables or total-least-squares regression, obtains the

model parameters by minimizing the sum of squares (SS)

of the orthogonal distances from the model to the data

points. The fitting program was able to account for a

background slope and uncertainties in both x (wavelength) and y (transmitted power). A Voigt profile is a

convolution of Lorentzian and Gaussian profiles; it results

when there is a combination of Gaussian broadening (resulting from Doppler broadening, for example) and

Lorentzian line shape (resulting from the natural linewidth or pressure broadening, for example). In our situation the natural linewidth is small compared with the

Gaussian Doppler broadening and the Lorentzian pressure broadening. For the low-pressure data, the width of

the Lorentzian component and the width of the Gaussian

component are comparable. For the intermediate- and

the high-pressure data, the Lorentzian component dominates because of the larger pressure broadening. For the

Fig. 1. Acetylene (12C2H2) spectrum taken by passing LED light through a 5-cm-long absorption cell and recording the spectrum of the

transmitted light with an optical spectrum analyzer with 0.05-nm resolution. This spectrum has been normalized to the LED spectrum.

Fig. 2. Diagram of pressure shift measurement apparatus.

Fig. 3. Tunable diode laser scan of the 12C2H2 line P4 showing

the transmittance through the low- and the high-pressure cells.

1264 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert
line fitting, we fixed the Gaussian Doppler linewidth at

3.7 pm (Ref. 4) and allowed other model parameters to

vary.

Since the spectra for the low- and the high-pressure

cells were measured simultaneously, the absolute accuracy of the wavelength meter was not of critical importance for the relative pressure shift measurement. However, the short-term statistical variation of the

wavelength measurement did add noise to the data. To

determine this statistical variation we took repeated measurements of a laser stabilized to a narrow rubidium line.

The statistical variation of repeated measurements

yielded a Gaussian distribution with a standard deviation

of 0.1 pm. We determined the experimental uncertainty

in transmitted power by measuring the statistical variation of the data within a region of the line wing. The

standard deviation of these fluctuations was 1 part in 104

of the transmitted power.

Each data point was assigned a standard uncertainty

of 0.1 pm for the wavelength and a fractional uncertainty

of 1 part in 104 for the transmitted power. The fitting

program determined the line centers and their widths,

the corresponding uncertainties, and the reduced

residual-SS (x2) value for the fit. Several factors can

complicate the fitting procedure and can cause uncertainty in the line center measurement. Our approaches

to minimizing and measuring the effect of these contributions are discussed below.

A. Background Signal Variation

A slope or a variation in the background level can shift

the apparent center of a line, particularly for the wide

lines of the intermediate- and the high-pressure cells.

Interference fringes due to reflected laser light, wavelength dependence of the optical components, beam pointing stability, and variations in the laser power can cause

background variation. As mentioned above, we removed

common-mode laser power variations by dividing the cell

transmittance data by the power monitor data. Owing to

the wavelength dependence of optical fiber couplers (splitters), we used free-space beam splitters to send the laser

light to the cells and the power monitor. We minimized

interference effects by using wedged cell windows and

beam splitters, windowless detectors, and two optical isolators. These measures reduced the statistical power

fluctuations to 1 part in 104 and the residual slope to less

than 5 parts in 104 over a 250-pm scan. This residual

slope was ;1 order of magnitude less than that caused by

small spectra features discussed below and is consequently insignificant compared with spectral effects.

B. Overlap with Nearby Lines

Wings of nearby lines can skew the shape of the line being

measured and can shift its apparent center. In addition

to the strong lines of the n 1 1 n 3 band, there are a number of weak lines throughout the spectrum that are due to

hot bands (transitions that are not out of the ground vibrational state).8 Figure 4 is a plot of the absorbance between 1526 and 1529 nm, showing lines P2 –P6 of the

n 1 1 n 3 band and weaker hot band lines. To minimize

the effect of neighboring lines on our pressure shift measurement we deliberately avoided measuring lines in the

spectrum that have significant lines very close to the primary line (such as line P2). We used high-resolution

spectra8 to select lines that were relatively isolated from

other lines. This eliminated the large perturbations, but

some smaller lines were present in the vicinity of several

measured primary lines.

