High-precision identification of morphology-dependent resonances in optical processes in microdroplets

J. D. Eversole; H.-B. Lin; A. L. Huston; A. J. Campillo; P. T. Leung; S. Y. Liu; K. Young

doi:10.1364/JOSAB.10.001955

High-precision identification of morphology-dependent resonances in optical processes in microdroplets

J. D. Eversole, H.-B. Lin, A. L. Huston, A. J. Campillo, P. T. Leung, S. Y. Liu, and K. Young

Journal of the Optical Society of America B
Vol. 10,
Issue 10,
pp. 1955-1968
(1993)
•https://doi.org/10.1364/JOSAB.10.001955

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J. D. Eversole, H.-B. Lin, A. L. Huston, A. J. Campillo, P. T. Leung, S. Y. Liu, and K. Young, "High-precision identification of morphology-dependent resonances in optical processes in microdroplets," J. Opt. Soc. Am. B 10, 1955-1968 (1993)

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History
- Original Manuscript: December 23, 1992
- Revised Manuscript: April 16, 1993
- Published: October 1, 1993

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Abstract

The spectroscopy of the morphology-dependent resonances of a microdroplet has been studied at high precision. The line positions are shown to reveal optical dispersion and permit the refractive index to be determined with sufficient accuracy to provide an estimate of the droplet cooling that is due to evaporation. Comparison of the remaining discrepancies in mode positions for different radial modes indicates a small temperature gradient near the surface. Both the cooling and the temperature gradient are compatible with thermodynamic estimates. The mode quantum numbers are identified with high confidence, and the systematics of the line intensities permit an estimate of the extra radiative loss 1/Q_L over and above that predicted by Lorenz–Mie theory for a perfect homogeneous microsphere, for example, that which is due to internal scattering, with Q_L ≈ 2 × 10⁸ for first-order modes.

