near-field observation of anomalous optical propagation in photonic crystal coupled-cavity...

Near-field observation of anomalous optical

propagation in photonic crystal coupled-cavity

waveguides

Haihua Tao,1, 2

Cheng Ren,2 Yazhao Liu,

2 Qingkang Wang,

1 Daozhong Zhang,

2 and

Zhiyuan Li2,*

1RIMNST, Shanghai Jiao Tong University, Shanghai 200240, China

2Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

*[email protected]

Abstract: An air-bridged silicon-based photonic crystal coupled-cavity

waveguide (PCCCW) connected with an input and output W1 PC waveguide

(PCW) was designed and fabricated. We mapped its intensity distributions

with a near-field scanning optical microscope (NSOM) at near-infrared

wavelengths around 1550 nm. Surprisingly, the intensity distributions

demonstrate that the second odd eigenmode dominates in such a PCCCW,

even though it possesses a much slower group velocity of light than that of the

first even one. Further considering the measured transmission spectrum, we

find that the modal profile and impedance matching between the eigenmodes

in the PCW and PCCCW plays an important role in the optical propagation

efficiency. Mode conversion between the first even and the second odd

eigenmode was also detected at the interfaces between the W1 PCW and

PCCCW.

©2010 Optical Society of America

OCIS codes: (130.5296) Photonic crystal waveguides; (180.4243) Near-field microscopy;

(230.4555) Coupled resonators; (999.9999) Slow light.

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1. Introduction

Slow light has attracted significant interest recently as a potential solution for optical delay line,

time-domain optical signal processing, and amplifiers of nonlinear optical effects in the

integrated photonic circuits [1–6]. For realizing slow light, two-dimensional silicon photonic

crystal waveguides (PCWs) have proven to be a powerful platform, as it is compatible with

on-chip integration and can offer wide bandwidth [5,6]. One way for this purpose is to utilize

the flat edges of photonic band dispersion curves, which consequently result in slow group

velocity [7–9]. The other one is to design photonic crystal coupled-cavity waveguides

(PCCCWs), in which the eigenmodes usually have relatively narrow bandwidth with slow

group velocity in the whole band range. For PCCCWs, the optical propagation is different from

the conventional PCWs, in which light propagates by hopping from one cavity to another in the

form of local resonant modes [5,10–17]. In all waveguides, transmission efficiency is an

important issue for its applications. Usually, slow light could intrinsically result in rather low

transmission efficiency due to increasing light-matter interaction as well as the extrinsic

influence from index and group velocity mismatches at interfaces [1,2,14–20]. As is well

known, near-field scanning optical microscopy (NSOM) provides an efficient tool to uncover

the essence of light propagation by mapping the optical field distributions with a subwavelength


resolution in nanophotonics [8,9,21–28]. Till now, slow light propagation in such specific

PCCCWs is still not experimentally studied via NSOM technique. In this article, we design a

silicon-based air-bridged PCCCW structure with slow light and study its optical propagation at

near-infrared wavelengths. The measured transmission spectrum, near-field optical mapping of

intensity distributions, and theoretical simulation results all demonstrate that the second odd

eigenmode of the PCCCW has significantly higher transmission efficiency than that of the first

even one, even though it possesses a lower group velocity. This anomalous optical propagation

has not been reported in previous literatures. Mode conversion between the first even and the

second odd eigenmode is also found at the interfaces between the W1 PCWs and PCCCW.

2. Theoretical design

PCCCW structures based on a conventional W1 PCW (a triangular lattice photonic crystal

membrane with a line of air holes unetched along the ΓΚ direction) with alternate identical air

holes have attracted specific attention and been studied especially for improving the optical

coupling efficiency from external medium [12,15–17]. However, to our knowledge, this kind of

PCCCW with decreased alternate air holes, which can improve the transmission efficiency, has

not been reported. In this study, we design such kind of silicon-based air-bridged PCCCW

structure working at around 1580 nm by means of the three-dimensional (3D) finite-difference

time-domain (FDTD) method [29,30]. As for the silicon-on-insulator (SOI) substrate, the

thickness of the silicon film is 235 nm with the refractive index to be 3.5. The refractive index of

the air background is taken to be 1. The lattice constant and the radius of the air holes in the

background triangular lattice photonic crystal are designed to be α = 455 nm and R0 = 126 nm,

respectively. For such a design, the W1 PCW could transmit TE-polarized light in the region

from 1500 to 1640 nm. The radius of the alternate small holes (radius) along the central

waveguide axis is Rd = 112 nm, forming a guided band centered at around 1580 nm for the

PCCCW.

