1. INTRODUCTION

The multitude of refinements of fluorescence microscopy from first attempts at the beginning of the 20th century [1] to single-molecule sensitivity in living cells [2–4] has transformed biological exploration over the last hundred years. Meanwhile, stimulated emission (StE), an alternative radiation process theoretically described by Einstein in 1917 [5,6], has seen relatively little development as an image-forming signal. The sensitivity of fluorescence microscopy can be attributed to the de-coupling of excitation light properties and the resulting spontaneous emission: the dipole radiation pattern of this Stokes-shifted light can be easily separated from its excitation source both spatially and in wavelength, resulting in background-free imaging for good-quality samples. This sensitivity of fluorescence comes at several costs: i) not all emission angles can be collected, ii) the resulting light is spectrally broadband and of random phase, so it is unsuitable for conventional interferometry with a reference source except at low temperatures [7], and iii) the dwell-time in the bleaching-prone excited state is not a simply controlled parameter, but rather a property of the molecule and its environment, which sets an ultimate limit on rate of emission.

The processes of fluorescence and stimulated emission both begin by pumping a molecule in a low electronic state (often the ground state singlet, ${{\rm S}_0}$) to an excited state (e.g. ${{\rm S}_1}$), as shown in Fig. 1(a). In condensed phase media, after a fast (picosecond) vibrational relaxation, the molecule lingers in the vibrational ground state of this excited electronic state for the excited state lifetime on the order of ns for electric-dipole-allowed transitions. The process of StE occurs when the molecule is not allowed to then relax spontaneously by either fluorescence emission or internal conversion, but is instead driven to a lower state (such as a vibrationally excited state of ${{\rm S}_0}$) by incident light, radiating light with the same energy as the incident field. For this transition to be favorable, this StE-driving field, the probe, is chosen to be red shifted from the original pumping wavelength to account for the energy lost by vibrational relaxation in the excited and ground states with probability given by Frank-Condon overlap integrals.

 

Fig. 1. (a) Jablonski diagram showing the energy levels relevant for stimulated emission (StE), fluorescence, and internal conversion is assumed small. Input pump (yellow) and (red, optionally delayed) probe photons are drawn on the side, as are the exiting probe and probe-wavelength StE photons. (b) ATTO 647N absorption (black) and emission spectra (red) for fluorescence (fluor.), partially depleted fluorescence (light blue), and the effective emission spectra when StE is being generated (dashed purple). The pump and probe wavelengths are shown on the lower axis, along with our fluorescence and StE channel transmission spectra (orange and blue, respectively). (c) Diagram of the total internal reflection (TIR) probe setup. (d) Two-channel detection path diagram. NF: notch filter, LP: long pass.

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The resonant interaction with the incident light imparts a coherence, implying a fixed phase and wavelength of StE. Rather than emitting fluorescence, with its broad probability distribution of resulting wavelength [see Fig. 1(b)], the spectral width of StE will be set by the probe. StE competes with fluorescence as a relaxation pathway from the excited state, leading to (partial) depletion of fluorescence across most of the emission spectrum, other than the probe spectral region for which there is an increase in emission signal due to StE gain. This effective emission spectrum is depicted in Fig. 1(b) for the highly fluorescent ATTO 647N emitter given a 10% fluorescence depletion effect (simplifying here by ignoring quantum yield and excited state absorption).

The propagation direction and spatial profile are, however, not necessarily implied by the coherence of StE. The extent to which the structure and orientation of the molecule play a role has been given little attention, in part because the emission pattern of StE from an extended distribution of emitters, as found in laser gain media, is clearly dominated by the spatial pattern of the probe. Multiple ideas remain prevalent in the literature about the directionality of stimulated emission from a subwavelength emitter, ranging from StE itself radiating in a straightforward dipole pattern [8] to spatially mode-matched directional emission [9,10], as well as careful theoretical studies where StE arises from the interference between a dipole field and the probe field [11,12]. Experimental groups targeting stimulated emission imaging have formed images working with different physical pictures for StE propagation; however, these experiments have all used a transmitted light configuration, meaning some stimulated emission would reach their detectors regardless of the nature of its propagation.

