Resonance of a dielectric cavity inside a fiber

Nikolaos K. Uzunoglu

doi:10.1364/AO.20.000857

Applied Optics
Vol. 20,
Issue 5,
pp. 857-861
(1981)
•https://doi.org/10.1364/AO.20.000857

Resonance of a dielectric cavity inside a fiber

Nikolaos K. Uzunoglu

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Nikolaos K. Uzunoglu, "Resonance of a dielectric cavity inside a fiber," Appl. Opt. 20, 857-861 (1981)

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Abstract

Resonance phenomena for a dielectric spherical cavity embedded inside a fiber waveguide are treated analytically. The interaction of fiber and scatterer fields is described in terms of an internal equation which is reduced into an infinite system of equations. The case of optically small but dense spheres is considered in detail. The resonance phenomena occurring for this case permit a decoupling procedure to be developed for the infinite system of equations. Analytic expressions are derived for the low-order mode central frequencies and quality factors. Numerical results are presented.

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p/n	1	2	3	4	5
1	3.141593	4.49309	5.763459	6.987932	8.182561
2	6.283185	7.725252	9.095011	10.417119	11.704907
3	9.424778	10.904122	12.322941	13.698023	15.039665
4	12.566370	14.066194	15.514603	16.923621	18.301256
5	15.707963	17.220755	18.689036	20.121806	21.525418
6	18.849556	20.371303	21.853874	23.304247	24.727566

√K	k₀ = 1, k₁ = 1.3, α = 1.4, d = 0		k₀ = 1, k₁ = 1.6, α = 1.6, d = 0
√K	$({\tilde{f}}_{11}^{m} - f_{11}^{m}) / f_{11}^{m}$	$({\tilde{Q}}_{11}^{m} - Q_{11}^{m}) / Q_{11}^{m}$	$({\tilde{f}}_{11}^{m} - f_{11}^{m}) / f_{11}^{m}$	$({\tilde{Q}}_{11}^{m} - Q_{11}^{m}) / Q_{11}^{m}$
3	−1.33(−2)	5.57(−2)	3.42(−3)	9.38(−2)
4	−4.21(−3)	4.71(−2)	1.08(−3)	6.73(−2)
5	−1.73(−3)	3.90(−2)	4.43(−4)	5.27(−2)
6	−8.33(−4)	3.29(−2)	2.14(−4)	4.33(−2)
7	−4.49(−4)	2.83(−2)	1.15(−4)	3.68(−2)
8	−2.63(−4)	2.48(−2)	6.76(−5)	3.21(−2)
9	−1.64(−4)	2.21(−2)	4.22(−5)	2.84(−2)
10	−1.08(−4)	1.99(−2)	2.77(−5)	2.55(−2)

√K	k₀ = 1, k₁ = 1.3, α = 1.5, α = 0		k₀ = 1, k₁ = 1.6, α = 1.6, d = 0
√K	$({\tilde{f}}_{11}^{e} - f_{11}^{e}) / f_{11}^{e}$	$({\tilde{Q}}_{11}^{e} - Q_{11}^{e}) / Q_{11}^{e}$	$({\tilde{f}}_{11}^{e} - f_{11}^{e}) / f_{11}^{e}$	$({\tilde{Q}}_{11}^{e} - Q_{11}^{e}) / Q_{11}^{e}$
3	−2.63(−3)	2.42(−1)	−5.26(−3)	2.41(−1)
4	−7.04(−4)	1.84(−1)	−1.41(−3)	1.84(−1)
5	−2.29(−4)	1.46(−1)	−4.58(−4)	1.47(−1)
6	−8.79(−5)	1.21(−1)	−1.76(−4)	1.21(−1)
7	−3.82(−5)	1.03(−1)	−7.64(−5)	1.03(−1)
8	−1.83(−5)	8.91(−2)	−3.66(−5)	8.96(−2)
9	−9.51(−6)	7.87(−2)	−1.90(−5)	7.92(−2)
10	−5.26(−6)	7.05(−2)	−1.05(−5)	7.09(−2)

p/n	1	2	3	4	5
1	3.141593	4.49309	5.763459	6.987932	8.182561
2	6.283185	7.725252	9.095011	10.417119	11.704907
3	9.424778	10.904122	12.322941	13.698023	15.039665
4	12.566370	14.066194	15.514603	16.923621	18.301256
5	15.707963	17.220755	18.689036	20.121806	21.525418
6	18.849556	20.371303	21.853874	23.304247	24.727566

√K	k₀ = 1, k₁ = 1.3, α = 1.4, d = 0		k₀ = 1, k₁ = 1.6, α = 1.6, d = 0
√K	$({\tilde{f}}_{11}^{m} - f_{11}^{m}) / f_{11}^{m}$	$({\tilde{Q}}_{11}^{m} - Q_{11}^{m}) / Q_{11}^{m}$	$({\tilde{f}}_{11}^{m} - f_{11}^{m}) / f_{11}^{m}$	$({\tilde{Q}}_{11}^{m} - Q_{11}^{m}) / Q_{11}^{m}$
3	−1.33(−2)	5.57(−2)	3.42(−3)	9.38(−2)
4	−4.21(−3)	4.71(−2)	1.08(−3)	6.73(−2)
5	−1.73(−3)	3.90(−2)	4.43(−4)	5.27(−2)
6	−8.33(−4)	3.29(−2)	2.14(−4)	4.33(−2)
7	−4.49(−4)	2.83(−2)	1.15(−4)	3.68(−2)
8	−2.63(−4)	2.48(−2)	6.76(−5)	3.21(−2)
9	−1.64(−4)	2.21(−2)	4.22(−5)	2.84(−2)
10	−1.08(−4)	1.99(−2)	2.77(−5)	2.55(−2)

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Equations (42)

Applied Optics