Open access peer-reviewed chapter

Review on Optical Waveguides

Written By

Shankar Kumar Selvaraja and Purnima Sethi

Submitted: 07 March 2018 Reviewed: 10 April 2018 Published: 01 August 2018

DOI: 10.5772/intechopen.77150

From the Edited Volume

Emerging Waveguide Technology

Edited by Kok Yeow You

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Optical devices are necessary to meet the anticipated future requirements for ultrafast and ultrahigh bandwidth communication and computing. All optical information processing can overcome optoelectronic conversions that limit both the speed and bandwidth and are also power consuming. The building block of an optical device/circuit is the optical waveguide, which enables low-loss light propagation and is thereby used to connect components and devices. This chapter reviews optical waveguides and their classification on the basis of geometry (Non-Planar (Slab/Optical Fiber)/Planar (Buried Channel, Strip-Loaded, Wire, Rib, Diffused, Slot, etc.)), refractive index (Step/Gradient Index), mode propagation (Single/Multimode), and material platform (Glass/Polymer/Semiconductor, etc.). A comparative analysis of waveguides realized in different material platforms along with the propagation loss is also presented.


  • optical waveguides
  • integrated optics
  • optical devices
  • optical materials
  • photonics integrated circuits

1. Introduction

Waveguides are indispensable for communication and computing applications as they are immune to electromagnetic interference and induced cross talk and also counter diffraction. Next-generation high-end information processing (bandwidths >1 Tb/s and speed >10 Gb/s) is immensely challenging using copper-based interconnects. Optical interconnects transmit data through an optical waveguide and offer a potential solution to improve the data transmission [1, 2]. There are predominantly two classes of optical waveguide: those in which “classical optical elements, placed periodically along the direction of propagation of the wave, serve to confine the wave by successive refocusing in the vicinity of the optical axis (laser resonators and multiple lens waveguides); and those in which the guiding mechanism is that of multiple total internal reflection from interfaces parallel to the optical axis” (fiber optical waveguides, slab waveguides, and resonators) [3].

Historically, high-frequency microwave sources had created a furore on guided wave photonics pioneered by Rayleigh and Sommerfeld. The first theoretical description of mode propagation along a dielectric guide was done by Hondros and Debye in 1910 [3]. The first dielectric waveguide to be examined at optical frequencies was the glass fiber used primarily for fiber optics imaging applications [4].

A waveguide can be defined as any structure (usually cylindrical) used for guiding the flow of electromagnetic wave in a direction parallel to its axis, confining it to a region either within or adjacent to its surfaces. In order to understand the propagation of light in a waveguide, it is imperative to derive the wave equation. The electromagnetic wave equation can be derived from the Maxwell’s equation, assuming that we are operating in a source free ρ=0J=0, linear (εandμ are independent of EandH), and an isotropic medium. EandH are the electric and magnetic field amplitudes, respectively, ε is the electric permittivity of the medium, and μ is the magnetic permeability of the medium. The equations are:


Here, B and D are magnetic and electric fluxes, respectively. The wave equation derived from the above expressions is:


The right-hand side of Eq. (5) is nonzero when there is a gradient in permittivity of the medium. Guided wave medium has a graded permittivity; however, in most structures, the term is negligible. Thus, the wave equation can be written as:


for electric and magnetic field amplitudes, respectively.


2. Classification of waveguides

Optical waveguides can be classified according to their geometry, mode structure, refractive index (RI) distribution, and material. A dielectric optical waveguide comprises a longitudinally extended high-index medium called the Core, which is transversely surrounded by a low-index medium, called the Cladding. A guided optical wave propagates in the waveguide along the longitudinal direction. The characteristics of a waveguide are determined by the transverse profile of its dielectric constant (x, y), which is independent of the z coordinate. For a waveguide made of optically isotropic media, the waveguide can be characterized merely with a single spatially dependent transverse profile of the index of refraction, n(x, y). Broadly, the waveguides can be classified as [5]:

  • Planar/2-D waveguides: Optical confinement is only in one transverse direction, the core is sandwiched between cladding layers in only one direction (Figure 1(a)). Optical confinement is only in the x-direction with index profile n(x). They are primarily used for high-power waveguide lasers and amplifiers.

  • Non-planar/3-D/channel optical waveguide: Comprises 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 as shown in Figure 1(b). A channel waveguide (with guidance in both directions) has a guiding structure in the form of a stripe with a finite width. Examples: channel waveguides (Section 2.3.II) and circular optical fibers [6].

Figure 1.

(a) Planar optical waveguide of 1-d transverse (x) optical confinement, (b) non-planar optical waveguide of 2-D transverse (x, y) optical confinement.

A waveguide in which the index profile changes abruptly between the core and the cladding is called a step-index waveguide, while one in which the index profile varies gradually is called a graded-index waveguide as shown in Figure 2. Recently, hybrid index profile waveguide was shown combining both inverse-step index waveguide and graded index waveguides for high-power amplification of a Gaussian single-mode beam [7].

Figure 2.

(a) Step-index type waveguide, (b) Graded-index waveguide, and (c) Hybrid waveguide.

2.1. Waveguide mode

A waveguide mode is an electromagnetic wave that propagates along a waveguide with a distinct phase velocity, group velocity, cross-sectional intensity distribution, and polarization. Each component of its electric and magnetic field is of the form fxyeiωtihz, where z is the axis of the waveguide. Modes are referred to as the “characteristic waves” of the structures because their field vector satisfies the homogenous wave equation in all the media that make up the guide, as well as the boundary conditions at the interfaces. The electric and magnetic fields of a mode can be written as Evrt=Evxyexpiβvziωt and Hvrt=Hvxyexpiβvziωt, where ν is the mode index, Evxy and Hvxy are the mode field profiles, and βv is the propagation constant of the mode.

