MAT'L INST. OF STAND & TECH

1110b

NIST SPECIAL PUBLICATION 260-133

^'ST 2001 Edition

PUBLICATIONS

U. S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

Standard Reference Materials

Acetylene C2H2 Absorption Reference

for 1510 nm to 1540 nm Wavelength

Calibration—SRM 2517a

Sarah L. Gilbert and William C. Swann

0

57

;60-133

01

onal Institute of Standards and Technology

"lology Administration, U.S. Department of Commerce NIST CENTENNIALI
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NIST Special Publication 260-133 2001 Edition

Standard Reference Materials®

Acetylene ^^CiRi 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 tine 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 Tectinology Special Publication 260-133 2001 ED

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

CODEN: NSPUE2

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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
NIST Special Publication 260-133 (revised February 2001)

Standard Reference Materials: Acetylene ^^CiRi 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 25 1 7a extends the use to higher resolution and higher accuracy applications. The center wavelengths of 56 lines of the

Vi + V3 rotational-vibrational band of acetylene ^^CtHi 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

1
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 ^^CiHi Vi + V3 rotational-vibrational combination band, shown in Fig. 1, contains about 50 strong lines between 1510 nm and 1540 nm. The corresponding band

in '^C2H2 extends from about 1520 nm to 1550 nm. Hydrogen cyanide also has a good spectrum, with lines between 1530 nm and 1565 nm for H'''c''*N. 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 ('^C2H2) 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. Acetylene has more than 50 accurately measured absorption lines in the 1500 nm wavelength region. This SRM can be used for high

resolution applicafions, 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 Vi + V3 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 lO"'' 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 pressure2
induced shift and broadening for 15 lines in the Vi + V3 rotational-vibrational band of acetylene '^CiHi 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 ^^C2H2 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 Vi + V3 rotational-vibrational band of acetylene ^'^€2^2 [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 ±2a).

Figure 2 shows the results of our pressure shift measurements. The pressure shift varies with line number and is largest for lines far fi-om 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 Rl 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 1 5 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 least- squares 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:

Rshifiipm) = 0.04 + 0. 1 1 3« - 7.8 x 1 0''

P5/2//?(;?w) = 0. 1 0 + 0.0044« - 5 .4 1 X 1 0"' «

' + 1 .93 X 1 0"'

,

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 Vi + V3 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 (vi + V3) 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 (la) for the measurement of these selected line centers was 0.05 pm [5].

3
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

Vi + V3 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 V] + V3

lines. Lines RO, PI, and PI 8 are notable exceptions to this. Line RO is weak, has significant hot band lines in the vicinity, and can be difficult to identify. For these reasons, we do not certify

line RO. Lines PI and PI 8 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 hne. Since most of

these smaller lines have fractional strengths of less than 1 5 %, 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 (la) of 0.14 pm (=0.25/V3) [7]. For lines PI and PI 8, 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 hne

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

4. Summary

Table 3 gives the SRM certified wavelengths for 56 lines of the Vi + V3 band of acetylene '^C2H2. The uncertainties were obtained by combining the pressure shift uncertainty and the line center measurement uncertainty in quadrature. The 1 5 NIST-measured lines are certified with expanded uncertainties (2a) 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.

4
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, CM. Hydrogen cyanide H^^C'^^N 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-|am bands of acetylene. J. Opt. Soc. Am. B 13: 2708-2714; 1996.

[4] Demtroder, 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 j^m.

J. Mol. Spectrosc. 68: 183-194; 1977; Guelachvih, 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; Jan. 1993.

5
Table 1. Pressure Shift Measurement Results

Pressure shift results from Ref. 5 for the 15 measured lines of the Vi + V3 band of acetylene

^'^CiHi- 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 ±2a).