The apparent shift due to smaller lines is most significant for the broader high-pressure lines, where small

lines can be buried within the primary line. We estimated the effect of these lines by modeling the worst

cases. The high-pressure data were modeled with

Lorentzian line shapes that approximate the spectra in

the vicinity of lines R1, P4, and P14. These primary

lines had small lines located ;35 pm from their line centers. The line parameters were obtained from the lowpressure data, with the linewidths scaled up to account

for pressure broadening. White noise was added to the

pure Lorentzian shapes to simulate real data. We initially limited the line fitting to the central portion of the

line within 85% of the maximum absorbance. Adding

small lines, modeled as described above, resulted in a

shift in the line center value returned by the fitting program for the (modeled) primary line. We found that the

fitted line center of the primary line is most sensitive to

additional lines that are very near the line center. Even

a very small line (absorbance '1% of the primary line)

can cause an apparent line shift of ;0.2 pm if it is within

50 pm of the center of the primary line. In our modeling

of the three primary lines the apparent shift due to small

neighboring lines was as much as 0.4 pm, and the reduced

x2 value was as large as 6. Restricting the fit range to

the central portion of the line, within 65% of the maximum absorbance, reduced the x2 values to ;1, indicating

a good fit, and restored the original (unperturbed) line

center. Restricting the fit range further did not significantly effect the results.

We compared the modeling results with those obtained

from the measured data and observed similar trends.

For the high-pressure data, primary lines with nearby

weak lines gave relatively poor fits (x2 between 1.6 and

3.4) when fitted over 85% of the maximum absorbance.

Narrowing the fit range to within 65% of maximum absorbance reduced the x2 values to ;1 and changed the fitFig. 4. Plot of 12C2H2 absorbance aL between 1526 and 1529

nm for the low- and the high-pressure cells.

W. C. Swann and S. L. Gilbert Vol. 17, No. 7/July 2000/J. Opt. Soc. Am. B 1265
ted line center by as much as 0.2 pm; further narrowing of

the fit range had a negligible effect.

The combination of avoiding primary lines with significant nearby lines and reducing the fit range to within

65% of the maximum absorbance eliminates the lineoverlap skewing effect for most cases. To first order, the

small line wings could be approximated by a slope in the

background when the fit was restricted to a narrow region

around the line center. The fitting program was able to

remove this effect by removing a slope in the region of the

main line. If the fit range was too wide, however, the

simple slope approximation was not adequate. Since we

cannot be certain that there are no small lines closer than

35 pm from a primary line center, we assign a standard

uncertainty (estimated standard deviation) for each of the

relative line centers: of 0.07 pm for the high-pressure

data and 0.04 pm for the intermediate-pressure data, owing to residual effects of additional lines. These uncertainty estimates are derived from the variation of the line

centers as we changed the width of the fitting region. In

view of the good x2 values obtained, we believe that this

uncertainty estimate is conservative.

C. Line Fitting Reproducibility

To test the reproducibility of the line fit we took several

scans of the same lines and determined the pressure shift

for each scan. Since the wavelength meter could drift

slightly between each scan, we compared only the shift

measurement, not the individual line center measurements. From these measurements we estimate that the

standard deviation for the line shift is 0.03 pm. Since

this is an uncertainty in the shift measurement and not

an uncertainty in the individual line centers, we then divide this value by A2 and assign a standard uncertainty

of 0.02 pm for both the low-pressure and the higherpressure cell data.

Table 1. Uncertainty Budgeta

Source of Uncertainty

Relative Line Center Standard Uncertainty (pm)

Low-Pressure Cell Intermediate-Pressure Cell High-Pressure Cell

(6.7 kPa) (29.7 kPa) (66 kPa)

Nearby line contribution – 0.04 0.07

Fit statistical uncertainty 0.02 0.02 0.02

Fit reproducibility 0.02 0.02 0.02

Combined standard

uncertainty

uc(low) 5 0.03 uc(int) 5 0.05 uc(high) 5 0.08

aThis uncertainty budget was used for the determination of relative line centers for the low-, intermediate-, and high-pressure cells. The combined

standard uncertainties are the root SS of the standard uncertainties due to the sources listed. The absolute accuracy of the wavelength meter is not

included.

