Optical Waveguide and IoT
Gurjit Kaur and Pradeep Tomar
Introduction about Optical Waveguide The propagation of an electricfield through a waveguide can be intuitively understood by the use of the ray opticsmodel described by Snell’s Law :
Snell’s Law relates the incident angle θ1 of light in a medium with index n1, impinging on the interface of a material with index n2, to the resulting angle θ2 that the light is refracted to when it enters the new medium.A diagram of the physical representation is shown below :
If n1, n2, are correctly chosen then the angle can become 90°, a conditiontermed as Total Internal Reflection(TIR) occurs, where the incident light impinging on the interface is
reflected back into the starting medium. The angle of incidence at which this condition occurs is called the critical angle and is calculated to be θc = arcsin(n2 / n1). A waveguiding structure works in such a way that each interface reflection occurs at an angle larger then critical angle as a result the light ray will theoretically continue in the core region indefinitely.
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The simplest structure that can be understood by this method is the slab waveguide. This 2D waveguide consists of a high index material sandwiched between two low index materials. If light is injected into the edge of this structure within the acceptance angle of the waveguide, it will be confined to the high index region. A very common example of the 2D waveguide is the rib structure waveguide.
For the analysis of waveguide devices the basic equations from which all the basic conditions and solutions are derived are the Maxwell’s Equations which are given below:
By default , ρ and J are considered to be zero.
∇ ⃗×εE ⃗=ρ
∇ ⃗×E ⃗=-d/dt μH ⃗
∇ ⃗×H ⃗=-d/dt εH ⃗+J ⃗
∇ ⃗×μE ⃗=0
Solving Maxwell curl equations:
Consequently the equations simplify as :
By solving these equations we can acquire transverse components of E and H. Upon solving we get :
2. Silicon Waveguides
Silicon as a substrate is used primarily for its electrical properties. As a semiconductor it can be doped with a wide variety of impurities, such as boron and phosphorus, to accurately control its electrical characteristics. Silicon is unique from many other semiconductors in that it has a natural oxide (SiO2), that is adhering, an excellent electrical insulator as well as diffusion barrier, and highly selective to etching.
These SOIsubstrates provide several advantages in micro-optical systems, primarily as a result ofthe large index contrast between Si (n=3.45) and SiO2 (n=1.46)the core of the waveguide is fabricated out of the thin silicon top layer, and theunderlying oxide is used as a cladding. This configuration provides an high index difference between the core and the substrate. These optical properties of silicon and its native oxide allow for light tobe confined at the material interface by total internal reflection (TIR). Because the light is so highly confined, single mode waveguides can have core crosssectionwith dimensions of only a few hundred nanometers and bending radii of a fewmicrometers with minimal losses. Because field leakage into the substrate andsurrounding cladding is so low, these waveguides can be fabricated closer togetherwithout coupling occurring between them. The high index of silicon also allows devicesto be shorter. SOI waveguides are so small they are commonly referred to as nanophotonicwires.
The high thermal conductivity of silicon allows for dense integration as heat generated by devices can be easily dissipated .SOI technology is allowing for the miniaturization of these photonic structures on an order of ten to ten thousand leading to ultra dense integration.
Another advantage of silicon is that it is optically transparent at long haul communication wavelengths, between 1.3μm and 1.7μm . This allows SOI waveguides as well as other nano-photonic devices fabricated on this platform to be easily integrated into existing silica based fiber optic networks.
A few undesirable properties of silicon that limit the degree of integration and level of performance of photonic components. These problems include the several poor optical properties of silicon, as well as waveguide sensitivity to losses. One major disadvantage of silicon is that it doesn’t exhibit the first order electro-optic effect or Pockel’s effect as III-V semiconductors do.
Silicon waveguides have several loss mechanisms that contribute to losses in the waveguide. These methods include absorption, scattering from volumetric refractive index inhomogeneity, coupling of guided modes to substrate modes, and interface induced scattering .Additional losses not associated with propagation occur during the coupling of light in and out of the device. Other losses solely caused by waveguide structure, such as bends, can occur as well . Waveguide losses are typically quantified in terms of dB/cm.
