Spectral structure of continuous-wave two-photon transitions in Na<sub>2</sub>

G. P. Morgan; H.-R. Xia; A. L. Schawlow

doi:10.1364/JOSA.72.000315

Journal of the Optical Society of America
Vol. 72,
Issue 3,
pp. 315-320
(1982)
•https://doi.org/10.1364/JOSA.72.000315

Spectral structure of continuous-wave two-photon transitions in Na₂

G. P. Morgan, H.-R. Xia, and A. L. Schawlow

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G. P. Morgan, H.-R. Xia, and A. L. Schawlow, "Spectral structure of continuous-wave two-photon transitions in Na₂," J. Opt. Soc. Am. 72, 315-320 (1982)

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Abstract

We have observed 79 two-photon transitions in Na₂ by using cw dye-laser excitation. The transitions are enhanced by the near coincidence of the laser frequency with a suitable one-photon transition. Of these two-photon lines, 57 have been assigned to transitions from the X ¹∑_g⁺ ground state to two recently reported ¹∑_g⁺ and one ¹Π_g state at 33000 cm⁻¹. We discuss the spectral structures of the observed lines that arise from the requirements of near-resonant enhancement.

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Number	Laser Frequency (cm⁻¹)	Branch	Ground State X ¹∑_g⁺ (v″, J″)	Enhancing State A ¹∑_u⁺ (v′, J′)	Upper State ¹∑_g⁺ (3s + 5s) (v, J)	Offset Δ (cm⁻¹)	Upper-State Energy (cm⁻¹)

							Observed (E₀)	Predicted (E_p)	E_p − E₀
1	16583.591	S	(3, 47)	(23, 48)	(19, 49)	−0.099	34053.963	34056.31	2.35
2	16601.803	Q₁	(2, 50)	(22, 49)	(18, 50)	−0.014	33981.777	33982.53	0.75
3	16611.073	Q₂	(2, 27)	(21, 28)	(17, 27)	0.066	33730.312	33730.48	0.17
4	16614.564	O	(2, 22)	(21, 21)	(17, 20)	0.003	33699.365	33698.41	−0.86
5	16635.586	S	(1, 36)	(20, 37)	(16, 38)	0.330	33711.469	33711.07	−0.40
6	16647.220	S	(0, 46)	(19, 47)	(15, 48)	0.025	33704.635	33703.57	−1.07
7	16648.413	Q₁	(0, 42)	(19, 41)	(15, 42)	0.256	33653.447	33652.09	−1.36
8	16672.645	Q₁	(3, 18)	(23, 17)	(20, 18)	−0.368	33944.306	33945.59	1.28
9	16690.544	S	(2, 34)	(22, 35)	(19, 36)	0.085	33954.927	33954.88	−0.05
10	16691.560	Q₁	(2, 30)	(22, 29)	(19, 30)	0.276	33917.645	33917.76	0.11
11	16694.185	Q₂	(4, 31)	(25, 32)	(23, 31)	−0.121	34238.395	34237.92	−0.48
12	16698.830	O	(4, 26)	(25, 25)	(23, 24)	−0.449	34204.314	34202.99	−1.32
13	16704.169	S	(1, 44)	(21, 45)	(18, 46)	−0.027	33946.766	33947.318	0.55
14	16720.465	Q₁	(0, 48)	(20, 47)	(17, 48)	−0.044	33879.942	33879.57	−0.37
15	16737.980	S	(0, 19)	(19, 20)	(16, 21)	0.488	33613.873	33613.52	−0.35
16	16738.018	Q₁	(0, 15)	(19, 14)	(16, 15)	0.038	33592.401	33592.00	−0.40
17	16745.753	S	(2, 45)	(23, 46)	(21, 47)	−0.036	34197.813	34198.316	0.51
18	16781.767	Q₁	(0, 55)	(21, 54)	(19, 55)	0.755	34112.573	34112.318	−0.25
19	16785.420	Q₂	(1, 19)	(21, 20)	(19, 19)	0.015	33866.074	33866.425	0.36
20	16789.655	O	(1, 13)	(21, 12)	(19, 11)	−0.018	33844.239	33843.07	−1.17
21	16792.618	Q₁	(1, 11)	(21, 10)	(19, 11)	0.126	33842.504	33843.07	0.57
22	16823.384	Q₂	(2, 23)	(23, 24)	(22, 23)	0.116	34123.990	34123.23	−0.76
23	16824.030	O	(2, 19)	(23, 18)	(22, 17)	0.414	34099.150	34100.886	1.74
24	16850.653	Q₂	(0, 46)	(21, 47)	(20, 46)	−0.117	34111.502	34111.369	−0.13
25	16882.874	O	(1, 45)	(23, 44)	(23, 43)	−0.283	34317.766	34316.87	−0.90
26	16890.420	Q₂	(0, 57)	(22, 58)	(22, 57)	0.230	34363.914	34364.73	0.82
27	16914.976	S	(0, 53)	(22, 54)	(22, 55)	−0.849	34344.432	34345.51	1.08
28	16922.369	Q₁	(0, 48)	(22, 47)	(22, 48)	−0.042	34283.750	34282.88	−0.87
29	16949.700	Q₂	(0, 15)	(21, 16)	(21, 15)	−0.050	34015.825	34016.66	0.83
30	16970.528	O	(1, 23)	(23, 22)	(24, 21)	−0.487	34261.613	34263.66	2.05
31	16979.237	S	(1, 23)	(23, 24)	(24, 25)	−0.021	34279.996	34280.32	0.32
32	16979.201	Q₁	(2, 53)	(26, 52)	(29, 53)	0.018	34783.080	34783.16	0.08
33	17006.295	Q₂	(0, 54)	(23, 55)	(25, 54)	1.598	34548.263	34547.69	−0.57
34	17103.224	O	(0, 30)	(23, 29)	(26, 28)	1.493	34431.781	34432.06	0.28