Figure 1 plots band diagrams of the PCCCW (with an inset of the supercell for calculation)

and the traditional W1 PCW for TE-polarized modes with parameters as designed above. The

W1 PCW model structure is coherent with the discussion in the rest of the article, in which it

works as the input and output waveguides of the actual structure and helps to increase the

coupling efficiency between the ridge waveguides and the PCCCW [15–17]. For both

structures, there exist two low-order eigenmodes, i.e., the first even mode and the second odd

mode, which are denoted by the triangular and circular dotted lines, respectively. Here the even

and odd eigenmodes have the mirror-reflection symmetry with respect to the plane passing

through the central axis of the waveguide and perpendicular to the slab. Comparing the

calculated band diagrams of the PCCCW and W1 PCW, we can clearly see that both resonant

eigenmodes of the PCCCW in the whole frequency region is completely covered by the

corresponding guided mode band in the W1 PCW. On the other hand, at a certain frequency the

W1 PCW supports eigemodes while they are absent in the PCCCW. In addition, the bandwidth

of the odd eigenmode is totally covered by that of the even mode in both the W1 PCW and

PCCCW.

The bandwidth of both eigenmodes in the PCCCW is much narrower than that of the W1

PCW. This means, in general, the group velocity Vg = dω/dk is supposed to be greatly reduced

in the whole range of the PCCCW. Figures 2(a) and 2(b) plots the curves of the normalized

group velocity (c the vacuum speed of light) varying with the frequency for the guided TE-like

polarized eigenmodes of the PCCCW and W1 PCW, respectively, which are derived from their

calculated band diagrams in Fig. 1. For the PCCCW, one notable characteristic is that the group

velocity of the second odd eigenmode (with a peak value of 0.054) is much lower than that of

the first even one (with a peak value of 0.131) within the whole bandwidth. Comparing Fig. 2(a)

with Fig. 2(b), the peak velocities of both the first even and the second odd eigenmodes for the

PCCCW are lower than that of the W1 PCW.


0.0 0.1 0.2 0.3 0.4 0.50.26

0.27

0.28

0.29

0.30

0.31

0.32

1750

1700

1650

1600

1550

1500

1450

Fre

qu

en

cy

(

/)

Wavevector (2/)

Odd Mode

Even Mode

light cone

(:n

m)

(b)

0.00 0.05 0.10 0.15 0.20 0.25

0.270

0.275

0.280

0.285

0.290

0.295

0.300

0.305

0.310

1680

1650

1620

1590

1560

1530

1500

1470

Even mode

Odd mode

Wavevector (2) (:n

m)

Fre

qu

en

cy

(

/)

(a)

Fig. 1. Calculated band diagrams of (a) the PCCCW with an inset of the supercell model (Rd =

112 nm) and (b) the traditional W1 PCW for the TE-like polarized modes.

0.270 0.285 0.300 0.315 0.330

0.00

0.05

0.10

0.15

0.20

0.25

high K

low K

W1 even mode

W1 odd modeV

g(c

)

Frequency (/)

(b)

0.280 0.285 0.290 0.2950.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Vg(c

)

Frequency (/)

CCW even mode

CCW odd mode (a)

Fig. 2. (a) Normalized group velocity as a function of frequency for TE-like polarized

eigenmodes of PCCCW and (b) that of the traditional W1 PCW derived from Fig. 1.