Pressure shift slope Pressure shift, Line P = 6.7±1.3kPa

(pm/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)

6
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)

29 0.30 28 0.30 27 0.29 26 0.28 25 0.27 24 0.27 23 0.26 22 0.25

21 0.24 20 0.23 19 0.23 18 0.22 17 0.21 16 0.20 15 0.19 14 0.18 13 0.17 12 0.16

11 0.15 10 0.15 9 0.14 8 0.13 7 0.11 6 0.11 5 0.09 4 0.08 3 0.07 2 0.06

1 0.05 0 0.04

P Branch Shift (pm)

1 0.10 2 0.11 3 0.11 4 0.11 5 0.11 6 0.11 7 0.11 8 0.11 9 0.11 10 0.11

11 0.11 12 0.11 13 0.11 14 0.11 15 0.11 16 0.11 17 0.11 18 0.12 19 0.12 20 0.13

21 0.13 22 0.14 23 0.15 24 0.16 25 0.17 26 0.19 27 0.20 28 0.22

7
Table 3. Certified Wavelengths for SRM 2517a

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

(50 Torr) cell pressure. These vacuum wavelengths of the Vi + V3 band '^C2H2 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 ±2a). The

lines in bold were accurately characterized by NIST [5] and have the lowest uncertainty. R Branch Wavelength (nm) P Branch Wavelength (nm)

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1 1 1 f^lQ 1 'tRRRM 1^ 1 3 1 9. 1 OOOD^ 1 1 ) 1Q 1 '^'^fi 719Rn^

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)

8
Figure 1. Spectrum of the acetylene ^^CtHj Vi + V3 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).

9
0.05

R Branch P Branch

Q QQ I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Q QQ

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

'

Line Number

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 ^^Cjili Vi + V3 band. Data are from Ref 5.

10
CD

0.40

0.35

0.30

0.25

0.20

CO ? 0.15 ^ 0.10

0.05

0.00 6

'o ,

oo-o-o.

-•- - 2nd line 20% of main line -O- - 2nd line 15% of main line -- - 2nd line 10% of main line -o- - 2nd line 5% of main line

o~ , ~ - - _ J , I . I I I

. ^

3 4 5 6 7 { Offset of Second Line (pm)10 11

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

a measured (main) Hne 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.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Fractional Strength of Second Line

0.35

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 resuhs. A quadratic fit (dashed line) yields:

shift (pm) = 1.492 x + 1.076 x

the main line.

, where jc is the fractional strength of the second line relative to

11

Appendix A

Standard Reference Material® 2517a

High Resolution Wavelength Calibration Reference for 1510 nm - 1540 nm

Acetylene ^^€2^2

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 ('-CjHj) 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 v, + Vj rotational-vibrational band of ''CjH, 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 I 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 ± 2a).

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 CM. 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.

Serial No.:

Gordon W. Day, Chief

Optoelectronics Division

Gaithersburg, MD 20899

Certificate Issue Date: 1 1 December 2000 Nancy M. Trahey, Chief

Standard Reference Materials Program

SRM 2517a Page 1 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 v, + V3 band '-C2H2 are certified with the uncertainty indicated in parenthesis for the last digits. The uncertainties quoted are the expanded uncertainty using a coverage factor A = 2 (i.e., the quoted

uncertainty is ± 2a). The lines in bold were accurately characterized by NIST [2] and have the lowest uncertainty. R Branch Wavelength P Branch Wavelength

(nm) (nm)

29 1511.7304(3) 28 1512.0884(3) 27 1512.45273(12) 26 1512.8232(3) 25 1513.2000(3) 24 1513.5832(3) 23 1513.9726(3) 22 1514.3683(3)

21 1514.7703(3) 20 1515.1786(3)

19 1515.5932(3)

18 1516.0141(3)

17 1516.44130(11)

16 1516.8747(3)

15 1517.3145(3)

14 1517.7606(3)

13 1518.2131(3)

12 1518.6718(3) i^iQ i36R6nn^

10 1519.6083(3)

9 1520.0860(3)

8 1520.5700(3)

7 1521.06040(10)

6 1521.5572(3)

5 1522.0603(3) 4 1522.5697(3)

3 1523.0855(3)

2 1523.6077(3) 1524.13609(10)

1 1525.7599(6) 2 1526.3140(3)

3 1526.87435(10)

4 1527.44114(10)

5 1528.01432(10)

6 1528.59390(10)

7 1529.1799(3)

8 1529.7723(3)

9 1530.3711(3)

10 1530.97627(10)

11 1531.5879(3)

12 1532.2060(3)

13 1532.83045(10)

14 1533.46136(10)

15 1534.0987(3)

16 1534.7425(3)

17 1535.3928(3)

18 1536.0495(6)

19 1536.7126(3) 20 1537.3822(3)

21 1538.0583(3) 22 1538.7409(3) 23 1539.42992(10) 24 1540.12544(11) 25 1540.82744(11) 26 1541.5359(3) 27 1542.2508(3)

SRM 2517a Page 2 of 6
Storage and Handling: The protective caps provided for tlie 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 '"C^H^ 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 pni 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. SRM 25 1 7a Page 3 of 6
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 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.