Here, we present an experiment that generates StE using a driving field that is not incident on our detector [see Fig. 1(c)], yet features high detection sensitivity for radiation emitted in a dipole pattern. This unique configuration allows us to test whether StE from a sub-wavelength ensemble of emitters can be detected as classical torus-like dipole emission in the far-field or not. We perform our tests using ATTO 647N, a molecule that has been shown to efficiently produce StE, with a small excited state absorption rate at our chosen probe wavelength, such that observed fluorescence depletion serves as a calibration of the amount of StE generated [13]. Imaging sample emission in two spectral windows simultaneously [Fig. 1(d)], we can directly compare the signal modulation due to probe excitation in a fluorescence-only window as well as in a probe-overlapping spectral window. Using ATTO 647N-doped subwavelength polymer beads, we observe only fluorescence depletion in both the fluorescence and StE channels, proving that StE does not radiate into a simple dipole pattern.

2. METHODS

A. Probe-TIR Microscope

We introduce our pump beam in a typical epifluorescence configuration, from an air-space objective below the sample [see Figs. 1(c) and S1, Table S1, and Supplement 1 Note 1]. To stimulate emission from a sample without collecting incident probe light on our detector, we introduce the ${ s}$-polarized probe at a 45° angle from above and through a prism. After the probe is incident on an index-matched sample layer, it undergoes total internal reflection (TIR) off the bottom coverglass-air interface, and is reflected upward and thereby diverted from our detection path below. The objective below the sample collects dipole radiation: fluorescence emission, probe scatter, and potentially stimulated emission.

A Glan-laser polarizer is placed in infinity space to attenuate remaining probe scatter collected by the imaging objective, as shown in Fig. 1(d). This scattering signal results from imperfections in the sample itself or in the glass surfaces, and from small refractive index differences between the polymers and the glass. The probe will preferentially drive StE from pumped molecular emitters according to their transition dipole projection along the probe’s linear polarization, which is the same orientation nulled by the emission path polarizer. Considering a large ensemble of fixed-orientation dipole emitters, the net field from their combined emission will cancel away from the probe polarization and will tend to be nulled by the polarizer unless symmetry is broken by preferentially pumping dipoles oriented away from the probe polarization. We therefore introduce the pump beam with linear polarization at 45° (see Fig. S2).

 

Fig. 2. Pump-probe pulse timing schemes for differential StE and fluorescence measurements. (a) Pump-probe pulse timing suitable for generating StE (termed, P0), where the pump beam arrives just before the probe beam such that the probe interacts with a large excited state population. (b) Pump-probe pulse timing P1, where the pump beam arrives after the probe beam, and several 3.5 ns fluorescence lifetimes before the next probe beam pulse arrives (12.5 ns period), such that no stimulated emission is generated. (c) Long-pulse P0 pulse timing, again suitable for generating stimulated emission, using camera frames synchronized to a 50% duty-cycle chopper in the probe beam path. (d) Long-pulse P1 pulse timing, where no stimulated emission is generated but the pump and probe fluences are the same as for a P0 camera frame.

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The 45° polarization difference between the pump and probe beam reduces the efficiency of generating StE by ${1/3}$. We expect the polarizer to transmit half of the fluorescence emission, which we denote as ${T_{\rm f}} = 0.5$, and to transmit a lesser portion of generated StE, ${T_{\rm s}} \approx 0.15$. We refine these values to ${T_{\rm f}} = 0.57$ and ${T_{\rm s}} \approx 0.21$ using measured pump and polarizer orientations (see Fig. S3 and Supplement 1 Note 2).

A tube lens after the polarizer forms the primary image plane, which is then relayed by a ${4f}$ telescope and split into two spectral windows using a dichroic mirror. One spectral window collects fluorescence emission (698/70 nm), the fluorescence channel, while the other is matched to the probe beam excitation filtering (750/10 nm), the StE channel. Both spectral channels are imaged simultaneously on two regions of the same sCMOS camera.