Table 2. Pressure Shift Resultsa

Line

Intermediate – Low Pressure

DP 5 23.0 6 0.6 kPa

High – Low Pressure

DP 5 59.3 6 1.3 kPa Weighted Average

Shift

(pm)

Shift Slope

(pm/kPa)

Shift

(pm)

Shift Slope

(pm/kPa)

Shift Slope

(pm/kPa)

Shift Slope

(MHz/Torr)

R27 0.99(12) 0.043(5) 2.56(17) 0.043(3) 0.043(2) 20.73(3)

R17 0.72 0.031 1.89 0.032 0.032(2) 20.55(3)

R11 0.53 0.023 1.39 0.023 0.023(2) 20.39(3)

R7 0.39 0.017 1.02 0.017 0.017(2) 20.29(3)

R1 0.15 0.007 0.46 0.008 0.008(2) 20.14(3)

P3 0.37 0.016 0.98 0.017 0.016(2) 20.27(3)

P4 0.42 0.018 1.02 0.017 0.017(2) 20.29(3)

P5 0.40 0.017 1.01 0.017 0.017(2) 20.29(3)

P6 – – 0.96 0.016 0.016(3) 20.27(5)

P10 0.35 0.015 1.02 0.017 0.017(2) 20.29(3)

P13 0.35 0.015 0.98 0.017 0.016(2) 20.27(3)

P14 0.37 0.016 0.98 0.017 0.016(2) 20.27(3)

P23 0.50 0.022 1.36 0.023 0.023(2) 20.39(3)

P24 – – 1.44 0.024 0.024(3) 20.41(5)

P25 0.58 0.025 1.53 0.026 0.026(2) 20.44(3)

aPressure shift results obtained from the two cell pairs for the measured lines of the n 1 1 n 3 band of acetylene 12C2H2 are shown. The uncertainties in

the final digits of the values are indicated in parentheses. For the data in columns 2–5, all the values in a particular column have the uncertainty listed

for the first value in the column. The uncertainties quoted are the expanded uncertainties obtained by use of a coverage factor k 5 2 (i.e., our quoted

uncertainty is 62s).

1266 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert
D. Wavelength Accuracy

Although the absolute accuracy of the wavelength measurement was not relevant to the pressure shift measurement, extrapolating our line center measurements to zero

pressure and comparing with literature values serves as a

good verification of our measurements. To determine the

line center accuracy for our measurements we first

checked the accuracy of the wavelength meter used in the

measurements. We have set up a high-accuracy wavelength reference for this purpose.2 Diode laser light at

1560.5 nm is amplified with an erbium-doped fiber amplifier and is frequency doubled in a periodically poled

lithium niobate crystal. The resultant 780-nm light is

then used to conduct saturated absorption spectroscopy

on the 5S1/2 → 5P3/2 transitions of rubidium (85Rb and 87Rb). The line centers of the hyperfine components of

these transitions have been measured with an uncertainty of 60.4 MHz (Ref. 9); a subset of these lines has

been measured to higher accuracy.10 We stabilized the

laser to several different hyperfine components of the

87Rb transition and compared the wavelength meter reading (vacuum wavelength) to the literature values multiplied by 2. Since the lines were very narrow (less than

10 MHz), the absolute stability of the laser was much better than the quoted wavelength meter uncertainty of 1

part in 107 (;20 MHz at 1560 nm). From measurements

taken before and after our pressure shift scans we found

that the wavelength meter reading was offset by

20.20 6 0.06 pm (125 6 8 MHz). The uncertainty (2s)

is derived from the standard deviation of 10 measurements made over a six-month period. During this time

the wavelength meter offset varied from 20.16 to 20.23

pm.

