Spontaneous emission enhancement and saturable absorption of colloidal quantum dots coupled to photonic crystal cavity Shilpi Gupta1,∗ and Edo Waks1,2 1 Department
of Electrical and Computer Engineering, Institute for Research in Electronics and Applied Physics, and Joint Quantum Institute, University of Maryland College Park, Maryland 20742, USA 2 [email protected] ∗ [email protected]
Abstract: We demonstrate spontaneous emission rate enhancement and saturable absorption of cadmium selenide colloidal quantum dots coupled to a nanobeam photonic crystal cavity. We perform time-resolved lifetime measurements and observe an average enhancement of 4.6 for the spontaneous emission rate of quantum dots located at the cavity as compared to those located on an unpatterned surface. We also demonstrate that the cavity linewidth narrows with increasing pump intensity due to quantum dot saturable absorption. © 2013 Optical Society of America OCIS codes: (230.5590) Quantum-well, -wire and -dot devices; (230.5298) Photonic crystals; (270.5580) Quantum electrodynamics.
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#197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29612
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1.
Introduction
Colloidally synthesized quantum dots are excellent emitters for developing light sources [1–5] and non-linear devices [6–12] operating at room temperature. These quantum dots exhibit high photoluminescence efficiency at room temperature [13,14] and emission wavelength tunability [15,16]. The spontaneous emission rate of the quantum dots can be enhanced by coupling them to small mode-volume cavities [17,18]. Photonic crystals create extremely small mode-volume cavities [19] that can reduce lasing threshold [20–28] and enable nonlinear devices at low lightlevels [11, 29–32]. #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29614
Previous measurements of CdSe quantum dots coupled to photonic crystal cavities have shown increased brightness when the quantum dots are resonant with the cavity mode [33–36]. Similar results have been shown for quantum dots near the band edge of two dimensional photonic crystals [37, 38]. Spontaneous emission rate enhancement and suppression of CdSe quantum dots coupled to band-edge modes of three dimensional photonic crystals have also been demonstrated [39]. Here, we demonstrate spontaneous emission rate enhancement and saturable absorption of CdSe(ZnS) colloidal quantum dots coupled to a nanobeam photonic crystal cavity. Using timeresolved measurements, we show an average spontaneous emission rate enhancement of 4.6 for an ensemble of quantum dots located at the cavity. We also demonstrate cavity linewidth narrowing due to quantum dot saturable absorption. These results represent an important step towards development of integrated nanophotonic devices operating at room temperature. 2.
Time-resolved lifetime measurements
Nanobeam photonic crystal cavities have been extensively studied numerically [40–42], and have been experimentally demonstrated in a number of previous works [43–46]. We utilize a cavity design proposed by Khan et al. [45]. Figure 1(a) shows the device structure and the calculated mode profile for the cavity. We calculate the cavity mode using numerical three dimensional finite-difference time-domain simulations (Lumerical Solutions). The cavity design consists of a 200-nm-thick and 300-nm-wide silicon nitride (SiN) beam with a one-dimensional periodic array of air holes (a = 250 nm and r = 70 nm). The cavity is formed by linearly reducing the lattice constant from a = 250 nm to a0 = 205 nm and the hole radius from r = 70 nm to r0 = 55 nm over a span of 4 holes at the center of the beam (symmetrically on both sides). r
r0
a
(c) 2500 a0
0
(b)
1
Intensity (a.u.)
(a)
Cavity Unpatterned surface
2000 1500 Q = 9900 1000
500 nm
640
645 650 655 Wavelength (nm)
660
Fig. 1. (a) Electric field intensity (|E|2 ) profile of the resonant cavity mode. (b) Scanning electron microscope image of a nanobeam photonic crystal cavity. (c) Photoluminescencespectra of CdSe (ZnS) colloidal quantum dots located at the cavity and on unpatterned silicon nitride surface at room temperature.
