Accurate absolute reference frequencies from 1511 to 1545 nm of the ν1+ν3 band of <sup>12</sup>C2H2 determined with laser frequency comb interval measurements

Alan A. Madej; A. John Alcock; Andrzej Czajkowski; John E. Bernard; Sergei Chepurov

doi:10.1364/JOSAB.23.002200

Journal of the Optical Society of America B
Vol. 23,
Issue 10,
pp. 2200-2208
(2006)
•https://doi.org/10.1364/JOSAB.23.002200

Accurate absolute reference frequencies from $1511 to 1545 nm$ of the $ν_{1} + ν_{3}$ band of ${}^{12}C_{2} H_{2}$ determined with laser frequency comb interval measurements

Alan A. Madej, A. John Alcock, Andrzej Czajkowski, John E. Bernard, and Sergei Chepurov

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Alan A. Madej, A. John Alcock, Andrzej Czajkowski, John E. Bernard, and Sergei Chepurov, "Accurate absolute reference frequencies from 1511 to 1545 nm of the ν1+ν3 band of ¹²C2H2 determined with laser frequency comb interval measurements," J. Opt. Soc. Am. B 23, 2200-2208 (2006)

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Abstract

Absolute frequency measurements, with uncertainties as low as $2 kHz$ $(1 \times 10^{- 11})$ , are presented for the $ν_{1} + ν_{3}$ band of ${}^{12}C_{2} H_{2}$ at $1.5 μ m$ $(194 - 198 THz)$ . The measurements were made using cavity-enhanced, diode-laser-based saturation spectroscopy. With one laser system stabilized to the $P (16)$ line of ${}^{13}C_{2} H_{2}$ and a system stabilized to the line in ${}^{12}C_{2} H_{2}$ whose frequency was to be determined, a Cr:YAG laser-based frequency comb was employed to measure the frequency intervals. The systematic uncertainty is notably reduced relative to that of previous studies, and the region of measured lines has been extended. Improved molecular constants are obtained.

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Source of Systematic Shift	Estimated Shift Uncertainty (kHz)
Uncertainty in modulation amplitude	0.5
Uncertainty in intracavity power	0.5
Uncertainty in operating cell pressure	0.9
Electronic offsets of laser lock to cavity	0.5
Frequency interval measurement offset due to reference oscillator	0.002
Uncertainty in laser 2, $P (16)$ reference frequency	1.2
Total shift	1.7

