Stress effects on the performance of optical waveguides

TLDR: In this paper, the photo-elastic relation and wave equations for inhomogeneous and anisotropic waveguides are reviewed and the effective refractive indexes and mode shapes of planar waveguide under different stress states are obtained analytically.

About: This article is published in International Journal of Solids and Structures.The article was published on 2003-04-01 and is currently open access. It has received 198 citations till now. The article focuses on the topics: Birefringence & Photoelasticity.

Figures

Fig. 3. Schematic of a symmetric three-layer planer waveguide.

Fig. 9. Normalized transverse field distribution of the fundamental mode (m ¼ 0) for a symmetric optical waveguide under different inplane stresses with t ¼ 1 lm: (a) TM mode; (b) TE mode. The curves from top are corresponding to C1r ¼ 0:01, C1r ¼ 0 and C1r ¼ 0:01 stress values.

Fig. 14. Stress caused radiation confinement loss of different stress states for a symmetric planar optical waveguide with t ¼ 1 lm when C1r ¼ 0:01, where r ¼ r for hydrostatic and in-plane stress states; r ¼ rm=10 for stress concentration state; and r ¼ s for pure shear state.

Fig. 15. Stress caused transition loss of different stress states for a symmetric planar optical waveguide with t ¼ 1 lm when C1r ¼ 0:01, where r ¼ r for hydrostatic and in-plane stress states; r ¼ rm=10 for stress concentration state; and r ¼ s for pure shear state.

Fig. 1. Finite element results of the stress distributions in a ridge silicon waveguide core: (a) rxx; (b) ryy ; (c) rzz. The stresses are induced by thermal mismatch of the top cladding layers. The unit of the stresses is MPa.

Fig. 2. Refractive index distributions caused by the stresses in Fig. 1: (a) nxx; (b) nyy ; (c) nzz.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Stress effects on the performance of optical waveguides" ?

In this paper, the photo-elastic relation and wave equations for inhomogeneous and anisotropic waveguides are reviewed. 

Q2. What is the effect of stress on the optical performance of buried waveguides?

For buried waveguides, which have rectangular core shape and embedded in other cladding materials, and straight optical fibers, their stress states are similar to the hydrostatic stress state, where stresses will not cause too much loss and birefringence, but may induce multimode. 

Q3. What is the eigenvalue of a planar waveguide?

For the planar waveguides, the light propagates in the z direction, is confined in the x direction within the central core region, and has no variation in the y direction. 

Q4. What are the main effects of stress on the optical performance?

Stress-induced refractive index non-uniformity and anisotropy may exist simultaneously, so many problems may be induced by stresses. 

Q5. What are the basic components in optical systems?

Optical waveguides are basic components in many optical systems, such as arrayed waveguide gratings (AWGs), lasers and tunable filters. 

Q6. Why is the field of the first mode zero?

Because the waveguide considered here is symmetric, the field of the first mode is zero at the center of the core, where the stress concentration happens. 

Q7. What is the temperature of the layers?

These layers are fabricated at high temperatures (e.g., 300 C for Al interconnect and 1000 C for silica cladding), and cooled down to room temperature. 

Q8. What is the function of a waveguide?

In modern optical systems, more and more components are integrated (or hybrid-packaged) in a single chip, where optical waveguides serve as interconnects for photonic components. 

Q9. What is the stress magnitude of the core?

In order to study the stress magnitude effect, the core is assumed to be under hydrostatic stress state, i.e., rxx ¼ ryy ¼ rzz ¼ r and rxy ¼ 0. 

Q10. Why does the stress concentration affect the refractive index?

The reason is that stress concentration causes the non-uniform distribution of the refractive index, and the light trends to propagate in the higher refractive index region. 

Q11. What is the eigenvalue equation for a planar waveguide?

Although most practical optical waveguides are channel waveguides, where the light is also confined in the y direction, planar waveguides are used to provide a basic understanding since analytical solutions may be obtained for this kind of structure. 

Q12. What are the effects of stress on the optical performance?

stresses could also cause problems, such as the increments of polarization dependent loss (PDL) and polarization shift (PS) (Min et al., 2000; Yan et al., 2002). 

Q13. What is the effect of stress on the optical performance?

As shown in this paper, this small index change, aided by non-uniformity and anisotropy, causes unacceptable optical performance degradation and different stress states play different roles: high stress value may induce multimode; in-plane stresses may induce PS and PDL; stress concentration may induce large transition loss; and pure shear stress has little effects on the effective refractive index. 

Q14. What is the effect of stress on optical performance?

Many efforts have been made to improve the optical performance by taking advantage of photo-elastic effect, such as stress release grooves to1616 M. Huang / International Journal of Solids and Structures 40 (2003) 1615–1632minimize the polarization shift (Nadler et al., 1999), thermal stress to control the temperature sensitivity of central wavelength (Cohen et al., 1996, 2000; Ooba et al., 2000; Huang and Yan, 2002), stress-induced optical waveguides and filters (Saitoh et al., 1999; Lea andWeiss, 1996; Almashary andKim, 1996; Rho and Jackson, 1999; Savin et al., 2000), stress effects on laser (Maciejko et al., 1989, 1993), and stress-induced birefringence behavior of the waveguides and fibers (Kilian et al., 2000; Okuno et al., 1994; Chowdhury andWilcox, 2000; Buda et al., 2000). 

Q15. What is the qualitative picture obtained in this paper?

Although this study is performed on the planar waveguides under four simple stress states, the qualitative picture obtained in this paper should be generic to other waveguide structures and under more complicated stress states. 

Q16. What is the effect of the photoelastic effect on the optical performance?

These stresses can change the refractive indexes of the waveguide by the acousto-optic (elasto-optic or photoelastic) effect (Xu and Stroud, 1992; Sapriel, 1979), which may affect the optical performance. 

Q17. What is the refractive index of microstructures?

The stresses in microstructures are usually on the order of 108 Pa, and the C values in Table 1 are on the order of 10 11 Pa 1; so the refractive index change caused by stress is normally between 0.01. 

Q18. What is the effective refractive index of the fundamental mode?

The solutions of the mode equations are listed in Table 4.M. Huang / International Journal of Solids and Structures 40 (2003) 1615–1632 1625Applying interface boundary conditions similar as the hydrostatic stress state, and solving these eigenvalue equations, the authors can obtain the effective refractive index and normalized mode shape. 

Q19. What is the refractive index of the core?

The number of modes allowed in a three-layer symmetric planar waveguide is (Boyd, 1994)M ffi 2t kffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 n21 q : ð34ÞStress can change the refractive index, which may change the number of modes in the waveguide. 

Q20. What is the effect index and mode shape for a planar waveguide?

In Section 3, the effect index and mode shape for a planar waveguide are solved analytically under four stress states: hydrostatic, in-plane, stress concentration, and pure shear.