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April 1, 2004 / Vol. 29, No. 7 / OPTICS LETTERS 697

Efficient input and output fiber couplingto a photonic crystal waveguide

Paul E. Barclay, Kartik Srinivasan, Matthew Borselli, and Oskar Painter

Department of Applied Physics, California Institute of Technology, Pasadena, California 91125

Received November 3, 2003The efficiency of evanescent coupling between a silica optical fiber taper and a silicon photonic crystal wave-guide is studied. A high-ref lectivity mirror on the end of the photonic crystal waveguide is used to recollect,in the backward-propagating fiber mode, the optical power that is initially coupled into the photonic crystalwaveguide. An outcoupled power in the backward-propagating fiber mode of 88% of the input power is mea-sured, corresponding to a lower bound on the coupler eff iciency of 94%. 2004 Optical Society of America

OCIS codes: 060.1810, 130.3120.

Evanescent coupling between optical fiber tapers 1 andphotonic crystal waveguides 2,3 (PCWGs) allows highlyefficient and mode-selective interfacing between fiberoptics and planar photonic crystal (PC) devices. Cir-cumventing the intrinsic spatial and refractive-indexmismatch of fiber to PCWG end-fire coupling, 4 thiscoupling scheme takes advantage of the strong disper-sion and undercut geometry inherent to PC membranestructures to allow eff icient power transfer betweenmodes of a PCWG and a f iber taper. The coherentinteraction over the length of the coupling regionbetween phase-matched modes of each waveguidemanifests in nearly complete resonant power transferbetween waveguides, and varying the position of thefiber taper makes it possible to tune the coupling strength and phase-matching frequency, allowing thedispersive and spatial properties of PCWG modes tobe efficiently probed. 5

In previous work 2,5 the coupling efficiency of this technique was studied by analyzing the signaltransmitted through the f iber taper as a functionof wavelength and fiber taper position. Althoughtransmission measurements are sufficient to infer theefficiency of this coupling scheme, a measurementof power coupled into and then back out of a PCWGis of interest since it allows the lower bound of theinput output coupling efficiency to be directly es-tablished. By studying light coupled into a PCWG,reflected by an end mirror at the PCWG termination,and then coupled into the backward-propagating fibermode, we show in this Letter that this coupling schemehas near-unity efficiency.

Figure 1(a) shows an illustration of the fiber taperevanescent coupling scheme. A fiber taper, formedby simultaneously heating and stretching a standardsingle-mode fiber until it has a minimum diameter of roughly 1 mm, is positioned above and parallel to anundercut planar PCWG. The small diameter of thefiber taper allows the evanescent tail of its fundamen-tal mode to interact with the PCWG, and the under-cut geometry of the PCWG prevents the fiber taperfrom radiating into the PC substrate. A schematicdetailing the optical path within the fiber taper andthe PCWG is shown in Fig. 1(b). To spectrally char-acterize the taperPCWG coupler, an external-cavityswept-wavelength source with a wavelength range of

15651625 nm was connected to the fiber taper inputby means of a 3-dB coupler. At the f iber taper out-put a photodetector (D T ) was connected to measure thetransmitted power past the taperPCWG coupling re-gion. An additional photodetector (D R ) was connectedto the second 3-dB coupler input to measure the lightreflected by the PCWG.

The PCWGs used in this work were fabricated froma silicon-on-insulator wafer. The airholes were pat-terned in the 300-nm-thick silicon layer with standardelectron-beam lithography and dry etching techniques,after which the suspended membrane structure wascreated by selective removal of the 2-mm-thick un-derlying silicon dioxide layer with a hydrofluoricacid wet etch. To form the PCWGs a grade in holeradius was introduced along the transverse directionof a compressed square lattice of airholes, 6 as shownin Figs. 2(a) and 2(b). Coupling in this case occursbetween the fundamental linearly polarized fiber

Fig. 1. (a) Schematic of the coupling scheme. (b) Illus-tration of the contradirectional coupling process and thefeedback within the PCWG caused by the ref lectivities r 1,2of the waveguide terminations.