R Branch 1

II 9 7

P Branch

1510 1515 1520 1525 1530 1535 1540 1545 Wavelength (nm)

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 ''C^H,

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/ .

SRM 2517a Page 4 of 6
0.7

0.6

0.5 1540.80

P25

I I I ^ I 1540.82 1540.84 Wavelength (nm)

i__

1540.86

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

1529.5 1530.0 1530.5 Wavelength (nm)

1531.0

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

1529.5 1530.5 Wavelength (nm)

1531.0

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

analyzer set to 0.05 nm resolution SRM 2517a Pa2e5of6
Optical Spectrum

Analyzer

Broadband

Source SRM

Unit

(a)

Tunable Source SRM

Unit Detector

(b)

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 |Lim 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 Sv^'ann, W.C, "Acetylene '"C^Hj 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 (301) 975-6776; fax (301) 926-4751; e-mail srminfo@nist.gov; or via

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

SRM 2517a Page 6 of 6
Appendix B

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

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 vi + rotational-vibrational band of acety- lene ^^C2H2. These lines are useful as wavelength references in the 1510-1540-nm region. We find that the pressure shift varies from +0.008(2) pm/kPa for line Rl to +0.043(2) pm/kPa for line i?27, with many of the

lines exhibiting a shift near +0.017 pm/kPa (or, equivalently, +2.3 X 10"^ pm/Torr or -0.29 MHz/Torr). In

addition, we have measured the pressure broadening of these lines and find that it also varies withJine number and is typically -0.7 pm/kPa (~12 MHz/Torr). We also evaluate the line sensitivity to temperature changes and electromagnetic fields. [80740-3224(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 re- gion to support wavelength-division-multiplexed optical

fiber communication systems. In a wavelength-division- multiplexed 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 in- struments that are used to characterize components and

monitor the wavelengths of the channels, wavelength ref- erences are needed. Fundamental atomic or molecular absorptions provide wavelength references that are stable under changing en- vironmental 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 ^^C2H2 +

rotational-vibrational combination band, shown in Fig. 1, contains —50 strong lines between 1510 and 1540 nm. The corresponding band in ^^C2H2 extends from —1520 to —1550 nm. Hydrogen cyanide also has a good spectrum, with lines between 1530 and 1565 nm for H^^C^^'N. The

National Institute of Standards and Technology (NIST)

has developed wavelength calibration transfer standards based on acetylene and hydrogen cyanide. ^'^ The vacuum wavelengths of the acetylene + lines have been measured at low pressure with an uncertainty

of —10"^ nm.^ For a wavelength reference, the stability of the wavelength of each absorption line is a critical characteristic. The symmetric isotopic species of acety- lene 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.'* Commonly called the pressure shift, this

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

Pa) has been reported for one acetylene line at low

pressure.^ 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 stron- gest signals for a given resolution bandwidth. We have measured the pressure-induced shift and

broadening for 15 lines in the vi + rotationalvibrational band of acetylene ^^C2H2. 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 electro- magnetic 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 fi-om 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 la- ser's wavelength with an uncertainty of 1 part in 10' (0.15 pm at 1500 nm). A computer controls the laser wavelength scan and records the readings of the three de- tectors and wavelength meter. Three absorption cells were filled with acetylene ^^C2H2

at low pressure (6.7 ± 0.1 kPa, —50 Torr), intermediate pressure (29.7 ± 0.5 kPa, —225 Torr), and high pressure

(66 ± 1 kPa, -500 Torr). The pressure uncertainty quoted here is the expanded uncertainty obtained with a

0740-3224/00/07 1263-08$ 15.00
1264 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert

R Branch P Branch

7 9 11

1510 1515 1520 1525 1530 1535 1540 Wavelength (nm)

Fig. 1. Acetylene (^^C2H2) 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. coverage factor ^ = 2 (i.e., our quoted uncertainty is ±2cr).^ 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% ^^C2H2). 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 pri- marily 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 1^ , is related to the absorption coefficient a and the absorption path length L by

Tunable nv^^ T

Fig. 2. Diagram of pressure shift measurement apparatus.

