Wave propagation in anisotropic thin-film optical waveguides

D. P. Gia Russo; J. H. Harris

doi:10.1364/JOSA.63.000138

Journal of the Optical Society of America
Vol. 63,
Issue 2,
pp. 138-145
(1973)
•https://doi.org/10.1364/JOSA.63.000138

Wave propagation in anisotropic thin-film optical waveguides

D. P. Gia Russo and J. H. Harris

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
D. P. Gia Russo and J. H. Harris, "Wave propagation in anisotropic thin-film optical waveguides," J. Opt. Soc. Am. 63, 138-145 (1973)

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

Abstract

Propagation of guided waves in layered crystalline media is investigated. Two-dimensional guided-mode dispersion curves are computed and classified for a three-layer uniaxial configuration with arbitrary optic-axis orientation in each layer. It is found that the dispersion curves can be either circular or elliptical and can also be discontinuous. Other interesting aspects of wave behavior include wave tilt of the evanescent fields and independent TE and TM mode-existence criteria.

Full Article | PDF Article

More Like This

Wave propagation in semileaky-type anisotropic thin-film optical waveguides

Y. Okamura, S. Yamamoto, and T. Makimoto
J. Opt. Soc. Am. 67(4) 539-545 (1977)

Uniaxial and biaxial anisotropy in thin-film optical waveguides

M. S. Kharusi
J. Opt. Soc. Am. 64(1) 27-35 (1974)

Mode dispersion in uniaxial optical waveguides*

W. K. Burns and J. Warner
J. Opt. Soc. Am. 64(4) 441-446 (1974)

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 (6)

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 (6)

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 (57)

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

(a)
∊₁₁ = ∊₁(sin²ϕ+cos²ϕcos²θ)+∊₃cos²ϕsin²θ
∊₂₂ = ∊₁(cos²ϕ+sin²ϕcos²θ)+∊₃sin²ϕsin²θ
∊₃₃ = ∊₁sin²θ+∊₃cos²θ
∊₂₃ = (∊₃ − ∊₁)sinϕsinθcosθ
∊₁₃ = (∊₃ − ∊₁)cosϕsinθcosθ
∊₁₂ = (∊₃ − ∊₁)sinϕcosϕsin²θ
(b)
	s = a	s = b		s = z
Y_s^o±	$\frac{ω ∊}{k_{t}} ε_{3} \cdot û^{o \pm}$	$\frac{ω ∊ {k_{z}}^{o \pm}}{{k_{ż}}^{o \pm 2}} {ε_{1}}^{'} \cdot û^{o \pm}$		$- \frac{k_{t}}{ω μ} û^{o \pm} \cdot â$
Z_s^e±	$- \frac{ω μ}{k_{t}} ẑ \cdot û^{e \pm}$	$\frac{ω μ}{{k_{z}}^{e \pm}} (\frac{(k^{e \pm} + α^{\pm} \hat{n}) \times ẑ}{k^{e \pm} \cdot (k^{e \pm} + α^{\pm} \hat{n})} k_{t} - â) \cdot û^{e \pm}$		$\frac{k_{t}}{ω ∊ {∊_{33}}^{'}} {u_{a}}^{o \pm} - \frac{{∊_{31}}^{'}}{{∊_{33}}^{'}} {Z_{a}}^{e \pm} - \frac{{∊_{32}}^{'}}{{∊_{33}}^{'}} {Z_{b}}^{e \pm}$
		u_a^o⁺ = û^o+·â, etc.	$ε_{3} = ∊_{13} \hat{x} + ∊_{23} ŷ + ∊_{33} ẑ$
		k_t = \|k_t\|	${ε_{1}}^{'} = {∊_{11}}^{'} â + {∊_{12}}^{'} \hat{b} + {∊_{13}}^{'} ẑ$