3. PRESSURE SHIFT, LINE CENTER, AND

PRESSURE BROADENING RESULTS

The uncertainty budget for the relative line center determinations is given in Table 1. Table 2 summarizes the

line-shift measurement results for the low–intermediatepressure pair and the low–high-pressure pair. We determined a weighted average slope for the pressure shift for

each line. In all cases the wavelength shift was positive

with increasing pressure. Figures 5(a) and 5(b) are plots

of line center versus pressure for the measured lines of

the R and the P branches, respectively. As expected,

each line’s shift is consistent with a linear dependence on

pressure. For most of the lines in the P branch, the shift

was approximately 10.017 pm/kPa (or, equivalently,

12.3 3 1023 pm/Torr or 20.29 MHz/Torr). The R branch

exhibited more variation in the pressure shift, with an approximately linear dependence on line number. For both

branches, the pressure shift was considerably larger for

lines far from the band center (i.e., transitions between

states with high rotational quantum numbers), rising to

10.043 pm/kPa for line R27.

Using the line center data adjusted for the wavelength

meter offset discussed in Subsection 2.D, we extrapolated

the line centers to zero pressure, using linear regression

fitting. Table 3 summarizes our determinations of the

line centers and compares them to the more accurate

measurements reported in Ref. 3, which were measured

at 1–4 Pa (10–30 mTorr). Our expanded uncertainty is

0.1 pm (coverage factor of 2), which is twice the root SS of

the relative line center standard uncertainty (0.03 pm),

the wavelength meter calibration standard uncertainty

(0.03 pm), and the linear regression fit uncertainty (0.03

pm). The estimated uncertainty given in Ref. 3 is 1.2

3 1026 nm. All our line center values are in good agreement with those of Ref. 3; the differences between our

measurements and those reported in Ref. 3 are within our

uncertainty for each line center. This gives us further

confidence in our analysis of the line center values.

Pressure broadening is responsible for the Lorentzian

component of the Voigt line shape. We found that the

pressure broadening also varied with line number. In

contrast to the pressure shift dependence, however, the

pressure broadening was largest for lines near the band

center (transitions between states with low rotational

quantum numbers). Table 4 summarizes our results for

the width of the Lorentzian component of the Voigt line

shape, where the Gaussian component (which is due to

Doppler broadening at room temperature) was fixed at 3.7

pm. The width variation with line number can be seen

more clearly in Fig. 6, where we plot the Lorentzian component of the linewidth for the lines measured in the R

branch and the associated linear fit results. The LorentFig. 5. (a) Pressure shift of the line centers for the measured

lines in the 12C2H2 R branch. Each line is shown with a linear

least-squares fit to the data. (b) Pressure shift of the line centers

for the measured lines in the 12C2H2 P branch, with corresponding linear least-squares fits. The uncertainties for the other

data shown in (a) and (b) are the same as those shown for R11.

W. C. Swann and S. L. Gilbert Vol. 17, No. 7/July 2000/J. Opt. Soc. Am. B 1267
zian linewidth slope versus pressure, derived from these

least-squares fits, is also given in Table 4. Our uncertainty for the Lorentzian linewidth values was derived

from the variation that we observed when using different

fitting algorithms for the Voigt profile. Although the fitting algorithms agreed for the line centers, values for the

Lorentzian component of the linewidth differed slightly.

We attribute this result to the fact that the Voigt profile is

generated numerically; small differences between algorithms can yield different model parameters. Since each

line is a convolution of its Gaussian and Lorentzian components, the convolved linewidth at low pressure will be

dominated by the width of the Gaussian component.

Our pressure broadening analysis does not include the

small effect of collisional narrowing due to velocity averaging. This effect is negligible at higher pressures,

where pressure broadening dominates, but can cause the

line shape to deviate from the expected Voigt profile at

low pressures.11 Since we do not observe significant discrepancies between our data and the Voigt function, we

conclude that the line-shape modification due to collisional narrowing is negligible at the level of our quoted

uncertainty.

4. SPECTRAL SENSITIVITY TO OTHER

ENVIRONMENTAL CONDITIONS

Other environmental conditions can affect molecular

spectra and can potentially shift line centers. For normal conditions, all these effects are small compared with

the pressure shift and broadening described in Section 3.

Below we discuss the effects of temperature variation and

electromagnetic fields.

