## Abstract

Tunable diode laser absorption spectroscopy using microresonator whispering-gallery modes (WGMs) is demonstrated. WGMs are excited around the circumference of a cylindrical cavity 125 µm in diameter using an adiabatically tapered fiber. The microresonator is very conveniently tuned by stretching, enabling the locking of an individual WGM to the laser. As the laser is scanned in frequency over an atmospheric trace-gas absorption line, changes in the fiber throughput are recorded. The experimental results of cavity-enhanced detection using such a microresonator are centimeter effective absorption pathlengths in a volume of only a few hundred microns cubed. The measured effective absorption pathlengths are in good agreement with theory.

©2007 Optical Society of America

## 1. Introduction

Numerous nonlinear all-optical switching devices implemented with resonant cavities have recently been demonstrated in semiconductor microstructures (for example, Si [1,2], GaAs [3]), where the efficiency of weak nonlinearity of the material is greatly enhanced due to accumulation of optical field (i.e., amplitude and phase) inside resonant cavities. It has been shown experimentally [1–3], numerically [2] and analytically [4,5] that the switching operations in such materials occur due to dominant free carrier nonlinearity exited via two-photon absorption (TPA) process as opposed to weaker but ultra-fast Kerr nonlinearity. Therefore, the demonstrated devices have response time limited by the free carrier lifetime of hundreds of picoseconds depending on the geometry. In order to achieve faster operation in such resonator-enhanced nonlinear devices, we need to identify a new waveguide material with a shorter carrier lifetime or with a smaller TPA coefficient (i.e., wide energy bandgap), and also compatible with the semiconductor or CMOS-compatible silicon on insulator (SOI) fabrication process.

In this manuscript, we investigate amorphous silicon as a candidate material to decrease carrier lifetime, utilizing its relatively large density of defects (localized states) as recombination centers leading to a shorter carrier lifetime (~10ps) [6]. Although pure amorphous silicon (a-Si) has a very high defect density preventing it from being useful electronic material, hydrogenated amorphous silicon (a-Si:H) has long been investigated for solar cells because the film is inexpensively deposited over a very large area and the hydrogen introduced into amorphous silicon terminates the defects [7]. The a-Si:H film can be deposited usually by plasma-enhanced chemical vapor deposition (PECVD) at low temperature (~400°C) on any substrate and therefore is compatible with the SOI fabrication process. Several works on its application to optical devices have been reported, including a single-mode waveguide with 2.0dB/cm loss [8] and a thermo-optical switch with 10µs response time [9, 10]. However, to the best of our knowledge, no information on nonlinear optical property of amorphous silicon is available in the literature. Here, we present the first measurements of nonlinear optical effects dominated by free carrier nonlinearity in amorphous silicon films using z-scan technique and find the enhanced nonlinearity mainly due to presence of midgap localized states. We also propose to exploit these materials in a new composite waveguide device, fabricate such a composite waveguide and validate experimentally the results on enhanced nonlinearity and shorter free-carrier lifetime.

## 2. Optical nonlinearity in amorphous silicon films: z-scan measurement

We use z-scan technique (see Fig. 1) [11] to investigate the nonlinear optical properties
of amorphous silicon films. We use a mode-locked Ti: Sapphire oscillator combined with a
regenerative optical amplifier, producing laser pulses with time duration of 100fs, beam
diameter of 6 mm at a wavelength of 1.55µm and 1kHz repetition rate. A beam splitter is
used to reflect a small fraction of the laser beam to a photodetector to monitor the
laser power. The transmitted beam is focused on the sample using a lens with focal
length *f*=100mm producing a 16.5µm beam waist and ~10mJ/cm^{2}
energy fluence. The incident optical field causes nonlinear refraction and absorption in
the sample as it is being scanned along the optical axis of the lens. The light
transmitted through the sample is detected by a detector with or without a small
aperture in front of it (see Fig. 1). When the
detection is performed with the aperture, the detected signal has a peak-valley trace,
depending on the sign of the nonlinear refraction, because the original Gaussian mode
distribution is distorted by the intensity-dependent nonlinear refraction at the focal
point. When the detection is performed without the aperture, the detected signal carries
only nonlinear absorption dip information when the sample is at *z*=0.
The intensity *I* of the field propagating within the sample satisfies
the differential equation,