We fabricate the device on 200-nm-thick stoichiometric SiN deposited on silicon using low pressure chemical vapor deposition. We pattern the nanobeam photonic crystal cavities using electron-beam lithography and fluorine-based inductively coupled plasma dry etching. The underlying silicon is etched by aqueous KOH to create a suspended beam. A scanning electron microscope image of a fabricated device is shown in Fig. 1(b). We disperse CdSe(ZnS) (Invitrogen Qtracker CdSe/ZnS 655 nm) quantum dots on the device by drop-casting a 10 nM aqueous solution and dabbing off the excess solution after 10 minutes. We note that due to this deposition technique, the quantum dots are not dispersed uniformly on the surface of the devices. Using atomic force microscopy, we determine the average density of the quantum dots on a nanobeam to be ≈50 μ m−2 . To avoid oxidation and photo-bleaching of the quantum dots during the experiment, we load #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29615
the device into a sealed chamber filled with purified nitrogen gas. For lifetime measurements, we illuminate the sample with 70 ps laser pulses at 405 nm wavelength and a repetition rate of 5 MHz (PDL800B, LDH-P-C-405B, PicoQuant). We set the average power to 500 nW to avoid creation of biexcitons and, thus, minimize the effect of excitation power on the measured lifetimes [47]. The laser excitation spot is about 1 μ m in diameter. The photoluminescence signal from the sample is collected using an objective lens with numerical aperture of 1.3. Of the collected signal, 25% is used for imaging and the rest is split equally between a grating spectrometer and a photon counting module (Picoquant MPD along with Picoharp 300) for simultaneous spectral and time-resolved lifetime measurements. We use a spatial filter to collect light only from a 1 μ m region around the cavity, and a spectral filter with 40 nm bandwidth (Semrock FF01-655/40-25) to reject all light outside the quantum dot bandwidth. Figure 1(c) shows typical photoluminescence spectra obtained by exciting the cavity region as well as an unpatterned region away from the nanobeam. The spectrum of ensemble of quantum dots located on an unpatterned region exhibits a broad homogenous linewidth of 21 nm. In contrast, the cavity spectrum exhibits a bright peak at the cavity resonant wavelength of 646.1 nm. We fit the cavity spectrum to a Lorentzian function to determine a quality factor of Q = 9900. Cavity Unpatterned surface
10−1 10−2 0
50 100 Time (ns)
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(b) 6
Measurements
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(a) 100
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14
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Fig. 2. (a) Time-resolved lifetime measurements of the quantum dots located at the cavity and on unpatterned silicon nitride surface (spectra shown in Fig. 1(c)). The stretched exponential fits are shown by solid curves. (b) Histogram of the lifetime (τavg from stretched exponential fit) from 29 different devices from 3 separately fabricated samples. The Gaussian fits are shown by dashed curves.
Figure 2(a) plots time-resolved lifetime measurement of the quantum dot emission collected from the cavity and an unpatterned region away from the nanobeam. We normalize the curves with respect to their count rates at time t = 0. The cavity fluorescence decays faster than the fluorescence from the unpatterned surface. Both temporal decays (on and off the cavity) exhibit a multi-exponential behavior. Multi-exponential decays in quantum dots have been previously studied and attributed to temporal fluctuations in non-radiative relaxation pathways due to changes in electronic or structural environment of the quantum dots [48, 49]. Cavities can induce additional fluctuations through variations in quantum dot positions and dipole orientations relative to the cavity field, which leads to different spontaneous emission enhancements [39, 50]. Two main decay models have been proposed for studying multi-exponential decay processes: stretched exponential fit [49] and log-normal fit [50, 51]. Here we use a stretched exponential fit given by β (1) I(t) = I0 + Ae−(t/τse ) where I(t) is the photoluminescence intensity at time t, I0 is the background intensity level, τse
#197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29616