Number	Laser Frequency (cm⁻¹)	Branch	Ground State X ¹∑_g⁺ (v″, J″)	Enhancing State A ¹∑_u⁺ (v′, J′)	Upper State ¹∑_g⁺ (3s + 4d) (v, J)	Offset Δ (cm⁻¹)	Upper-State Energy (cm⁻¹)

							Observed (E₀)	Predicted (E_p)	E_p − E₀
1	16611.893	Q₂	(0, 53)	(19, 54)	(7, 53)	−0.517	33739.941	33735.6	−4.34?
2	16641.980	O	(3, 29)	(23, 28)	(11, 27)	0.003	33963.323	33962.8	−0.52
3	16668.234	O	(7, 14)	(29, 13)	(17, 12)	0.363	34519.547	34518.1	−1.45
4	16724.839	O	(0, 21)	(19, 20)	(8, 19)	0.047	33600.200	33599.2	−1.00
5	16726.570	Q₂	(0, 24)	(19, 25)	(8, 24)	0.058	33624.867	33621.2	−3.67?
6	16738.726	O	(1, 32)	(21, 31)	(10, 30)	−0.045	33875.803	33872.7	−3.10?
7	16750.999	Q₂	(3, 30)	(24, 31)	(13, 30)	−0.622	34190.390	34189.4	−0.99
8	16751.109	O	(3, 26)	(24, 25)	(13, 24)	0.491	34156.281	34157.6	1.32
9	16767.436	S	(7, 16)	(30, 17)	(19, 18)	−0.101	34727.082	34727.6	0.52
10	16844.667	Q₁	(0, 13)	(20, 12)	(10, 13)	0.042	33796.765	33799.0	2.23
11	16845.549	Q₂	(1, 34)	(22, 35)	(12, 34)	0.224	34109.826	34110.5	0.67
12	16845.944	S	(0, 16)	(20, 17)	(10, 18)	−0.176	33813.180	33814.8	1.62
13	16940.221	O	(4, 57)	(29, 56)	(20, 55)	−0.066	35072.822	35069.2	−3.62?
14	16948.120	O	(0, 43)	(22, 42)	(13, 41)	0.393	34265.417	34265.3	−0.12
15	16949.730	O	(5, 22)	(29, 21)	(20, 20)	−0.222	34827.968	34828.4	0.43
16	16959.810	Q₁	(5, 18)	(29, 17)	(20, 18)	−0.592	34823.735	34821.3	−2.44
17	16970.553	S	(2, 39)	(25, 40)	(16, 41)	−0.045	34570.755	34566.6	−4.16?
18	17053.178	Q₂	(1, 32)	(24, 33)	(16, 32)	−0.137	34504.707	34504.3	−0.41
19	17065.486	S	(1, 28)	(24, 29)	(16, 30)	0.342	34492.165	34492.5	0.37