where *α* is the absorption coefficient, *β* is the TPA
coefficient, *z*’ is the coordinate within the sample, and
*L* is the thickness of the sample. The solution of Eq. (1) at the output surface of the sample
(*z*
^{’}=*L*) can be written as,

where *I*(0, *r*, *t*, *z*)
is the Gaussian mode behind the lens, *q*(*r*,
*t*, *z*)=*βI*(0, *r*,
*t*, *z*)*L*
* _{eff}*, with

*L*

*=(1-exp(-*

_{eff}*αL*))/

*α*. When the aperture is present, we calculate the field integral over the aperture area using Gaussian decomposition method or Fresnel integral. When the aperture is absent, we simply integrate Eq. (2) spatially and temporally, yielding the normalized transmittance at

*z*=0,

where *I*
_{0} is the center peak intensity of the original Gaussian pulse. Figure 2 shows the plot of
*T*(*z*=0) in Eq. (3a) with relation to the parameter *q*
_{0} in >Eq. (3b). Note that
*q*
_{0} is obtained from the measured normalized transmission dip corresponding to
the value of *T*(*z*=0) and its relation shown in Fig. 2. Once *q*
_{0} is found, we can then calculate *β* using Eq. (3b) with the known *I*
_{0} and *L*
* _{eff}*. We use this

*q*

_{0}for data analysis later.

We fabricated and prepared four samples for the z-scan measurement as summarized in
Table 1. One of the samples was a-Si
prepared using RF sputtering and two other samples were a-Si:H prepared by different
PECVD processes with saline and helium mixture. The fourth sample was crystalline
silicon (c-Si). The amorphous samples are deposited on silicon dioxide substrates with
thicknesses of several microns, much thinner than the thickness of the crystalline
sample. We measured the transmission spectra of the samples using a normally incident
beam from a 120nm-broadband source centered at a wavelength of 1.56µm. We estimate the
film thicknesses *L* from the observed Fabry-Perot resonance
oscillations, assuming the refractive index *n*
_{0} of 3.7 [12] for a-Si and 3.4 [9] for a-Si:H. The obtained thickness for a-Si was
close to the expected value estimated from the deposition rate and the total deposition
time. We also determined the material absorption *α* around 1.55µm of the
films from the peaks of the Fabry-Perot oscillations. Next, we measured the transmission
spectra of these samples using a super-continuum light source with the wavelength
ranging from 500nm (2.48eV) to 1100nm (1.13eV), as shown in Fig. 3(a). Figure 3(b)
shows the plot of absorption coefficient vs. photon energy which was extracted from the
transmission spectra in Fig. 3(a). Note that the
noisy data points with the transmission below -20dB was removed for the clarity of the
graph. For reference, we also include plots of the values from Ref. [9] for a-Si:H and c-Si. We conclude that the
measured *α* for c-Si is consistent with these of Ref. [9]. The measured *α* for a-Si is very
large, which means that the density of defect states in a-Si is very large. The measured
α for a-Si:H ranges between the values measured for c-Si and a-Si, indicating that
a-Si:H has a moderate defect density. We also observe that the a-Si:H(2) sample has a
higher quality (i.e. lower density of defects) than a-Si:H(1) sample. It should be noted
that the film quality of our samples decreases in the following order:
c-Si>a-Si:H(2)>a- Si:H(1)>a-Si.