is the 1/e decay lifetime, β is the stretch parameter, and A is a scaling constant. The stretch parameter β ranges between 0 and 1, and is inversely related to the variance of the decay rate (β = 1 corresponds to a single-exponential). From the stretched exponential fit, the average decay lifetime of the ensemble can be calculated by 1 τse (2) τavg = Γ β β where Γ is the Gamma function. We fit the lifetime data shown in Fig. 2(a) to Eq. (1) by treating τse , β , and A as fitting parameters. The solid lines in Fig. 2(a) represent the fitted values. These fits correspond to τse = 0.32 ns and β = 0.36 for quantum dots located at the cavity, and τse = 5.35 ns and β = 0.62 for quantum dots located on the unpatterned silicon nitride surface. Using Eq. (2), we calculate the average lifetime, τavg , for quantum dots located at the cavity to be 1.5 ns and quantum dots located at unpatterned silicon nitride surface to be 7.66 ns. We performed lifetime measurements on 29 different devices from 3 separately fabricated samples. Figure 2(b) plots τavg for all these measurements. The dashed curves are Gaussian fits to both the lifetime distributions. We observe a mean lifetime of 1.25 ns for quantum dots located at the cavity and 5.74 ns for quantum dots located on unpatterned silicon nitride surface, leading to an average spontaneous emission rate enhancement of 4.6. For quantum dots on the unpatterned surface we observe a shorter lifetime than those typically reported for single quantum dots deposited on glass [49, 52]. This reduction may be caused by modification of the local density of states due to the larger dielectric constant of SiN [53, 54] and Forster energy transfer between quantum dots [55]. Nonradiative decay may also contribute to the measured lifetimes. Because quantum dots are deposited on the device after the fabrication process, they are expected to have the same non-radiative decay rate regardless of whether they are deposited on the cavity or the unpatterned surface. In this case, the measured decrease in lifetime provides a lower bound on the actual spontaneous emission enhancement factor. The spontaneous emission enhancement factor for a quantum dot located at position r in the cavity, defined as F(r) = γ (r)/γ0 where γ (r) is the decay rate of the quantum dot located at the cavity and γ0 in free space, assuming dipole transition resonant and emitting in the same polarization as the cavity mode is given by [56]: F(r) = 1 +
3λ 3 Qqd ψ (r) 4π 2 n2 V
(3)
In the above equation, λ is the cavity-mode wavelength, Qqd = λ /Δλqd is the quantum dot quality factor, Δλqd is the quantum dot linewidth, n is the refractive index of the cavity dielectric, V = d 3 rε (r)|E(r)|2 /[ε (r)|E(r)|2 ]max is the cavity mode volume, ε (r) is the relative dielectric constant, and ψ (r) = |E(r)|2 /[|E(r)|2 ]max is the ratio of cavity-field intensity at location r to the maximum cavity field intensity. We note that the above equation is different from the conventional expression for the spontaneous emission rate enhancement factor and depends on the quality factor of the quantum dot, not the quality factor of the cavity. This difference is attributed to the fact that the homogeneous linewidth of the quantum dots is broader than the cavity, and therefore, our cavity-quantum dot system lies in the bad emitter limit [18, 57]. We set SiN refractive index to n = 2.01 [58] and single quantum dot linewidth to Δλqd = 15 nm [59]. Using finite-difference time-domain simulations, we calculate V = 0.57(λ /n)3 , λ = 642.6 nm, and ψ = 0.355 for a quantum dot located at the field maximum on the top surface of the nanobeam cavity. Plugging these values into Eq. (3), the maximum spontaneous emission rate enhancement is calculated to be 5.1. The calculated value for the spontaneous emission rate enhancement agrees with the measured value. #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29617
3.
Saturable absorption measurement
Just as the cavity can affect the quantum dots by enhancing spontaneous emission, the quantum dots can affect the cavity through absorption which degrades the cavity Q. Because quantum dots saturate at high pump intensity, the cavity will exhibit intensity-dependent linewidth. Saturable absorbers in a cavity can create enhanced nonlinear optical effects such as optical bistability [6–8, 60], optical switching [10, 12], and passive mode locking [61]. (b) 10000
measuremen t
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Time sequen ce of
8000
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po w
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(a)
6000 4000 2000 0
Increasing power Decreasing power fit
20 40 Input Power (μ W)
60
Fig. 3. (a) Normalized cavity spectrum for different input pump power levels. The green curved arrows show the time sequence in which the cavity spectra were measured. (b) Cavity Q as a function of input pump power. (c) Integrated cavity photoluminescence intensity as a function of input pump power.