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No.	Experimental			Theoretical
No.	Position	Height	Width	Position	μ	l	i
1	14 700.8	1.5	3.5	14 697.0	2	76	2
2	14 765.6	0.5	2.8	14 762.1	1	72	3
3	14 782.3	0.6	2.8	–	–	–	–
4	14 865.5	0.5	1.8	14 863.9	2	83	1
5	14 870.8	1.4	3.5	14 868.8	2	77	2
6	14 931.0	0.6	3.5	14 928.3	1	84	1
7	14 941.6	0.4	5.3	14 937.7	1	73	3
8	14 952.2	0.8	3.5	14 949.2	1	78	2
9	15 007.1	0.2	7.1	15 008.7	2	73	3
10	15 030.9	0.6	4.2	15 031.0	2	84	1
11	15 040.8	1.0	5.3	15 040.5	2	78	2
12	15 095.7	0.5	4.2	15 095.3	1	85	1
13	15 113.4	0.4	3.5	15 113.0	1	74	3
14	15 122.2	1.0	3.5	15 120.4	1	79	2
15	15 186.0	0.4	3.5	15 185.0	2	74	3
16	15 196.6	1.5	7.1	15 198.1	2	85	1
17	15 214.3	2.0	4.2	15 212.1	2	79	2
18	15 263.9	1.0	3.5	15 262.2	1	86	1
19	15 292.2	2.0	7.1	15 288.2	1	75	3
				15 291.5	1	80	2
20	15 363.0	1.8	5.3	15 361.1	2	75	3
				15 365.1	2	86	1
21	15 384.3	2.7	3.5	15 383.5	2	80	2
22	15 430.3	1.2	5.3	15 429.0	1	87	1
23	15 464.0	2.8	5.3	15 462.5	1	81	2
23	15 464.0	2.8	5.3	15 463.2	1	76	3
24	15 531.3	2.4	7.1	15 532.0	2	87	1
25	15 540.1	0.5	3.5	15 536.9	2	76	3
26	15 555.2	3.5	3.5	15 554.8	2	81	2
27	15 596.8	1.5	5.3	15 595.8	1	88	1
28	15 634.0	3.0	8.9	15 633.4	1	82	2
29	15 696.8	2.0	5.3	15 698.8	2	88	1
30	15 710.1	1.7	7.1	15 712.6	2	77	3
31	15 726.0	3.7	5.3	15 725.9	2	82	2
32	15 762.3	1.7	5.3	15 762.4	1	89	1
33	15 805.7	3.5	5.3	15 804.2	1	83	2
34	15 813.7	2.0	3.5	15 812.7	1	78	3
35	15 864.2	2.7	7.1	15 865.5	2	89	1
36	15 885.4	2.2	7.1	15 888.0	2	78	3
37	15 896.0	2.2	4.2	15 896.9	2	83	2
38	15 927.9	3.0	5.3	15 929.0	1	90	1
39	15 975.7	5.5	3.5	15 974.8	1	84	2
40	15 986.3	3.0	5.3	15 987.2	1	79	3
41	16 030.6	5.0	4.2	16 032.2	2	90	1
42	16 067.8	9.0	7.1	16 067.8	2	84	2
43	16 096.1	5.0	5.3	16 095.5	1	91	1
44	16 145.7	7.0	5.3	16 145.3	1	85	2
45	16 161.7	4.2	7.1	16 161.5	1	80	3
46	16 197.1	9.0	4.2	16 198.7	2	91	1
47	16 236.9	14.0	4.2	16 238.3	2	80	3
				16 238.6	2	85	2
48	16 260.8	8.0	4.2	16 261.9	1	92	1
49	16 314.8	9.2	4.2	16 315.7	1	86	2
50	16 335.2	6.0	6.4	16 335.6	1	81	3
51	16 363.5	17.0	3.5	16 365.2	2	92	1
52	16 406.9	20.0	5.3	16 409.2	2	86	2
53	16 425.5	11.0	4.2	16 428.3	1	93	1
54	16 483.9	12.0	5.3	16 486.0	1	87	2
55	16 508.7	8.5	5.3	16 509.5	1	82	3
56	16 530.0	53.0	1.8	16 531.6	2	93	1
57	16 577.8	21.0	2.8	16 579.7	2	87	2
58	16 586.6	10.0	1.8	16 587.7	2	82	3
59	16 593.7	15.0	5.3	16 594.6	1	94	1