A mode is characterized by an invariant transversal intensity profile and an effective index (neff). Each mode propagates through the waveguide with a phase velocity of c/neff, where c denotes the speed of light in vacuum and neff is the effective refractive index of that mode. It signifies how strongly the optical power is confined to the waveguide core. In order to understand modes intuitively, consider a simple step-index 2-D waveguide and an incident coherent light at an angle θ between the wave normal and the normal to the interface as shown in Figure 3. The critical angle at the upper interface is θc=sin1nc/nf and lower interface θs=sin1ns/nf and ns<nc(θs<θc).

Figure 3.

Ray-optical picture of modes propagating in an optical waveguide.

Optical modes with an effective index higher than the largest cladding index are (1) Guided modes (θs<θ<90°): As the wave is reflected back and forth between the two interfaces, it interferes with itself. A guided mode can exist only when a transverse resonance condition is satisfied so that the repeatedly reflected wave has constructive interference with itself. Modes with lower index are radiating and the optical power will leak to the cladding regions. They can be categorized as (2) Substrate radiation modes (θc<θ<θs): Total reflection occurs only at the upper interface resulting in refraction of the incident wave at the lower interface from either the core or the substrate, (3) Substrate-cover radiation modes (θ<θc): No total reflection at either interface. Incident wave is refracted at both interfaces, and it can transversely extend to infinity on both sides of the waveguide, and (4) Evanescent modes: Their fields decay exponentially along the z direction. For a lossless waveguide, the energy of an evanescent mode radiates away from the waveguide transversely.

The waveguide dimensions determine which modes can exist. Most waveguides support modes of two independent polarizations, with either the dominant magnetic (quasi-TM) or electric (quasi-TE) field component along the transverse (horizontal) direction. For most applications, it is preferable that the waveguides operate in a single-mode regime for each polarization. This single-mode regime is obtained by reducing the waveguide dimensions until all but the fundamental waveguide modes become radiating. Fields in the waveguide can be classified based on the characteristics of the longitudinal field components, namely (1) Transverse electric and magnetic mode (TEM mode): Ez=0, and Hz=0. Dielectric waveguides do not support TEM modes, (2) Transverse electric mode (TE mode): Ez=0 and Hz0, (3) Transverse magnetic mode (TM mode): Hz=0 and Ez0, and (4) Hybrid mode: Ez0 and Hz0. Hybrid modes exist only in non-planar waveguide.

2.2. Planar waveguide

Homogeneous wave equations exist for planar slab waveguides of any index profile n(x). For a planar waveguide, the modes are either TE or TM.

Infinite slab waveguide: The slab waveguide is a step-index waveguide, comprising a high-index dielectric layer surrounded on either side by lower-index material (Figure 4). The slab is infinite in the y-z plane and finite in x direction and the refractive index of ncore > ncladding,nsubstrate to ensure total internal reflection at the interface. For case (1): ncladding=nsubstrate, the waveguide is denoted as Symmetric and for case (2): ncladdingnsubstrate, waveguide is Asymmetric.

Figure 4.

Planar slab waveguide and transverse electric (TE) and transverse magnetic configuration (TM).

For the electromagnetic analysis of the planar slab waveguide (infinite width), assuming ncore>nsubstrate>ncladding, we consider two possible electric field polarizations—TE or TM. The axis of waveguide is oriented in z-direction: k vector of the guided wave will propagate down the z-axis, striking the interfaces and angles greater than critical angle. The field could be TE which has no longitudinal component along z-axis (electric field is transverse to the plane of incidence established by the normal to the interface, and the k vector) or TM depending on the orientation of the electric field.

I. For TE Asymmetric waveguide: E field is polarized along the y-axis, and assuming that waveguide is excited by a source with frequency ωo and a vacuum wave vector of magnitude ωoc, the allowed modes can be evaluated by solving the wave equation in each dielectric region through boundary conditions. For a sinusoidal wave with angular frequency ωo, the wave equation for the electric field components in each region can be written as (k=ωμε=k),


here, ni can be the refractive index of either core, cladding, or the substrate. The solution to Equation (7) can be written as:


due to the translational invariance of the waveguide in z-direction. β is the propagation constant along the z-direction (longitudinal). From Equation (8) and since d2ydx2=0, we can write:


The solution to the wave equation can be deduced by considering Case (1)β>k0ni and E0 is field amplitude at x = 0, solution is exponentially decaying and can be written as:


The attenuation constant ϓ=β2k02ni2. Case (2)β<k0ni, solution has an oscillatory nature and is given by:


The transverse wave vector κ=k02ni2β2 and the relation between β, κ and k are given by k2=β2+κ2.

The longitudinal wave vector β (z component of k) must satisfy k0nsubstrate<β<k0ncore (ncladdingncore) in order to be guided inside the waveguide. Eigen values for the waveguide can be derived using transverse components of electric field amplitudes in three regions as Eyx=Aeγcladdingxfor0<x;Eyx=Bcosκcorex+Csinκcorexforh<x<0; Eyx=Deγsubstratex+hforx<h, where A, B, C, and D are amplitude coefficients to be derived using boundary conditions (Ey,Hz,Eyxatx=0 are continuous). Solving the equation, we get A=B,C=Aϓcladdingκcore ,D=A[cosκcoreh+γcladdingkcoresin(kcoreh], and thus:


The Eigenvalue equation (Figure 5(a)) is given by:


Figure 5.

Plot for Eigen value equation for (a) Asymmetric TE mode slab waveguide, (b) Asymmetric TM mode slab Waveguide.