It = /oexp(-aL) (1) where /q 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 ob- tain the absorbance aL

Individual lines were then fitted to Voigt profiles'^ by

use of an orthogonal distance regression algorithm.^ The

orthogonal distance regression, called either error-in- variables 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 (re- sulting from Doppler broadening, for example) and

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

0.2 6.7 kPa (50 Torr) 66 kPa (500 Tot)

Wavelength (nm)

Fig. 3. Tunable diode laser scan of the '^'^€2^2 line P4 showing

the transmittance through the low- and the high-pressure cells. Gaussian Doppler broadening and the Lorentzian pres- sure 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
W. C. Swann and S. L. Gilbert Vol. 17, No. 7/JuIy 2000/J. Opt. Soc. Am. B 1265

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 accu- racy 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 stabiHzed 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 lO"* 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 10* for the transmitted power. The fitting program determined the line centers and their widths, the corresponding uncertainties, and the reduced

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

complicate the fitting procedure and can cause uncertainty in the fine 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 point- ing 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 (split- ters), we used free-space beam spHtters 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 iso- lators. These measures reduced the statistical power

fluctuations to 1 part in 10* and the residual slope to less than 5 parts in 10* 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 conse- quently 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 vi + 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 vi- brational state). ^ Figure 4 is a plot of the absorbance be- tween 1526 and 1529 nm, showing lines P2-P6 of the

vi + band and weaker hot band lines. To minimize

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

67 kPa (50 Torr) 66 kPa (500 Torr)

Wavelength (nm) Fig. 4. Plot of ^^CzHj absorbance aL between 1526 and 1529 nm for the low- and the high-pressure cells.

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

spectra^ to select lines that were relatively isolated from

other lines. This eliminated the l£u-ge perturbations, but some smaller lines were present in the vicinity of several measured primary lines. The apparent shift due to smaller lines is most signifi- cant for the broader high-pressure lines, where small hnes can be buried within the primary fine. We esti- mated 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 Rl, P4, and P14. These primary

lines had small Hnes located ~35 pm from their line centers. The line parameters were obtained from the low- pressure 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 ini- tially 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 pro- gram 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

x'^ value was as large as 6. Restricting the fit range to the central portion of the line, within 65% of the maxi- mum absorbance, reduced the x'^ values to ~1, indicating a good fit, and restored the original (unperturbed) line center. Restricting the fit range further did not signifi- cantly 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 ix"^ between 1.6 and

3.4) when fitted over 85% of the maximum absorbance. Narrowing the fit range to within 65% of maximum ab- sorbance reduced the x'^ values to ~ 1 and changed the fit-
1266 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert

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 signifi- cant nearby lines and reducing the fit range to within 65% of the maximum absorbance eliminates the line- overlap 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 fine centers as we changed the width of the fitting region. In view of the good values obtained, we believe that this uncertainty estimate is conservative.

C. Line Fitting Reproducibility To test the reproducibihty of the fine 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 di- vide this value by V2 and assign a standard uncertainty

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

Table 1. Uncertainty Budget"

Relative Line Center Standard Uncertainty (pm) Low-Pressure Cell Intermediate-Pressure Cell High-Pressure Cell Source of Uncertainty (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 M^dow) = 0.03 u<,(int) = 0.05 «e(high) = 0.08 uncertainty

"This 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 Results"

Intermediate - Low Pressure High - Low Pressure AP = 23.0 ± 0.6 kPa AP = 59.3 ± 1.3 kPa Weighted Average

Shift Shift Slope Shift Shift Slope Shift Slope Shift Slope Line (pm) (pm/kPa) (pm) (pm/kPa) (pm/kPa) (MHz/Torr) R21 0.99(12) 0.043(5) 2.56(17) 0.043(3) 0.043(2) -0.73(3) R\l 0.72 0.031 1.89 0.032 0.032(2) -0.55(3) R\\ 0.53 0.023 1.39 0.023 0.023(2) -0.39(3) Rl 0.39 0.017 1.02 0.017 0.017(2) -0.29(3) Rl 0.15 0.007 0.46 0.008 0.008(2) -0.14(3) P3 0.37 0.016 0.98 0.017 0.016(2) -0.27(3) P4 0.42 0.018 1.02 0.017 0.017(2) -0.29(3) P5 0.40 0.017 1.01 0.017 0.017(2) -0.29(3) P6 0.96 0.016 0.016(3) -0.27(5) PIO 0.35 0.015 1.02 0.017 0.017(2) -0.29(3) P13 0.35 0.015 0.98 0.017 0.016(2) -0.27(3) P14 0.37 0.016 0.98 0.017 0.016(2) -0.27(3) P23 0.50 0.022 1.36 0.023 0.023(2) -0.39(3) P24 1.44 0.024 0.024(3) -0.41(5) P25 0.58 0.025 1.53 0.026 0.026(2) -0.44(3)