3. ARROW WAVEGUIDES ANTIRESONANT Reflecting Optical Waveguides (ARROW) are integrated waveguides in which guided field is confined by antiresonant Fabry-Perot reflections rather than total internal reflection (TIR). The heart of the Fabry–Pérot interferometer is a pair of partially reflective glass optical flats spaced micrometers to centimeters apart, with the reflective surfaces facing each other.at least at one of the faces which is usually the substrate cladding . This fact implies some power leakage of antiresonant modes into the substrate although losses may be reasonably low with a convenient design of the structure. The (ARROW) waveguide has a silicon substrate and is multilayer waveguide where light is confined within the core by an anti-resonant reflection, with a very high reflection coefficient, at the two interference cladding layers underneath the core. Antiresonant waveguides fabricated using the advantages of silicon technology have attracted a great interest lately because they provide single mode operation in the transversal direction with a low index guiding layer (usually SiO2) and a size of the structure that allows good compatibility with single mode optical fibers which can be used in various daily life applications The most important characteristic of ARROW waveguides is that they can operate in single mode, even for core dimensions and rib parameters of a few micrometers, together with a low index cladding having a refractive index lower than the core cladding leading to various experimental advantages. .The basic characteristics of these waveguides are: Low losses for the basic mode implying maximum light confinement. High tolerance for the design of the refractive index and thickness of the cladding layers. Since low loss operation of the waveguide relies on properly phased reflections from all the cladding interfaces, one might conclude that the device only works over a narrow band of wavelengths . Strict fabrication tolerances.
Furthermore, ARROW structures have been studied because they present selective losses depending on the wavelength and on the polarization of the light, and accordingly, can be used as integrated wavelength filters and polarizers .Therefore, conditions for leakage of guided light are achieved by a suitable design of the structure, where ARROW operation is controlled by a proper use of refractive index and thickness of the antiresonant layers. Another advantage is that substrate cladding can be made reasonably thin because of the shielding effect of the antiresonant structure, avoiding the use of thick substrate claddings that require long deposition processes.
Lateral confinement of the slab antiresonant modes is achieved in the waveguides that are subject of this work by means of a rib structure. As much as the ARROW structure provides the conditions for power leakage from the waveguide, rib parameters such as rib depth and waveguide width determine the guiding conditions of the light in the ARROW. Rib parameters also have strong influence in the performance of rib-ARROW’S, and if they are not properly controlled, some problems such as the loss of the fundamental mode for narrow waveguides or too high losses may arise for waveguides with low rib heights. ARROW's are leaky structures which can be solved analytically, leading to modes with complex propagation constants. The imaginary part of the propagation constant accounts for radiation losses through the substrate which are dependent on the wavelength or polarization of the light and are determined by the thickness and refractive index of the ARROW layers. ARROWs can be realized as rib waveguides or slab waveguides (1D confinement). The ARROWs are practically formed by a low index layer, embedded between higher index layers. Note that the refractive indices of these ARROWs are reversed, when comparing to usual waveguides. ARROW structures are often used for guiding light in liquids for optofluidic applications, particularly in microfluidic systems. This is due to the difficulty of finding suitable optical cladding materials, with a lower refractive index than the liquid, which would be required to form a conventional waveguide structure.
4. Waveguide Modes
Waveguide modesare characteristic of a particularwaveguide structure. A waveguide mode is a transverse field patternwhoseamplitude and polarization profilesremain constant alongthe longitudinal z coordinate.
Therefore, the electric and magnetic fields of a mode can be written as follows :
where v is the mode index, Ev (x, y) and Hv (x, y) are the mode field profiles, and βυ is the propagation constantof the mode. For a waveguide of two-dimensional transverse optical confinement, there are two degrees of freedom in the transverse xy plane, and the mode index υ consists of two parameters for characterizing the variations of the mode fields in these two transverse dimensions. For ex. v represents two mode numbers, v = mn with integral m and n, for discrete guided modes. 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 that is the repeatedly reflected wave has constructive interference with itself. Modes can be classified as : Transverse Electric or Magnetic (TEM) Transverse Electric (TE) Transverse Magnetic (TM) Transverse electric (TE) fields are those whose electric field vector lies entirely in the x y plane that is transverse to the direction of net travel (the z direction). A TE wave has EZ=0 and HZ ≠ 0. Cut off frequencies for TE Modes :
Transverse electric (TM) fields are those the electric field is no longer purely transverse. It has a component along the z direction. However, the magnetic field points in the y direction for this type of mode is entirely transverse (i.e. Hz = 0).
