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Discrete optics v.s. Integrated optics
Mirrors, lens, mechanical mounts bulky labor intensive alignment ray optics environment sensitive Waveguide Bendable, portable Free-of-alignment wave optics robust more functionalities
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Discrete optics v.s. Integrated optics
Applications of Integrated optics: Transmitters and receivers, transceivers All optical signal processing Ultra-high speed communications (100Gbit/s), optical packet switching RF spectrum analyzer Smart sensors OEIC, bio/sensor Optical transceivers
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Optical waveguides 2-D Optical waveguide x Core, refractive index n1 Cladding, n2 z y n2 < n1 d 1 n2 n1 n0 = 1 0 90º-1 n0*sin(0) = n1*sin(1) Numerical aperture (NA) Critical angle n1*sin(90º-1)=n2*sin(90º) cos(1)=n2/n1
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: total acceptance angle
Optical waveguides 2-D Optical waveguide : total acceptance angle
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Optical waveguides Example 2: Calculate the acceptance angle of a core layer with index of n1= 1.468, and cladding layer of n0 = for wavelength of 1.3m and 1.55 m. Solution: acceptance angle: Wavelength independent:
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Reflections at the interface
Fresnel equations n2 < n1 x z E1s E3s y z 1 1 y 1 1 n1 n1 2 n2 2 E2s n2 s-polarized beam (senkrecht: perpendicular) p-polarized beam (parallel) Trans-electric beam (TE) Trans-magnetic beam (TM)
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Reflections at the interface
Fresnel equations n2 < n1 x z E1s E3s y z 1 1 y 1 1 n1 n1 2 n2 2 E2s n2 Poynting vector, energy flow rate
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Reflections at the interface
Phase shift of reflection n2 < n1 x E1s E3s z y 1 1 n1 n2 2 E2s when i.e. because In this case, is a real number The reflection is not associated with phase shift, or phase shift is 0
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Reflections at the interface
Phase shift of reflection n2 < n1 E1s x E3s z 1 1 y n1 n2 2 E2s when i.e. c 1
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Reflections at the interface
Evanescent wave n2 < n1 x E1s E3s z y 1 1 n1 Momentum conservation n2 2 E2s Attenuated wave, penetration depth: d
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Ray optics approach Optical modes C A 1 1 1 2 d 1 B k*n1*AC – k*n1*AB = 2m AC = AB*cos(21) AB = d/sin(1)
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Ray optics approach Optical modes C A 1 1 1 2 d 1 B Propagation constant Effective index:
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Ray optics approach Optical modes, considering phase shift at reflection C A 1 1 1 2 d 1 B k*n1*AC – k*n1*AB + 2* = 2m AC = AB*cos(21) AB = d/sin(1)
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V number, normalized thickness, or normalized frequency
Ray optics approach Optical modes C A 1 1 1 2 d 1 B V number, normalized thickness, or normalized frequency Cut-off wavelength :
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Example: estimate the number of modes
Ray optics approach Optical modes Example: estimate the number of modes waveguide thickness 100m, free-space wavelength 1m, 49 modes
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Normalized waveguide equation:
Ray optics approach Normalized waveguide equation: b: normalized propagation constant
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Ray optics approach Discussion: Attenuated wave, penetration depth: D
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mode numbers v.s. index difference and wavelength
Ray optics approach Discussions: mode numbers v.s. index difference and wavelength effective index difference of higher and lower order modes mode profiles dependence on index difference and wavelength Example 1: Calculate the thickness of a core layer with index of n1= 1.468, and cladding layer of n0 = 1.447 for wavelength of 1.3m. Solution: For single mode:
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Normalized waveguide equation:
Ray optics approach Normalized waveguide equation: V = 3.3 b
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Ray optics approach Asymmetric waveguide n2 n1 n0 = 1 n3
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Wave optics approach Maxwell equations: Dielectric materials Maxwell equations in dielectric materials: phasor
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Wave optics approach Helmholtz Equation: Free-space solutions 2-D Optical waveguide x Core, refractive index n1 Cladding, n2 z y n2 < n1 d TM mode: TE mode:
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Wave optics approach Core, refractive index n1 Cladding, n2 z y n2 < n1 d III n2 x d x y I n1 II n2
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Wave optics approach III n2 x d x y I n1 II n2
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Wave optics approach III n2 x d x y I n1 II n2
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Wave optics approach III n2 x d x y I n1 II n2
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Wave optics approach III n2 x d x y I n1 II n2
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Wave optics approach III n2 x d x y I n1 II n2
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Wave optics approach Graphic solution
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Dispersion Dispersion Time delay
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Example --- material dispersion
Calculate the material dispersion effect for LED with line width of 100nm and a laser with a line width of 2nm for a fiber with dispersion coefficient of Dm = 22pskm-1nm-1 at 1310nm. Solution: for the LED for the Laser
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Example --- waveguide dispersion
n2 = 1.48, and delta n = 0.2 percent. Calculate Dw at 1310nm. Solution: for V between 1.5 – 2.5.
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Waveguide mode dispersion
Higher order mode, Lower order mode,
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chromatic dispersion (material plus waveduide dispersion)
material dispersion is determined by the material composition of a fiber. waveguide dispersion is determined by the waveguide index profile of a fiber
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Dispersion induced limitations
For RZ bit With no intersymbol interference For NRZ bit With no intersymbol interference
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Dispersion induced limitations
Optical and Electrical Bandwidth Bandwidth length product
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Dispersion induced limitations
Example --- bit rate and bandwidth Calculate the bandwidth and length product for an optical fiber with chromatic dispersion coefficient 8pskm-1nm-1 and optical bandwidth for 10km of this kind of fiber and linewidth of 2nm. Solution: Fiber limiting factor absorption or dispersion?
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