B. Differential Measurement

To sense an effect due to StE in the presence of background signal from probe scatter, we employ a differential lock-in measurement scheme. We modulate the detected signal by generating two distinct pump-probe relative timings, which either generate stimulated emission (P0 timing) or do not generate stimulated emission (P1 timing), without changing the time-averaged illumination intensity present in either channel. In this way, we can subtract camera frames integrating P1 pulse trains from camera frames integrating P0 pulse trains to remove scatter and fluorescence to obtain a StE difference image. With short pulses (less than the fluorescence lifetime), it is possible to be very efficient at generating StE, using lower intensity than would be required for the same effect size with continuous wave (CW) beams. However, these short pulses serve to synchronize StE events from multiple emitters present in the sample, while long pulses (orders of magnitude longer than the fluorescence lifetime) result in more temporally spread events. We explore both regimes in our experiments.

In the short-pulse regime, we use pulsed lasers with a repetition rate of 76 MHz and pulse widths of 90 and 200 ps for the pump and probe, respectively, as is typical for previous stimulated emission depletion (STED) microscopy with these lasers [14]. In the P0 timing [Fig. 2(a)], the pump creates an excited state population just before the probe beam arrives, generating stimulated emission during the early part of the spontaneous emission excited state lifetime. In the P1 timing [Fig. 2(b)] the pump arrival time is delayed, so that the probe beam arrives early, when there is no excited state population, and stimulated emission is not driven. Each camera frame integrates over 10 ms of either P0 or P1 pulse trains, and a fast switch toggles between directing P0 or P1 trigger pulses to the pump, synchronously with each camera frame (see Fig. S4 and Table S2), that is, at a rate of 100 Hz.

In the long-pulse regime, the pump and probe are both CW lasers, chopped by either an acousto-optic modulator (AOM) or optical chopper, respectively. The camera is synchronized to the probe chopper, and each 56 ms integration time camera frame begins with the arrival of the 28 ms probe pulse. The P0 timing is generated by overlapping a 23 ms pump pulse with the probe pulse, generating stimulated emission [Fig. 2(c)]. The P1 timing is generated by the 23 ms pump pulse arriving after the probe [Fig. 2(d)]. A fast switch toggles on every frame whether the pump AOM driver is given the early P0 or late P1 trigger (see Fig. S5 and Table S2), at a rate of 17.9 Hz.

C. Sample

In order to image a dye known to efficiently radiate StE, and with minimal scatter, we produced covalently labeled ATTO 647N 112 nm diameter poly(methyl-methacrylate) PMMA beads (see Supplement 1 Note 3). We sonicated and then diluted the beads in 1% poly(vinyl alcohol–vinyl acetate) (PVAVA) and spin-coated this solution on a #1.5 coverglass that had been plasma-etched with argon. Using a small drop of immersion oil matched to glass, a second coverglass was then mated on top of the sample. After mounting on the microscope, immersion oil was placed on top of the upper coverslip before lowering the prism into position [see Fig. 1(c)].

These 112 nm diameter beads are subwavelength in size for our 750 nm probe beam. Given the refractive index of PMMA is 1.48, the maximum emitter spatial separation for these beads is about $0.22\lambda$. This $0.22\lambda$ is an upper bound on the furthest apart two dye molecules can be within the bead and is an over-estimate for the average separation. We regard these beads as a reasonable target to test StE properties in a regime that is not influenced by conventional phasing effects one would expect from an extended distribution of coherently radiating dipoles (which would yield directional radiation [15]).

D. Series Acquisition and Analysis

Our microscope is controlled by the PYthon Microscopy Environment [16] using acquisition protocols for our short-pulse and long-pulse experiments (see Supplement 1 Note 4). Our acquisitions begin by stopping live acquisition on the camera and zeroing the divide-by-2 circuit that counts camera frames and toggles P0 and P1 pulse timings for the pump beam. This allows us to label each frame as a P0 or P1 frame throughout the acquisition. The camera is then started, and several camera frames are acquired with the probe shutter open and the pump shutter closed. This is then reversed to acquire several pump-only frames, after which both shutters are opened. Acquisition events are timestamped when the pump and probe shutters are opened or closed, and additional frames are dropped during post-acquisition analysis such that pump-only, probe-only, and both-laser frames do not include frames partially exposed during shutter movement. Image intensities are dark subtracted and converted to units of ${{\rm e}^ -}/{\rm s}$, ignoring the duty cycle of illumination. The pump-only and probe-only frames are averaged in time. A pixel position corresponding to the center of the bead in each channel is manually selected using the fluorescence spot in the pump-only average image, and used as the center position to crop an ${11}\;{\times}\;{11}$ pixel ROI around the bead in each channel.