In order to create sufficient quantum dot absorption to decrease Q, we increase the quantum dot density by performing five deposition steps on the device, as opposed to the single deposition step used for lifetime measurements. Using atomic force microscopy, we determine the average quantum dot density on a nanobeam to be ≈ 250 μ m−2 . We increased the pulsed laser repetition rate to 20 MHz to get higher signal. The collected photoluminescence signal is sent to a grating spectrometer to measure the cavity spectrum. Figure 3(a) shows the normalized cavity spectrum for several different input powers (the green arrows show the time sequence in which the cavity spectra were measured). We gradually increase the input power from 10 nW to 70 μ W, and the corresponding spectra are shown in blue. Once the input power level is at 70 μ W, we gradually decrease the input power back to 10 nW, and the corresponding spectra are shown in red. We observe that the cavity spectrum narrows with higher input power and becomes broad again when the input power is decreased back. We also observe an irreversible shift in resonance wavelength at higher input powers, which may be caused by photo-induced damage to the quantum dots [59] or cavity membrane at high intensities. Figure 3(b) plots the cavity Q as a function of input power, determined by performing a Lorentzian fit to the cavity spectrum. The blue circles show the cavity Q when the input power is gradually increased from 10 nW to 70 μ W, and the red dots represent the Q when the input power is gradually decreased back to 10 nW. In the increasing power cycle, Q increases from 6700 at 10 nW to 10400 at 70 μ W. The increase in cavity Q as a function of pump power is due to quantum dot saturation, which reduces the absorption in the cavity. In the decreasing power cycle, the cavity Q does not fully recover to its original value, but reaches a slightly higher value of 7400. This behavior is attributed to photo bleaching of quantum dots at higher powers during the increasing power cycle, which leads to a slightly lower absorption. The solid curve, in Fig. 3(b), is a fit to a model based on a cavity coupled to a homogeneous saturable absorber, where Q is given by [62]: 1 1 1 1 = + (4) Q Qc Qab 1 + P/Psat where Qc is the quality factor of the bare cavity, Qab is the quality factor due to quantum dot #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29618
absorption at low (unsaturated) powers, P is the input power, and Psat is the saturation power. We fit the quality factor data, obtained for increasing power cycle, to the above equation, treating Qc , Qab and Psat as fitting parameters. We obtain the best fit, shown as a solid curve in Fig. 3(b), for Qc = 10500, Qab = 19600, and Psat = 2.98 μ W. The cavity emission intensity provides further evidence that saturable absorption is the dominant mechanism for linewidth narrowing. Figure 3(c) plots the integrated cavity photoluminescence intensity as a function of input power, determined by performing a Lorentzian fit to the cavity spectrum. The blue circles represent the intensity when the input power is gradually increased from 10 nW to 70 μ W, and the red dots represent the intensity when the input power is gradually decreased back to 10 nW. The integrated cavity photoluminescence intensity increases linearly with increasing input power and eventually saturates. The solid curve in Fig. 3(c) is a fit to a saturable absorption model given by [63] Ic =
αP 1 + P/Psat
(5)
where Ic is the photoluminescence intensity and α is a proportionality constant. Figure 3(c) shows the best-fit results where we treat α as a fitting parameter and use the calculated Psat from Eq. (4). The fit is performed for the data obtained for increasing power cycle, and exhibits good agreement with the experimental measurements. Both the intensity and the cavity Q saturate with the same Psat , providing strong support for saturable absorption as the dominant mechanism for the intensity dependent cavity linewidth. When the power is decreased back down, the observed intensity values during the decreasing power cycle are lower than those in the increasing power cycle. This behavior is irreversible, it does not recover when we increase the power back up on subsequent power cycles but instead further degrades. It is therefore not due to power hysteresis effects such as thermal or optical bistability, which typically require direct resonant excitation of the cavity mode. This reduction in intensity is caused by photo-bleaching of quantum dots at higher input powers, and is also consistent with the fact that Q does not drop down completely to its original value (Fig. 3(b)). 4.
Conclusion
In conclusion, we have demonstrated spontaneous emission rate enhancement and saturable absorption of CdSe quantum dots coupled to a nanobeam photonic crystal cavity. We obtained a factor of 4.6 increase in the average spontaneous emission rate. These results could be further increased by either embedding the quantum dots in the dielectric [35] or by designing cavities which confine the mode in the air [42], so that the quantum dots reside in the high cavityfield region. This device structure can be employed for developing low-threshold nanolasers and fast optical switches at room temperature, which could be useful for developing integrated nanophotonic devices. Acknowledgments We thank Chad Ropp for help with silicon nitride deposition, and Joseph L. Garrett and Jeremy Munday for help with atomic force microscopy. We acknowledge funding support from the Physics Frontier Center at the Joint Quantum Institute (grant number PHY-0822671). We acknowledge the support of the Maryland NanoCenter.