3. Fabrication and experimental results

We fabricated the PCCCW on the silicon-on-insulator wafers with a focused ion beam machine

followed by the chemical etching in hydrofluoric acid to form an air-bridged silicon membrane

2D PC structure. The transmission spectrum was detected by a far-field optical detection system

equipped with a continuous wave (cw) wavelength-tunable laser from 1500 to 1640 nm with the

power fixed at 3 mW. An infrared CCD camera (HAMAMATSU MODEL C2741-03), which

was connected with an objective (M Plan Apo NIR, 100X/0.5N.A.), could take a picture with

the field of view 127 × 95 µm2. The near-field intensity distribution profiles were mapped using

an NSOM system (NSOM-100 Nanonics, Israel) in collection mode with the same cw laser

source. The output signal was probed by an inhouse developed InGaAs single-photon detector.

The NSOM tip, a cantilever metal-coated fiber with an aperture diameter of 200 nm, was

controlled to scan at a constant-height position of ~10 nm above the sample surface. More

details of the fabrication and optical detection techniques can be found in Ref. 28.

Figure 3(a) displays the scanning electron microscope (SEM) image of the element

composed of the central PCCCW (encircled by a red square), two identical W1 PCWs, and the

input/output ridge waveguides before chemical etching with parameters as designed by the

aforementioned 3D FDTD method. Figure 3(b) is the corresponding transmission spectrum


with a guided band ranging from 1555 to 1614 nm as measured by the far-field optical detection

system. This narrow guided bandwidth is consistent with the calculated band curves in Fig. 1(a).

At outlet of the element, a bright spot is detectable in the region of guided band, as depicted by

a partial CCD image at 1580 nm in the inset of Fig. 3(b).

1500 1530 1560 1590 1620-70

-65

-60

-55

-50

-45

-40

-35

Tra

ns

mis

sio

n (

dB

m)

Wavelength (nm)

(b)

(a)

Fig. 3. (a) SEM image of the element composed of the central PCCCW, two identical W1 PCWs

and the input/output ridge waveguides; (b) Measured transmission spectrum with the inset of a

bright optical spot image at 1580 nm at the outlet observed by the infrared CCD camera.

Figure 4 displays the near-field optical intensity distribution patterns of the PCCCW at

different wavelengths within the guided bandwidth. The scanning area is 12 × 15 μm2 with the

incident light propagating upwards from the bottom of the image. The straight yellow lines in

Figs. 4(b)-4(d), and 4(f) are used to label the position for showing the cross-sectional profiles of

the field distribution patterns. The results are displayed in Fig. 5. For clarity, the SEM picture of

the PCCCW is inserted in Fig. 4(a) instead of the NSOM topography with the same scanning

area as the latter has a much coarser topographical resolution.

We first focus on the near-field optical images at 1550 and 1610 nm [Figs. 4(b) and 4(f)]

which appear dissipating pretty quickly along the PCCCW section with relatively low

transmission efficiency as indicated in the transmission spectrum of Fig. 3(b). The optical

intensity distribution patterns are different at 1550 and 1610 nm, even though both of them

mainly appear as a single narrow line along the central PCCCW region with a full width at half

maximum (FWHM) of ~350 nm. Precisely speaking, the pattern demonstrates a little bit

shoulder as a result of mode superposition at 1550 nm, since it comprises two eigenmodes. At

1610 nm, the pattern appears bright and wide with obvious interference nodes in the PCCCW

section.


Fig. 4. (a) SEM topographic image, and the near-field optical intensity distributions at (b) 1550

nm, (c) 1560 nm, (d) 1571 nm, (e) 1590 nm, and (f) 1610 nm. The white dotted lines in each

optical picture denote the interface between the W1 PCW and PCCCW. All pictures were

obtained for the same scanning area of 12 × 15 μm2.

Fig. 5. Typical NSOM transverse field distribution profiles of the PCCCW sections labeled in

Fig. 4 at (a) 1550 nm, (b) 1560 nm, (c) 1571 nm, and (d) 1610 nm.