Number	Laser Frequency (cm⁻¹)	Branch	Ground State X ¹∑_g⁺ (v″, J″)	Enhancing State A ¹∑_u⁺ (v′, J′)	Upper State ¹Π_g⁺ (3s + 4d) (v, J)	Offset Δ (cm⁻¹)	Upper-State Energy (cm⁻¹)

							Observed (E₀)	Predicted (E_p)	E_p − E₀
1	16948.120	Q₂	(3, 30)	(26, 31)	(6, 30)	0.013	34584.700	34584.92	0.22
2	16960.285	P	(4, 35)	(28, 34)	(8, 34)	−0.141	34810.700	34811.63	0.93
3	17049.480	R	(2, 1)	(25, 2)	(6, 2)	−0.182	34492.496	34490.65	−1.85
4	17086.985	Q₁	(1, 60)	(26, 59)	(7, 60)	0.178	34964.682	34963.16	−1.52

Number	Laser Frequency (cm⁻¹)	Branch	Ground State X ¹∑_g⁺ (v″, J″)	Enhancing State A ¹∑_u⁺ (v′, J′)	Upper State ¹∑_g⁺ (3s + 5s) (v, J)	Offset Δ (cm⁻¹)	Upper-State Energy (cm⁻¹)

							Observed (E₀)	Predicted (E_p)	E_p − E₀
1	16583.591	S	(3, 47)	(23, 48)	(19, 49)	−0.099	34053.963	34056.31	2.35
2	16601.803	Q₁	(2, 50)	(22, 49)	(18, 50)	−0.014	33981.777	33982.53	0.75
3	16611.073	Q₂	(2, 27)	(21, 28)	(17, 27)	0.066	33730.312	33730.48	0.17
4	16614.564	O	(2, 22)	(21, 21)	(17, 20)	0.003	33699.365	33698.41	−0.86
5	16635.586	S	(1, 36)	(20, 37)	(16, 38)	0.330	33711.469	33711.07	−0.40
6	16647.220	S	(0, 46)	(19, 47)	(15, 48)	0.025	33704.635	33703.57	−1.07
7	16648.413	Q₁	(0, 42)	(19, 41)	(15, 42)	0.256	33653.447	33652.09	−1.36
8	16672.645	Q₁	(3, 18)	(23, 17)	(20, 18)	−0.368	33944.306	33945.59	1.28
9	16690.544	S	(2, 34)	(22, 35)	(19, 36)	0.085	33954.927	33954.88	−0.05
10	16691.560	Q₁	(2, 30)	(22, 29)	(19, 30)	0.276	33917.645	33917.76	0.11
11	16694.185	Q₂	(4, 31)	(25, 32)	(23, 31)	−0.121	34238.395	34237.92	−0.48
12	16698.830	O	(4, 26)	(25, 25)	(23, 24)	−0.449	34204.314	34202.99	−1.32
13	16704.169	S	(1, 44)	(21, 45)	(18, 46)	−0.027	33946.766	33947.318	0.55
14	16720.465	Q₁	(0, 48)	(20, 47)	(17, 48)	−0.044	33879.942	33879.57	−0.37
15	16737.980	S	(0, 19)	(19, 20)	(16, 21)	0.488	33613.873	33613.52	−0.35
16	16738.018	Q₁	(0, 15)	(19, 14)	(16, 15)	0.038	33592.401	33592.00	−0.40
17	16745.753	S	(2, 45)	(23, 46)	(21, 47)	−0.036	34197.813	34198.316	0.51
18	16781.767	Q₁	(0, 55)	(21, 54)	(19, 55)	0.755	34112.573	34112.318	−0.25
19	16785.420	Q₂	(1, 19)	(21, 20)	(19, 19)	0.015	33866.074	33866.425	0.36
20	16789.655	O	(1, 13)	(21, 12)	(19, 11)	−0.018	33844.239	33843.07	−1.17
21	16792.618	Q₁	(1, 11)	(21, 10)	(19, 11)	0.126	33842.504	33843.07	0.57
22	16823.384	Q₂	(2, 23)	(23, 24)	(22, 23)	0.116	34123.990	34123.23	−0.76
23	16824.030	O	(2, 19)	(23, 18)	(22, 17)	0.414	34099.150	34100.886	1.74
24	16850.653	Q₂	(0, 46)	(21, 47)	(20, 46)	−0.117	34111.502	34111.369	−0.13
25	16882.874	O	(1, 45)	(23, 44)	(23, 43)	−0.283	34317.766	34316.87	−0.90
26	16890.420	Q₂	(0, 57)	(22, 58)	(22, 57)	0.230	34363.914	34364.73	0.82
27	16914.976	S	(0, 53)	(22, 54)	(22, 55)	−0.849	34344.432	34345.51	1.08
28	16922.369	Q₁	(0, 48)	(22, 47)	(22, 48)	−0.042	34283.750	34282.88	−0.87
29	16949.700	Q₂	(0, 15)	(21, 16)	(21, 15)	−0.050	34015.825	34016.66	0.83
30	16970.528	O	(1, 23)	(23, 22)	(24, 21)	−0.487	34261.613	34263.66	2.05
31	16979.237	S	(1, 23)	(23, 24)	(24, 25)	−0.021	34279.996	34280.32	0.32
32	16979.201	Q₁	(2, 53)	(26, 52)	(29, 53)	0.018	34783.080	34783.16	0.08
33	17006.295	Q₂	(0, 54)	(23, 55)	(25, 54)	1.598	34548.263	34547.69	−0.57
34	17103.224	O	(0, 30)	(23, 29)	(26, 28)	1.493	34431.781	34432.06	0.28