#197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29619
of Electrical and Computer Engineering, Institute for Research in Electronics and Applied Physics, and Joint Quantum Institute, University of Maryland College Park, Maryland 20742, USA 2 [email protected] ∗ [email protected]
Abstract: We demonstrate spontaneous emission rate enhancement and saturable absorption of cadmium selenide colloidal quantum dots coupled to a nanobeam photonic crystal cavity. We perform time-resolved lifetime measurements and observe an average enhancement of 4.6 for the spontaneous emission rate of quantum dots located at the cavity as compared to those located on an unpatterned surface. We also demonstrate that the cavity linewidth narrows with increasing pump intensity due to quantum dot saturable absorption. © 2013 Optical Society of America OCIS codes: (230.5590) Quantum-well, -wire and -dot devices; (230.5298) Photonic crystals; (270.5580) Quantum electrodynamics.
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#197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29612
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1.
Introduction
Colloidally synthesized quantum dots are excellent emitters for developing light sources [1–5] and non-linear devices [6–12] operating at room temperature. These quantum dots exhibit high photoluminescence efficiency at room temperature [13,14] and emission wavelength tunability [15,16]. The spontaneous emission rate of the quantum dots can be enhanced by coupling them to small mode-volume cavities [17,18]. Photonic crystals create extremely small mode-volume cavities [19] that can reduce lasing threshold [20–28] and enable nonlinear devices at low lightlevels [11, 29–32]. #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29614
Previous measurements of CdSe quantum dots coupled to photonic crystal cavities have shown increased brightness when the quantum dots are resonant with the cavity mode [33–36]. Similar results have been shown for quantum dots near the band edge of two dimensional photonic crystals [37, 38]. Spontaneous emission rate enhancement and suppression of CdSe quantum dots coupled to band-edge modes of three dimensional photonic crystals have also been demonstrated [39]. Here, we demonstrate spontaneous emission rate enhancement and saturable absorption of CdSe(ZnS) colloidal quantum dots coupled to a nanobeam photonic crystal cavity. Using timeresolved measurements, we show an average spontaneous emission rate enhancement of 4.6 for an ensemble of quantum dots located at the cavity. We also demonstrate cavity linewidth narrowing due to quantum dot saturable absorption. These results represent an important step towards development of integrated nanophotonic devices operating at room temperature. 2.
Time-resolved lifetime measurements
Nanobeam photonic crystal cavities have been extensively studied numerically [40–42], and have been experimentally demonstrated in a number of previous works [43–46]. We utilize a cavity design proposed by Khan et al. [45]. Figure 1(a) shows the device structure and the calculated mode profile for the cavity. We calculate the cavity mode using numerical three dimensional finite-difference time-domain simulations (Lumerical Solutions). The cavity design consists of a 200-nm-thick and 300-nm-wide silicon nitride (SiN) beam with a one-dimensional periodic array of air holes (a = 250 nm and r = 70 nm). The cavity is formed by linearly reducing the lattice constant from a = 250 nm to a0 = 205 nm and the hole radius from r = 70 nm to r0 = 55 nm over a span of 4 holes at the center of the beam (symmetrically on both sides). r
r0
a
(c) 2500 a0
0
(b)
1
Intensity (a.u.)
(a)
Cavity Unpatterned surface
2000 1500 Q = 9900 1000
500 nm
640
645 650 655 Wavelength (nm)
660
Fig. 1. (a) Electric field intensity (|E|2 ) profile of the resonant cavity mode. (b) Scanning electron microscope image of a nanobeam photonic crystal cavity. (c) Photoluminescencespectra of CdSe (ZnS) colloidal quantum dots located at the cavity and on unpatterned silicon nitride surface at room temperature.