II. TM Asymmetric waveguide: The field components of the waveguide can be written as:

HYxyt=Hmxeiωt, Exxzt=βωεHmxeiωtβz, and Ezxzt=iωε. The Eigen value for β (Figure 5(b)) is given by:


III. TE Symmetric waveguide: The field equation of a TE mode within the symmetric waveguide is given by:

Ey=Aeγxh2for xh2Ey=Acosκxcosκh2orAsinκxsinκh2forh2xh2Ey=±Aeγx+h2forxh2E14

The characteristic Eigen value equation for the TE modes in a symmetric waveguide is given by:

tanκh2=γk for even (cos) modes=ky for odd (sin) modesE15

In order to plot the Eigen values of the TE modes of the symmetric waveguide, solutions of Eq. (15) are plotted for a wavelength of 1.55 μm and different “h” values (15 μm and 3 μm respectively) as shown in Figure 6.

Figure 6.

Plot for Eigen value equation for Symmetric TE mode slab waveguide at a wavelength of 1.55 μm for waveguide width of (a) 15 μm and (b) 3 μm. Thick waveguide supports multimode transmission.

The longitudinal wave vector β is quintessential to describe the field amplitudes in all regions of the waveguide. (i) Every Eigen value β corresponds to a distinct confined mode of the system. The amplitude of the mode is established by the power carried in the mode; (ii) only a finite number of modes will be guided depending on the wavelength, index contrast, and waveguide dimensions; (iii) most modes will be unguided, and all modes are orthogonal to each other; (iv) some modes are degenerate. Degenerate modes will share the same value of β but will have distinguishable electric field distributions. The lower-order mode is expressed by βlowest orderkncore and higher-order mode by βlowest orderkncorecosθcriticalknsubstrate. A waveguide is generally characterized by its normalized frequency, given by,


The approximate number of modes (m) in the waveguide are given by mV/π. Graphical solution to the waveguide can be evaluated by:


where a is asymmetry parameter (ranges from 0 (symmetric waveguide) to infinity), b is normalized effective index (ranges from 0 (cutoff) to 1) and neff=β/ko is the effective index of the waveguide. The normalized dispersion relation is given by (Figure 7):


where ν is an integer. The cut-off condition (b = 0) for modes in a step-index waveguide is given by V=tan1a+vπ. The numerical aperture is defined as the maximum angle that an incident wave can have and still be guided within the waveguide. It is given by: N A=sinθmax=ncore2nsubstrate/cladding2.

Figure 7.

Normalized index b versus normalized frequency V for different values of asymmetry coefficient a (a = 0, a = 10, a = ).

IV. TM Symmetric waveguide: The characteristic Eigen value equation for the TM modes in a symmetric waveguide is given by:

tanκh2=ncore/nsubstrate2γκ: even (cos) modes=ncore/nsubstrate2κγ for odd (sin) modesE20

Graphical solution to the waveguide can be evaluated using:


2.3. Non-planar waveguide

The following section describes step-index circular and channel waveguides.

I. Step-index circular waveguide: The wave equation for the step-index circular waveguides in cylindrical coordinates is given by:


At z = 0, field is purely radial (Figure 8).The Ez component of the electric field couples only to itself and the scalar wave equation for Ez is given by:


Figure 8.

Schematic representation of step-index circular waveguide.

One can write Ezrϕz=RrϕφZz,Eq. (24) can be written as:


The solution to the wave equation is deduced from separation of variables, and we obtain:


The solution is given by Bessel functions: (1),Jνκr when k02n2β2ν2/r2 is positive (κ2=k02n2β2) and (2) Kνϓr when k02n2β2ν2/r2 is negative (γ2=β2k02n2). Bessel function (1) can be approximated by (κr is large) (Figure 9):


Figure 9.

Bessel Function of the (a) first kind (behaves as a damped sine wave) and (b) second kind (monotonic decreasing function).

And solution to (2) is


The equation for field distribution in the step-index fiber can be calculated through:

Er=κ2Jvκr+jωμvβrBJvκrejvϕejβz, Eϕ=κ2jvrAJvκrωμβJvκrejvϕejβz,Hr=κ2JvκrϵcorevβrAJvκrejvϕejβz and Hϕ=κ2jvrBJvκrωϵcoreβJvκrejvϕejβz for (r<a); a is core’s radius. In the cladding (r>a) Er=γ2Kvγr+jωμvβrDKvγrejvϕejβz, Eϕ=γ2jvrCKvγrωμβKvγrejvϕejβz and Hr=γ2KvγrϵcladvβrCKvγrejvϕejβz.

The V-number or the normalized frequency is used to characterize the waveguide and is defined as:

II. Rectangular dielectric Waveguide: Channel/rectangular waveguides are the most commonly used non-planar waveguides for device applications. Channel waveguides include buried waveguides, strip-loaded, ridge, rib, diffused, slot, ARROW, and so on. Figure 10 shows the schematic of few of the channel waveguides. The wave equation analysis of a rectangular waveguide can be done by writing the scalar wave equation:


Figure 10.

Schematic representation of various channel waveguides.

The general representation of the dielectric waveguide along with the electromagnetic field distribution in the regions is shown below:

expγ3x                   3
expγ5x                      5
Cosκyy+Φy            1
expγ4yb           4
expγ2xa         2

where ϕx and ϕy are phase constants. The characteristic equations are given by tanκyb=κyγ4+γ5κy2γ4γ5 and tanκxa=n12κxn22γ3+n32γ2n22n32κx2n12γ2γ3 (γi) are exponential decay constants. The critical cut-off condition is given by:


The following section describes various types of channel waveguides.

1. Wire waveguide: The schematic of silicon photonic wire waveguide is shown in Figure 11(a). The waveguide consists of a silicon core and silica-based cladding. Since the single-mode condition is very important in constructing functional devices, the core dimension should be determined so that a single-mode condition is fulfilled. The primary requisite is single-mode guiding of the TE00 and TM00 mode. When the effective refractive index is larger than the cladding and smaller than the core, mode is guided in the waveguide, and guiding will be stronger for higher values of effective index neff. Thus, modes with effective indices above nSiO2 will not be radiated into the buffer layer and thus will be guided. Figure 11(b) depicts the quasi-TE mode of a 220-nm-high and 450-nm-wide silicon waveguide at wavelength of 1.55 μm [8].

