A novel method is proposed for generating sharper fluorescent super-resolution spot by azimuthally polarized beam in stimulated emission depletion (STED) microscopy. The incoherent superposition of azimuthally polarized beam with five-zone binary phase plate and the same beam with quadrant phase plate can yield a tightly focused doughnut spot surrounded completely and uniformly. And azimuthally polarized beam modulated by a vortex 0—2π phase plate works as pump beam. Compared with known effective excitation spot yielded by circular polarized STED beam, the azimuthally polarized beam result is shaper, as well as energy-saving, costing only ~50% of the energy cost by circular polarized beam. A STED beam of less intensity has the potential to reduce fluorescence photobleaching and photodamage in living cell imaging. In addition, the influence of Ez absence as well as FWHM of pump beam in the focal field is discussed.
© 2012 OSA
Breaking of the diffraction limit is widely discussed nowadays. STED is one of the methods that can realize it. In STED microscopy, switching of fluorophores into a dark state is used to confine the fluorescence to a small volume in the focal field. After its theoretical description in 1994 , STED microscopy was experimentally demonstrated in 1999 . Since its first implementation, the attainable resolution has been improved in several steps [3–6] to reach the current record of 5.8nm . Following these steps, it is found that resolution improvement depends mostly on the increasing of STED beam intensity, say from 450MW/cm2  to 8.6GW/cm2 . According to the relationship between resolution and the maximum intensity of STED beam that , the higher intensity of STED beam, the better resolution that will be achieved. High intensity may face a problem of stronger fluorescence photobleaching. Such as 5.8nm resolution can be realized only when crystal color centers are observed rather than fluorescent samples. How to achieve equally high-resolution using STED beam with low intensity is still a pending problem. Thus, more effective STED beams with different polarizations are being investigated.
In STED microscopy, circular polarized beam is widely used in generation of either 2D super-resolution spots  or 3D super-resolution spots . 3D super-resolution is also realized by STED-4pi technology [3, 9]. On the other hand, cylindrical vector beams receive more attention in STED microscopy recently, especially radially polarized beam and azimuthally polarized beam [10–13]. Applying radially polarized beam to total internal reflection (TIR) fluorescence in STED microscopy provides a way to achieve super-resolution . At the same time, 3D super-resolution spot can be generated by overlapping two beams as STED beam [12, 13]. Most of these researches just used cylindrical vector beams as either pump beam [10, 11] or STED beam , but rarely both pump beam and STED beam. Polarization match of cylindrical vector beams is crucial in STED microscopy. If the polarization direction of STED beam is in the same direction with the pumped fluorescent molecular orientation, the depletion effect will be most obvious. Using cylindrical vector beams of the same polarization as both STED beam and pump beam is gaining popularity for its strong depletion ability .
By only using azimuthally polarized Gaussian beam, a sharper fluorescent super-resolution spot with FWHM of ~19nm () but costing much less energy is achieved in this paper. The incident beam is split into two and modified by two phase plates respectively. The first beam is modified by a five-zone binary phase plate and generates a tightly focused dark spot (beam (1)). The second beam is modified by a quadrant phase plate and generates beam (2) which compensates the polarization of beam (1). The incoherent superposition of beam (1) and beam (2) generates the STED beam, and another azimuthally polarized beam passing though vortex phase plate works as pump beam.
2. Basic setup and theory analysis
Figure 1 shows the system constructed to create the STED spot. A linear polarized beam through the azimuthally polarization converter becomes azimuthally polarized beam. Then the azimuthally polarized beam is split into two branches. One passes through the five-zone binary phase plate (beam (1)), while the other one is modified by a quadrant phase plate (beam (2)) Then these two beams are overlapped incoherently and finally coaxially focused by an apochromatic lens. In this way, the STED beam is yielded.
The focusing is assumed to be done with a high numerical aperture (NA) oil-immersion apochromatic lens (AL) with NA = 1.4, and the refractive index of the oil is 1.518. All aberrations are ignored so that a diffraction-limited paraxial image can be expected to form exactly at the focal spot of the image plane. In case of high NA focusing, the scalar approximation is no longer valid, and polarization effects play a prominent part [14, 15]. According to the full vector diffraction theory, the electric field vectors near the focal spot can be obtained from the generalized Debye integral as [16, 17]18]Fig. 2 . And are marked in the figure.
For a quadrant phase plate, the phase plate is divided into four quadrants. The phase delay is
3. Result and discussion
3.1 Analysis of pump beam and STED beam focal fields
The simulated results are presented in the following intensity maps with side length of 2λ. Different focal patterns, that is, azimuthally polarized STED beam and circular polarized STED beam, are normalized to equal energy. For azimuthally polarized STED beam, it has two branches, beam (1) and beam (2). Beam (1) and beam (2) don’t share the input energy equally, but share by a certain ratio. When this ratio is used, the maximum intensities of STED beam’s four lobes, which form the doughnut-like spot, are equal. That is, the maximum intensity of beam (1) is equal to the maximum intensity of beam (2).At the same time, the input power of beam (1) and beam (2) is probably not equal. In this way, the STED beam achieves best special uniformity in terms of its depletion effect. The center of each intensity map is the geometrical focal point.
