Using a coupled mode theory and finite-difference time-domain calculations nearly complete evanescent power transfer between a fiber taper and a photonic crystal defect waveguide which is ideal for probing high-Q cavities is predicted

Barclay, Paul E.

Painter, Oskar

Srinivasan, Kartik

English

Caltech Authors - Main

JWB2 
Evanescent coupling from optical fiber tapers to photonic 
crystal waveguides and resonators 
Paul E. Barclay, Kartik Srinivasan, Oskar Painter 
Department ofApphed Physics, Calrfornia Institute of Technolw, Pasadena Calrfornia 91 125 
phone: (626) 395-6269, fax (626) 795-7258, email: pbarclay@caltech edu 
Abstract: Using a coupled mode theory and finite-difference time-domain calculations nearly complete 
evanescent power transfer between a fiber taper and a photonic crystal defect waveguide which is ideal 
for probing high-Q cavities is predicted. 
@ 2003 Optical Society of Amenca 
OCIS codes: (1 30.2790) Guided waves, (230.7370) Waveguides 
Evanescent coupling from fiber tapers to air bridge photonic crystal (PC) waveguides provides a wafer-scale probe 
of PC devices for applications ranging from optoelectronics to quantum optics. By relying on matching momentum 
rather than spatial overlap, evanescent coupling circumvents the problems caused by the intrinsic spatial mismatch 
between PCs and traditional optics. We dwuss the general k-space design of a PC waveguide for efficient evanescent 
coupling to the fiber taper, and show how tlus same waveguide can couple efficiently to a high-Q ( lo5) defect cavity. 
Fig. 1. (a) Schematic of coupling scheme. (b) Coupling geometry. (c) Waveguide unit cell. (d) Effective index bandstructure 
and fiber taper dispersion. (e) Transverse momentum distribution of defect modes A and 5. (Q 3D FDTD PC bandstructure 
and dispersion for a fiber taper of radius 7Az/6. 
Two dimensional PC membrane waveguides are ideally suited to evanescent coupling as their zone-folded disper- 
sibn enables optical coupling to waveguides with a dissimilar refractive index, and their undercut structure prevents 
radiation into the substrate. Evanescent coupling between two parallel waveguides (Fig. lb) requires that there exist a 
pair of modes (one in each waveguide) which (i) are phase matched in the propagation direction for maximum power 
transfer, and (ii) share similar symmetry and transverse Fourier components, resulting in a significant total transverse 
overlap of their evanescent tails and an acceptable coupling length. Since the fundamental fiber mode varies slowly 
in the transverse direction compared to the PC, to maximize the PC-fiber coupling the transverse Fourier spectrum of 
the PC mode must have a large zero frequency component. This corresponds to waveguide modes formed from bulk 
PC modes whose dominant Fourier components lie parallel to the defect waveguide (the r -X band in thls case). 
Refering to Fig. 1 which describes coupling to a waveguide formed in a square lattice, mode A satisfies this criteria, 
while mode B does not. By using a compressed-lattice graded-defect waveguide (Fig. IC) we obtain a defect mode 
which couples efficiently to a fiber taper and is ideal for tunneling light into and out of the high-Q cavities designed in 
JWB2 
Barclay et.al., Evanescent coupling to photonic crystals from optical fibers CLE0/2003 Page 2 
[l]. The graded defect results in a mode profile similar to [ll’s high-Q cavity mode (I(B~GIB~”)xyI M 0.988), and the 
compressed lattice matches the frequencies of the waveguide mode and the uncompressed defect cavity mode without 
requiring any lattice stitchng (choosing A? = A? requires A p / A y  = hcav/ihiPc). 
150 0.98 3000 0.48 
<“ -2 
\ \ 
-I J 
0 0 0 n 
Fig. 2. (a) Coupled power to mode A.  The fiber has radius r = 7Az/6, and is placed d = A, above the PC. (b) Coupled power 
to mode B. r = 10Az,/6 and d = A=. 
Using the coupled mode theory discussed in [2], the power transfered to the PC wavegwde (mode.4) as a functionof 
coupler length and detuning from phase matching was calculated (Fig. 2a). For w = wo and L = 50% the coupled power 
is greater than 90%, and reaches 98% for L = 80A,. Additionally, phase matched coupling to mode B was calculated 
(Fig. 2b) and found to be very weak, consistent with the k-space analysis discussed above. These results suggest that 
light can be efficiently evanescently coupled into a well designed PC waveguide which can be subsequently used to 
passively probe the resonant properties of high-Q defect cavities. 
References 
1. E;. Srinivasan and 0. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670 (2002). 
http :!iwu~~.opticsexprrss.org:abstra~~, cfin?UKI+PEX- 10- 15-670 
2. P. E. Barclay, I;. Srinivasan and 0. Painter, “Evanescent coupling between photonic crystal waveguides and optical fiber tapers,” Opt. Lett., 
(submitted). 
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Evanescent coupling from optical fiber tapers to photonic

crystal waveguides and resonators

Evanescent coupling between photonic crystal waveguides and optical fiber tapers,”

Momentum space design of high-Q photonic crystal optical cavities,”

https://authors.library.caltech.edu/27341/1/BARcleo03b.pdf

Evanescent coupling from optical fiber tapers to photonic crystal waveguides and resonators

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