Figure 4 summarizes the z-scan measurement
results: Figure 4(a) shows normalized
transmittance vs. z-coordinate when we use an aperture for a 1mm-thick SiO_{2}
substrate and a- Si sample. Figure 4(b) shows
the normalized transmittance traces vs. z-coordinate for our 4 samples described in
Table 1 using laser beam with a different
average powers, when we did not use the aperture. It is evident that we can neglect the
effect of the SiO_{2} substrate on our characterization of Si films, since the
laser beam at very high power of 90µW generated only a small signal for SiO_{2}
substrate (see Fig. 4(a)) in contrast to these
in the Si samples. For the analytic fit (see the solid curve in Fig. 4(a)), we used a value *n*
_{2}=4.3×10^{-16}cm^{2}/W, which is only two times larger than
the values of *n*
_{2} for SiO_{2} found in the literature [13], indicating a good accuracy of our measurements. The discrepancy
might be due to an error in the confocal parameters we used since the beam from the
femto-second light source was not a very clean Gaussian. The trace for a-Si in Fig. 4(a) is inverted in z direction, in comparison
to that for SiO_{2} substrate, indicating that the dominant nonlinear effect in
a-Si corresponds to negative nonlinear refraction due to free carrier nonlinearity. From
the results in Fig. 4(b), we note that the
signals for a-Si and c-Si are very close, although the thickness of a-Si is much less
than that of c-Si. Therefore, we expect that the nonlinear effect in a-Si will be much
larger than that in c-Si. In contrast, for a-Si:H samples, since higher input powers are
required to obtain similar level of signals as these observed in a-Si, we anticipate
that the nonlinear effect in a- Si:H should be smaller than in a-Si. To quantify these
observations, we plot the parameter *q*
_{0} vs. average power (see Fig. 5(a))
which are found from z-scan dips *T*(*z*=0) using their
relation through Eq. (3a) plotted in
Fig. 2, together with the linear fits (dotted
lines) from the analytic formula given by Eq.
(3b). The values of *β*s are estimated from the dotted lines
providing the values of 4.4cm/GW, 12cm/GW, 40cm/GW and 120cm/GW for our 4 samples c-Si,
a-Si:H(2), a-Si:H(1) and a-Si respectively, corresponding to the order of the film
quality. The estimated value of 4.4cm/GW for c-Si is only several times larger than that
found in the literature [14]. Again, this
discrepancy might be due to an error in the confocal parameters we used. The values for
a-Si and a-Si:H are extremely large as we have expected. We attribute such a large
nonlinear absorption to the “two-step” absorption (TSA) process through the midgap
localized states (See Fig. 6). We discuss this
effect further in the next section. *n*
_{2} could be directly measured at much lower fluence levels but the
*n*
_{2} signal in our setup was unfortunately not able to be distinguished from the
noise. It should be noted that accurate measurements of *n*
_{2} can be achieved using waveguide structures with longer interaction length
[15], however these measurements are not in
the scope of our current study.

## 3. Discussion – enhanced optical nonlinearity via two-step absorption

For more accurate analysis of the nonlinear interactions, we modify Eq. (1) by including the free-carrier absorption term, yielding,

where *σ* is the change in the attenuation per unit photo-excited free
carrier density *N*. Since we assume that the free carriers in a-Si and
a-Si:H samples are mainly generated via TSA, the σ and *N* are described
by

where we reproduced *σ* from ref. [16] and *N* is found from integrating Gaussian temporal
variation of *I*, *e*
_{0} is the electron charge, *ε*
_{0} is the vacuum permittivity, *m*
* _{e}* and

*m*

*are the effective masses of electrons and holes,*

_{h}*µ*

*and*

_{e}*µ*

*are the mobilities of electrons and holes,*

_{h}*n*

_{0}is the refractive index of the material and

*τ*

*is the time duration of the laser pulses. Therefore, we can combine the second and the third terms on the right-hand side of Eq. (4) and define an enhanced nonlinear absorption coefficient*

