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
Numerous nonlinear all-optical switching devices implemented with resonant cavities have recently been demonstrated in semiconductor microstructures (for example, Si [1,2], GaAs ), 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  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) . 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 . 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  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)  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/cm2 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 eff=(1-exp(-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  for a-Si and 3.4  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.  for a-Si:H and c-Si. We conclude that the measured α for c-Si is consistent with these of Ref. . 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 SiO2 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 SiO2 substrate on our characterization of Si films, since the laser beam at very high power of 90µW generated only a small signal for SiO2 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=4.3×10-16cm2/W, which is only two times larger than the values of n 2 for SiO2 found in the literature , 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 SiO2 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 βs 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 . 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 , 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.  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 h are the effective masses of electrons and holes, µ e and µ h are the mobilities of electrons and holes, n 0 is the refractive index of the material and τ p 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 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 ), m e=0.5m 0, m h=1.0m 0, µ e=2.0cm2/Vs and µ h=0.4cm2/Vs . 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 Δn via TSA can be calculated in the similar way  with Δn=-(e 2 λ 2/8π2 c 2 ε 0 n 0)[1/m e+1/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 . 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) . 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  or 450ps ). 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 . Even in an ion-implanted PhC resonator, the lifetime was reported to be around 70ps . 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.
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.
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.
References and links
2. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005). [CrossRef]
3. V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002). [CrossRef]
5. K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007). [CrossRef]
6. P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan Jr., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids. 141, 76–87 (1992). [CrossRef]
7. R. A. Street, Hydrogenated Amorphous Silicon, (Cambridge University Press, Cambridge NY1991). [CrossRef]
8. A. Harke, M. Krause, and J. Mueller, “Low-loss singlemode amorphous silicon waveguides,” Electron. Lett. 41, 1377–1379 (2005). [CrossRef]
9. G. Cocorullo, F. G. Della Corte, R. De Rosa, I. Rendina, A. Rubino, and E. Terzini, “Amorphous siliconbased guided-wave passive and active devices for silicon integrated optoelectronics,” IEEE J Sel. Top. Quantum Electron. 4, 997–1002 (1998). [CrossRef]
10. M. Iodice, G. Mazzi, and L. Sirleto, “Thermo-optical static and dynamic analysis of a digital optical switch based on amorphous silicon waveguide,” Opt. Express 14, 5266–5278 (2006). [CrossRef] [PubMed]
11. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992). [CrossRef]
12. M. J. A. de Dood, A. Polman, T. Zijlstra, and E. W. J. M. van der Drift, “Amorphous silicon waveguides for microphotonics,” J. Appl. Phys. 92, 649–653 (2002). [CrossRef]
13. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 mu m,” Opt. Lett. 21, 1966–1968 (1996). [CrossRef] [PubMed]
14. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003). [CrossRef]
15. M. N. Islam, C. E. Soccolich, R. E. Slusher, A. F. J. Levi, W. S. Hobson, and M. G. Young, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” J. Appl. Phys. 71, 1927–1935 (1992). [CrossRef]
16. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J Quantum Electron. , QE-23, 123–129 (1987). [CrossRef]
17. T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, K. Yamada, T. Tsuchizawa, T. Watanabe, and H. Fukuda, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007). [CrossRef]
18. V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, M. A. Foster, D. G. Ouzounov, and A. L. Gaeta, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869 (2004). [CrossRef]