A. Temperature

Aside from the obvious effect that thermal distribution of

population in rotational levels has on line strengths, thermally induced changes in molecular spectra are usually

small for moderate temperatures. Moderate thermal

changes can slightly modify the pressure shift and broadening of a molecular line by changing the collision frequency; both these collision-induced effects are proportional to the density of collision partners and their mean

relative velocity.4 In a closed cell containing only the gas

phase, the density is fixed. The mean relative velocity is

Fig. 6. Pressure broadening (Lorentzian component of the linewidth) for the measured lines in the 12C2H2 R branch. Each line

is shown with a linear least-squares fit to the data. The uncertainties are approximately the same size as the data points.

Table 3. Unperturbed Line Center Valuesa

Line

Line Center

This Measurement

(nm)

Line Center

from Ref. 3

(nm)

Difference

(pm)

R27 1512.45242 1512.45244 20.02

R17 1516.44113 1516.44109 0.04

R11 1519.13678 1519.13671 0.07

R7 1521.06034 1521.06029 0.05

R1 1524.13602 1524.13604 20.02

P3 1526.87430 1526.87424 0.06

P4 1527.44111 1527.44103 0.08

P5 1528.01428 1528.01421 0.07

P6 1528.59388 1528.59379 0.09

P10 1530.97621 1530.97616 0.05

P13 1532.83042 1532.83034 0.08

P14 1533.46131 1533.46125 0.06

P23 1539.42979 1539.42977 0.02

P24 1540.12535 1540.12528 0.07

P25 1540.82729 1540.82727 0.02

aLine center results for very-low-pressure conditions (less than 5 Pa).

Our measurements (column 2) are values obtained by use of line centers at

the different pressures extrapolated to zero pressure. Our expanded uncertainty for each line center is 1 3 1024 nm (0.1 pm). The data in column 3 are from Ref. 3, measured at very low pressure with an estimated

uncertainty of 1.2 3 1026 nm.

Table 4. Pressure Broadening Resultsa

Line

Lorentzian Component of Linewidth (pm) Linewidth Slope

6.7-kPa

Cell

29.7-kPa

Cell

66-kPa

Cell

(pm/

kPa)

(MHz/

Torr)

R27 3.3(8) 13.3(8) 29.4(8) 0.44(2) 7.5(3)

R17 4.3 18.3 40.2 0.61 10.1

R11 4.9 22.6 50.2 0.76 13.0

R7 5.1 23.5 51.6 0.78 13.3

R1 6.1 25.2 55.8 0.84 14.3

P3 5.9 24.7 54.2 0.81 13.8

P4 5.6 23.5 51.9 0.78 13.3

P5 5.4 22.7 50.5 0.76 13.0

P6 5.3 – 48.1 0.72 12.3

P10 5.0 20.6 45.3 0.68 11.6

P13 4.9 20.6 44.9 0.67 11.4

P14 4.7 19.7 43.1 0.65 11.1

P23 3.9 15.7 34.4 0.51 8.7

P24 3.7 – 33.4 0.50 8.5

P25 3.6 15.6 32.3 0.48 8.2

aWidth of the Lorentzian component of the Voigt line profile derived

from fitting the lines with the Gaussian component, which is due is Doppler broadening, fixed at 3.7 pm. Results were obtained at the three pressures for selected lines of the n 1 1 n 3 band of acetylene 12C2H2. All the

values in a column have the expanded uncertainty (coverage factor of 2)

listed for the first value in the column.

1268 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert
proportional to the square root of the temperature. Thus

the temperature dependence of the pressure shift, Dn(T),

is simply

Dn~T! 5 Dn~Tm!AT/Tm, (2)

where Dn(Tm) is the pressure shift measured at temperature Tm and the temperatures T and Tm are in degrees

Kelvin. From Eq. (2) it can be seen that the line center is

fairly insensitive to temperature changes; a 50 K increase

from room temperature would increase the pressure shift

by only 8%. For the measurements reported here, the

temperature was (22 6 2) °C. This temperature range

would cause a 60.3% change in the pressure shift, which

is negligible compared with our other sources of uncertainty.