60	16 655.7	14.5	4.2	16 656.2	1	88	2
61	16 684.0	11.0	5.3	16 683.3	1	83	3
62	16 696.4	Off scale	4.2	16 698.0	2	94	1
63	16 747.8	22.0	1.8	16 750.1	2	88	2
64	16 759.3	29.5	4.2	16 760.8	1	95	1
65	16 825.7	17.0	4.2	16 826.2	1	89	2
66	16 857.5	14.0	1.8	16 857.0	1	84	3
67	16 862.9	Off scale	3.5	16 864.2	2	95	1
68	16 919.5	30.0	1.8	16 920.4	2	89	2
69	16 926.6	34.0	3.5	16 926.9	1	96	1
70	16 935.5	21.0	3.5	16 936.4	2	84	3
71	16 995.7	21.0	5.3	16 996.2	1	90	2
72	17 029.3	Off scale	2.8	17 030.4	2	96	1
				17 030.5	1	85	3
73	17 091.3	Off scale	3.5	17 090.6	2	90	2
				17 093.0	1	97	1
74	17 109.0	23.0	4.2	17 110.5	2	85	3
75	17 165.7	25.0	6.4	17 166.0	1	91	2
76	17 195.8	56.0	2.8	17 196.5	2	97	1
77	17 204.6	21.0	6.4	17 203.8	1	86	3
78	17 259.5	Off scale	3.5	17 258.9	1	98	1
				17 260.6	2	91	2
79	17 284.3	29.0	3.5	17 284.4	2	86	3
80	17 300.2	2.0	12.4	17 298.2	1	82	4
81	17 335.6	30.0	5.3	17 335.8	1	92	2
82	17 360.4	27.0	3.5	17 362.6	2	98	1
83	17 377.3	24.0	7.1	17 377.0	1	87	3
84	17 413.2	19.0	1.8	–	–	–	–
85	17 431.2	50.0	3.5	17 430.5	2	92	2
86	17 457.8	30.0	5.3	17 458.1	2	87	3
87	17 477.3	3.0	15.9	17 474.7	1	83	4
88	17 505.6	32.0	4.2	17 505.4	1	93	2
89	17 528.7	18.0	3.5	17 528.5	2	99	1
				17 531.8	2	83	4
90	17 551.7	33.0	6.4	17 550.0	1	88	3
91	17 588.8	6.0	3.5	17 590.7	1	100	1
92	17 599.5	48.0	2.8	17 600.4	2	93	2
93	17 631.3	50.0	3.5	17 631.6	2	88	3
94	17 652.5	5.0	15.9	17 651.0	1	84	4
95	17 675.6	22.0	5.3	17 674.9	1	94	2
96	17 693.3	4.0	5.3	17 694.4	2	100	1
97	17 709.3	2.0	8.9	17 709.3	2	84	4
98	17 725.2	36.0	5.3	17 722.9	1	89	3
99	17 757.1	2.0	7.1	17 756.5	1	101	1
100	17 771.2	30.0	2.1	17 770.1	2	94	2
101	17 804.9	53.0	3.5	17 805.0	2	89	3
102	17 829.7	4.0	8.9	17 827.1	1	85	4
103	17 845.6	8.0	5.3	17 844.4	1	95	2
104	17 859.8	2.0	5.3	17 860.3	2	101	1
105	17 882.8	3.0	3.5	17 886.6	2	85	4
106	17 897.0	37.0	4.2	17 895.6	1	90	3
107	17 939.5	11.0	3.5	17 939.7	2	95	2
108	17 978.4	47.0	3.5	17 978.2	2	90	3
109	18 006.7	6.0	10.6	18 003.1	1	86	4
110	18 015.6	3.0	3.5	18 013.7	1	96	2
111	18 070.5	29.0	6.4	18 068.2	1	91	3
112	18 109.4	2.0	2.1	18 109.2	2	96	2
113	18 151.9	26.0	3.5	18 151.3	2	91	3
114	18 183.8	4.0	10.6	18 182.9	1	97	2
115	18 242.3	11.0	6.4	18 240.6	1	92	3
				18 240.7	2	87	4
116	18 325.5	4.5	5.3	18 324.2	2	92	3
117	18 355.6	1.0	10.6	18 352.1	1	98	2
				18 354.7	1	88	4
118	18 414.0	1.0	3.5	18 413.0	1	93	3
				18 417.5	2	88	4