We calculate the P0–P1 subtraction first in the time-forward direction, subtracting each P1 frame from the P0 frame that came before it, resulting in a series of frame-pair subtraction images. Leveraging that photobleaching is monotonic in time, we mitigate its effect in our lock-in measurement by additionally calculating the P0–P1 subtraction in the time reversed direction (subtracting each P1 frame from the P0 frame that came after it) and averaging. The resulting time-balanced P0–P1 subtraction therefore largely cancels the effect of photobleaching. We use the same bead ROI identified previously to calculate the ROI sum of this P0–P1 subtraction in time, and additionally average this P0–P1 subtraction series in time to reconstruct a StE difference image. Finally, we implement a negative control, where we perform the subtraction at half the frequency. This is accomplished by averaging a P0 and P1 frame together, and subtracting the average of the next P0 and P1 frames. This half-frequency negative control P0–P1 is again performed in the time-forward and time-reversed direction and averaged to mitigate the influence of photobleaching.

E. Expected Rate of StE

Imaging the sample with the same collection optics and direction in both fluorescence-only and probe-overlapping spectral windows, acquired simultaneously on the same camera, provides a useful internal calibration for our data where the common assumption is made that depleted fluorescence photons lead to StE events. For a measured rate of fluorescence depletion, ${D_{{\rm meas}}}[{{{\rm e}^ -}/{\rm s}}]$, we calculate an expected total rate of StE events in the sample, ${S_{{\rm abs}}}\;[{{\rm event}/{\rm s}}]$, as

We additionally wish to estimate what the detection rate of StE would be under the hypothesis that it emits into a simple classical dipole pattern, $S_{{\rm meas}}^{{\rm dipole}}$, which is given by

3. RESULTS

We first imaged 112 nm diameter ATTO 647N-labeled PMMA beads with the short-pulse train [Figs. 2(a) and 2(b)]. Pump-only fluorescence images in both channels are shown in Figs. 3(a) and 3(b), and as expected the signal strength is about 40-fold larger in the fluorescence-only channel than the StE channel (StE ROI sum/Fluor ROI sum: 0.020 measured, 0.025 expected). Probe-only images show some weak probe-excited fluorescence in the fluorescence channel [Fig. 3(c)] and are dominated by probe scatter in the StE channel [Fig. 3(d), note colorbar scales]. Looking in time at the bead ROI emission value summed in each channel on each frame [Fig. 3(e)], we see a clear modulation (note the vertical separation between the open and closed circles) that requires the presence of both beams, and calculate a fractional fluorescence depletion modulation of 12.5% [averaged over the first ${\tau _b}$ ($1/e$ time) of photobleaching]. The time-averaged P0–P1 subtraction image was averaged in time over the first ${\tau _b}$ ($1/e$ time) of photobleaching. Clear fluorescence depletion can be seen in the fluorescence channel [Fig. 3(f)]. Signal of the same (negative) sign, but lesser magnitude, is present in the StE channel subtraction image [Fig. 3(g)]. The half-frequency P0–P1 negative control analysis, averaged over the same duration, shows effectively no modulation in either channel [Figs. 3(h) and 3(i); colorbars are the same as for Figs. 3(f) and 3(g), respectively].