B. Electromagnetic Fields

An excellent discussion of the effects of electromagnetic

fields on molecular spectra can be found in Ref. 12. The

ground state of acetylene and most other molecules is

the 1S electronic state, where the angular momentum of

the electronic cloud is zero. Consequently, magnetic field

effects such as hyperfine structure (arising from the internal magnetic field) and the Zeeman effect (interaction of a

magnetic moment with an external magnetic field) are

much smaller than those normally found in atoms. This

is simply due to the nature of the molecular chemical

bond, where unpaired electrons in atoms pair up with

electrons from another atom. Magnetic moments for

these molecules are proportional to the overall rotational

angular momentum and are ;1/1000 that of an electron.

Thus a moderately large magnetic field of 0.1 T (1000 G)

would cause a Zeeman splitting of less than 1 MHz (;0.01

pm).

Electric quadrupole hyperfine structure (arising from

the interaction of a nuclear electric quadrupole moment

and the surrounding charge distribution) is absent in

acetylene because it lacks a nuclear quadrupole moment.

First- and second-order Stark shifts (arising from the interaction of the molecular electric dipole moment and an

external electric field) are also absent; owing to its symmetry, the molecule has no permanent electric dipole moment. An electric field can polarize a molecule; this effect is ;104 times smaller than second-order Stark effects

and is therefore negligible, except in the case of extremely

high electric fields.12

High-intensity ac electric fields can split and shift line

centers.12 This effect is referred to as the Autler–Townes

effect, the ac Start effect, or light shift and is significant

when the laser intensity is comparable with the saturation intensity IS of a transition. The saturation intensity

has been estimated for line P13 of 13C2H2 (Ref. 13) as

IS (W/m2) 5 15 3 106(0.1 1 10p)2 where p is the pressure in torr. For the lowest pressure used in our work

(6.7 kPa 5 50 Torr), this gives a saturation intensity of

4 3 108 W/cm2

. Our measurements were made with an

intensity of less than 1 W/cm2

, so we are clearly operating

far from the regime in which this effect is significant.

This effect may need to be taken into account for experiments done at low pressure and high intensity, such as

those in which a power buildup cavity is used.

5. CONCLUSIONS

We have measured the pressure-induced shift for 15 lines

of the n 1 1 n 3 rotational–vibrational band of acetylene 12C2H2. Although there is some variation with line number, over half the lines measured exhibit a shift near

10.017 pm/kPa (or, equivalently, 12.3 3 1023 pm/Torr or

20.29 MHz/Torr). We have also measured the pressure

broadening of these lines and find that it also varies with

line number and is typically ;0.7 pm/kPa (12 MHz/Torr).

For a pressure of 27 kPa (;200 Torr, the conditions of

NIST Standard Reference Material 25171

), the line shift

is typically near 0.5 pm but can be as large as 1.2 pm for

lines far from the band center and can be as low as 0.2 pm

for lines near the band center. The Lorentzian component of the linewidths at this pressure varies from 12 pm

(1.5 GHz) for lines far from the band center to 23 pm (2.9

GHz) near the band center.

Although the pressure shift and the pressure broadening are both due to the interactions of molecules during

collisions, they depend on line number rather differently.

The pressure shift is largest for lines far from the band

center (transitions between states with high rotational

quantum number J), whereas the pressure broadening is

largest for lines near the band center (transitions between states with low J). One explanation for the pressure broadening line dependence is that rotational averaging of the potential during a collision causes states with

high rotational angular momentum (high J) to be perturbed less than states with low J. The pressure shift is

more difficult to interpret; it represents the difference between the shift of the excited state and the shift of the

ground state. We would need to conduct a more extensive study before drawing any conclusions about the shift

of a particular state. Measurements of the pressure

broadening and the pressure shift of carbon monoxide

lines14 show trends that are very similar to those that we

observe in acetylene.

We also evaluated the line sensitivity to temperature

changes and to electromagnetic fields. We conclude that

these effects are small compared with the collisioninduced pressure broadening and pressure shift. In most

cases thermal and electromagnetic effects can be neglected, although they can be significant at extreme temperatures and field strengths.

ACKNOWLEDGMENTS

The authors are grateful to C. Wang for discussions and

suggestions on the uncertainty analysis and to D. Nesbitt

and L. Hollberg for discussions and comments on the

manuscript.