Number	Laser Frequency (cm⁻¹)	Branch	Ground State X ¹∑_g⁺ (v″, J″)	Enhancing State A ¹∑_u⁺ (v′, J′)	Upper State ¹∑_g⁺ (3s + 4d) (v, J)	Offset Δ (cm⁻¹)	Upper-State Energy (cm⁻¹)

							Observed (E₀)	Predicted (E_p)	E_p − E₀
1	16611.893	Q₂	(0, 53)	(19, 54)	(7, 53)	−0.517	33739.941	33735.6	−4.34?
2	16641.980	O	(3, 29)	(23, 28)	(11, 27)	0.003	33963.323	33962.8	−0.52
3	16668.234	O	(7, 14)	(29, 13)	(17, 12)	0.363	34519.547	34518.1	−1.45
4	16724.839	O	(0, 21)	(19, 20)	(8, 19)	0.047	33600.200	33599.2	−1.00
5	16726.570	Q₂	(0, 24)	(19, 25)	(8, 24)	0.058	33624.867	33621.2	−3.67?
6	16738.726	O	(1, 32)	(21, 31)	(10, 30)	−0.045	33875.803	33872.7	−3.10?
7	16750.999	Q₂	(3, 30)	(24, 31)	(13, 30)	−0.622	34190.390	34189.4	−0.99
8	16751.109	O	(3, 26)	(24, 25)	(13, 24)	0.491	34156.281	34157.6	1.32
9	16767.436	S	(7, 16)	(30, 17)	(19, 18)	−0.101	34727.082	34727.6	0.52
10	16844.667	Q₁	(0, 13)	(20, 12)	(10, 13)	0.042	33796.765	33799.0	2.23
11	16845.549	Q₂	(1, 34)	(22, 35)	(12, 34)	0.224	34109.826	34110.5	0.67
12	16845.944	S	(0, 16)	(20, 17)	(10, 18)	−0.176	33813.180	33814.8	1.62
13	16940.221	O	(4, 57)	(29, 56)	(20, 55)	−0.066	35072.822	35069.2	−3.62?
14	16948.120	O	(0, 43)	(22, 42)	(13, 41)	0.393	34265.417	34265.3	−0.12
15	16949.730	O	(5, 22)	(29, 21)	(20, 20)	−0.222	34827.968	34828.4	0.43
16	16959.810	Q₁	(5, 18)	(29, 17)	(20, 18)	−0.592	34823.735	34821.3	−2.44
17	16970.553	S	(2, 39)	(25, 40)	(16, 41)	−0.045	34570.755	34566.6	−4.16?
18	17053.178	Q₂	(1, 32)	(24, 33)	(16, 32)	−0.137	34504.707	34504.3	−0.41
19	17065.486	S	(1, 28)	(24, 29)	(16, 30)	0.342	34492.165	34492.5	0.37

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Figures (7)

Tables (4)

Equations (2)

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