Guide d’onda

propagazione guidata

modi

n2

z

y

O

i

n1

Ai

ri

Incident Light BiAr

Br

t t

t

Refracted Light

Reflected Light

kt

At

Bt

BA

B

A

Ar

ki

kr

A light wave travelling in a medium with a greater refractive index (n1 > n2) suffersreflection and refraction at the boundary.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Leggi di Snell

• Raggio incidente riflesso e rifratto sono complanari, in un piano normale alla superficie.

• L’angolo di incidenza è eguale all’angolo di riflessione

• n1 sin 1 = n2 sin 2

Incidenza normale

• Per non si distinguono le due direzioni di polarizzazione

• r = (n1 – n2) / (n1 + n2) campo elettrico

• R = [(n1 – n2) / (n1 + n2)]2

Riflessione totale

k i

n2

n1 > n2

t=90°Evanescent wave

Reflectedwave

Incidentwave

i r

Er,//

Er,Ei,

Ei,//

Et,

(b) i > c then the incident wavesuffers total internal reflection.However, there is an evanescentwave at the surface of the medium.

z

y

x into paper i r

Incidentwave

t

Transmitted wave

Ei,//

Ei,Er,//

Et,

Et,

Er,

Reflectedwave

k t

k r

Light wave travelling in a more dense medium strikes a less dense medium. The plane ofincidence is the plane of the paper and is perpendicular to the flat interface between thetwo media. The electric field is normal to the direction of propagation . It can be resolvedinto perpendicular () and parallel (//) components

(a) i < c then some of the waveis transmitted into the less densemedium. Some of the wave isreflected.

Ei,

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Riflessione totale

Salto di fase

Light

n2

A planar dielectric waveguide has a central rectangular region ofhigher refractive index n1 than the surrounding region which hasa refractive index n2. It is assumed that the waveguide isinfinitely wide and the central region is of thickness 2a. It isilluminated at one end by a monochromatic light source.

n2

n1 > n2

Light

Light Light

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

n2

n2

d = 2a

k1

Light

A

B

C

E

n

1

A light ray travelling in the guide must interfere constructively with itself topropagate successfully. Otherwise destructive interference will destroy thewave.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

z

y

x

Wilson&Hawkes: Optoelectronics and introduction Cap.8

Cutoff

Numero di modi singolo modo

Sopra il cutoff:

m /2 <= V –

m <= ( V – 2

Numero di modi

N = m + 1

Costante di propagazione

• Il vettore d’onda k della radiazione che si propaga nella guida può essere scomposto in una componente parallela ed una perpendicolare all’asse ottico

• Detto m l’angolo del modo m, la componente parallela m (costante di propagazione) ed il corrispondente campo elettrico, sono dati da:

m = k sin m (2n1/) sin m

E(y,z,t) = 2Em(y) cos (t – mz)

Dove Em(y) rappresenta la distribuzione dei campo elettrico in direzione nperpendicolare all’asse per il modo di ordine m

n2

Light

n2

n1

y

E(y)

E(y,z,t ) = E(y)cos(t – 0z)

m = 0

Field of evanescent wave(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest . It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an1

n2

n2

The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fieldpenetration into the cladding.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)