Figure 11.

(a) Silicon-on-insulator wire waveguide, (b) quasi-TE mode of a 220-nm-high and 450-nm-wide silicon waveguide at wavelength of 1.55 μm, and (c) effective refractive index (neff) at 1550 nm for a 220-nm-high silicon photonic wire waveguide. The left of the hashed line is the single-mode region.

Each mode propagates through the waveguide with a phase velocity of c/neff, where c denotes the speed of light in vacuum and neff is the effective refractive index felt by that mode. It signifies how strongly the optical power is confined to the waveguide core. Most waveguides support modes of two independent polarizations, with either the major magnetic (quasi-TM) or electric (quasi-TE) field component along the transverse (horizontal) direction.

Figure 11(c) shows neff as a function of the width of the photonic wire. The neff depends on the waveguide cross-section, waveguide materials, and the cladding material. Higher-order modes travel with a different propagation constant compared to the lowest-order mode and are less confined in the waveguides. As a consequence of the dissimilar propagation constants, there is modal dispersion which reduces the distance-bandwidth product of the waveguide. Due to the low confinement, first, a large field decay outside the waveguide reduces the maximum density of the devices and, second, in the waveguide bends the higher-order modes become leaky resulting in propagation losses. It is desirable that the difference between neff of the fundamental quasi-TE and quasi-TM modes be large so that the coupling between the modes is limited due to difference in mode profiles and also the phase-mismatch. For widths below ∼550 nm, silicon photonic wire will be single mode for each polarization.

2. Rib waveguide: Figure 12(a) and (b) shows the schematic and the fundamental quasi-TE mode of a silicon photonic rib waveguide (H = 220 nm, r = 70 nm). Although a rib waveguide can never truly be single mode, by optimizing the design, the power carried by the higher-order modes will eventually leak out of the waveguide over a very short distance, thus leaving only the fundamental mode. Figure 12(c) shows the dispersion neff as a function of the width of the photonic rib waveguide. For widths below ∼800 nm, silicon photonic rib waveguide will be single mode for each polarization.

Figure 12.

(a) Silicon-on-insulator rib waveguide, (b) quasi-TE mode of a 220-nm-high and 700-nm-wide silicon rib waveguide at wavelength of 1.55 μm, and (c) effective refractive index (neff) at 1550 nm for 220-nm-high silicon rib waveguide for ridge height (r) = 70 nm.

Wire waveguides are advantageous as they provide a small bending radius and realization of ultra-dense photonic circuits. However, they have higher propagation losses. On the one hand, wire waveguide allows low-loss sharp bends in the order of a few micrometres, while, on the other hand, the device structures produced are susceptible to geometric fluctuations such as feature drift size (resulting in degradation of device performance) and waveguide sidewall roughness (resulting in propagation losses) [9, 10]. Rib waveguides typically require bend radii >50 μm in SOI to ensure low bend losses, which eventually result in a larger device/circuit footprint. Figure 13 shows the TE mode loss in silicon wire and rib waveguide for a bend of 90°.

Figure 13.

Mode loss for silicon wire (cross-section: 450 × 220 nm2) and rib (cross-section: 600 × 220 nm2) waveguides for a 90° bend with increasing bending radii.


3. Slot waveguide

Slot waveguides are used to confine light in a low-index material between two high-index strip waveguides by varying the gap and dimensions (width and height) of the strip waveguides (Figure 14(a)). The normal component of the electric field (quasi TE) undergoes very high discontinuity at the boundary between a high- and a low-index material, which results into higher amplitude in the low-index slot region. The amplitude is proportional to the square of the ratio between the refractive indices of the high-index material (Si, Ge, Si3N4) and the low-index slot material (air). On the other hand, the effect of the presence of the slot is minimal on quasi-TM mode, which is continuous at the boundary. When the width of the slot waveguides is comparable to the decay length of the field, electric field remains across the slot and the section has high-field confinement [11, 12, 13, 14], which results into propagation of light in the slot section; unlike in a conventional strip waveguide, where the propagating light is confined mainly in the high-index medium.

Figure 14.

(a) Silicon-on-insulator slot waveguide, (b) Quasi-TE mode of a 220-nm-high (Gap = 100 nm) slot waveguide, (b) variation of effective refractive index with waveguide width for slot gap of 100, 150, and 200 nm, respectively, at a wavelength of 1.55 μm.

Figure 14(c) shows the variation in effective index with the waveguide width for different slot gaps. The advantage of a slot waveguide is the high-field confinement in the slot section, which normally cannot be achieved using a simple strip- or a ridge-based waveguide, making it a potential candidate for applications that require light-matter interaction such as sensing [12] and nonlinear photonics [13]. The launching of light into a slot waveguide is normally done by phase matching the propagation constant of the strip waveguide and the slot waveguide. However, efficient coupling still remains a challenge because of scattering loss and mode mismatch of the slot and strip waveguides, with a reported propagation loss between 2 and 10 dB/cm [14].


4. Strip-loaded waveguide

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, as shown in Figure 15(a). Strip-loaded waveguides do not require half-etching in waveguide fabrication and is therefore easier to fabricate. Figure 15(a) shows the schematic of a hydrogenated amorphous silicon strip-loaded waveguide where a thermal oxide is inserted between the layers for passivation [15]. Figure 15(b) shows the optical field for the waveguide for a 75-nm-thick and 800-nm-wide strip-loaded waveguide and Figure 15(c) depicts the variation in effective index with the strip waveguide width.

Figure 15.