_{p}*β*

^{’}as,

The last equation indicates that free carrier absorption excited by TSA is of the same
order as TPA, whereas, in comparison, free carrier absorption due to TPA is of the
higher order. Thus, Eq. (4) can be solved
in the same way as Eq. (1) but by
replacing *β* with *β*
^{’}, yielding the relation *q*
_{0}=*β*
^{’}
*I*
_{0}
*L*
* _{eff}* instead of Eq. (3b) plotted for
a-Si and a-Si:H as solid lines in Fig. 5(b). We
used the following parameters;

*β*=0.8cm/GW (from c-Si [14]),

*m*

*=0.5*

_{e}*m*

_{0},

*m*

*=1.0*

_{h}*m*

_{0},

*µ*

*=2.0cm*

_{e}^{2}/Vs and

*µ*

*=0.4cm*

_{h}^{2}/Vs [6]. The calculated

*β*

^{’}s are 104cm/GW for a-Si, 6.7cm/GW for a-Si:H(1) and 1.4cm/GW for a-Si:H(2). We observe that the

*q*

_{0}-

*P*plots with the

*β*

^{’}in Fig. 5(b) are fairly close to the measured z-scan data especially at lower powers. The discrepancy at higher power will be from an additional free carrier absorption excited via TPA. Figure 7 shows the plot of

*β*

^{’}with relation to

*α*from Eq. (6) with example waveguide losses of 1dB/cm for a channel waveguide and 1dB/mm for a slab photonic crystal (PhC) waveguide. Since we are using laser pulses of 100fs, a higher

*α*(>10dB/mm) comparing to PhC waveguide or channel waveguide is required to have an enhanced nonlinearity and this will lead to device degradation. However, if we are to use picosecond pulses, the enhancement occurs even at a lower value of

*α*(<1dB/mm), comparable to these waveguide losses. Therefore, amorphous silicon with small

*α*can be useful to enhance the nonlinear effects in waveguide devices without device degradation. Please note that the enhancement of free carrier refraction Δ

*n*via TSA can be calculated in the similar way [16] with

*Δn*=-(

*e*

^{2}

*λ*

^{2}/8π

^{2}

*c*

^{2}

*ε*

_{0}

*n*

_{0})[1/

*m*

*+1/*

_{e}*m*

*]*

_{h}*N*.

## 4. Amorphous-crystalline composite waveguide structures

We exploit the results discussed above by constructing a novel composite waveguide
consisting of a-Si and c-Si (ac-Si) for use in Si photonics applications. The advantage
of our structure is that the effect from midgap states can be tailored by controlling
the fraction of a- Si in the ac-Si composite, instead of depositing different films with
different recipes. Additionally, the c-Si layer can act as a heat sink for a-Si since
thermal conductivity of c-Si is much higher than that of a-Si [10]. Figure 8 shows SEM
micrograph of a fabricated composite rib waveguide with about 3dB/mm loss. We measured
*β*
^{’} of this waveguide using picosecond laser pulses with repetition rate of
76MHz, using the solution of Eq. (1) with
replaced *β* by *β*
^{’}, yields

where *T*
_{0} is the transmission at low power (linear regime), *C* is the
coupling loss to the waveguide, *P* is the input peak power,
*A*
* _{eff}* is the effective core area of the waveguide. If we measure and plot the
inverse transmittance

*T*

^{-1}of this waveguide with regard to the input peak power

*P*, we can extract

*β*

^{’}from the tilt of the plot since we know the other parameters in the second term of the right-hand side of Eq. (7) [15]. Figure 9(a) is the result for the ac-Si composite rib waveguide and Fig. 9(b) is the result for pure c-Si rib waveguide with similar dimensions. The measured

*β*

^{’}s are 0.55cm/GW and 4cm/GW for c-Si and ac-Si, respectively. Since the data points in Fig. 9 do not appear exactly linear, it might include a higher order nonlinear absorption probably from the free carrier absorption via TPA. Therefore, the estimated values might not be very accurate. Even so, we can clearly see from the data that the nonlinear absorption in ac-Si waveguide is much larger than that in c-Si waveguide. Since some part of waveguide loss should come from scattering, the loss due to midgap states

*α*will be a little smaller than 3dB/mm. Also, we used pulses with about 10 picosecond time duration. Therefore, this measurement corresponds to the area indicated by the red solid circle in Fig. 7.