We fabricate the device on 200-nm-thick stoichiometric SiN deposited on silicon using low pressure chemical vapor deposition. We pattern the nanobeam photonic crystal cavities using electron-beam lithography and fluorine-based inductively coupled plasma dry etching. The underlying silicon is etched by aqueous KOH to create a suspended beam. A scanning electron microscope image of a fabricated device is shown in Fig. 1(b). We disperse CdSe(ZnS) (Invitrogen Qtracker CdSe/ZnS 655 nm) quantum dots on the device by drop-casting a 10 nM aqueous solution and dabbing off the excess solution after 10 minutes. We note that due to this deposition technique, the quantum dots are not dispersed uniformly on the surface of the devices. Using atomic force microscopy, we determine the average density of the quantum dots on a nanobeam to be ≈50 μ m−2 . To avoid oxidation and photo-bleaching of the quantum dots during the experiment, we load #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29615
the device into a sealed chamber filled with purified nitrogen gas. For lifetime measurements, we illuminate the sample with 70 ps laser pulses at 405 nm wavelength and a repetition rate of 5 MHz (PDL800B, LDH-P-C-405B, PicoQuant). We set the average power to 500 nW to avoid creation of biexcitons and, thus, minimize the effect of excitation power on the measured lifetimes [47]. The laser excitation spot is about 1 μ m in diameter. The photoluminescence signal from the sample is collected using an objective lens with numerical aperture of 1.3. Of the collected signal, 25% is used for imaging and the rest is split equally between a grating spectrometer and a photon counting module (Picoquant MPD along with Picoharp 300) for simultaneous spectral and time-resolved lifetime measurements. We use a spatial filter to collect light only from a 1 μ m region around the cavity, and a spectral filter with 40 nm bandwidth (Semrock FF01-655/40-25) to reject all light outside the quantum dot bandwidth. Figure 1(c) shows typical photoluminescence spectra obtained by exciting the cavity region as well as an unpatterned region away from the nanobeam. The spectrum of ensemble of quantum dots located on an unpatterned region exhibits a broad homogenous linewidth of 21 nm. In contrast, the cavity spectrum exhibits a bright peak at the cavity resonant wavelength of 646.1 nm. We fit the cavity spectrum to a Lorentzian function to determine a quality factor of Q = 9900. Cavity Unpatterned surface
10−1 10−2 0
50 100 Time (ns)
150
(b) 6
Measurements
Normalized Counts
(a) 100
Cavity Unpatterned surface
4 2 0 0
2
4
6
8 10 12 Lifetime, τavg (ns)
14
16
18
20
Fig. 2. (a) Time-resolved lifetime measurements of the quantum dots located at the cavity and on unpatterned silicon nitride surface (spectra shown in Fig. 1(c)). The stretched exponential fits are shown by solid curves. (b) Histogram of the lifetime (τavg from stretched exponential fit) from 29 different devices from 3 separately fabricated samples. The Gaussian fits are shown by dashed curves.
Figure 2(a) plots time-resolved lifetime measurement of the quantum dot emission collected from the cavity and an unpatterned region away from the nanobeam. We normalize the curves with respect to their count rates at time t = 0. The cavity fluorescence decays faster than the fluorescence from the unpatterned surface. Both temporal decays (on and off the cavity) exhibit a multi-exponential behavior. Multi-exponential decays in quantum dots have been previously studied and attributed to temporal fluctuations in non-radiative relaxation pathways due to changes in electronic or structural environment of the quantum dots [48, 49]. Cavities can induce additional fluctuations through variations in quantum dot positions and dipole orientations relative to the cavity field, which leads to different spontaneous emission enhancements [39, 50]. Two main decay models have been proposed for studying multi-exponential decay processes: stretched exponential fit [49] and log-normal fit [50, 51]. Here we use a stretched exponential fit given by β (1) I(t) = I0 + Ae−(t/τse ) where I(t) is the photoluminescence intensity at time t, I0 is the background intensity level, τse
#197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29616
