Source: http://aoot.osa.org/ome/abstract.cfm?uri=ome-9-3-1320
Timestamp: 2019-04-21 03:05:30+00:00

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Fig. 1 Scheme of the physical space for a waveguide coupler with a cosine transition function, m(x), with power of 2.
Fig. 2 Output matched dielectric constant versus the Brewster angle based on Eq. (8) for a device with scaled parameters and M = 0.5. (a) M2s(d) < 1 and “+” sign and (b) M2s(d) < 1 and “−” sign. (c) M2s(d) > 1 and “+” sign and (d) M2s(d) > 1 and “−” sign.
Fig. 3 Simulated magnetic field for the TM0 mode. The medium in both left and right waveguides is a vacuum. (a) Real part and (b) magnitude of Hz without the non-magnetic coupler. (c) Real part and (d) magnitude of Hz for the non-magnetic coupler with the Brewster angle of zero.
Fig. 4 Simulated magnetic field for the non-magnetic Brewster-angle coupler for the TM3 mode. The medium in both left and right waveguides is a vacuum. (a) Real part and (b) magnitude of Hz for the design with Brewster angle of 49°. (c) Real part and (d) magnitude of Hz for the design with Brewster angle of 0 (normal incidence).
Fig. 5 Simulated magnetic field for the non-magnetic all-mode coupler impedance-matched to ε2 = M−2 = 4. (a) Real part and (b) magnitude of Hz for TM0 mode. (c) Real part and (d) magnitude of Hz for TM1 mode.
Fig. 6 Simulated magnetic field for the non-magnetic all-mode coupler impedance-matched to ε2 = M−2 = 4. (a) Real part and (b) magnitude of Hz for TM2 mode. (c) Real part and (d) magnitude of Hz for TM3 mode.
Fig. 7 Coupling efficiency of the non-magnetic coupler versus the incidence angle for TM3 mode.
(1) m 1 ( x ) = ( 1 − M ) ∑ n = 1 N α n ( 1 − x / d ) n + M .
(2) m 2 ( x ) = ( 1 − M ) ∑ n = 1 N α n cos n ( π x / 2 d ) + M .
(3) m 3 ( x ) = ∑ n = 1 N α n M ( x / d ) n .
(4) ε = μ = J J T det ( J ) .
(6) ε u ε v | i = ε i 2 .
(7) ε x x μ z z | i = ε i .
(8) cos 2 θ B | x = d = ε 2 ( 1 / M 2 − ε 2 ) s 2 ( d ) − ε 2 2 → ε 2 = 1 ± 1 − M 4 s 2 ( d ) sin 2 ( 2 θ B ) 2 M 2 sin 2 θ B .
(12) s ( x ) = ( 1 − s ( d ) ) ( 3 ( 1 − x / d ) 2 − 2 ( 1 − x / d ) 3 ) + s ( d ) .
(13) m ( x ) = ( 1 − M ) cos 2 ( π x / 2 d ) + M .
(14) f ( x ) = ∫ m ( x ) d x = x ( M + 1 ) / 2 − d ( M − 1 ) sin ( π x / d ) / ( 2 π ) .

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