S. Gilbert can be reached by e-mail at

sgilbert@boulder.nist.gov.

REFERENCES

1. S. L. Gilbert, T. J. Drapela, and D. L. Franzen, ‘‘Moderateaccuracy wavelength standards for optical communications,’’ in Technical Digest—Symposium on Optical Fiber

Measurements, NIST Spec. Publ. 839 (National Institute of

Standards and Technology, Boulder, Colo., 1992), pp. 191–

194; S. L. Gilbert and W. C. Swann, ‘‘Acetylene 12C2H2 abW. C. Swann and S. L. Gilbert Vol. 17, No. 7/July 2000/J. Opt. Soc. Am. B 1269
sorption reference for 1510–1540 nm wavelength

calibration—SRM 2517,’’ NIST Spec. Publ. 260–133 (National Institute of Standards and Technology, Gaithersburg, Md., 1998).

2. S. L. Gilbert, W. C. Swann, and C. M. Wang, ‘‘Hydrogen

cyanide H13C14N absorption reference for 1530–1560 nm

wavelength calibration—SRM 2519,’’ NIST Spec. Publ.

260–137 (National Institute of Standards and Technology,

Gaithersburg, Md., 1998).

3. K. Nakagawa, M. de Labachelerie, Y. Awaji, and M.

Kourogi, ‘‘Accurate optical frequency atlas of the 1.5-mm

bands of acetylene,’’ J. Opt. Soc. Am. B 13, 2708–2714

(1996).

4. W. Demtro ̈der, Laser Spectroscopy, 2nd ed. (SpringerVerlag, Berlin, 1996), pp. 67–82.

5. Y. Sakai, S. Sudo, and T. Ikegami, ‘‘Frequency stabilization

of laser diodes using 1.51–1.55 mm absorption lines of 12C2H2 and 13C2H2,’’ IEEE J. Quantum Electron. 28, 75–81

(1992).

6. B. N. Taylor and C. E. Kuyatt, ‘‘Guidelines for evaluating

and expressing the uncertainty of NIST measurement results,’’ NIST Tech. Note 1297 (National Institute of Standards and Technology, Gaithersburg, Md., 1993).

7. P. A. Boggs, R. H. Byrd, J. E. Rogers, and R. B. Schnabel,

‘‘User’s reference guide for ODRPACK version 2.01: software for weighted orthogonal distance regression,’’ NIST

Interagency Rep. 4834 (National Institute of Standards and

Technology, Gaithersburg, Md., 1992).

8. A. Baldacci, S. Ghersetti, and K. N. Rao, ‘‘Interpretation of

the acetylene spectrum at 1.5 mm,’’ J. Mol. Spectrosc. 68,

183–194 (1977); G. Guelachvili and K. N. Rao, Handbook of

Infrared Standards II (Academic, San Diego, Calif., 1993),

pp. 564–571.

9. G. P. Barwood, P. Gill, and W. R. C. Rowley, ‘‘Frequency

measurements on optically narrowed Rb-stabilised laser diodes at 780 nm and 795 nm,’’ Appl. Phys. B: Photophys. Laser Chem. 53, 142–147 (1991).

10. J. Ye, S. Swartz, P. Jungner, and J. L. Hall, ‘‘Hyperfine

structure and absolute frequency of the 87Rb 5P3/2 state,’’

Opt. Lett. 21, 1280–1282 (1996).

11. P. L. Varghese and R. K. Hanson, ‘‘Collisional narrowing effects on spectral line shapes measured at high resolution,’’

Appl. Opt. 23, 2376–2385 (1984).

12. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy

(Dover, New York, 1975), Chaps. 10 and 11.

13. M. de Labachelerie, K. Nakagawa, and M. Ohtsu, ‘‘Ultranarrow 13C2H2 saturated-absorption lines at 1.5 mm,’’ Opt.

Lett. 19, 840–842 (1994).

14. J. Henningsen, H. Simonsen, T. Mo”gelberg, and E. Trudso”,

‘‘The 0 → 3 overtone band of CO: precise linestrengths

and broadening parameters,’’ J. Mol. Spectrosc. 193, 354–

362 (1999).

1270 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert