Integrated Optics / Photonic Integrated Circuits (PIC)

and

Waveguide Structures

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 Integrated Optics/Photonic Integrated Circuits (PIC)

• Technology of integrating various optical devices and

components for the generation, focusing, splitting, combining,
isolation, polarization, coupling, switching, modulation and
detection of light, all on a single chip.

• Optical versions of electronic IC

• Goal: Miniaturization of optical devices/systems in much the

same way that integrated circuits have miniaturized electronics

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Fig: An example of an integrated optics used as an optical transceiver. Light from a
LASER is GUIDED, MODULATED and COUPLED into an optical fiber. Received
light is COUPLED into a WAVEGUIDE and directed to a PHOTODIODE.

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 Importance of Waveguides in PIC

• Most prevalent
• They are the interconnects between devices/components in a PIC.

• Many optical devices (for generation, focusing, splitting,

combining, isolation, polarization, coupling, switching,
modulation and detection of light) are nothing but some kind
of waveguides or modified waveguides.

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Optical Waveguide:
A light conduit consisting of a slab, strip, or cylinder of dielectric
material surrounded by another dielectric material of lower
refractive index

Fig: Optical waveguides: (a) Slab, (b) Strip, (c) cylindrical

Light is transported through the inner medium without radiating

into the surrounding medium.
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WAVEGUIDE STRUCTURES

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Optical Waveguides
• Basic elements for confinement and transmission of light over various
distances, ranging from tens or hundreds of µm in PIC to hundreds or
thousands of km in long-distance fiber-optic transmission.

• Optical waveguides also form key structures in semiconductor lasers, and act
as passive and active devices such as waveguide couplers and modulators.

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Waveguide Structures

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There are two basic types of waveguides: Planar and Non-Planar

• Planar waveguide: In a planar waveguide that has optical confinement in only one
transverse direction, the core is sandwiched between cladding layers in only one
direction, say the x direction, with an index profile n(x). The core of a planar
waveguide is also called the film, while the upper and lower cladding layers are called
the cover and the substrate.

• Non-planar waveguide: In a non-planar waveguide of two-dimensional transverse

optical confinement, the core is surrounded by cladding in all transverse directions, and
n(x, y) is a function of both x and y coordinates.

e.g. the strip waveguides and the optical fibers

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 Planar Mirror Waveguides

• Made of two parallel infinite mirrors separated by a distance d. The mirrors

are assumed ideal, i.e. they reflect light without loss.

• Not used in practical applications mainly because of the difficulty and cost of
fabricating low-loss mirrors.

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 Planar Dielectric Waveguides

• A planar dielectric waveguide is a slab of dielectric material sandwiched

between media of lower refractive indices.

• The light is guided inside the slab by total internal reflection.

• In thin-film devices the slab is called the “film” and the upper and lower
media are called the “cover” and the “substrate,” respectively.
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 Symmetric and Asymmetric Planar Waveguides

Fig: Asymmetric Planar waveguide

• Here, n2 ≠ n3

• Symmetric, if , n2 = n3

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 Non-planar/Two-Dimensional Waveguides
• The planar-mirror waveguide and the planar dielectric waveguide studied
earlier confine light in one transverse direction while guiding it along the z
direction. They are 1D waveguides.

• Two-dimensional waveguides confine light in the two transverse directions

(the x and y directions).

(b) (c)
(a)
Fig: Geometries of (a) a rectangular mirror waveguide; (b) a rectangular
dielectric waveguide; (c) an optical fiber (cylindrical) 13
Channel Waveguides
• Most waveguides used in device applications are non-planar waveguides.

• An important group of non-planar waveguides is the channel waveguides,

which include
 The buried channel waveguides

 The strip-loaded waveguides

 The ridge waveguides

 The rib waveguides

 The diffused waveguides.

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Representative Channel Waveguides
• A buried channel waveguide is formed with a high-index core buried in a
low-index surrounding medium.

 The waveguide core can have any cross-sectional geometry though it is

often a rectangular shape.

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• A strip-loaded waveguide is formed by loading a planar waveguide, which
already provides optical confinement in the x direction, with a dielectric strip
of index n3<n1 or a metal strip to facilitate optical confinement in the y
direction.

 The core of a strip waveguide is the n1 region under the loading strip,
with its thickness d determined by the thickness of the n1 layer and its
width w defined by the width of the loading strip.
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• A ridge waveguide has a structure that looks like a strip waveguide, but the
strip, or the ridge, on top of its planar structure has a high index and is
actually the guiding core.

 A ridge waveguide has strong optical confinement because it is

surrounded on three sides by low-index air (or cladding material).

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• A rib waveguide has a structure similar to that of a strip or ridge waveguide,
but the strip has the same index as the high-index planar layer beneath it and
is part of the guiding core.

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• A diffused waveguide is formed by creating a high-index region in a substrate
through diffusion of dopants; example: LiNbO3 waveguide with a core formed by
Ti diffusion.

 Because of the diffusion process, the core boundaries in the substrate are not
sharply defined.

 It has an effective thickness, d, defined by the diffusion depth of the dopant

in the x direction and an effective width, w, defined by the distribution of the
dopant in the y direction.
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 Different Configurations

Fig: (a) Straight; (b) S bend; (c) Y branch; (d) Mach-Zehnder; (e)
directional coupler; (f) intersection
Fabrications may be done in different configurations for diffused waveguides
• S bends – to offset the propagation axis.
• The Y branch – beam splitter or combiner.
• Two Y branches – a Mach-Zehnder interferometer.
• Two waveguides in close proximity (or intersecting) can exchange power and
may be used as directional coupler.

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Channel Waveguide Technologies

• Ti:LiNbO : The most advanced technology for fabricating waveguides is

Ti:LiNbO.

 A diffused or embedded-strip waveguide is fabricated by diffusing

titanium (Ti) into a Lithium Niobate (LiNbO) substrate to raise its
refractive index in the region of the strip.

• GaAs: Strip waveguides are made by using layers of GaAs and AlGaAs of
lower refractive index.

• Glass waveguides are made by ion exchange.

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Silicon Optical Waveguides (Nanophotonic Wires)

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Remarks on Non-Planar Waveguides
• One distinctive property of non-planar dielectric waveguides over their planar
counterpart is that a non-planar waveguide supports hybrid modes in addition
to TE and TM modes, whereas a planar waveguide supports only TE and TM
modes.

• Except for those few exhibiting special geometric structures, such as circular
optical fibers, non-planar dielectric waveguides generally do not have
analytical solutions for their guided mode characteristics.

• Numerical methods exist for analyzing such waveguides.

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Geometrical Optics Description
• Ray picture valid only within geometrical-optics approximation.

• Useful for a physical understanding of waveguiding mechanism.

• Limitation: One must resort to wave-optics description for thin waveguides

(thickness d ∼ λ).

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Wave Optics
Maxwell’s Equations:
1.
Explanation: The vortices of the electric field E are caused by temporal variations
of the magnetic induction B (Faraday’s law of induction).
2.
Explanation: The vortices of the magnetic field H are either caused by an electric
current with density j or by temporal variations of the electric displacement D
(Ampere’s law + Maxwell’s extension). The quantity ∂D/∂t is called the electric
displacement current
3.
Explanation: The sources of the electric displacement D are the electric charges
with density ρ (Gauss’ law)
4.
Explanation: The magnetic field (induction) is solenoidal, i.e. there exist no
‘magnetic charges’ (Gauss’ law for magnetism).

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• The 4 Maxwell’s equations are not all independent. The two divergence
equations can be derived from the two curl equations.

• The 4 field vectors E, D, H and B (each having 3 components) represent 12

unknowns. 12 scalar equations are required for the determination of these 12
unknowns.

Constitutive Relations:

• The required equations are supplied by the 2 vector curl equations and the 2
vector constitutive relations.

• NOTE: E and H are the macroscopic electric and magnetic fields; D and B are
the derived fields. 26
Maxwell’s Equations: Integral Forms
• The Maxwell’s equations are formulated in the differential form by using the
so-called Nabla operator:

• These equations can also be expressed in integral forms (by using Stoke’s
Theorem and Divergence theorem)

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Material Effects
• The constitutive parameters are used to characterize the electronic properties
of materials.

• Materials are characterized based on their predominant phenomenon:

 Dielectric: polarization (electric displacement current density) is the

predominant phenomenon

 Magnetic: magnetization (magnetic displacement current density) is the

predominant phenomenon.

 Conductor: conduction (conduction current density) is the predominant

phenomenon.

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Materials Classifications
According to lattice structures and behaviors, materials can be classified as:

• Linear/non-linear: Materials whose constitutive parameters are not functions

of applied field strength are called linear; otherwise nonlinear.

• Homogeneous/non-homogenous (inhomogeneous): Materials whose

constitutive parameters are not functions of positions are known as
homogeneous; otherwise non-homogeneous.

• Isotropic/non-isotropic (anisotropic): Materials whose constitutive

parameters are not functions of direction of the applied field are isotropic;
otherwise anisotropic.

• Dispersive/non-dispersive: Materials whose constitutive parameters are

functions of frequency are dispersive materials; otherwise non-dispersive.

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For Isotropic Dielectric Materials
• The constitutive relations become:

𝜖 is the dielectric function of the material and µ the magnetic permeability. Both
are functions of the position r.

• The dielectric constant of the vacuum 𝜖𝑜 = 8.8542·10−12 A sV−1 m−1 and the
magnetic permeability of the vacuum µ0 = 4π ·10−7 V s A−1 m−1 are related
with the light speed in vacuum c via:

with c = 2.99792458·108 m s−1

• Also for isotropic dielectric materials,

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Wave Equation in Homogeneous Dielectrics
 In homogeneous materials the dielectric function є and the magnetic
permeability µ are both constants (are not function of r).

 A special case is the vacuum where both constants are one (є = 1, µ =1).

 The Maxwell’s equation now becomes:

 These equations are completely symmetrical to a simultaneous replacement

of E with H and є0є with −µ0µ.

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We know the following vector identity:

Here, the Laplacian Operator:

So, we can write:

The wave equation for the electric vector in a homogeneous dielectric is

obtained:

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By using the equation, into the previous equation, we have:

The refractive index n of a homogeneous dielectric is defined as:

 Because of the symmetry in E and H of the Maxwell’s equations in

homogeneous dielectrics the same equation also holds for the magnetic
vector:

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