Line	Offset from $P (16)$ (kHz)	$U_{c}$ (kHz)	Frequency (kHz)	$U_{c}$ (kHz)	Vacuum Wavelength (nm)	$U_{c}$ (nm)	Offset (this work and Ref. [24]) (kHz)
$12 P 31$	$- 351 195 291.6$	4 .0	194 018 374 094.3	4.1	1 545.175 602	$3.3 \times 10^{- 8}$	0.2
$12 P 30$	$- 258 109 650.9$	1.5	194 111 459 735.0	1.9	1 544.434 617	$1.5 \times 10^{- 8}$	6.2
$12 P 29$	$- 165 753 448.2$	1.2	194 203 815 937.8	1.8	1 543.700 141	$1.4 \times 10^{- 8}$	$- 4.7$
$12 P 28$	$- 74 128 756.4$	1.5	194 295 440 629.5	2.0	1 542.972 172	$1.6 \times 10^{- 8}$	2.5
$12 P 27$	16 762 897.6	1.5	194 386 332 283.6	2.0	1 542.250 705	$1.6 \times 10^{- 8}$	$- 9.2$
$12 P 26$	106 919 478.4	2.0	194 476 488 864.4	2.4	1 541.535 739	$1.9 \times 10^{- 8}$	$- 8.5$
$12 P 25$	196 340 804.5	1.3	194 565 910 190.5	1.8	1 540.827 259	$1.4 \times 10^{- 8}$	$- 9.7$
$12 P 24$	285 023 746.4	2.0	194 654 593 132.4	2.4	1 540.125 271	$1.9 \times 10^{- 8}$	$- 6.5$
$12 P 23$	372 967 336.9	1.2	194 742 536 722.9	1.8	1 539.429 767	$1.4 \times 10^{- 8}$	$- 7.4$
$12 P 22$	460 170 032.2	1.5	194 829 739 418.2	1.9	1 538.740 743	$1.5 \times 10^{- 8}$	$- 6.4$
$12 P 21$	546 630 314.5	1.6	194 916 199 700.5	2.0	1 538.058 194	$1.6 \times 10^{- 8}$	$- 7.7$
$12 P 20$	632 346 688.8	1.3	195 001 916 074.7	1.8	1 537.382 114	$1.4 \times 10^{- 8}$	$- 7.6$
$12 P 19$	717 317 679.1	1.3	195 086 887 065.0	1.8	1 536.712 500	$1.4 \times 10^{- 8}$	$- 5.5$
$12 P 18$	801 541 820.8	1.3	195 171 111 206.7	1.8	1 536.049 347	$1.4 \times 10^{- 8}$	$- 6.8$
$12 P 17$	885 017 681.1	2.2	195 254 587 067.1	2.6	1 535.392 651	$2.0 \times 10^{- 8}$	$- 4.1$
$12 P 16$	967 743 824.0	1.4	195 337 313 210.0	1.9	1 534.742 406	$1.5 \times 10^{- 8}$	$- 5.0$
$12 P 15$	1 049 718 850.4	1.5	195 419 288 236.3	2.0	1 534.098 608	$1.6 \times 10^{- 8}$	$- 2.6$
$12 P 14$	1 130 941 360.2	2.8	195 500 510 746.2	3.0	1 533.461 252	$2.4 \times 10^{- 8}$	$- 1.5$
$12 P 13$	1 211 409 984.4	3.5	195 580 979 370.4	3.7	1 532.830 334	$2.9 \times 10^{- 8}$	$- 0.7$
$12 P 12$	1 291 123 355.4	2.9	195 660 692 741.4	3.1	1 532.205 850	$2.5 \times 10^{- 8}$	$- 3.8$
$12 P 11$	1 370 080 137.4	3.1	195 739 649 523.4	3.3	1 531.587 794	$2.6 \times 10^{- 8}$	$- 1.3$
$12 P 10$	1 448 278 992.7	3.6	195 817 848 378.7	3.8	1 530.976 162	$3.0 \times 10^{- 8}$	$- 3.6$
$12 P 9$	1 525 718 615.7	2.4	195 895 288 001.6	2.7	1 530.370 950	$2.1 \times 10^{- 8}$	0.05
$12 P 8$	1 602 397 698.5	1.9	195 971 967 084.5	2.3	1 529.772 153	$1.8 \times 10^{- 8}$	$- 1.4$
$12 P 7$	1 678 314 964.8	2.7	196 047 884 350.7	3.0	1 529.179 766	$2.3 \times 10^{- 8}$	0.5
$12 P 6$	1 753 469 134.1	1.3	196 123 038 520.1	1.8	1 528.593 786	$1.4 \times 10^{- 8}$	$- 1.3$
$12 P 5$	1 827 858 961.3	3.4	196 197 428 347.2	3.6	1 528.014 208	$2.8 \times 10^{- 8}$	1.5
$12 P 4$	1 901 483 194.4	1.2	196 271 052 580.4	1.8	1 527.441 026	$1.4 \times 10^{- 8}$	$- 1.5$
$12 P 3$	1 974 340 616.0	2.6	196 343 910 002.0	2.9	1 526.874 238	$2.2 \times 10^{- 8}$	1.4
$12 P 2$	2 046 430 009.0	1.3	196 415 999 394.9	1.8	1 526.313 839	$1.4 \times 10^{- 8}$	$- 4.2$