" Pressure shift results obtained from the two cell pairs for the measured lines of the + band of acetylene ^^C2H2 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 = 2 (i.e., our quoted

uncertainty is ±2a).
W. C. Swann and S. L. Gilbert Vol. 17, No. 7/July 2000/J. Opt. Soc. Am. B 1267

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.^ Diode laser hght 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 5Sv2 ^Pm transitions of rubidium (^^Rb and

^''Rb). The fine centers of the hj^^erfine components of these transitions have been measured with an uncertainty of ±0.4 MHz (Ref 9); a subset of these lines has been measured to higher accuracy.^*' We stabilized the

laser to several different hyperfine components of the ^^Rb transition and compared the wavelength meter read- ing (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 bet- ter than the quoted wavelength meter uncertainty of 1 part in 10^ (—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

-0.20 ± 0.06 pm (-H25 ± 8 MHz). The uncertainty (2o-) is derived from the standard deviation of 10 measure- ments made over a six-month period. During this time

the wavelength meter offset varied from -0.16 to -0.23 pm.

3. PRESSURE SHIFT, LINE CENTER, AND

PRESSURE BROADENING RESULTS

The uncertainty budget for the relative line center deter- minations 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 deter- mined 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 -1-0.017 pm/kPa (or, equivalently,

-H2.3 X 10"^ pmyTorr or -0.29 MHz/Torr). The R branch

exhibited more variation in the pressure shift, with an ap- proximately 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 +0.043 pm/kPa for line R21.

Using the hne center data adjusted for the wavelength meter offset discussed in Subsection 2.D, we extrapolated

the hne centers to zero pressure, using hnear 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

30 40 Pressure (kPa)

Fig. 5. (a) Pressure shift of the line centers for the measured

lines in the ^^C2H2 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 ^^C2H2 P branch, with correspond- ing linear least-squares fits. The uncertainties for the other data shown in (a) and (b) are the same as those shown for R\l.

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 X 10"^ nm. All our line center values are in good agree- ment 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 hne

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 com- ponent of the linewidth for the lines measured in the R

branch and the associated linear fit results. The Lorent-
1268 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L, Gilbert

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 fit- ting algorithms agi'eed for the line centers, values for the Lorentzian component of the linevvddth differed slightly. Table 3, Unperturbed Line Center Values"

Line Center Line Center

Line

This Measurement

(nm) from Ref. 3 (nm)

Difference (pm) R21 1512.45242 1512.45244 -0.02 Rll 1516.44113 1516.44109 0.04 RU 1519.13678 1519.13671 0.07 Rl 1521.06034 1521.06029 0.05 Rl 1524.13602 1524.13604 -0.02 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 PIO 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

" Line 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 x 10"'' nm (0.1 pm). The data in col- umn 3 are from Ref. 3, measured at very low pressure with an estimated

uncertainty of 1.2 x 10"^ nm.

Table 4. Pressure Broadening Results"

Lorentzian Component of Linewidth (pm) Linewidth Slope 6.7-kPa 29.7-kPa 66-kPa (pm/ (MHz/

Line Cell Cell Cell kPa) Torr) R27 3.3(8) 13.3(8) 29.4(8) 0.44(2) 7.5(3) Rn 4.3 18.3 40.2 0.61 10.1 RU 4.9 22.6 50.2 0.76 13.0 Rl 5.1 23.5 51.6 0.78 13.3 Rl 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 PIO 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 "Width 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 pres- sures for selected Hnes of the vi + band of acetylene ^"C2H2. All the values in a column have the expanded uncertainty (coverage factor of 2) listed for the first value in the column.

