Resonator studies with the Gardner–Fresnel–Kirchhoff propagator

W. P. Latham; T. C. Salvi

doi:10.1364/OL.5.000219

Optics Letters
Vol. 5,
Issue 6,
pp. 219-221
(1980)
•https://doi.org/10.1364/OL.5.000219

Resonator studies with the Gardner–Fresnel–Kirchhoff propagator

W. P. Latham and T. C. Salvi

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
W. P. Latham and T. C. Salvi, "Resonator studies with the Gardner–Fresnel–Kirchhoff propagator," Opt. Lett. 5, 219-221 (1980)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

The Gardner–Fresnel–Kirchhoff (GFK) propagation algorithm is an efficient way of evaluating the Fresnel diffraction formula in cylindrical coordinates. However, the resolution requirements for this algorithm are not clearly established in the literature. In this Letter, eigenvalues for a simple resonator are calculated with the GFK propagator to establish resolution requirements for the algorithm.

Full Article | PDF Article

More Like This

Effect of gain on the electrodynamics of marginally stable resonators

J. Nagel, D. Rogovin, and P. Avizonis
Opt. Lett. 5(3) 90-92 (1980)

Optical resonators with phase-conjugate mirrors

Juan F. Lam and Wilbur P. Brown
Opt. Lett. 5(2) 61-63 (1980)

Synthesis of the vector resonator modes from scalar results

G. A. Tyler and W. H. Southwell
Opt. Lett. 5(2) 42-44 (1980)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (1)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (14)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

			GFK (N = 512)				GFK (N = 1024

	AGL (N = 64)		k₂ = 5.6, k₁ = 934.8, α = α₀, r₀ = 1.07 × 10⁻⁴		k₂ = 5.6, k₁ = 934.8, α = α_c, r₀ = 1.06 × 10⁻⁴		k₂ = 11.2, k₁ = 934.8, α = α₀, r₀ = 1.07 × 10⁻⁴		k₂ = 11.2, k₁ = 934.8, α = α_c, r₀ = 1.06 × 10⁻⁴		k₂ = 19.6, k₁ = 18.6, α = α_c, r₀ = 5.4 × 10⁻⁴

l	Mag.	Phase	Mag.	Phase	Mag.	Phase	Mag.	Phase	Mag.	Phase	Mag.	Phase
0	0.523	−0.5	0.5295	7.4	0.5397	−0.3	0.5248	3.4	0.5266	−0.5	0.5237	−0.6
1	0.421	14.5	0.4500	28.3	0.4377	14.5	0.4281	21.1	0.4256	14.5	0.4228	14.5
2	0.378	−40.8	0.3916	−25.8	0.3981	−39.8	0.3798	−32.8	0.3827	−40.6	0.3793	−40.7
3	0.341	149.0	0.3714	167.3	b	b	0.3504	158.5	b	b	b	b
4	0.306	173.4	0.3269	−164.7	0.3274	173.6	0.3100	−176.4	0.3113	173.5	0.3077	173.4
5	0.239	−69.1	0.2627	30.0	0.2524	−71.3	0.2448	−59.6	0.2425	−69.5	0.2403	−69.2
6	0.275	169.9	0.3133	−164.8	0.2981	169.0	0.2845	−177.9	0.2807	169.8	0.2767	169.9
7	0.298	−37.4	0.3424	−14.6	0.3151	−38.9	0.3111	−26.6	0.3030	−37.7	0.3000	−37.5
8	0.315	−9.7	0.3253	16.4	0.3520	−8.8	0.3171	3.5	0.3228	−9.7	0.3176	−9.7
9	0.265	18.7	0.2746	41.3	0.2801	20.4	0.2629	30.0	0.2694	19.1	0.2667	18.8
10	0.202	35.3	b	b	0.2138	34.7	0.2078	45.8	0.2042	35.3	0.2024	35.2