In the central PCCCW region, the optical intensity distribution patterns continue evolving

with the wavelength. At 1560 nm, it presents an obvious snake-like profile. The transverse field

distribution profile analysis in Fig. 5(b) further confirms this feature by showing a wide total

FWHM of ~950 nm, which is composed of a single peak with a large shoulder on the right side.

At 1571 or 1590 nm, two parallel lines show up in the PCCCW region along the central

waveguide axis. As shown in Fig. 5(c), the total FWHM of the field distribution profile is ~900

nm with the distance of ~500 nm between the dual-peak centers. It is notable that all optical

intensity distribution patterns present snake-like structure in the input W1 PCW section in Figs.

4(b)-4(e).


4. Analysis and discussion

With the calculated band diagrams of the PCCCW and W1 PCW in Fig. 1 at hand, we now

move forward to get the field distributions at different wavelengths by means of the 3D FDTD

method. The light source has a Gaussian profile with even or odd symmetry relative to the

waveguide axis. Figures 6(a1)-6(e1) show the calculated optical field distribution profiles at

different wavelengths with a simulation model schematized in Fig. 6(M1). When it contains

only the first even eigenmode, an even symmetric source is used [at 1610 nm in Fig. 6(e1)]. In

this case, only the first even eigenmode can be excited. The calculated result consists well with

the experimental one in Fig. 4(f) presenting a single line along the whole waveguide. When the

first even and the second odd eigenmodes coexist, a superposed continuous wave source with

equal even and odd eigenmode amplitudes is used [Figs. 6(a1)-6(d1)]. In this case, both the first

even and the second odd eigenmodes can be excited. The simulated field distribution profiles in

the W1 PCW sections agree well with the detected ones at all these wavelengths, which show a

snake-like/single-line profile in the input/output W1 PCW except that of a snake-like profile in

the output W1 PCW at 1560 nm. In addition, the simulated field distribution patterns of the

snake-like profile in the PCCCW section appear deviating greatly from the detected ones at

1550, 1571, and 1590 nm. In order to explain such discrepancies, we use a model of the

PCCCW in Fig. 6(M2) for further theoretical simulation. The optical field distribution patterns

at 1550, 1560, and 1571 nm are displayed in Figs. 6(a2)-6(c3) with the even-to-odd amplitude

ratios of 1:4, 1:1, 1:4, and 1:6, respectively. The calculated field distributions at 1590 nm, which

are similar to those at 1571 nm with the same trend as the experimental results in Fig. 4, are not

otherwise displayed for concision. With this model, the simulated results are consistent with the

experimental patterns evolving from single, to snake-like, and then to double-line structures for

the PCCCW section. Calculation of the field distribution displayed in Fig. 6(a2) further shows

that the first even eigenmode still dominates in the PCCCW even if the even-to-odd amplitude

ratio is only 1:4. This means that the component of the odd eigenmode increases when the

wavelength grows from 1550 to 1571 nm.

As pointed out in Fig. 2(a), in general, the group velocity of the second odd eigenmode is

much slower than that of the first even one. According to previous studies, a slow group

velocity means long transit time per distance, and this can result in large dissipation due to

material absorption and radiation losses [14,15,17]. Furthermore, a slow group velocity means

low coupling efficiency at the interfaces due to large impedance mismatch [18,19]. However, in

our current study, the second odd eigenmode dominates with a result of high total transmission

efficiency in the central frequency region. This means that the group velocity of different modes

is not a critical factor in determining the transmission efficiency of the PCCCW. The reason

might be that the PCCCW has a distance comprising only seven cavities, and therefore the

group velocity induced loss is not a dominant factor.