0146-9592/04/070697-03$15.00/0 2004 Optical Society of America

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Fig. 2. (a) Waveguide geometry and finite-difference time-domain calculated magnetic field profile ( By ) of the TE-1mode. (b) Scanning electron microscopy image of the high(r 1 ) ref lectivity waveguide termination. The PCWG hasa transverse lattice constant L x 415 nm, a longitudi-nal lattice constant L z 536 nm, and length L 200 L z .(c) Dispersion of the TE-1 PCWG mode. Also shown arethe mirror termination band edges for momentum along thewaveguide axis ( z ). The corresponding partial bandgap of the mirror region is indicated by the shaded region.

mode and the TE-1 PCWG mode, the field profile of which is shown in Fig. 2(a). This PCWG mode has anegative group velocity, resulting in contradirectionalcoupling as depicted in Fig. 1, and was designed tobe integrated with recently demonstrated 7 high- Qcavities formed with a similar grading in hole radius.

In previous studies of evanescent coupling to suchPCWGs 5 the waveguide termination consisted of a2-mm region of undercut silicon, followed by an 8-mmlength of nonundercut silicon on insulator and a finalair interface. The interference from multiple reflec-tions at the three interfaces within the waveguide ter-mination resulted in a highly wavelength-dependentreflection coefficient, making quantitative analysis of

signals ref lected by the PCWG difficult. Here, thewaveguide terminations were engineered to have ei-ther high or low broadband reflectivities. On one endof the PCWG, shown in Fig. 2(b), a PC mirror with highmodal reflectivity ( r 1 ) for the TE-1 PCWG mode wasused. This high-ref lectivity end mirror was formedby removal of the lattice compression of the waveguidewhile maintaining the transverse grade in hole radius.The change in lattice compression results in the TE-1PCWG mode lying within the partial bandgap 6 of thehigh-ref lectivity end mirror section [Fig. 2(c)] whilethe transverse grade in hole radius reduces diffractionloss within the mirror. On the opposite end of thePCWG a poor reflector with low reflectivity ( r 2 ) wasrealized by removal (over several lattice constants) of the transverse grade in hole radius while keeping thecentral waveguide hole radius fixed, resulting in aloss of transverse waveguiding within the end mirrorsection and allowing the TE-1 PCWG mode to diffractinto the unguided bulk modes of the PC.

In the absence of reflections caused by the PCWGtermination (i.e., r 1, 2 0) the fiber PCWG junctioncan be characterized by

"a 1F La 2PC 0 # " t k 0k t0#" a1F 0

a 2PC L #, (1)

where k and k 0 are coupling coefficients; t and t0 aretransmission coefficients; and a 1F z and a

2PC z are the

amplitudes of the forward-propagating fundamentalfiber taper mode and the backward-propagating TE-1PCWG mode, respectively. The coupling region ex-tends along the z axis, with z 0 corresponding to theinput and z L to the output of the coupler. As illus-trated in Fig. 1(b), nonzero r 1, 2 introduce feedback intothe system. This allows input light coupled from theforward-propagating fundamental f iber taper modeinto the TE-1 PCWG mode to be partially reflectedby the PCWG termination and subsequently coupledto the backward-propagating fundamental fiber tapermode. In the presence of this feedback within thePCWG, the normalized reflected and transmittedpowers in the fiber taper are given by 8

T ja 1F L j2 t 1 kk 0t 0r 1 r 21 2 r 1 t 0r 2 t 02

, (2)

R ja 2F 0 j2 kk 0r 11 2 r 1 t 0r 2 t 02

, (3)

for a 1F 0 1 and a 2PC L 0 . By measuring T and Rand considering Eqs. (2) and (3), we can determine theefficiency of the fiber PCWG coupling as measured by