				Eigenvalue

N	k₂	k₁	r₀	Mag.	Phase
512	5	2.4	0.016	0.5196	−1.598
512	14	0.17	0.231	0.250	−23.17
1024	4	1120.0	3 × 10⁻⁵	0.5272	−0.505
1024	7	13.9	3 × 10⁻³	0.5243	−0.555
1024	8	6.7	6 × 10⁻³	0.5235	−0.644
1024	10	2.4	0.016	0.5178	−1.598
2048	5	521894.0	7 × 10⁻⁸	0.5267	−0.520
2048	14	13.9	0.003	0.5233	−0.560
2048	16	6.7	0.005	0.5227	−0.649
2048	18	3.8	0.011	0.5212	−0.753
2048	20	2.4	0.016	0.5173	−1.597
4096	14	4836.7	8 × 10⁻⁶	0.5234	−0.539
4096	25	28.07	0.0014	0.5231	−0.546
				0.5231b	−0.541 b

			GFK (N = 512)				GFK (N = 1024

	AGL (N = 64)		k₂ = 5.6, k₁ = 934.8, α = α₀, r₀ = 1.07 × 10⁻⁴		k₂ = 5.6, k₁ = 934.8, α = α_c, r₀ = 1.06 × 10⁻⁴		k₂ = 11.2, k₁ = 934.8, α = α₀, r₀ = 1.07 × 10⁻⁴		k₂ = 11.2, k₁ = 934.8, α = α_c, r₀ = 1.06 × 10⁻⁴		k₂ = 19.6, k₁ = 18.6, α = α_c, r₀ = 5.4 × 10⁻⁴

l	Mag.	Phase	Mag.	Phase	Mag.	Phase	Mag.	Phase	Mag.	Phase	Mag.	Phase
0	0.523	−0.5	0.5295	7.4	0.5397	−0.3	0.5248	3.4	0.5266	−0.5	0.5237	−0.6
1	0.421	14.5	0.4500	28.3	0.4377	14.5	0.4281	21.1	0.4256	14.5	0.4228	14.5
2	0.378	−40.8	0.3916	−25.8	0.3981	−39.8	0.3798	−32.8	0.3827	−40.6	0.3793	−40.7
3	0.341	149.0	0.3714	167.3	b	b	0.3504	158.5	b	b	b	b
4	0.306	173.4	0.3269	−164.7	0.3274	173.6	0.3100	−176.4	0.3113	173.5	0.3077	173.4
5	0.239	−69.1	0.2627	30.0	0.2524	−71.3	0.2448	−59.6	0.2425	−69.5	0.2403	−69.2
6	0.275	169.9	0.3133	−164.8	0.2981	169.0	0.2845	−177.9	0.2807	169.8	0.2767	169.9
7	0.298	−37.4	0.3424	−14.6	0.3151	−38.9	0.3111	−26.6	0.3030	−37.7	0.3000	−37.5
8	0.315	−9.7	0.3253	16.4	0.3520	−8.8	0.3171	3.5	0.3228	−9.7	0.3176	−9.7
9	0.265	18.7	0.2746	41.3	0.2801	20.4	0.2629	30.0	0.2694	19.1	0.2667	18.8
10	0.202	35.3	b	b	0.2138	34.7	0.2078	45.8	0.2042	35.3	0.2024	35.2

				Eigenvalue

N	k₂	k₁	r₀	Mag.	Phase
512	5	2.4	0.016	0.5196	−1.598
512	14	0.17	0.231	0.250	−23.17
1024	4	1120.0	3 × 10⁻⁵	0.5272	−0.505
1024	7	13.9	3 × 10⁻³	0.5243	−0.555
1024	8	6.7	6 × 10⁻³	0.5235	−0.644
1024	10	2.4	0.016	0.5178	−1.598
2048	5	521894.0	7 × 10⁻⁸	0.5267	−0.520
2048	14	13.9	0.003	0.5233	−0.560
2048	16	6.7	0.005	0.5227	−0.649
2048	18	3.8	0.011	0.5212	−0.753
2048	20	2.4	0.016	0.5173	−1.597
4096	14	4836.7	8 × 10⁻⁶	0.5234	−0.539
4096	25	28.07	0.0014	0.5231	−0.546
				0.5231b	−0.541 b

Abstract

Cited By

Figures (1)

Tables (2)

Equations (14)

Optics Letters