 

Fig. 3. Typical short-pulse experimental results. 112 nm ATTO 647N-labeled PMMA bead in the focus of our microscope imaged concomitantly in a (a), (c), (f), (h) fluorescence-only channel and (b), (d), (g), (i) probe-overlapping spectral channel using ${\sim}{100}\;{\rm ps}$ pump and probe pulses. Units for each image are in detected photoelectrons/s. (a), (b) Pump-only frames show simple fluorescence images of the bead in both channels. (c), (d) Probe-only frames detect probe-excited fluorescence in the fluorescence channel (c) and are dominated by probe scatter in the probe-overlapping channel (d). (e) The bead ROI signal in each channel is summed over each of the first 100 frames and plotted. The fluorescence data points are filled or hollow for P0 or P1 frames, respectively. The vertical black line indicates the first time point considered in the following subtraction analysis (f)–(j). (f), (g) ${\rm P}0 - {\rm P}1$ subtraction images, averaged over the first ${\tau _b}$, show fluorescence depletion in both channels. (h), (i) Half-frequency negative control subtraction images averaged over the same period show no modulation in either channel. Colorbar scales for (h) and (i) are the same as (f) and (g), respectively. (h) is outlined in black to show the border despite the low contrast. (j) The ${\rm P}0 - {\rm P}1$ subtraction images are summed in each channel over the bead ROI and plotted. An arrow points to the slight negative dip observed in the StE channel data. The expected fluorescence depletion present in the StE channel is plotted (black), as well as the hypothetical StE channel gain for dipole-patterned StE. Similar results occurred for ${\sim}{10}\;{\rm s}$ of other beads and with other samples.

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The fluorescence depletion signal clearly serves as a useful calibration to be able to estimate the expected size of any StE signal, if the StE signal has a dipole emission pattern like fluorescence. Using the ratio of pump-only fluorescence detection between the fluorescence and StE channels, we scale the fluorescence depletion signal [Fig. 3(j), orange], to calculate the fluorescence depletion signal we would expect to observe in the StE channel in the absence of any StE gain [Fig. 3(j), black]. We find excellent agreement between the expected fluorescence depletion in the StE channel, and the measured StE channel subtraction signal [Fig. 3(j), blue], with the average difference between the two well within one standard deviation of zero (${1.7 \times 10^3}$ [${{\rm e}^ -}/{\rm s}$] average difference over the first ${\tau _b}$, ${1.4 \times 10^4}$ [${{\rm e}^ -}/{\rm s}$] standard deviation). Given that any hypothetical dipole-patterned StE should result in a large positive StE gain signal in that channel [Fig. 3(j), purple], we conclude that for the case of a subwavelength-extent ensemble of emitters simultaneously driven to radiate StE, StE is about 139-fold smaller (averaging ${\le} {1.7 \times 10^3}$ [${{\rm e}^ -}/{\rm s}$] over the first ${\tau _b}$) than expected for dipole emission (purple curve, $2.3 \times {10^5}$ [${{\rm e}^ -}/{\rm s}$] average over the first ${\tau _b}$), strongly showing that StE does not radiate in a simple dipole pattern.

To explore conditions with different collective coherence properties, we repeated our experiment using continuous wave lasers chopped to centisecond pulses [see Figs. 2(c) and 2(d)] and present the results in Fig. 4. While these long pulses reduce the efficiency with which we can modulate StE (here we achieve 3.6% fractional fluorescence depletion), the emission events are now dramatically spread out in time. The ${\sim}{5 \times 10^4}$ [${{\rm e}^ -}/{\rm s}$] fluorescence depletion measured at the start of the acquisition before photobleaching [see Fig. 4(j)] corresponds to an expected ${1.3 \times 10^6}$ StE events per second. Under the assumption these events are uniformly random in time, their average separation would be about 0.77 ms. With emission events separated an average of about 220 fluorescence lifetimes, we consider this regime to be quasi-single emitter and a valid test of whether StE radiates into a dipole pattern in the absence of ensemble effects. Here, we again see clear fluorescence depletion in the fluorescence channel [Fig. 4(f)], and this modulation disappears when the subtraction is done at half the frequency [Fig. 4(h)], or in the absence of both lasers [Fig. 4(e)]. While the signal-to-noise is degraded relative to the short-pulse case, the subtraction analysis in the StE channel [see Fig. 4(g), and blue points in Fig. 4(j)] clearly does not show strong StE gain. The difference between the StE channel subtraction signal and the expected fluorescence depletion in that channel [Fig. 4(j), black] is within one standard deviation of zero (190 [${{\rm e}^ -}/{\rm s}$] average difference over the first ${\tau _b}$, ${6.3 \times 10^3}$ [${{\rm e}^ -}/{\rm s}$] standard deviation), and 104-fold lower than would be expected for a hypothetical dipole emitter [Fig. 4(j), purple, ${2.0\times 10^4}$ [${{\rm e}^ -}/{\rm s}$] average over the first ${\tau _b}$]. We therefore conclude that even in the absence of ensemble effects, StE does not radiate in a simple dipole pattern.