$12 P 1$	2 117 750 175.7	1.3	196 487 319 561.7	1.8	1 525.759 823	$1.4 \times 10^{- 8}$	$- 5.3$
$12 R 0$	2 258 078 098.8	1.2	196 627 647 484.7	1.7	1 524.670 929	$1.4 \times 10^{- 8}$	$- 3.4$
$12 R 1$	2 327 083 532.0	1.7	196 696 652 917.9	2.1	1 524.136 042	$1.6 \times 10^{- 8}$	$- 2.4$
$12 R 2$	2 395 315 080.4	3.1	196 764 884 466.3	3.3	1 523.607 522	$2.6 \times 10^{- 8}$	$- 5.0$
$12 R 3$	2 462 771 621.3	1.3	196 832 341 007.2	1.8	1 523.085 365	$1.4 \times 10^{- 8}$	$- 6.0$
$12 R 4$	2 529 452 039.9	2.2	196 899 021 425.9	2.6	1 522.569 568	$2.0 \times 10^{- 8}$	$- 5.5$
$12 R 5$	2 595 355 239.0	1.2	196 964 924 625.0	1.8	1 522.060 126	$1.4 \times 10^{- 8}$	$- 2.6$
$12 R 6$	2 660 480 130.6	1.5	197 030 049 516.5	1.9	1 521.557 035	$1.5 \times 10^{- 8}$	$- 1.2$
$12 R 7$	2 724 825 646.8	1.3	197 094 395 032.7	1.8	1 521.060 292	$1.4 \times 10^{- 8}$	$- 0.6$
$12 R 8$	2 788 390 730.7	1.2	197 157 960 116.6	1.7	1 520.569 891	$1.3 \times 10^{- 8}$	$- 3.9$
$12 R 9$	2 851 174 350.5	1.3	197 220 743 736.5	1.8	1 520.085 830	$1.4 \times 10^{- 8}$	$- 0.5$
$12 R 10$	2 913 175 471.7	1.2	197 282 744 857.7	1.7	1 519.608 105	$1.3 \times 10^{- 8}$	—
$12 R 11$	2 974 393 096.1	1.3	197 343 962 482.1	1.8	1 519.136 710	$1.4 \times 10^{- 8}$	—
$12 R 12$	3 034 826 223.5	2.7	197 404 395 609.4	3.0	1 518.671 644	$2.3 \times 10^{- 8}$	—
$12 R 13$	3 094 473 893.8	2.0	197 464 043 279.7	2.3	1 518.212 901	$1.8 \times 10^{- 8}$	—
$12 R 14$	3 153 335 123.6	1.2	197 522 904 509.6	1.7	1 517.760 478	$1.3 \times 10^{- 8}$	—
$12 R 15$	3 211 408 993.5	1.3	197 580 978 379.4	1.8	1 517.314 371	$1.4 \times 10^{- 8}$	—
$12 R 16$	3 268 694 565.8	2.1	197 638 263 951.8	2.5	1 516.874 577	$1.9 \times 10^{- 8}$	—
$12 R 17$	3 325 190 939.9	1.3	197 694 760 325.9	1.8	1 516.441 091	$1.4 \times 10^{- 8}$	—
$12 R 18$	3 380 897 227.8	1.3	197 750 466 613.7	1.8	1 516.013 910	$1.4 \times 10^{- 8}$	—
$12 R 19$	3 435 812 557.1	1.2	197 805 381 943.0	1.7	1 515.593 029	$1.3 \times 10^{- 8}$	—
$12 R 20$	3 489 936 076.3	1.4	197 859 505 462.2	1.8	1 515.178 446	$1.4 \times 10^{- 8}$	—
$12 R 21$	3 543 266 956.9	1.4	197 912 836 342.9	1.9	1 514.770 156	$1.5 \times 10^{- 8}$	—
$12 R 22$	3 595 804 386.5	1.6	197 965 373 772.4	2.0	1 514.368 156	$1.5 \times 10^{- 8}$	—
$12 R 23$	3 647 547 589.4	1.3	198 017 116 975.3	1.8	1 513.972 441	$1.4 \times 10^{- 8}$	—
$12 R 24$	3 698 495 209.9	1.7	198 068 064 595.9	2.1	1 513.583 013	$1.6 \times 10^{- 8}$	—
$12 R 25$	3 748 648 054.0	1.2	198 118 217 439.9	1.8	1 513.199 855	$1.3 \times 10^{- 8}$	—
$12 R 26$	3 798 003 983.5	1.3	198 167 573 369.4	1.8	1 512.822 976	$1.4 \times 10^{- 8}$	—
$12 R 27$	3 846 562 721.7	1.6	198 216 132 107.7	2.0	1 512.452 366	$1.5 \times 10^{- 8}$	—
$12 R 28$	3 894 323 473.2	5.5	198 263 892 859.1	5.6	1 512.088 024	$4.3 \times 10^{- 8}$	—
$12 R 29$	3 941 286 000.1	2.1	198 310 855 386.0	2.4	1 511.729 942	$1.9 \times 10^{- 8}$	—
$12 R 30$	3 987 450 177.5	9.1	198 357 019 563.5	9.1	1 511.378 113	$7.0 \times 10^{- 8}$	—
$12 R 31$	4 032 805 511.4	4.4	198 402 374 897.3	4.6	1 511.032 608	$3.5 \times 10^{- 8}$	—

