Periodic stratified structure in a multilayer planar optical waveguide

Yi-Fan Li; Keigo lizuka; John W. Y. Lit

doi:10.1364/JOSAA.9.000559

Periodic stratified structure in a multilayer planar optical waveguide

Yi-Fan Li, Keigo lizuka, and John W. Y. Lit

Journal of the Optical Society of America A
Vol. 9,
Issue 4,
pp. 559-568
(1992)
•https://doi.org/10.1364/JOSAA.9.000559

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Yi-Fan Li, Keigo lizuka, and John W. Y. Lit, "Periodic stratified structure in a multilayer planar optical waveguide," J. Opt. Soc. Am. A 9, 559-568 (1992)

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About this Article
History
- Original Manuscript: August 14, 1991
- Revised Manuscript: October 28, 1991
- Manuscript Accepted: October 29, 1991
- Published: April 1, 1992

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Abstract

The contribution of a periodic stratified structure to the optical guiding properties of a multilayer planar waveguide is analyzed. We present an equivalent-layer method for the periodic stratified structure in a multiplayer waveguide that not only allows the whole periodic stratified structure to be treated as a single layer but offers exact solutions for the propagation constant of the waveguide and the power-confinement factor within the periodic stratified structure in a multilayer waveguide. This method is applied to study the optical guiding characteristics of multiquantum-well waveguides, such as the propagation constant, the field distribution, the power-confinement factor, and the group refractive index. The effective indices and the confinement factors of several practical GaInAsP/InP multiquantum-well lasers are calculated and analyzed.

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m	N	n_q	d_q (μm)	Γ_mqw	Γ_w	Γ_w′
1	3.2021	3.3219	1.000 × 10⁻²	9.156 × 10⁻⁴	9.156 × 10⁻⁴	9.156 × 10⁻⁴
2	3.2022	3.2824	3.001 × 10⁻²	5.446 × 10⁻³	3.629 × 10⁻³	3.631 × 10⁻³
3	3.2025	3.2744	5.004 × 10⁻²	1.351 × 10⁻²	8.106 × 10⁻³	8.110 × 10⁻³
4	3.2029	3.2710	7.007 × 10⁻²	2.491 × 10⁻²	1.422 × 10⁻²	1.423 × 10⁻²
5	3.2034	3.2690	9.012 × 10⁻²	3.943 × 10⁻²	2.189 × 10⁻²	2.191 × 10⁻²
6	3.2039	3.2678	1.102 × 10⁻¹	5.674 × 10⁻²	3.091 × 10⁻²	3.095 × 10⁻²
7	3.2046	3.2669	1.303 × 10⁻¹	7.657 × 10⁻²	4.116 × 10⁻²	4.123 × 10⁻²
8	3.2053	3.2663	1.503 × 10⁻¹	9.852 × 10⁻²	5.245 × 10⁻²	5.255 × 10⁻²

m	N	n_q	d_q (μm)	Γ_mqw	Γ_w	Γ_w′
1	3.1011	3.3219	1.000 × 10⁻²	1.149 × 10⁻²	1.149 × 10⁻²	1.149 × 10⁻²
2	3.1051	3.2824	3.001 × 10⁻²	3.932 × 10⁻²	2.620 × 10⁻²	2.621 × 10⁻²
3	3.1096	3.2743	5.004 × 10⁻²	7.250 × 10⁻²	4.344 × 10⁻²	4.350 × 10⁻²
4	3.1142	3.2708	7.007 × 10⁻²	1.097 × 10⁻¹	6.254 × 10⁻²	6.267 × 10⁻²
5	3.1191	3.2688	9.012 × 10⁻²	1.496 × 10⁻¹	8.287 × 10⁻²	8.310 × 10⁻²
6	3.1241	3.2675	1.102 × 10⁻¹	1.911 × 10⁻¹	1.039 × 10⁻¹	1.042 × 10⁻¹
7	3.1291	3.2666	1.303 × 10⁻¹	2.332 × 10⁻¹	1.251 × 10⁻¹	1.256 × 10⁻¹
8	3.1342	3.2659	1.504 × 10⁻¹	2.751 × 10⁻¹	1.461 × 10⁻¹	1.467 × 10⁻¹

m	N	n_q	d_q (μm)	Γ_mqw	Γ_w	Γ_w′
1	3.2021	3.3219	1.000 × 10⁻²	9.156 × 10⁻⁴	9.156 × 10⁻⁴	9.156 × 10⁻⁴
2	3.2022	3.2824	3.001 × 10⁻²	5.446 × 10⁻³	3.629 × 10⁻³	3.631 × 10⁻³
3	3.2025	3.2744	5.004 × 10⁻²	1.351 × 10⁻²	8.106 × 10⁻³	8.110 × 10⁻³
4	3.2029	3.2710	7.007 × 10⁻²	2.491 × 10⁻²	1.422 × 10⁻²	1.423 × 10⁻²
5	3.2034	3.2690	9.012 × 10⁻²	3.943 × 10⁻²	2.189 × 10⁻²	2.191 × 10⁻²
6	3.2039	3.2678	1.102 × 10⁻¹	5.674 × 10⁻²	3.091 × 10⁻²	3.095 × 10⁻²
7	3.2046	3.2669	1.303 × 10⁻¹	7.657 × 10⁻²	4.116 × 10⁻²	4.123 × 10⁻²
8	3.2053	3.2663	1.503 × 10⁻¹	9.852 × 10⁻²	5.245 × 10⁻²	5.255 × 10⁻²

m	N	n_q	d_q (μm)	Γ_mqw	Γ_w	Γ_w′
1	3.1011	3.3219	1.000 × 10⁻²	1.149 × 10⁻²	1.149 × 10⁻²	1.149 × 10⁻²
2	3.1051	3.2824	3.001 × 10⁻²	3.932 × 10⁻²	2.620 × 10⁻²	2.621 × 10⁻²
3	3.1096	3.2743	5.004 × 10⁻²	7.250 × 10⁻²	4.344 × 10⁻²	4.350 × 10⁻²
4	3.1142	3.2708	7.007 × 10⁻²	1.097 × 10⁻¹	6.254 × 10⁻²	6.267 × 10⁻²
5	3.1191	3.2688	9.012 × 10⁻²	1.496 × 10⁻¹	8.287 × 10⁻²	8.310 × 10⁻²
6	3.1241	3.2675	1.102 × 10⁻¹	1.911 × 10⁻¹	1.039 × 10⁻¹	1.042 × 10⁻¹
7	3.1291	3.2666	1.303 × 10⁻¹	2.332 × 10⁻¹	1.251 × 10⁻¹	1.256 × 10⁻¹
8	3.1342	3.2659	1.504 × 10⁻¹	2.751 × 10⁻¹	1.461 × 10⁻¹	1.467 × 10⁻¹

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Tables (2)

Equations (79)

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