Cut off frequencies for TM Modes:
The Transverse Electric and Magnetic (TEM) Mode are characterized by EZ =0 and HZ = 0. In order for this to occur fc= 0. In other words there is no cut off frequency for waves that support TEM modes.
5 6 Important Characteristics of the Waveguide
Effective Index
The effective refractive index is a key parameter in guided propagation, just as the refractive index is in unguided wave travel.The effective refractive index changes with the wavelength(i.e. dispersion) in a way related to that the bulk refractive index does. We can define the waveguide Phase velocity vpas vp = ω / β We now define an effective refractive index neffas the free-space velocity divided by the waveguide phase velocity. neff = c / vp neff = cβ / ω = β / k Waveguide effective index: neff = n1sin θ For waveguiding at n1-n2 interface, we see that n2 ≤ neff ≤ n1. At θ = 90o, neff = n1implies a ray traveling parallel to the slab (core) has an effective index that depends on the guiding medium alone. At θ = θc,neff = n2implies the effective index for critical-angle rays depends only on the outer material n2. The effective wavelength as measured in the waveguide is: λz = λ/neff
Gain in a Optical Waveguide
Gain in an optical waveguide is generally defined as : G = Pout/Pin where Poutis the signal output power that comes out of the waveguide and Pin is the input power coupled into the waveguide.
Since g(ω) depends on the incident optical power when P ≈ PS, Gain will start to
decrease with an increase in optical power P. Therefore ,we cannot increase the optical power of the signal beyond the saturation level as it will not lead to constant increase in gain.
Where go is the peak gain, ω is the optical frequency of the incident signal, ωo is the transition frequency, P is the optical power of the incident signal and Psis thesaturation power. To achieve maximum Gain , we always assume that the incident frequency is tuned for peak gain ω= ω0 ). Losses in an Optical Waveguide There are 3 major types of losses in an optical waveguide : Scattering Losses: These are mainly caused by the surface roughness of the sidewalls in the waveguide.Sidewall roughness is mainly generated during etching process. This type of propagation loss is high for a small-dimension waveguide.
The scattering loss is further divided into :
Volume Scattering loss: This type of propagation loss is caused by imperfections. These imperfections can be due to design flaw or due to contamination of the structure due to doping. These are negligible as compared to surface scattering losses.
Surface Scattering loss : These type of propagation losses are dominant in optical waveguides. These are created by the roughness or the irregular nature of the waveguide surface. Absorption Losses:
These type of propagation losses occur when photons are incident on the waveguide surface . When light is incident on the waveguide surface, light energy (in the form of photons) is absorbed by the surface and only some of it passes through. The energy that is absorbed by the surface is lost as it is used to excite electrons from the valence band into the conduction band and thus because of these absorption losses we get less energy at the output as compared to the input .
Radiation Losses :These types of losses only occur when the waveguides are bent. They are absent in linear waveguides. When we design a waveguide which has bends and curves then these types of losses are significant.
6. Dispersion in an Optical Waveguide :
This phenomenon is basically described as the broadening of the pulse during its propagation .What it does is it limits the rate of the information that is transferred per pulse.Dispersion is also classified into various categories : Modal dispersion:Modal dispersion is a distortion mechanism occurring in multimode fibers and other waveguides, in which the signal is spread in time because the propagation velocity of the optical signal is not the same for all modes.Modal dispersion limits the bandwidth of multimode fibers. Modal dispersion should not be confused with chromatic dispersion, a distortion that results due to the differences in propagation velocity of different wavelengths of light. Modal dispersion occurs even with an ideal, monochromatic light source. Material and Waveguide dispersion:Material dispersion can be a desirable or undesirable effect in optical applications. Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion, in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal), whether or not the waves are confined to some region. In a waveguide, both types of dispersion will generally be present, although they are not strictly additive. For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a Zero-dispersion wavelength, important for fast Fiber-optic communication.
