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Phase matching using Bragg reflection waveguides for monolithic nonlinear optics applications

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Abstract

A novel design to achieve phase matching between modes of a vertical distributed Bragg reflector waveguide and those of a conventional total internal reflection waveguide is reported for the first time. The device design and structure lend themselves to monolithic integration with active devices using well developed photonic fabrication technologies. Due to the lack of any modulation of the optical properties in the direction of propagation, the device promises very low insertion loss. This property together with the large overlap integral between the interacting fields dramatically enhances the conversion efficiency. The phase matching bandwidth, tunability and dimensions of these structures make them excellent contenders to harness optical nonlinearities in compact, low insertion loss monolithically integrable devices.

©2006 Optical Society of America

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Figures (5)

Fig. 1.
Fig. 1. A schematic diagram of a BRW with the propagation direction orthogonal to the Bragg stack.
Fig. 2.
Fig. 2. Plot of the refractive index dispersion of a BRW similar to that shown in Fig. 1. The waveguide structure that resulted in this dispersion curve is a 200 nm core (nc) of Al0.24G0.76aAs, sandwiched in a Bragg stack made of alternating layers of Al0.3G0.7aAs and Al0.5G0.5aAs (n1 and n2).
Fig. 3.
Fig. 3. A graphical example of the solution of both the TIR and BR modes. The waveguide structure that resulted in this dispersion curve is a 310 nm core of 30% AlGaAs, sandwiched in a Bragg stack made of alternating quarter wave layers of 20% and 40% AlGaAs.
Fig. 4.
Fig. 4. Field profiles of both the TE-polarized TIR mode @ 1550 nm and the TM-polarized BRW mode at 775nm.
Fig. 5.
Fig. 5. Modal index of both the TIR and BR modes due to the change of the core bandgap, and hence refractive index.

Equations (14)

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E ( x , z , t ) = { E K ( x d c 2 ) e iK ( x d c 2 ) e i ( ωt βz ) x > d c 2 [ C 1 cos ( k c x ) + C 2 sin ( k c x ) ] e i ( ωt βz ) d c 2 < x d c 2 E K ( x d c 2 ) e iK ( x + d c 2 ) e i ( ωt βz ) x d c 2
k c 2 = ( ω . n c c ) 2 = β 2 + k x 2
k ix d i = π 2 , i = 1,2
k ix 2 = ( ω . n i c ) 2 β 2 , i = 1,2
i k 1 x e iK Λ + k 1 x k 2 x e iK Λ + k 2 x k 1 x = { k c tan ( k c d c ) for even TE modes k c cot ( k c d c ) for odd TE modes
i k 1 x n c 2 e iK Λ + n 2 2 k 1 x n 1 2 k 2 x e iK Λ + n 1 2 k 2 x n 2 2 k 1 x = { k c n 1 2 tan ( k c d c ) for even TE modes k c n 1 2 cot ( k c d c ) for odd TE modes
K = Λ ± i κ i , m = 1,2 . .
Λ κ i { ln ( k 2 x k 1 x ) for TE modes ln ( n 1 2 k 2 x n 2 2 k 1 x ) for TE mode
M structure = ( m 11 m 12 m 21 m 22 ) = j = 1 l M j , total number of layers = l
M j = ( cos Φ j i γ j sin Φ j i γ j sin Φ j cos Φ j )
Φ j = k jx d j
γ j = { n j 2 n eff 2 c μ o for TE modes n j 2 n eff 2 c ε o for TM modes
χ M ( n eff ) = γ c m 11 + γ c γ s m 12 + m 21 + γ s m 22 ,
Δ ω gap ω o 2 π ( k 2 x k 1 x k 2 x ) ,
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