(a) Hydrogenated amorphous strip-loaded waveguide, (b) Quasi-TE mode of a 220-nm-high, 800-nm-wide, 75-nm-thick strip Waveguide, (c) Variation of effective refractive index with strip width at a wavelength of 1.55 μm.


5. Suspended waveguide

Suspended waveguides have enabled new types of integrated optical devices for applications in optomechanics, nonlinear optics, and electro-optics. Fabrication involves removing a sacrificial layer above or below a waveguide core layer to design these waveguides [16]. Increasing absorption loss of SiO2 at longer wavelengths makes it challenging to utilize SOI for low-loss components in the mid-infrared (MIR) [17]. Removing the SiO2 layer opens the possibility of extending the low-loss SOI wavelength range up to ∼8 μm. For MEMS, it is imperative to have waveguides that can be mechanically actuated. This requires waveguides that are released from the substrate, for example, through surface micromachining [17]. Figure 16 shows the schematic of a suspended waveguide [18].

Figure 16.

Schematic of a suspended waveguide.


6. TriplexTM technology

TriPleX waveguides are a family of waveguide geometries that is based on an alternating layer stack consisting of two materials: Si3N4 and SiO2. The waveguide geometries are categorized as box shell, single stripe (propagation loss <0.03 dB/cm), symmetric double stripe (propagation loss <0.1 dB/cm), and asymmetric double stripe (propagation loss <0.1 dB/cm) as shown in Figure 17(a) [19]. Different confinement regimes can be optimized for specific applications for these waveguides and tunable birefringence- and polarization dependent loss (PDL) can be achieved. Propagation losses (<0.1 dB/cm), very low PDL (< 0.1 dB/cm), and easy interconnection with optical fibers (<0.15 dB/facet) have been demonstrated in single-mode box-shaped waveguides [20]. Moreover, fabrication of the waveguide is a low-cost and simple process.

Figure 17.

(a) Schematic of different type of TriPleX waveguides, (b) Variation in waveguide size of the box-shaped waveguide, and (c) its diffraction angle versus the index contrast.

LioniX TriPleX technology is a versatile photonics platform suited for applications such as communications, biomedicine, sensing, and so on, over a broadband range of 0.4 to 2.35 μm [21]. Figure 17(b) and (c) depicts the variation in waveguide size and diffraction angle with index contrast of the box-shaped geometry for a wavelength of 1.55 μm.


7. Photonic crystal waveguide

Photonic crystal waveguides guiding mechanism is different from that of a traditional waveguide, which is based on internal reflection. A photonic crystal is a periodic dielectric structure with a photonic band gap, that is, a frequency range over which there is no propagation of light. The introduction of line defects into a photonic crystal structure creates an optical channel for propagation of light. If the line defect is properly designed, the resulting guiding mode falls within a photonic band gap, is highly confined, and can be used for guiding light. The guiding mode can also be designed to be broadband and thus gives rise to a compact, broadband photonic crystal waveguide [22]. Application of these waveguides includes nanofluidic tuning, RI measurements, optical characterization of molecule orientation, and biosensing.


8. Diffused waveguide

A diffused waveguide is formed by creating a high-index region in a substrate through diffusion of dopants, such as a LiNbO3 waveguide with a core formed by Titanium (Ti) diffusion. Due to the diffusion process, the core boundaries in the substrate are not sharply defined. A diffused waveguide has a thickness defined by the diffusion depth of the dopant and a width defined by the distribution of the dopant. Alternatively, the material can be exchanged with the substrate. Ion-exchanged glass waveguide is fabricated by diffusing mobile ions originally in glass with other ions of different size and polarizability [23].The additional impurities cause a change in refractive index that is approximately proportional to their concentration. A material can also be implanted using an ion implanter within the waveguide. However, this process damages the lattice and is therefore followed by annealing.


9. ARROW waveguide

In anti-resonant reflecting optical (ARROW) waveguides, light confinement is realized by choosing the cladding layer thicknesses accordingly to create an anti-resonant Fabry-Perot reflector for the transverse component of the wave vector at the desired wavelength. Even though the ARROW mode is leaky, low-loss propagation over large distances can be achieved. Yin et al. have designed an ARROW waveguide exhibiting single-mode confinement and low-loss light propagation in a hollow air core on a semiconductor chip [24]. ARROW waveguides with non-solid low-index cores have applications in gas and liquid sensing, quantum computing, quantum communications, and Raman scattering spectroscopy. Chalcogenide rib ARROW structures have also been shown with propagation loss ∼6 dB/cm to design opto-chemical sensors in the near- and mid-IR region [25].


10. Augmented waveguide

Light confinement in a low-index media has been shown in ARROW, slot, and plasmonic waveguides. However, ARROW waveguide has low confinement and is thus leaky. Strong light confinement in the low-index medium can be achieved by using silicon slot and plasmonic waveguide. Fabrication of the slot waveguide is cumbersome and hybrid plasmonic waveguide suffers from additional propagation losses due to the presence of metal. Augmented waveguide confines light efficiently in the low-index region by reducing the reflection at the high index-low index interface in a high-index contrast waveguide, which results in enhancement of light confinement in the low-index region [26]. Figure 18 shows the schematic of an augmented low-index waveguide.

Figure 18.

Schematic of an augmented waveguide.

Waveguides can be classified on the basis of different material platforms. Wavelength range, ease of fabrication, compactness, and CMOS compatibility are few of the determining factors when selecting a material for a specific application. Table 1 compares various waveguide platforms along with their propagation losses [27]. Figure 19 shows variation of index contrast with footprint for few material platforms.