Molecular Constant $({cm}^{- 1})$	This Work	Reference [24]	Reference [8]
$B^{″}$	1.176 646 487 7 (9)	1.176 646 497 4 (14)	1.176 646 29 (5)
$D^{″}$ $(\times 10^{6})$	1.626 966 (3)	1.627 067 (13)	1.625 84 (9)
$H^{″}$ $(\times 10^{12})$	1.518 (5)	1.90 (6)	—
$L^{″}$ $(\times 10^{18})$	$- 4.5$ (2.3)	—	—
$B^{'}$	1.163 777 834 9 (8)	1.163 777 842 6 (23)	1.163 777 53 (5)
$D^{'}$ $(\times 10^{6})$	1.607 282 (3)	1.607 372 (12)	1.605 53 (10)
$H^{'}$ $(\times 10^{12})$	2.574 (3)	3.03 (7)	—
$ν_{o}$	6556.464 783 18 (4)	6556.464 783 32 (33)	6556.464 783 (1)

Source of Systematic Shift	Estimated Shift Uncertainty (kHz)
Uncertainty in modulation amplitude	0.5
Uncertainty in intracavity power	0.5
Uncertainty in operating cell pressure	0.9
Electronic offsets of laser lock to cavity	0.5
Frequency interval measurement offset due to reference oscillator	0.002
Uncertainty in laser 2, $P (16)$ reference frequency	1.2
Total shift	1.7