30 40 50 60 70 Pressure (kPa)

Fig. 6. Pressure broadening (Lorentzian component of the line- width) for the measured lines in the ^^C2H2 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. We attribute this result to the fact that the Voigt profile is generated numerically; small differences between algo- rithms 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 coUisional narrowing due to velocity aver- aging. 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. Since we do not observe significant dis- crepancies between our data and the Voigt function, we

conclude that the line-shape modification due to coUi- sional 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 nor- mal 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, ther- mally induced changes in molecular spectra are usually small for moderate temperatures. Moderate thermal changes can sHghtly modify the pressure shift and broad- ening of a molecular line by changing the collision fre- quency; both these collision-induced effects are proportional to the density of collision partners and their mean

relative velocity."* In a closed cell containing only the gas

phase, the density is fixed. The mean relative velocity is
W. C. Swann and S. L. Gilbert Vol. 17, No. 7 /July 2000/J. Opt. Soc. Am. B 1269

proportional to the square root of the temperature. Thus

the temperature dependence of the pressure shift, A v( T)

,

is simply Ap{T) = Ai^(T„)VT/r„, (2) where AviT„) is the pressure shift measured at temperature r„ and the temperatures T and T„ 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 ± 2) °C. This temperature range would cause a ±0.3% 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 electronic state, where the angular momentum of the electronic cloud is zero. Consequently, magnetic field effects such as hyperfine structure (arising from the inter- nal 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 in- teraction 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 ef- fect is —10'* times smaller than second-order Stark effects and is therefore negligible, except in the case of extremely

high electric fields. High-intensity ac electric fields can split and shift line centers. 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 Ig of a transition. The saturation intensity has been estimated for line P13 of ^^CaHa (Ref. 13) as /s(W/m2) = 15 X 10^(0.1 + lOpf where p is the pres- sure in torr. For the lowest pressure used in our work

(6.7 kPa = 50 Torr), this gives a saturation intensity of 4 X 10^ W/cm^. Our measurements were made with an

intensity of less than 1 W/cm^, 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 experi- ments 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 vi + V3 rotational-vibrational band of acetylene

^^C2H2. Although there is some variation with line number, over half the lines measured exhibit a shift near +0.017 pm/kPa (or, equivalently, +2.3 X 10"^ pm/Torr or -0.29 MHz/Torr). We have also measured the pressure broadening of these lines and find that it also varies with

line number and is t3T3ically -0.7 pm/kPa (12 MHz/Torr). For a pressure of 27 kPa (-200 Torr, the conditions of NIST Standard Reference Material 2517^), the fine 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 line§ 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 be- tween states with low J). One explanation for the pres- sure broadening line dependence is that rotational aver- aging of the potential during a collision causes states with

high rotational angular momentum (high J) to be per- turbed less than states with low J. The pressure shift is more difficult to interpret; it represents the difference be- tween 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

lines^* 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 colhsion- induced 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 ^^CjHa ab-
1270 J. Opt. Soc. Am. B/Vol. 17, No. 7/July 2000 W. C. Swann and S. L. Gilbert

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 H^^C^''N 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-yum bands of acetylene," J. Opt. Soc. Am. B 13, 2708-2714

(1996).

4. W. Demtroder, Laser Spectroscopy, 2nd ed. (Springer- Verlag, Berlin, 1996), pp. 67-82.

5. Y. Sakai, S. Sudo, and T. Ikegami, "Frequency stabihzation

of laser diodes using 1.51-1.55 /^m absorption lines of and ^^CzHz," IEEE J. Quantum Electron. 28, 75-81

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6. B. N. Taylor and C. E. Kuyatt, "Guidelines for evaluating and expressing the uncertainty of NIST measurement re- sults," NIST Tech. Note 1297 (National Institute of Stan- dards and Technology, Gaithersburg, Md., 1993).

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

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8. A. Baldacci, S. Ghersetti, and K N. Rao, "Interpretation of the acetylene spectrum at 1.5 /xm," 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. 0. Rowley, "Frequency measurements on optically narrowed Rb-stabilised laser di- odes 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 ®'Rb 5P3/2 state," Opt. Lett. 21, 1280-1282 (1996).

11. P. L. Varghese and R. K. Hanson, "Collisional narrowing ef- fects 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, "Ultra- narrow ^^C2H2 saturated-absorption lines at 1.5 yu,m," Opt.

Lett. 19, 840-842 (1994).

14. J. Henningsen, H. Simonsen, T. M^gelberg, and E. Truds^, "The 0 — 3 overtone band of CO: precise linestrengths and broadening parameters," J. Mol. Spectrosc. 193, 354-

362 (1999).
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