 

Fig. 4. Typical long-pulse experimental results. 112 nm ATTO 647 N-labeled PMMA bead in the focus of our microscope imaged concomitantly in a (a), (c), (f), (h) fluorescence-only channel and (b), (d), (g), (i) probe-overlapping spectral channel using ${\sim}{25}\;{\rm ms}$ pump and probe pulses. Units for each image are in detected photoelectrons/s. (a), (b) Pump-only frames show simple fluorescence images of the bead in both channels. (c), (d) Probe-only frames detect probe-excited fluorescence in the fluorescence channel (c) and are dominated by probe scatter in the probe-overlapping channel (d). (e) The bead ROI signal in each channel is summed over each of the first 100 frames and plotted. The fluorescence data points are filled or hollow for P0 or P1 frames, respectively. The vertical black line indicates the first time point considered in the following subtraction analysis (f)–(j). (f), (g) ${\rm P}0 - {\rm P}1$ subtraction images, averaged over the first ${\tau _b}$, show fluorescence depletion in both channels. (h), (i) Half-frequency negative control subtraction images averaged over the same period show no modulation in either channel. Colorbar scales for (h) and (i) are the same as (f) and (g), respectively. (h) is outlined in black to show the border despite the low contrast. (j). The ${\rm P}0 - {\rm P}1$ subtraction images are summed in each channel over the bead ROI and plotted. The expected fluorescence depletion present in the StE channel is plotted in black, as well as the hypothetical StE channel gain for dipole-patterned StE (purple). Similar results occurred for other beads.

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4. DISCUSSION

Whether StE shares the same spatial profile and propagation direction as the incident field or radiates in a dipole pattern, as spontaneous emission does, has been a question of recent discussion [8,12]. The coherent properties of StE are appealing as an imaging contrast; however, reaching single-molecule sensitivity with StE has so far been impractical using standard fluorophores due to the difficulty in detecting StE appearing at the same wavelength as the probe in the presence of scattering backgrounds. A scheme to image StE without the probe beam being incident on the detector, as it is for standard transmission setups, could greatly benefit achievable sensitivity, but the feasibility of such a scheme would hinge on StE radiating in a manner distinct from the probe.

Treatment of StE from a two-state atom using quantum field theory leads to the result that StE photons share both the wave-vector and polarization of the probe [17]. This is consistent with our experiment results, but is distinct from the classical Lorentz oscillator picture of an oscillating charge on a spring (or in the simple quantum picture, the oscillation of the transition dipole moment) [15,18,19]. In these treatments, one would think that the driving field induces a polarization that could radiate (see Supplement 1 Note 5); however, most authors focus on calculating the energy contained in the interference between the probe and emitted field in the forward direction using the Poynting vector [11,12,15]. This interference is contained within the spatial extent of the probe beam, and so could not be detected without shot noise arising from the probe-only component of the Poynting vector.

Here, we configured a measurement, with non-zero probe fields in the sample, to produce stimulated emission fields with an off-axis detection path where the probe field ${E_{\rm p}} \cong 0$. Detecting from such an angle, the only (non-fluorescent) energy flowing towards the detector would be from the dipole-only component of the Poynting vector, which could occur from StE or Rayleigh scattering. Since Rayleigh scattering is not detectable in our modulated experiment (see Supplement 1 Note 5), by calibrating with the observed fluorescence depletion, we find that our results are not consistent with StE radiating in a classical dipole pattern. In other words, StE is not readily detectable in directions away from the probe beam. We hope applications relying on StE from subwavelength emitters benefit from this insight.