Ch4Sec2 - THE FIBER FORUM Fiber Optic Communications...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
THE FIBER FORUM Fiber Optic Communications JOSEPH C. PALAIS PRESENTED BY
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Joseph C. Palais 4.2 2 Section 4.2 MODES IN THE SYMMETRIC-SLAB WAVEGUIDE n 2 n 2 n 1 n 1 > n 2 θ Range of θ for bound waves: ° 90 θ c
Background image of page 2
Joseph C. Palais 4.2 3 Mode in The Symmetric-Slab Waveguide For an axial ray, θ = 90 ° and n eff = n 1 For a critical angle ray θ = θ c and 2 1 2 1 1 sin n n n n n n c eff = = θ The range of n eff is now (4.9) 1 2 n n n eff Define the effective index of refraction: sin 1 n n eff
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Joseph C. Palais 4.2 4 4.2.1 Mode Condition The two boundaries (upper and lower) form a cavity. A cavity is resonant when the round trip phase shift is 2 π m (where m = 1,2,3 …). Expressing this mathematically, we get ∆ φ = m2 π (4.10)
Background image of page 4
Joseph C. Palais 4.2 5 Mode Condition ∆ φ is the phase shift for one complete cycle of the zigzag path. It includes the phase shift at the two totally reflected surfaces. Equation (4.10) can be satisfied (for a given λ ) for several distinct ray angles (between θ c and 90º). The waves traveling at these allowed angles are the modes of the waveguide. Waves traveling at other angles will interfere destructively and will not propagate.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Joseph C. Palais 4.2 6 4.2.2 and 4.2.3 TE and TM Polarization and TE Mode Chart Derivation of fields in the symmetric waveguide: E d n 2 n 2 n 1 z y 1 2 0 2 0 2 1 0 1 k k n k k n μ = = = = TE polarization (Transverse Electric) This is the same as perpendicular polarization (s). z θ
Background image of page 6
Joseph C. Palais 4.2 7 TE Mode Chart Consider a TE wave in the middle layer where: ( ) ˆ j t k r x E u E e ϖ - = r v y z k 1 θ (1) 1 1 0 1 n c n k k = = z z y y x x k u k u k u k ˆ ˆ ˆ + + = 2 2 2 z y x k k k k + + = z u y u x u r z y x ˆ ˆ ˆ + + =
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Joseph C. Palais 4.2 8 TE Mode Chart Example: ) sin cos ( 1 1 ˆ θ ϖ z k y k t j x e E u E - - + + = This represents the upward traveling wave. If θ = 90º this reduces to the equation of a z- directed wave. (2) sin ˆ cos ˆ 1 1 1 k u k u k z y + = z y x u z u y u x r ˆ ˆ ˆ + + = z k 1 θ y
Background image of page 8
Joseph C. Palais 4.2 9 y z k 1 θ TE Mode Chart For the downward wave - + - + - - = = E E e E u E z k y k t j x ) sin cos ( 1 1 ˆ θ ϖ (3) Because of total reflection the magnitudes are equal
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Joseph C. Palais 4.2 10 TE Mode Chart The total field is (5) (4) 1 1 1 sin cos cos jk z jk y jk y j t E E E E e e e e θ ϖ + - - - + = + = + ) cos cos( 2 1 sin 1 y k e e E E z jk t j - + = Define β sin , cos 1 1 k k h + E E 2 1
Background image of page 10
Joseph C. Palais 4.2 11 TE Mode Chart (6) 0 1 0 1 cos , sin h k n k n θ β = = Then 2 2 - d y d (7) ) ( 1 ) cos( z t j e hy E E ϖ - = This equation is valid in the middle layer where
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Joseph C. Palais 4.2 12 TE Mode Chart This is a plane wave traveling in the z-direction with propagation constant β . The amplitude varies spatially sinusoidally in the transverse (y) direction.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/11/2010 for the course EEE EEE-448 taught by Professor Palais during the Fall '09 term at ASU.

Page1 / 54

Ch4Sec2 - THE FIBER FORUM Fiber Optic Communications...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online