Material platformsWaveguidesRangeConfigurationPropagation Loss
Semiconductor materialsSiliconMid-IRSilicon nanophotonic waveguide∼4 dB/cm (2030 nm)
∼10 dB/cm (2500 nm) [28]
Mid/Near-IRSuspended silicon-membrane ridge waveguide (TM mode)2.8±0.5 dB/cm (3.39 μm)
5.6±0.3 dB/cm (1.53 μm) [29]
Mid/Near-IRSilicon on porous silicon (SiPSi)2.1±0.2 dB/cm (1.55 μm) ∼3.9±0.2 dB/cm (3.39 μm) [30]
GermaniumMid-IRGermanium on silicon strip waveguide2.53dB dB/cm [31] (∼5.15-5.4 μm)
Far-IRGermanium on silicon strip waveguide2.5dB dB/cm [32] (∼5.8 μm)
Mid-IRGermanium on silicon rib waveguide2.4±0.2 dB/cm [33] (∼3.8 μm)
Mid-IRGermanium-rich silicon germanium platform-based rib waveguide1.5±0.5 dB/cm [34] (∼4.6 μm)
Mid IR/Far-IRSilicon germanium/silicon-based graded index waveguides1 dB/cm (4.5 μm) ∼2 dB/cm (7.4 μm) [35]
Mid-IRGermanium-on-silicon-on-insulator waveguides3.5 dB/cm (3.682 μm) [36]
Mid-IRSilicon germanium ridge waveguide on a silicon substrate0.5 dB/cm (4.75 μm) [37]
Far-IRGermanium on GaAs ridge waveguide4 .2 dB/cm (10 μm) [38]
Gallium arsenide (GaAS)Near-IRGaAS/Al0.3 Ga0.7As ridge waveguide for manipulation of single-photon and two-photon states1.6 dB/cm (1.55 μm) [39]
Near-IRSuspended GaAs waveguide0.4 dB/mm (TE) (1.55 μm) and 6 dB/mm (TM) (1.03 μm) [40]
Near-IRGaAs-based single-line defect photonic crystal slab waveguide0.76 dB/mm (1050–1580 nm) [41]
Indium phosphide (InP)Near-IRInP waveguides based on localized Zn-diffusion process (MOVPE) to mitigate passive loss by p-dopants0.4 dB/cm (1.55 μm) [42]
Near-IRSuspended InP dual-waveguide structures for MEMS-actuated optical buffering2.2 dB/cm (1.5–1.6 μm) [43]
Gallium antimonyMid-IRGaSb waveguides based on quasi-phase matching (QPM)0.7/1.1 dB/cm [44] ∼(2/4 μm)
Quantum dotesNear-IRPolymer waveguides containing infrared-emitting nanocrystal quantum dots (PbSe and InAs)5 dB/cm (inclusive of fiber coupling loss) [45] (∼1550 nm)
Doped semiconductorVis/Near-IRRare-earth-doped GaN (gallium nitride) channel waveguide5.4/4.1 dB/cm [46] (∼633/1550 nm)
Near-IRErbium-Doped Phosphate Glass Strip-loaded Waveguide on Silicon4.1 dB/cm [47] (∼1535 nm)
Semiconductor nanomaterialsMid-IRSilicon-on-Sapphire Suspended Nanowire1±0.3 dB/cm [48] (∼4 μm)
VisTin-oxide nanoribbons-based subwavelength waveguide10 dB/cm [49] (∼400-550 nm)
Near-IRAmorphous silicon nanowire4.5 dB/cm [50] (∼1550 nm)
Near-IRInP/benzocyclobutene optical nanowires on a GaAs substrate0.8 dB/mm [51] (∼1550 nm)
Silicon-on-insulator waveguidesSilicon-on-SilicaNear-IRSilicon-on-silica strip waveguide0.6 dB/cm [52] (∼1550 and 2000 nm)
Near-IRSilicon-on-silica rib (70-nm etch depth) waveguide0.10.2 dB/cm [52] (∼1550 and 2000 nm)
Mid-IRSilicon-on-silica rib (70-nm etch depth) waveguide1.5 dB/cm [53] (∼3800 nm)
Near-IRSilicon-on-silica slot waveguide2.28±0.03 dB/cm [54] (∼1064 nm)
Near-IRSilicon-on-Silica slot waveguide3.7 dB/cm [55] (∼1550 nm)
Mid-IRSuspended silicon waveguide∼3.1 dB/cm (7.67 μm) [56]
Near-IRSilicon-on-silica strip waveguide coated with amorphous TiO22±1 dB/cm [57] (∼1550 nm)
Silicon-on-SapphireMid-IRSilicon-on-sapphire ridge waveguide4.0±0.7 dB/cm [58] (∼5.4-5.6 μm)
Mid-IRSilicon-on-sapphire ridge waveguide4.3±0.6 dB/cm [59] (∼4.5 μm)
Mid-IRSilicon-on-sapphire slot waveguide11 dB/cm [60] (∼3.4 μm)
Near/Mid-IRSilicon-on-sapphire nanowire waveguide0.8 dB/cm [61] (∼1550 nm).
1.11.4 dB/cm [61] (∼2080 nm)
<2 dB/cm [61] (∼5.18 μm)
Silicon-on-nitrideMid-IR and Near-IRSilicon-on-nitride ridge waveguide5.2±0.6 dB/cm [62] (∼3.39 μm)
Thallium-doped SOI Rib/Indium-doped SOI RibNear-IRThallium-doped silicon waveguide3 dB/cm [63] (∼1.55 μm)
Near-IRIndium-doped silicon waveguide, decrease in absorption coefficient ∼16 dB/cm [64] (wavelength ∼1.55 μm).
Glass waveguidesSilica glassVisLaser-written waveguide in fused silica for vertical polarization (VP)/horizontal polarization (HP) beam0.06/0.1 dB/cm [65] (∼777 nm)
Mid-IR3D laser-written silica glass step-index high-contrast (HIC) waveguide1.3 dB/cm3 [66] (∼3.39 μm)
Near-IRGraded-index (GRIN) Cladding in HIC glass waveguides1.5 dB/cm [67] (∼1.55 μm)
Near-IRHigh-index, doped silica glass material (Hydex) waveguides0.06 dB/cm [68] (∼1.55 μm)