jkk 0j.In the measurements presented here a fiber taperwith 2-mm diameter was used to probe the PCWG of Fig. 2(b). Figures 3(a) and 3(b) show T and R as afunction of wavelength when the taper is aligned withthe PCWG at a height of g 0.20 mm and indicatethat the phase-matched wavelength is l 1598 65 nm. As described in Ref. 5, coupling to the guidedTE-1 mode of the PCWG was confirmed by study of the coupling dependence upon polarization, lateraltaper displacement, and fiber taper diameter. Fig-ure 3(c) shows T and R at the resonant wavelengthof the PCWG nearest the phase-matching condition[the minima and maxima in T l and R l ] a s afunction of taper height g above the PCWG. Includedin Fig. 3(c) is the off-resonant (away from phasematching) transmission, T off , through the fiber. A maximum normalized ref lected power Rmax 0.88was measured at a height of g 0.25 mm, wherethe corresponding transmission was T , 0.01 . Ascan be seen in the wavelength scans of Fig. 3(a),at this taper height the Fabry Perot resonancescaused by multiple ref lections from the end mirrorsof the PCWG are suppressed for wavelengths withinthe coupler bandwidth due to strong coupling to thefiber taper. Ignoring for the moment the effects of multiple ref lections in Eq. (3), the maximum opticalpower coupling eff iciency is then jkk 0j p R max jr 1j,where the square-root dependence upon Rmax is aresult of the light passing through the coupler twice inreturning to the backward-propagating fiber mode. Assuming the high-ref lectivity mirror is perfect (unityref lection), for the measured R max 0.88 this implies94% coupling of optical power from taper to PC wave-guide (and vice versa).

By further comparison of T g and R g withthe model given above, this time including feedback

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Fig. 3. (a) Reflection and (b) transmission of the fibertaper as a function of wavelength for a taper height of 0.20 mm. Both signals were normalized to the taper trans-mission with the PCWG absent. (c) Measured taper trans-mission minimum ( l 1600 nm), ref lection maximum ( l1600 nm), and off-resonant transmission ( l 1565 nm) asa function of taper height. Also shown are fits to the data,and the resulting predicted coupler efficiency, jk j2 . Asym-metry in the fiber taper loss about the coupling region wastaken into account by repeating the measurements with thedirection of propagation through the taper and the orien-tation of the PCWG sample reversed; the geometric meanof the values obtained from the two orientations takes anyasymmetry into account.

within the PCWG, we find that the high-reflectivityPCWG end mirror is imperfect and that Rmax is infact limited by mirror ref lectivity, not the eff iciencyof the coupling junction. For this comparison wetake the elements of the coupling matrix to satisfythe relations jt j2 1 jk j2 1, k 0 k , and t0 tof an ideal (lossless) coupling junction. 8 For thephase-matched contradirectional coupling consideredhere, the dependence of k on g can be approximatedby jk g j tanh k , 0 exp 2 g g 0 L ,9 where k , 0 andg 0 are constants. Substituting these relations intoEqs. (2) and (3), we can fit T and R to the experi-mental data with r 1, 2 , k , 0 , and g 0 as free parame-ters. 10 Waveguide loss can also be included in themodel; however, it is found to be small compared with

the mirror loss and will be studied in detail elsewhere.Figure 3(c) shows the fits to the data for g $ 0.20 mm;for g , 0.20 mm nonresonant scattering loss is nolonger negligible and the ideal coupling junctionmodel breaks down. Note that this scattering lossis observed to affect the ref lected signal at a smallertaper PCWG gap than for the transmitted signal; T off begins to decrease for g # 0.30 mm, whereas R beginsto decrease for g # 0.20 mm. This indicates that,within the coupler bandwidth, 1 2 T off is an overesti-mate of the amount of power scattered into radiationmodes. From the fits in Fig. 3(c) the PCWG end mir-ror ref lectivities are estimated to be jr 1j2 0.90 andjr 2j2 0.52 , and the optical power coupling efficiency(jk j2 ) occurring at R max (g 0.25 mm) is approxi-mately 97%.

In conclusion, these results indicate that this cou-pling scheme allows highly efficient input and outputcoupling between photonic crystal devices and fiber ta-pers and is promising for efficient probing of future in-tegrated planar PC devices.

K. Srinivasan thanks the Hertz Foundation and M.

Borselli thanks the Moore Foundation for f inancialsupport. P. Barclay s e-mail address is pbarclay@ caltech.edu.

References

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4. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C.Takahashi, and I. Yokohama, IEEE J. Quantum Elec-tron. 38, 736 (2002).

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9. P. Yeh and H. F. Taylor, Appl. Opt. 19, 2848 (1980).10. We take r 1 t 0r 2 t 0 jr 1 t 0r 2 t 0j 1 , corresponding to a reso-nant condition within the PCWG.