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6. lecture=9 10 filters
- 3. Optical Filters Optical filters are used for example to separate a single of multiple optical signals from a WDM signal Optical filters are also widely used to reject out-of-band ASE noise imposed on the desired signals Some of the desirable features of an optical filter are: 1. A high out-of-band signal rejection, 2. Temperature independent operation, 3. Low insertion loss, 4. Compact size and 5. low cost
- 4. Optical Filters In this course, we will discuss the four most common optical filters used in communications namely: 1. Grating Based Filter 2. Arrayed Waveguide Grating Filter 3. Fabry-Perot Filters 4. Fiber Bragg Grating Filter
- 5. Grating Filters Grating filters exploit the phenomenon of light-diffraction to different wavelengths of an input optical signal It uses a diffraction grating, which is essentially a glass having a rectangular cross-section and multiple slits or groves When light composed of different wavelengths impinges on such a grating, it passes through the narrow slits and spreads out at the output due to diffraction Hence each slit effectively acts like a separate source of light
- 7. Grating Filters An important quality of diffraction grating is that for a unique set of discrete angles, the light diffracted from the multiple slits facing in different directions are in phase This coherent phase relationship results in constructive interference among various diffracted wavefronts at spatially separate points at the opposite side of the diffraction grating The condition for constructive interference to occur for a grating having a uniform slit spacing of d between two consecutive slits and an incident light of wavelength λ is given by:
- 8. Grating Filters Where m is the diffraction order and θ is the diffraction angle The operating principle of a grating filter based on a diffraction grating can be understood from the simplified diagram The optical signal to be filtered impinges on a diffraction grating, which results in a diffraction pattern at the opposite side The diffraction pattern is composed of multiple bright spots of light at different wavelengths separated spatially
- 9. Grating Filters The spatial distance among the different bright spots depends both upon: 1. The slit spacing of the grating and 2. The distance of the screen used for observing the pattern A narrow bandwidth of light can be filtered out by using an exit slit located at some distance from the diffraction grating The bandwidth retained depends upon the size of the exit slit
- 10. Grating Filters In order to construct a tunable grating filter, the diffraction grating is mounted on a mechanical structure that can be rotated externally When the diffraction grating rotates, the diffraction pattern on the screen also shifts, resulting in different retained wavelengths exiting the exit slit
- 11. Arrayed Waveguide Grating Filter The grating filter described in the previous section uses a diffraction grating for achieving spatial dispersion of the input optical signal Now we discuss the Arrayed Waveguide Grating (AWG) filter, which uses optical waveguides for achieving a spatial separation similar to the grating filter AWG filters rely on the principle of optical interferometers
- 12. Arrayed Waveguide Grating Filter The simplest interferometer is the Mach-Zehnder Interferometer (MZI) MZI is composed of two optical couplers connected by two separate waveguides in order to filter a single wavelength, in a fashion that is reminiscent of the MZM Similarly, the AWG is composed of two optical couplers that are connected by more than two waveguides in order to filter multiple wavelengths
- 13. Arrayed Waveguide Grating Filter
- 14. Arrayed Waveguide Grating Filter Observe that the AWG consists of input and output waveguides, two slab waveguides and a set of arrayed waveguides, which are made up of silica When the optical signal passing through the input waveguide enters the first slab waveguide, it diverges in the free propagation region of the slab waveguide The signal that spreads in the first slab waveguide is captured by the set of arrayed waveguides which function as dispersive elements and are arranged to have a constant length-difference between the adjacent waveguides
- 15. Arrayed Waveguide Grating Filter The length of each waveguide is chosen by ensuring that a particular wavelength undergoes the same dispersion in each waveguide Therefore, after travelling through the free propagation region of the second slab waveguide, all the optical signals having a particular wavelength constructively focus their output on a single output waveguide
- 16. Arrayed Waveguide Grating Filter The length-difference △L of the adjacent arrayed waveguides required for achieving the constructive focusing of all the optical signals having a particular wavelength can be written as: Where m is the order and ng is the effective refractive index of the arrayed waveguide The central wavelength of the incident optical signal is represented by λ𝑐
- 17. Fiber Bragg Grating Filter - Concept From a practical standpoint, a diffraction grating is defined as any optical element capable of imposing a periodic variation in the amplitude or phase of light incident on it Clearly, an optical medium whose refractive index varies periodically acts as a grating since it imposes a periodic variation of phase when light propagates through it Such gratings are called index gratings
- 18. Bragg Diffraction The diffraction theory of gratings shows that when light is incident at an angle θi (measured with respect to the planes of constant refractive index), it is diffracted at an angle θr such that: Λ is the grating period, λ is the wavelength of the light inside the medium 𝑛 is the average refractive index m is the order of the Bragg diffraction
- 19. Fiber Bragg Grating Filter In the case of single-mode fibers, the incident and diffracted light lie along the fiber axis As a result, the diffracted light propagates backward Therefore: If m = 1, the period of the grating is related to the vacuum wavelength as: This condition is known as the Bragg condition
- 20. Fiber Bragg Grating Filter A fiber grating acts as a reflector for a specific wavelength of light for which the phase-matching condition is satisfied
- 21. Fiber Bragg Grating Filter Gratings satisfying Bragg condition are referred to as Bragg gratings Physically, the Bragg condition ensures that weak reflections occurring throughout the grating add up in phase to produce a strong reflection For a fiber grating reflecting light in the wavelength region near 1550 nm, the grating period is:
- 22. Fabry-Perot Filter A Fabry-Perot (FP) filter exploits the interference of light in a resonating cavity The resonating cavity of the FP filter consists of two highly reflective mirrors that are placed parallel to each other at a distance L The input light enters into the cavity through the left mirror and after traveling a distance of L it falls on the reflective side of the right mirror
- 23. Fabry-Perot Filter A part of the light exits through the right mirror, while a part of it is reflected back into the cavity The percentage of light refracted or reflected depends upon the reflectivity of the mirrors The resonating cavity structure of the FP filter can be used to filter out a particular wavelength by choosing the length of the cavity to be an integer multiple of half the wavelength That is L = mλ/2, where m is an integer and λ is the wavelength to be retained
- 25. Fabry-Perot Filter Light having a particular wavelength λ interferes constructively after going through a round-trip inside the cavity, the resultant high intensity light exits through the right facet The power transfer function PTF of the filter in terms of wavelength is given by: A and R are the absorption loss and reflectivity of the each mirror’s respectively and n is the refractive index of the cavity