(a)
$(\begin{array}{l} - {u_{a}}^{o +} & {u_{a}}^{o -} & - {Z_{a}}^{e +} & {Z_{a}}^{e -} \\ - {Y_{b}}^{o +} & {Y_{b}}^{o -} & - {u_{b}}^{e +} & {u_{b}}^{e -} \\ - {u_{b}}^{o +} & {u_{b}}^{o -} & - {Z_{b}}^{e +} & {Z_{b}}^{e -} \\ - {Y_{a}}^{o +} & {Y_{a}}^{o -} & - {u_{a}}^{e +} & {u_{a}}^{e -} \end{array}) \begin{array}{l} {E_{⊥}}^{+} \\ {E_{⊥}}^{-} \\ {H_{⊥}}^{+} \\ {H_{⊥}}^{-} \end{array}) = (\begin{array}{l} - {u_{i a}}^{o +} & {u_{i a}}^{o -} & - {Z_{i a}}^{e +} & {Z_{i a}}^{e -} \\ - {Y_{i b}}^{o +} & {Y_{i b}}^{o -} & - {u_{i b}}^{e +} & {u_{i b}}^{e -} \\ - {u_{i b}}^{o +} & {u_{i b}}^{o -} & - {Z_{i b}}^{e +} & {Z_{i b}}^{e -} \\ - {Y_{i a}}^{o +} & {Y_{i a}}^{o -} & - {u_{i a}}^{e +} & {u_{i a}}^{e -} \end{array}) \begin{array}{l} {E_{i ⊥}}^{+} \\ {E_{i ⊥}}^{-} \\ {H_{i ⊥}}^{+} \\ {H_{i ⊥}}^{-} \end{array})$
(b)
TE_x	TM_x
$\frac{{E_{y 2}}^{-}}{{E_{y 2}}^{+}} = exp (j 2 ({tan}^{- 1} \frac{j {k_{z 1}}^{o +}}{{k_{z 2}}^{o +}} - {k_{z 2}}^{o +} w))$	$\frac{{H_{y 2}}^{-}}{{H_{y 2}}^{+}} = exp (j 2 ({tan}^{- 1} \frac{Δ_{1} {(\| B_{1} \|)}^{\frac{1}{2}}}{Δ_{2} {(B_{2})}^{\frac{1}{2}}} - {(B_{2})}^{\frac{1}{2}} 2 w))$
$\frac{{E_{y 1}}^{+}}{{E_{y 2}}^{+}} = (1 + exp (j 2 {tan}^{- 1} \frac{j {k_{z 1}}^{o +}}{{k_{z 2}}^{o +}})) exp (- j {k_{z 2}}^{o +} w)$	$\frac{{H_{y 1}}^{+}}{{H_{y 2}}^{+}} = (1 + exp (j 2 {tan}^{- 1} \frac{Δ_{1} {(\| B_{1} \|)}^{\frac{1}{2}}}{Δ_{2} {(B_{2})}^{\frac{1}{2}}})) exp (- j {k_{z 2}}^{e +} w)$
$\frac{{E_{y 3}}^{-}}{{E_{y 2}}^{+}} = (1 + exp (- j 2 {tan}^{- 1} \frac{j {k_{z 3}}^{o -}}{{k_{z 2}}^{o +}})) exp (j {k_{z 2}}^{o +} w)$	$\frac{{H_{y 3}}^{-}}{{H_{y 2}}^{+}} = (1 + exp (j 2 {tan}^{- 1} \frac{Δ_{3} {(\| B_{3} \|)}^{\frac{1}{2}}}{Δ_{2} {(B_{2})}^{\frac{1}{2}}})) exp (j {k_{z 2}}^{e +} w)$

Crystal	Principal indices n₁, n₃	Maximum phase tilt angle χ_max
LiNbO₃	2.286, 2.200	−2.2°
BaTiO₃	2.440, 2.370	−1.7°
KDP	1.510, 1.470	−1.5°
NaNO₃	1.585, 1.336	−9.7°
Rutile	2.616, 2.903	+6.0°
Calcite	1.658, 1.486	−6.2°

i =	1	2	3
z′ =	−w	0	w
l =	o⁺, e⁺	o^±, e^±	o⁻, e⁻

−u_a1^o+	u_a2^o+e^−jk_z2o+w	u_a2^o⁻e^{−jk_z2o−w}	0	−Z_a₁^e⁺	Z_a₂^e⁺e^−jk_z2e+w	Z_a₂^e^{−e−jk_z2e−w}	0
−Y_b₁^o+	Y_b₂^o+e^−jk_z2o+w	Y_b₂^o−e^{−jk_z2o−w}	0	−u_b1^e⁺	u_b2^e⁺e^−jk_z2e+w	u_b2^e^{−e−jk_z2e−w}	0
0	u_a2^o+e^jk_z2o+w	u_a2^o−e^jk_z2o−w	−u_a3^o−	0	Z_a₂^e⁺e^jk_z2e+w	Z_a₂^e⁻e^jk_z2e−w	−Z_a₃^e⁻
0	Y_b₂^o+e^jk_z2o+w	Y_b₂^o−e^jk_z2o−w	−Y_b₃^o−	0	u_b2^e⁺e^jk_z2e+w	u_b2^e⁻e^jk_z2e−w	−u_b3^e⁻
−u_b1^o+	u_b2^o+e^−jk_z2o+w	u_b2^o−e^{−jk_z2o−w}	0	−Z_b₁^e⁺	Z_b₂^e⁺e^−jk_z2e+w	Z_b₂^e^{−e−jk_z2e−w}	0
−u_b1^o+	Y_a₂^o+e^−jk_z2o+w	Y_a₂^o−e^{−jk_z2o−w}	0	−u_a1^e⁺	u_a2^e⁺e^−jk_z2e+w	u_a2^e^{−e−jk_z2e−w}	0
0	u_b2^o+e^jk_z2o+w	u_b2^o−e^jk_z2o−w	−u_b3^o−	0	Z_b₂^e⁺e^jk_z2e+w	Z_b₂^e⁻e^jk_z2e−w	−Z_b₃^e⁻
0	Y_a₂^o+e^jk_z2o+w	Y_a₂^o−e^jk_z2o−w	−Y_a₃^o−	0	u_a2^e⁺e^jk_z2e+w	u_a2^e⁻e^jk_z2e−w	−u_a3^e⁻

Abstract

Cited By

Figures (6)

Tables (6)

Equations (57)

Journal of the Optical Society of America