is the 1/e decay lifetime, β is the stretch parameter, and A is a scaling constant. The stretch parameter β ranges between 0 and 1, and is inversely related to the variance of the decay rate (β = 1 corresponds to a single-exponential). From the stretched exponential fit, the average decay lifetime of the ensemble can be calculated by 1 τse (2) τavg = Γ β β where Γ is the Gamma function. We fit the lifetime data shown in Fig. 2(a) to Eq. (1) by treating τse , β , and A as fitting parameters. The solid lines in Fig. 2(a) represent the fitted values. These fits correspond to τse = 0.32 ns and β = 0.36 for quantum dots located at the cavity, and τse = 5.35 ns and β = 0.62 for quantum dots located on the unpatterned silicon nitride surface. Using Eq. (2), we calculate the average lifetime, τavg , for quantum dots located at the cavity to be 1.5 ns and quantum dots located at unpatterned silicon nitride surface to be 7.66 ns. We performed lifetime measurements on 29 different devices from 3 separately fabricated samples. Figure 2(b) plots τavg for all these measurements. The dashed curves are Gaussian fits to both the lifetime distributions. We observe a mean lifetime of 1.25 ns for quantum dots located at the cavity and 5.74 ns for quantum dots located on unpatterned silicon nitride surface, leading to an average spontaneous emission rate enhancement of 4.6. For quantum dots on the unpatterned surface we observe a shorter lifetime than those typically reported for single quantum dots deposited on glass [49, 52]. This reduction may be caused by modification of the local density of states due to the larger dielectric constant of SiN [53, 54] and Forster energy transfer between quantum dots [55]. Nonradiative decay may also contribute to the measured lifetimes. Because quantum dots are deposited on the device after the fabrication process, they are expected to have the same non-radiative decay rate regardless of whether they are deposited on the cavity or the unpatterned surface. In this case, the measured decrease in lifetime provides a lower bound on the actual spontaneous emission enhancement factor. The spontaneous emission enhancement factor for a quantum dot located at position r in the cavity, defined as F(r) = γ (r)/γ0 where γ (r) is the decay rate of the quantum dot located at the cavity and γ0 in free space, assuming dipole transition resonant and emitting in the same polarization as the cavity mode is given by [56]: F(r) = 1 +
3λ 3 Qqd ψ (r) 4π 2 n2 V
(3)
In the above equation, λ is the cavity-mode wavelength, Qqd = λ /Δλqd is the quantum dot quality factor, Δλqd is the quantum dot linewidth, n is the refractive index of the cavity dielectric, V = d 3 rε (r)|E(r)|2 /[ε (r)|E(r)|2 ]max is the cavity mode volume, ε (r) is the relative dielectric constant, and ψ (r) = |E(r)|2 /[|E(r)|2 ]max is the ratio of cavity-field intensity at location r to the maximum cavity field intensity. We note that the above equation is different from the conventional expression for the spontaneous emission rate enhancement factor and depends on the quality factor of the quantum dot, not the quality factor of the cavity. This difference is attributed to the fact that the homogeneous linewidth of the quantum dots is broader than the cavity, and therefore, our cavity-quantum dot system lies in the bad emitter limit [18, 57]. We set SiN refractive index to n = 2.01 [58] and single quantum dot linewidth to Δλqd = 15 nm [59]. Using finite-difference time-domain simulations, we calculate V = 0.57(λ /n)3 , λ = 642.6 nm, and ψ = 0.355 for a quantum dot located at the field maximum on the top surface of the nanobeam cavity. Plugging these values into Eq. (3), the maximum spontaneous emission rate enhancement is calculated to be 5.1. The calculated value for the spontaneous emission rate enhancement agrees with the measured value. #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29617
3.
Saturable absorption measurement
Just as the cavity can affect the quantum dots by enhancing spontaneous emission, the quantum dots can affect the cavity through absorption which degrades the cavity Q. Because quantum dots saturate at high pump intensity, the cavity will exhibit intensity-dependent linewidth. Saturable absorbers in a cavity can create enhanced nonlinear optical effects such as optical bistability [6–8, 60], optical switching [10, 12], and passive mode locking [61]. (b) 10000
measuremen t
Q
Time sequen ce of
8000
)
644 Wavelength644.5 (nm)
10 645 70
po w
1
er
(μW
1 0.5 0
Intensity (a.u.)
6000 0.01 (c) 0.1
Inp ut
Normalized intensity
(a)
6000 4000 2000 0
Increasing power Decreasing power fit
20 40 Input Power (μ W)
60
Fig. 3. (a) Normalized cavity spectrum for different input pump power levels. The green curved arrows show the time sequence in which the cavity spectra were measured. (b) Cavity Q as a function of input pump power. (c) Integrated cavity photoluminescence intensity as a function of input pump power.