Line	Offset from $P (16)$ (kHz)	$U_{c}$ (kHz)	Frequency (kHz)	$U_{c}$ (kHz)	Vacuum Wavelength (nm)	$U_{c}$ (nm)	Offset (this work and Ref. [24]) (kHz)
$12 P 31$	$- 351 195 291.6$	4 .0	194 018 374 094.3	4.1	1 545.175 602	$3.3 \times 10^{- 8}$	0.2
$12 P 30$	$- 258 109 650.9$	1.5	194 111 459 735.0	1.9	1 544.434 617	$1.5 \times 10^{- 8}$	6.2
$12 P 29$	$- 165 753 448.2$	1.2	194 203 815 937.8	1.8	1 543.700 141	$1.4 \times 10^{- 8}$	$- 4.7$
$12 P 28$	$- 74 128 756.4$	1.5	194 295 440 629.5	2.0	1 542.972 172	$1.6 \times 10^{- 8}$	2.5
$12 P 27$	16 762 897.6	1.5	194 386 332 283.6	2.0	1 542.250 705	$1.6 \times 10^{- 8}$	$- 9.2$
$12 P 26$	106 919 478.4	2.0	194 476 488 864.4	2.4	1 541.535 739	$1.9 \times 10^{- 8}$	$- 8.5$
$12 P 25$	196 340 804.5	1.3	194 565 910 190.5	1.8	1 540.827 259	$1.4 \times 10^{- 8}$	$- 9.7$
$12 P 24$	285 023 746.4	2.0	194 654 593 132.4	2.4	1 540.125 271	$1.9 \times 10^{- 8}$	$- 6.5$
$12 P 23$	372 967 336.9	1.2	194 742 536 722.9	1.8	1 539.429 767	$1.4 \times 10^{- 8}$	$- 7.4$
$12 P 22$	460 170 032.2	1.5	194 829 739 418.2	1.9	1 538.740 743	$1.5 \times 10^{- 8}$	$- 6.4$
$12 P 21$	546 630 314.5	1.6	194 916 199 700.5	2.0	1 538.058 194	$1.6 \times 10^{- 8}$	$- 7.7$
$12 P 20$	632 346 688.8	1.3	195 001 916 074.7	1.8	1 537.382 114	$1.4 \times 10^{- 8}$	$- 7.6$
$12 P 19$	717 317 679.1	1.3	195 086 887 065.0	1.8	1 536.712 500	$1.4 \times 10^{- 8}$	$- 5.5$
$12 P 18$	801 541 820.8	1.3	195 171 111 206.7	1.8	1 536.049 347	$1.4 \times 10^{- 8}$	$- 6.8$
$12 P 17$	885 017 681.1	2.2	195 254 587 067.1	2.6	1 535.392 651	$2.0 \times 10^{- 8}$	$- 4.1$
$12 P 16$	967 743 824.0	1.4	195 337 313 210.0	1.9	1 534.742 406	$1.5 \times 10^{- 8}$	$- 5.0$
$12 P 15$	1 049 718 850.4	1.5	195 419 288 236.3	2.0	1 534.098 608	$1.6 \times 10^{- 8}$	$- 2.6$
$12 P 14$	1 130 941 360.2	2.8	195 500 510 746.2	3.0	1 533.461 252	$2.4 \times 10^{- 8}$	$- 1.5$
$12 P 13$	1 211 409 984.4	3.5	195 580 979 370.4	3.7	1 532.830 334	$2.9 \times 10^{- 8}$	$- 0.7$
$12 P 12$	1 291 123 355.4	2.9	195 660 692 741.4	3.1	1 532.205 850	$2.5 \times 10^{- 8}$	$- 3.8$
$12 P 11$	1 370 080 137.4	3.1	195 739 649 523.4	3.3	1 531.587 794	$2.6 \times 10^{- 8}$	$- 1.3$
$12 P 10$	1 448 278 992.7	3.6	195 817 848 378.7	3.8	1 530.976 162	$3.0 \times 10^{- 8}$	$- 3.6$
$12 P 9$	1 525 718 615.7	2.4	195 895 288 001.6	2.7	1 530.370 950	$2.1 \times 10^{- 8}$	0.05
$12 P 8$	1 602 397 698.5	1.9	195 971 967 084.5	2.3	1 529.772 153	$1.8 \times 10^{- 8}$	$- 1.4$
$12 P 7$	1 678 314 964.8	2.7	196 047 884 350.7	3.0	1 529.179 766	$2.3 \times 10^{- 8}$	0.5
$12 P 6$	1 753 469 134.1	1.3	196 123 038 520.1	1.8	1 528.593 786	$1.4 \times 10^{- 8}$	$- 1.3$
$12 P 5$	1 827 858 961.3	3.4	196 197 428 347.2	3.6	1 528.014 208	$2.8 \times 10^{- 8}$	1.5
$12 P 4$	1 901 483 194.4	1.2	196 271 052 580.4	1.8	1 527.441 026	$1.4 \times 10^{- 8}$	$- 1.5$
$12 P 3$	1 974 340 616.0	2.6	196 343 910 002.0	2.9	1 526.874 238	$2.2 \times 10^{- 8}$	1.4
$12 P 2$	2 046 430 009.0	1.3	196 415 999 394.9	1.8	1 526.313 839	$1.4 \times 10^{- 8}$	$- 4.2$
$12 P 1$	2 117 750 175.7	1.3	196 487 319 561.7	1.8	1 525.759 823	$1.4 \times 10^{- 8}$	$- 5.3$