Silicon oxynitride (SiON)Near-IRSiON deposited by inductively coupled PECVD-based waveguides0.5±0.05 dB/cm,1.6±0.2 dB/cm and 0.5±0.06 dB/cm [69] (∼1330, 1550 and 1600 nm)
Ion—exchanged glassVisTi+/Na+ ion-exchanged single-mode waveguides on silicate glass9±1 dB/cm [70] (∼0.405 μm)
Near-IRAlkaline aluminum phosphate glasses for thermal ion-exchanged waveguide0.53 dB/cm [71] (∼1.534 μm)
Sol-gel glassNear-IRHybrid organic-inorganic glass sol-gel ridge waveguides0.1 dB/cm [72] ∼(1.55 μm)
VisSol-gel derived silicon titania slab waveguides films0.2 dB/cm [73] ( 677 nm)
VisSol–gel-derived glass-ceramic photorefractive films-based waveguide0.5±0.2 dB/cm [74] (∼635 nm)
Tungsten tellurite glassNear-IROptical planar channel waveguide-based on tungsten-tellurite glass fabricated by RF Sputtering0.44 dB/cm [75] (∼1.53 μm)
Laser-writtenNear-IRLaser-written waveguide in planar light-wave circuit (PLC) glass doped with Boron and Phosphorous0.35 dB/cm [76] (∼1.55 μm)
VisLaser-written waveguide in fused silica for vertical polarization (VP)/horizontal polarization (HP) beam0.06/0.1 dB/cm [65](∼777 nm)
Near-IRLaser-written ferroelectric crystal in glass waveguide2.64 dB/cm [77] (∼1530 nm)
VisFemtosecond laser-written double-line waveguides in germanate and tellurite glasses2.0 dB/cm [78] (∼632 nm)
Near-IRUltrafast laser-written waveguides in flexible As2S3 chalcogenide glass tape<0.15 dB/cm [79] (∼1550 nm)
Electro-optic waveguidesLithium niobateNear-IRLithium niobate on insulator rib waveguide0.4 dB/cm [80] (∼1.55 μm)
Near-IRLithium niobate ridge waveguide0.3 dB/cm(TE) and 0.9 dB/cm(TM) [81] (∼1.55 μm)
Near-IRPeriodically poled lithium niobate waveguide<1 dB/cm [82] (∼1.55 μm)
Near-IRHeterogeneous lithium niobate on silicon nitride waveguide<0.2±0.4 dB/cm [83] (∼1.54 μm)
Near-IRLithium Niobate on Insulator Ridge Waveguide1 dB/cm [84] (∼1.55 μm)
Near-IRThin film strip-loaded (SiN) lithium niobate waveguide5.8 dB/cm (TE)14 dB/cm (TM) [85] (∼1.55 μm)
Near-IRThin film strip-loaded (a-Si) lithium niobate waveguide42 dB/cm (TE)20 dB/cm (TM) [86] (1.55 μm)
Near-IRThin film lithium niobate ridge waveguide0.268 dB/cm (TE)1.3 dB/cm (TM) [87]
(∼1.55 μm)
Lithium tantalateNear-IRGa3+-diffused lithium tantalate waveguide0.2 dB/cm (TE)0.4 dB/cm (TM) [88] (∼1.55 μm)
Barium titanate (BTO)VisBTO thin films on MgO-based ridge waveguide2 dB/cm (TE) [89] (∼633 nm)
Mid-IRBTO thin films on Lanthanum Aluminate (LAO) with a-Si ridge waveguide4.2 dB/cm [90] (∼3.0 μm)
Electro-optic polymerNear-IRHybrid Electro-Optic Polymer and TiO2 Slot Waveguide5 dB/cm [91] (∼1550 nm)
Liquid crystalNear-IRPDMS (poly (dimethyl siloxane))-liquid crystal-based optical waveguide8 dB/cm [92] (∼1550 nm)
VisLiquid-crystal core channel waveguide encapsulated in semicircular grooves with glass substrate1.3 dB/cm [93] (∼632.8 nm)
Near-IRLiquid crystal clad shallow-etched SOI waveguide4.5 dB/cm [94] (1570 nm)
Polymer-basedConventional optical polymersVisPMMA (poly(methyl methacrylate) )-based optical waveguide0.2 dB/cm [95] (∼850 nm)
Vis/Near-IRPolyurethane (PU)-based optical waveguide0.8 dB/cm [95] (∼633 and 1064 nm)
Vis/Near-IREpoxy resin-based optical waveguide0.3/0.8 dB/cm [95] (∼633/1064 nm)
VisPolymer PMMA-based waveguide using femtosecond laser0.3 dB/cm [96] (∼638 and 850 mm)
Novel optical polymersVis/Near-IRPolymeric waveguides (WIR30 photopolymer) with embedded micro-mirror0.18 dB/cm [97] (∼850 nm )
Vis/Near-IRAcrylate-based waveguide pattern using photo exposure/laser ablation0.02/0. 3 and 0.8 dB/cm [95] (∼840/1300 and 1550 nm)
Vis/Near-IRTelephotonics-OASIC-based optical waveguide<0.01,0.03,0.1 dB/cm [95]
(∼840/1300/1550 nm)
Near-IRDow chemical perfluorocyclobutane(XU 35121)-based waveguide0.25 dB/cm [95] (∼1300/1550 nm)
Near-IRCircular-core UV-curable epoxies-based optical waveguide0.79 dB/cm [98] (∼1550 nm)
Vis/Near-IRMulti-mode Siloxane-based polymer waveguide, single-mode siloxane-based polymer waveguide0.05 dB/cm [99] (∼850 nm)/ ∼0.5/1 dB/cm [99] (∼1.31/1.55μm)
Surface plasmon polariton waveguideNear-IRPolymer-Silicones-based long range surface plasmon polariton waveguide (LRSPPW)0.51 dB/mm [100] (∼1.55 μm)