Experimental		Theoretical
No.	Position	Position	μ	l	i
1	16 141.7	16 141.9	2	86	3
2	16 191.6	16 191.0	1	92	2
3	16 214.1	16 215.9	2	98	1
4	16 230.0	16 229.1	1	87	3
5	16 274.0	16 274.4	1	99	1
6	16 279.3	16 279.0	2	92	2
7	16 304.3	16 304.2	2	87	3
8	16 350.1	16 349.4	1	93	2
9	16 369.9	16 370.9	2	99	1
		16 372.2	2	83	4
10	16 392.6	16 390.7	1	88	3
11	16 428.9	16 429.2	1	100	1
12	16 437.8	16 437.6	2	93	2
13	16 466.5	16 466.3	2	88	3
14	16 508.3	16 507.7	1	94	2
15	16 524.7	16 525.8	2	100	1
16	16 553.5	16 552.2	1	89	3
17	16 583.3	16 584.0	1	101	1
18	16 596.3	16 596.1	2	94	2
19	16 628.4	16 628.2	2	89	3
20	16 650.8	16 649.0	1	85	4
21	16 666.4	16 665.9	1	95	2
22	16 678.8	16 680.6	2	101	1
23	16 714.7	16 713.5	1	90	3
24	16 737.5	16 738.7	1	102	1
25	16 754.3	16 754.5	2	95	2
26	16 790.2	16 789.9	2	90	3
27	16 824.8	16 824.1	1	96	2
28	16 834.2	16 835.4	2	102	1
29	16 875.8	16 874.7	1	91	3
30	16 892.4	16 893.4	1	103	1
31	16 912.6	16 912.8	2	96	2
32	16 952.0	16 951.6	2	91	3
33	16 982.5	16 982.1	1	97	2
34	16 988.7	16 990.1	2	103	1
35	17 036.8	17 034.1	2	87	4
		17 035.7	1	92	3
36	17 046.9	17 048.0	1	104	1
37	17 070.8	17 070.9	2	97	2
38	17 113.4	17 113.0	2	92	3
		17 140.0	1	98	2
39	17 141.0	17 141.7	1	88	4
		17 144.7	2	104	1
		17 140.0	1	98	2
40.	17 143.1	17 141.7	1	88	4
		17 144.7	2	104	1
41	17 198.0	17 196.6	1	93	3
		17 199.2	2	88	4
42	17 201.5	17 199.2	2	88	4
		17 202.5	1	105	1
43	17 228.6	17 229.0	2	98	2
44	17 274.5	17 274.4	2	93	3
45	17 298.2	17 297.8	1	99	2
		17 299.3	2	105	1
46	17 357.9	17 357.0	1	106	1
		17 357.4	1	94	3
47	17 386.8	17 387.0	2	99	2
48	17 435.5	17 435.6	2	94	3
49	17 455.3	17 453.8	2	106	1
		17 455.6	1	100	2
50	17 470.2	17 469.3	1	90	4
51	17 510.8	17 511.4	1	107	1
52	17 518.6	17 518.1	1	95	3
53	17 529.4	17 528.8	2	90	4
54	17 544.8	17 544.9	2	100	2
55	17 596.8	17 596.6	2	95	3
56	17 607.1	17 608.2	2	107	1
57	17 613.7	17 613.2	1	101	2
58	17 633.9	17 632.9	1	91	4
59	17 664.9	17 665.7	1	108	1
60	17 679.7	17 678.6	1	96	3
61	17 692.6	17 693.3	2	91	4
62	17 702.0	17 702.7	2	101	2
63	17 757.5	17 757.5	2	96	3
64	17 771.0	17 770.8	1	102	2
65	17 797.3	17 796.4	1	92	4
66	17 818.4	17 820.0	1	109	1
67	17 839.6	17 839.1	1	97	3
68	17 859.4	17 857.7	2	92	4
		17 860.4	2	102	2
69	17 918.5	17 916.9	2	109	1
		17 918.3	2	97	3
70	17 960.6	17 959.7	1	93	4
71	18 000.1	17 999.4	1	98	3
72	18 019.6	18 018.0	2	103	2
		18 021.9	2	93	4
73	18 079.1	18 079.0	2	98	3
74	18 124.1	18 122.8	1	94	4
75	18 160.3	18 159.6	1	99	3
76	18 185.1	18 185.8	2	94	4
77	18 239.7	18 239.5	2	99	3
		18 243.0	1	105	2
78	18 286.7	18 285.8	1	95	4
79	18 320.3	18 319.7	1	100	3
80	18 349.6	18 349.6	2	95	4
81	18 399.8	18 399.9	2	100	3
		18 400.2	1	106	2
82	18 449.4	18 448.7	1	96	4
83	18 480.0	18 479.7	1	101	3
84	18 512.9	18 513.3	2	96	4
85	18 559.7	18 557.3	1	107	2
		18 560.2	2	101	3
86	18 611.9	18 611.4	1	97	4
87	18 640.1	18 639.5	1	102	3
88	18 676.3	18 676.7	2	97	4
89	18 719.9	18 720.3	2	102	3
90	18 774.3	18 774.0	1	98	4
91	18 799.7	18 799.3	1	103	3
92	18 839.0	18 840.0	2	98	4
		18 841.4	2	115	1
93	18 879.0	18 880.4	2	103	3
94	18 936.0	18 936.4	1	99	4

Data Set	n	a (μm)	C	S	l^*
A	1.348	7.301	0.792	110 (93%)	97
B	1.347	7.897	0.722	72 (77%)	–

Data Set	n	a (μm)	Δx	C	S	l^*
A	1.364	7.226	0.85	0.909	117 (99%)	96
B	1.364	7.763	1.12	0.954	94 (100%)	–

Data Set	n₀	n₁(10⁻⁶ cm)	a (μm)	C	S	l^*
A	1.366	0.964	7.133	0.883	116 (98%)	96
B	1.365	1.06	7.652	0.962	94 (100%)	–

Polarization	Mode Order i
Polarization	1	2	3
TE	4 × 10⁻⁷	5 × 10⁻⁶	<10⁻⁴
TM	4 × 10⁻⁷	4 × 10⁻⁶	<10⁻⁴

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