$12 R 0$	2 258 078 098.8	1.2	196 627 647 484.7	1.7	1 524.670 929	$1.4 \times 10^{- 8}$	$- 3.4$
$12 R 1$	2 327 083 532.0	1.7	196 696 652 917.9	2.1	1 524.136 042	$1.6 \times 10^{- 8}$	$- 2.4$
$12 R 2$	2 395 315 080.4	3.1	196 764 884 466.3	3.3	1 523.607 522	$2.6 \times 10^{- 8}$	$- 5.0$
$12 R 3$	2 462 771 621.3	1.3	196 832 341 007.2	1.8	1 523.085 365	$1.4 \times 10^{- 8}$	$- 6.0$
$12 R 4$	2 529 452 039.9	2.2	196 899 021 425.9	2.6	1 522.569 568	$2.0 \times 10^{- 8}$	$- 5.5$
$12 R 5$	2 595 355 239.0	1.2	196 964 924 625.0	1.8	1 522.060 126	$1.4 \times 10^{- 8}$	$- 2.6$
$12 R 6$	2 660 480 130.6	1.5	197 030 049 516.5	1.9	1 521.557 035	$1.5 \times 10^{- 8}$	$- 1.2$
$12 R 7$	2 724 825 646.8	1.3	197 094 395 032.7	1.8	1 521.060 292	$1.4 \times 10^{- 8}$	$- 0.6$
$12 R 8$	2 788 390 730.7	1.2	197 157 960 116.6	1.7	1 520.569 891	$1.3 \times 10^{- 8}$	$- 3.9$
$12 R 9$	2 851 174 350.5	1.3	197 220 743 736.5	1.8	1 520.085 830	$1.4 \times 10^{- 8}$	$- 0.5$
$12 R 10$	2 913 175 471.7	1.2	197 282 744 857.7	1.7	1 519.608 105	$1.3 \times 10^{- 8}$	—
$12 R 11$	2 974 393 096.1	1.3	197 343 962 482.1	1.8	1 519.136 710	$1.4 \times 10^{- 8}$	—
$12 R 12$	3 034 826 223.5	2.7	197 404 395 609.4	3.0	1 518.671 644	$2.3 \times 10^{- 8}$	—
$12 R 13$	3 094 473 893.8	2.0	197 464 043 279.7	2.3	1 518.212 901	$1.8 \times 10^{- 8}$	—
$12 R 14$	3 153 335 123.6	1.2	197 522 904 509.6	1.7	1 517.760 478	$1.3 \times 10^{- 8}$	—
$12 R 15$	3 211 408 993.5	1.3	197 580 978 379.4	1.8	1 517.314 371	$1.4 \times 10^{- 8}$	—
$12 R 16$	3 268 694 565.8	2.1	197 638 263 951.8	2.5	1 516.874 577	$1.9 \times 10^{- 8}$	—
$12 R 17$	3 325 190 939.9	1.3	197 694 760 325.9	1.8	1 516.441 091	$1.4 \times 10^{- 8}$	—
$12 R 18$	3 380 897 227.8	1.3	197 750 466 613.7	1.8	1 516.013 910	$1.4 \times 10^{- 8}$	—
$12 R 19$	3 435 812 557.1	1.2	197 805 381 943.0	1.7	1 515.593 029	$1.3 \times 10^{- 8}$	—
$12 R 20$	3 489 936 076.3	1.4	197 859 505 462.2	1.8	1 515.178 446	$1.4 \times 10^{- 8}$	—
$12 R 21$	3 543 266 956.9	1.4	197 912 836 342.9	1.9	1 514.770 156	$1.5 \times 10^{- 8}$	—
$12 R 22$	3 595 804 386.5	1.6	197 965 373 772.4	2.0	1 514.368 156	$1.5 \times 10^{- 8}$	—
$12 R 23$	3 647 547 589.4	1.3	198 017 116 975.3	1.8	1 513.972 441	$1.4 \times 10^{- 8}$	—
$12 R 24$	3 698 495 209.9	1.7	198 068 064 595.9	2.1	1 513.583 013	$1.6 \times 10^{- 8}$	—
$12 R 25$	3 748 648 054.0	1.2	198 118 217 439.9	1.8	1 513.199 855	$1.3 \times 10^{- 8}$	—
$12 R 26$	3 798 003 983.5	1.3	198 167 573 369.4	1.8	1 512.822 976	$1.4 \times 10^{- 8}$	—
$12 R 27$	3 846 562 721.7	1.6	198 216 132 107.7	2.0	1 512.452 366	$1.5 \times 10^{- 8}$	—
$12 R 28$	3 894 323 473.2	5.5	198 263 892 859.1	5.6	1 512.088 024	$4.3 \times 10^{- 8}$	—
$12 R 29$	3 941 286 000.1	2.1	198 310 855 386.0	2.4	1 511.729 942	$1.9 \times 10^{- 8}$	—
$12 R 30$	3 987 450 177.5	9.1	198 357 019 563.5	9.1	1 511.378 113	$7.0 \times 10^{- 8}$	—
$12 R 31$	4 032 805 511.4	4.4	198 402 374 897.3	4.6	1 511.032 608	$3.5 \times 10^{- 8}$	—

Abstract

Cited By

Figures (4)

Tables (3)

Equations (6)

Journal of the Optical Society of America B