Near-IRExguide ZPU/LFR-based long range surface plasmon polariton waveguide (LRSPPW)1.72 dB/cm [101] (∼1.55 μm).
Hollow waveguidesMetal/Dielectric CoatedTHzGold-coated waveguide using liquid phase chemical deposition process1.98/1.89 dB/cm [102] (∼215/513 μm)
THzSilver-coated waveguide using liquid phase chemical deposition Process1.77/1.62 dB/cm [102] (∼215/513 μm)
Mid-IRCadmium sulfide CdS) and PbS (Lead Sulfide) on Ag (Silver)-coated hollow glass waveguide0.037 dB/cm [103] (∼2.94 μm)
THzHigh-refractive index composite photonics band-gap Bragg fiber0.3 dB/cm [104] (∼300 μm)
THzSilver/polystyrene-coated hollow glass waveguides1.9 dB/m [105] (∼300 μm)
Vis/Near-IRSilver/cyclic olefin hollow glass waveguide0.549/0.095and0.298 dB/m [106]
(∼808/1064 and 2940 nm)
Hollow glassNear-IRHollow-core optical waveguide (Si Substrate)1.7 dB/cm [107] (∼1.52-1.62 μm)
Far-IRTapered hollow-air core waveguide1.27 dB/cm [108] (∼6.2 μm)
VisAir-core anti-resonant reflecting Optical Waveguide (ARROW)4 dB/cm [109] (∼820-880 nm)
ChalcogenideNear-IRChalcogenide waveguides (Ge23Sb7S70) fabricated through CMOS-compatible lift-off process: Strip/rib2-6 /<0.5 dB/cm [110] (∼1550 nm)
Mid-IRChalcogenide waveguides (Ge11.5As24Se64.5)<1 dB/cm (0.3dB at 2000 cm−1 )
(1500-4000 cm−1) [111]
Near-IRChalcogenide waveguides Ge23Sb7S70 (chlorine-based plasma etching)<0.42 dB/cm−1 (1550 nm) [112]
Liquid coreVisLiquid core/(ethylene glycol) air-cladding waveguide0.14 dB/cm ( 464-596 nm) [113]
VisNano porous solid liquid core Waveguide0.6 dB/cm ( 632.8 nm) [114]
Metamaterial optical waveguidesMid-IRSuspended silicon waveguide with lateral cladding (subwavelength grating metamaterial)∼0.82 dB/cm (3.8μm) [115]
Titanium dioxide TiO2Vis/Near-IRAtomic layer deposition (ALD) TiO2 slab waveguide∼2.0-3.5 dB/cm (633 nm) [116]
<1 dB/cm (1530 nm) [65]
Near-IRAmorphous TiO2 strip waveguide∼2.4-0.2 dB/cm (1.55μm) [117]
Silicon carbideNear-IRPECVD silicon-carbide-silicon oxide horizontal slot waveguide23.9±1.2 dB/cm (1.3 μm)-TM mode [118]
Silicon nitride on silica30VisSilicon-nitride strip waveguide2.25 dB/cm. [119] (∼532 nm)
VisSilicon-nitride strip waveguide0.51 dB/cm. [120] (∼600 nm)
VisSilicon-nitride strip waveguide1.30 dB/cm. [119] (∼780 nm)
Near-IRLPCVD Silicon-nitride strip waveguide0.04 dB/cm. [121] (∼1550 nm)
Near-IRTripleX TM LPCVD silicon-nitride planar waveguide0.02 dB/cm. [122] (∼1550 nm)
Near-IR900-nm-thick LPCVD Silicon-nitride strip waveguide0.37 dB/cm. [123] (∼1550 nm)
Mid—IRLPVCD silicon-nitride strip waveguide0.60 dB/cm. [124] (∼2600 nm)
Mid-IRSilicon-rich LPVCD silicon-nitride strip waveguide0.16 dB/cm. [125] (∼2650 nm)/2.10 dB/cm. [126] (∼3700 nm)
Tantalum pentoxide (Ta2O5)-core/silica-clad/silicon substrateNear IRPlanar waveguide0.03 dB/cm. [127] (∼1550 nm)
Suspended silicon-on-insulator waveguideMid-IRWaveguide with Subwavelength grating3.4 dB/cm. [17] (∼3.8 μm).
Photonic crystal fibers based waveguidesTHzSemiconductor silicon photonic crystal slab waveguides0.1/0.04 dB/cm. [128] (∼905.7/908 μm).
THz3-D printed THz waveguide based on Kagome photonic crystal structure0.1/0.04 dB/cm. [129] (∼905.7/908 μm).
THZKagome-lattice hollow-core silicon photonic crystal slab-based waveguide0.875 dB/cm [129] (∼400 μm).

Table 1.

Material platforms.

Figure 19.

Comparison of different waveguide platforms as a function of index contrast and compactness.

11. Conclusion

Classification of waveguides on the basis of geometry (planar/non-planar), mode propagation (Single/Multi-Mode), refractive index distribution (Step/Gradient Index), and material platform is described briefly. An overview of different kinds of channel waveguides, namely wire, rib, slot, strip-loaded, diffused, TriPleX, suspended, photonic crystal, ARROW, and augmented waveguide is given. A comparative analysis of material platforms used along with their propagation losses and wavelength range is also shown.


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Written By

Shankar Kumar Selvaraja and Purnima Sethi

Submitted: 07 March 2018 Reviewed: 10 April 2018 Published: 01 August 2018