Another factor, i.e. the modal profile and impedance matching between the eigenmodes in

the W1 PCW and PCCCW, seems to play a more important role in the transmission efficiency

of the PCCCW. In the PCCCW, the waveguide along the alternate small air hole axis has a

relatively low effective refractive index. For the second odd eigenmode, its energy distributes

mainly away from the central axis, therefore the modal profile mismatch between the PCW odd

mode and the PCCCW odd mode could be relatively small. In contrast, for the first even mode,

its energy mainly concentrates on the central line, light sees very different environment in the

PCW and PCCCW and the modal impedance is strong. Light could thus suffer more serious

interface reflection and radiation losses when it propagates across the interfaces between the

W1 PCW and PCCCW. As a result, the transmission efficiency gets relatively lower for the first

even eigenmode, even though its group velocity is higher than that of the second odd mode. For

the second odd eigenmode at around 1550 nm, the low propagation efficiency could be related

to the spreading structure of the second odd mode due to its extremely slow group velocity near

the cutoff of the PCCCW. When the incident wavelength gets larger, the mode group velocity


increases, and therefore the transport efficiency across the whole element grows due to less loss

from the modal profile and impedance mismatch. It should be pointed out that from the

discussion of the detected transmission spectrum and the variable component of the second odd

eigenmode, the group velocity still influence the transmission efficiency in the conventional

way for the same eigenmode. As discussed in the above, the calculated patterns in the input W1

PCW consist with the experimental results by using the even-to-odd amplitude ratio of 1:1.

Variation of the proportion of the second odd eigenmode in the PCCCW from 1550 to 1571 nm

with increasing transmission efficiency and the single-line profile at the outlet W1 PCW at 1550

nm, 1571 nm and 1590 nm indicate that there exists mode conversion between the first even and

the second odd one at the interfaces between the W1 PCW and PCCCW. Mode conversion at

the interfaces has been previously discovered by NSOM techniques [22,23].

Fig. 6. (M1) Simulation model and calculated optical field distributions at (a1) 1550 nm, (b1) 1560

nm, (c1) 1571 nm, (d1) 1590 nm, and (e1) 1610 nm; (M2) Simulation model and calculated optical

field distributions at 1550 nm, 1560 nm, and 1571 nm with the even-to-odd amplitude ratios of

(a2) 1:4, (b2)1:1, and (c2) 1:4, (c3) 1:6, respectively.

As is well known, decreasing the loss as much as possible is very important for design of all

optical waveguides, especially for the PCCCW transmitting slow light. As indicated by the field

distributions in Fig. 4 with severely decreasing intensity along the whole waveguide, the

coupling efficiency at the interfaces between the W1 PCW and PCCCW is very low, resulting

in an inefficient slow-light device. The use of adaptive structure between the W1 PCW and

PCCCW, such as adiabatic coupling or other structures, could enhance the coupling efficiency

as well as change the mode propagation [15,17]. Furthermore, the PCCCW part discussed in

this article is not well optimized. For instance, by further decreasing radius of the alternate air

holes in a certain scope, the optical propagation could be further improved. The detailed

discussion on structure optimization and loss dependence on the PCCCW length is out of the

scope of this paper, and it would be discussed elsewhere.


5. Conclusion

In summary, we designed an air-bridged silicon-based PCCCW connected with an input/output

W1 PCW and mapped its near-field optical distributions at different wavelengths around 1550

nm with the NSOM. The simulated dispersion relations and field distributions derived by means

of the 3D FDTD method give a good explanation of the experimental phenomena. For the

PCCCW, the higher transmission efficiency of the second odd eigenmode with a slower group

velocity indicates that the modal profile and impedance matching between the eigenmodes in

the PCW and PCCCW could play a crucial role in optical propagation efficiency. Mode

conversion occurs at the interfaces between the W1 PCW and PCCCW. Combination of the

near-field optical detection and theoretical simulation shows that NSOM is an efficient tool to

study the optical propagation in the PCCCW and can help to design slow light elements.

Acknowledgements

The authors would like to acknowledge the financial support of the National Natural Science

Foundation of China Nos. 10525419 and 60345008, the National Key Basic Research Special

Foundation of China No. 2007CB613205, as well as the technical support of Prof. Ling-an Wu,

Prof. Zebo Zhang, Dr. Haiqiang Ma, and the Laboratory of Microfabrication in the IoP, CAS.


near-field observation of anomalous optical propagation in photonic crystal coupled-cavity...

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