In order to create sufficient quantum dot absorption to decrease Q, we increase the quantum dot density by performing five deposition steps on the device, as opposed to the single deposition step used for lifetime measurements. Using atomic force microscopy, we determine the average quantum dot density on a nanobeam to be ≈ 250 μ m−2 . We increased the pulsed laser repetition rate to 20 MHz to get higher signal. The collected photoluminescence signal is sent to a grating spectrometer to measure the cavity spectrum. Figure 3(a) shows the normalized cavity spectrum for several different input powers (the green arrows show the time sequence in which the cavity spectra were measured). We gradually increase the input power from 10 nW to 70 μ W, and the corresponding spectra are shown in blue. Once the input power level is at 70 μ W, we gradually decrease the input power back to 10 nW, and the corresponding spectra are shown in red. We observe that the cavity spectrum narrows with higher input power and becomes broad again when the input power is decreased back. We also observe an irreversible shift in resonance wavelength at higher input powers, which may be caused by photo-induced damage to the quantum dots [59] or cavity membrane at high intensities. Figure 3(b) plots the cavity Q as a function of input power, determined by performing a Lorentzian fit to the cavity spectrum. The blue circles show the cavity Q when the input power is gradually increased from 10 nW to 70 μ W, and the red dots represent the Q when the input power is gradually decreased back to 10 nW. In the increasing power cycle, Q increases from 6700 at 10 nW to 10400 at 70 μ W. The increase in cavity Q as a function of pump power is due to quantum dot saturation, which reduces the absorption in the cavity. In the decreasing power cycle, the cavity Q does not fully recover to its original value, but reaches a slightly higher value of 7400. This behavior is attributed to photo bleaching of quantum dots at higher powers during the increasing power cycle, which leads to a slightly lower absorption. The solid curve, in Fig. 3(b), is a fit to a model based on a cavity coupled to a homogeneous saturable absorber, where Q is given by [62]: 1 1 1 1 = + (4) Q Qc Qab 1 + P/Psat where Qc is the quality factor of the bare cavity, Qab is the quality factor due to quantum dot #197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29618
absorption at low (unsaturated) powers, P is the input power, and Psat is the saturation power. We fit the quality factor data, obtained for increasing power cycle, to the above equation, treating Qc , Qab and Psat as fitting parameters. We obtain the best fit, shown as a solid curve in Fig. 3(b), for Qc = 10500, Qab = 19600, and Psat = 2.98 μ W. The cavity emission intensity provides further evidence that saturable absorption is the dominant mechanism for linewidth narrowing. Figure 3(c) plots the integrated cavity photoluminescence intensity as a function of input power, determined by performing a Lorentzian fit to the cavity spectrum. The blue circles represent the intensity when the input power is gradually increased from 10 nW to 70 μ W, and the red dots represent the intensity when the input power is gradually decreased back to 10 nW. The integrated cavity photoluminescence intensity increases linearly with increasing input power and eventually saturates. The solid curve in Fig. 3(c) is a fit to a saturable absorption model given by [63] Ic =
αP 1 + P/Psat
(5)
where Ic is the photoluminescence intensity and α is a proportionality constant. Figure 3(c) shows the best-fit results where we treat α as a fitting parameter and use the calculated Psat from Eq. (4). The fit is performed for the data obtained for increasing power cycle, and exhibits good agreement with the experimental measurements. Both the intensity and the cavity Q saturate with the same Psat , providing strong support for saturable absorption as the dominant mechanism for the intensity dependent cavity linewidth. When the power is decreased back down, the observed intensity values during the decreasing power cycle are lower than those in the increasing power cycle. This behavior is irreversible, it does not recover when we increase the power back up on subsequent power cycles but instead further degrades. It is therefore not due to power hysteresis effects such as thermal or optical bistability, which typically require direct resonant excitation of the cavity mode. This reduction in intensity is caused by photo-bleaching of quantum dots at higher input powers, and is also consistent with the fact that Q does not drop down completely to its original value (Fig. 3(b)). 4.
Conclusion
In conclusion, we have demonstrated spontaneous emission rate enhancement and saturable absorption of CdSe quantum dots coupled to a nanobeam photonic crystal cavity. We obtained a factor of 4.6 increase in the average spontaneous emission rate. These results could be further increased by either embedding the quantum dots in the dielectric [35] or by designing cavities which confine the mode in the air [42], so that the quantum dots reside in the high cavityfield region. This device structure can be employed for developing low-threshold nanolasers and fast optical switches at room temperature, which could be useful for developing integrated nanophotonic devices. Acknowledgments We thank Chad Ropp for help with silicon nitride deposition, and Joseph L. Garrett and Jeremy Munday for help with atomic force microscopy. We acknowledge funding support from the Physics Frontier Center at the Joint Quantum Institute (grant number PHY-0822671). We acknowledge the support of the Maryland NanoCenter.
#197171 - $15.00 USD Received 6 Sep 2013; revised 10 Oct 2013; accepted 8 Nov 2013; published 22 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.029612 | OPTICS EXPRESS 29619