Next, we measured the free-carrier lifetime of the composite rib waveguide, by introducing the same picosecond pulses at 1.54µm as a pump and a CW source at 1.57um as a probe signal. This composite waveguide has oscillations in the transmission spectrum that is described by Fabry-Perot effect due to impedance mismatch on the input-output faces. Since the picosecond pump pulses excite the free carriers by TSA or TPA, the refractive index is modulated by the free carriers, causing the transmitted Fabry-Perot spectrum to shift to shorter wavelengths. We detected the modulated probe signal using a 45GHz PD and oscilloscope (see Fig. 10). The modulated signal has 300ps decay time, which is shorter than the reported values in the literature for pure c-Si waveguides (for example, 1ns [17] or 450ps [18]). It should be noted that our ac-Si composite rib waveguide was fabricated with E-beam writing process followed by lift-off process, without any etching procedures, and therefore we anticipate that the surface is very smooth. Therefore, the density of surface states in this rib waveguide should be small and this fast recombination is attributed to the defect state in a-Si. Faster recombination will be investigated using a-Si:H or microcrystalline silicon. Finally, we fabricated a ring resonator (see Fig. 11(a)) using ac-Si composite channel waveguide with the cross section and the mode profile shown in Fig. 11(b). The same pure a-Si film without hydrogen of about 20nm thickness was deposited on top of c-Si layer, followed by E-beam writing and RIE etching processes. The measured spectrum for quasi-TM mode is shown in Fig. 11(c) and the quality factor was measured to be 2200 at 1550nm. We demonstrate switching operation using 430nm femtosecond pump pulses illuminating the ring resonator from the top and a 1550nm CW probe signal propagating through the device at the resonant wavelength. We achieved 30% modulation of the probe signal using 17pJ/pulse as shown in Fig. 12(a). Notice that the carrier lifetime was around 30ps, which is much shorter than the reported value in similar experiment [18]. Even in an ion-implanted PhC resonator, the lifetime was reported to be around 70ps [17]. We also measured the carrier lifetime in pure c-Si ring resonator (see Fig. 12(b)) and found that the carrier lifetime (~40ps) was similar to that observed in ac-Si. Since we measured about 20dB/mm waveguide loss for both waveguides, we hypothesize that the main recombination centers for the generated free carriers in these waveguides were the surface states due to the rough sidewall resulting from our lithography and RIE processes. The results from these resonators unfortunately do not demonstrate the advantage of the faster recombination originating from the a-Si due to the roughness of the structure, however, do demonstrate that we can make a resonant device using the ac-Si waveguide structure.

## 5. Conclusions

We measured enhanced nonlinearities in a-Si using z-scan technique. Free-carrier nonlinearity due to TSA through midgap states explained this effect. We introduced, fabricated and characterized composite ac-Si waveguides made of a-Si and c-Si. The fabricated composite rib waveguide is confirmed to have the enhanced free-carrier nonlinearity at the estimated value of 4cm/GW, seven times larger than that of a pure c-Si waveguide. We measured the free-carrier lifetime in the composite rib waveguide (~300ps), which was shorter than the reported values in the literature for similar geometries of c-Si. We also fabricated a ring resonator using the composite waveguide approach and demonstrated modulation function using femto-second pump pulses. The resonator had a very short carrier lifetime of ~30ps, which was attributed to the high density of surface states.

## Acknowledgements

The authors thank Robert Saperstein, Nikola Alic and other group members for their support in the experimental setups. Financial support from the National Science Foundation, the Air Force Office of Scientific Research, and the Defense Advanced Research Projects Agency are gratefully acknowledged. K. Ikeda acknowledges the scholarship from Nakajima Foundation, Japan.

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