Beam (1) is azimuthally polarized Gaussian beam which passes through the five-zone binary phase plate. This phase plate was used to create a needle of longitudinally polarized light by radially polarized beam at first . When we apply azimuthally polarized beam instead of radially polarized beam to the system, a doughnut like spot with sharper focal dark center is created. Figure 3 shows the intensity of beam (1), as well as the vector components. The dark center is focused quite tight, and the light ring is circular symmetric (Fig. 3(a)). The tighter dark spots focus, the more depletion effective they are, and finally smaller the effective excitation spot is. Nevertheless, side-lobes are the negative side-effect caused by the binary phase plate. The influence of side lobes will be discussed in section 3.2. Figure 3(b) shows that the energy of Ex component is mainly distributed along Y axis. In Fig. 3(c), the energy of Ey is mostly distributed in X direction. The azimuthally polarized beam has no Ez component in the focal field.
Although beam (1) alone can generate uniform intensity doughnut-like spot (Fig. 3(a)), there is still a deficiency in polarization. In XY plane, Ex is only in Y axis, and Ey is only in X axis. Theoretically, when a pump beam has round shape Ex and Ey focal field, the STED beam should be circular ring so that it can deplete fluorescence uniformly in all three components. As for beam (1), Ex lacks energy distributed in X axis while Ey lacks that in Y axis. It is necessary to take the fluorescent molecular orientation into account. Every fluorescent molecule is in a certain orientation. If the polarization of the pump beam is in the same direction with orientation of fluorecent molecules, fluorescence will be excited to the maximum degree. It’s the same with STED beam. When polarization of STED beam is in the same direction with the excited fluorescent molecular orientation, the depletion effect is most obvious . Therefore, if beam (1) alone is applied as STED beam, Ex component of excited fluorescent molecules in X axis cannot be depleted by this STED beam. It’s the same with Ey component of excited fluorescent molecules in Y axis. Another beam is indispensible to compensate the polarization drawback of beam (1), which should have strong Ex component in X axis and Ey component in Y axis. Azimuthally polarized beam converted by quadrant phase plate matches the requirement (beam (2), Fig. 4 ). The intensity distribution is a symmetric cross shape with a very tightly-focused dark spot in the center (Fig. 4(a)). Although the light around the dark spot is not uniform, it is adequate as a compensation of beam (1) in the polarization. There is also no Ez in the focal field.
The incoherent superposition of beam (1) and beam (2) forms the STED beam in the simulated experiment (Fig. 5 ). The coherent superposition of beam (1) and beam (2) would lead to spot distortion. This phenomenon widely exists in the combination of different beams into one STED beam [12, 19], and several methods to avoid the distortion, that is, generate incoherent superposition, were realized [8, 12, 20, 21]. To achieve incoherent superposition, these two beams should be manipulated to work in temporal difference or spectral difference. For example, two beams forming a STED beam converge in turn, not at the same time . According to Fig. 5(a), the dark spot in the center of the STED beam focal field is quite tight, while the light around is symmetric and almost uniform. Side-lobes of STED beam will not result in serious problems. On the contrary, it may be helpful to deplete the side-lobes of the pump beam. In Fig. 5(b) and Fig. 5(c), the superposition of beam (1) and beam (2) successfully generates Ex and Ey , in both of which dark spot in the center is uniformly and completely surrounded with light, making a uniform depletion effect on the pump beam.
To match the polarization, the pump beam in the super-resolution fluorescent microscopy is also azimuthally polarized beam. Azimuthally polarized beam with no phase plate can yield a doughnut like spot . Azimuthally polarized beam with a vortex phase plate can generate a sharper focal spot than that generated by circular polarized beam [11, 22]. In the simulated experiment, we used azimuthally polarized beam modified by a vortex phase plate as pump beam (Fig. 6 ). After being depleted by STED beam, the effective excitation super-resolution spot is achieved.
To illustrate advantages of this method, we compared this result with STED microscopy using circular polarized beam, which is more widely used nowadays since it can excite the most potential fluorescence out of samples [5, 8, 23]. Using circular polarized beam as pump beam and STED beam yields a uniform effective excitation spot. And circular polarized beam can excite fluorescent molecules in all three directions, so fluorescent potential is excited mostly. However, it is faced with the problem of fluorescent bleaching sometimes for its strong excitation ability. For example, right handed circular polarized beam works as pump beam, and STED beam is generated by right handed circular polarized beam modified by vortex phase plate (Pump beam and STED beam are shown in Fig. 7 and Fig. 8 . After STED beam depletes the fluorescence excited by the pump beam, a super-resolution spot is generated.
Circular polarized beam excites fluorescence in all three local electric field components (Fig. 7 and Fig. 8). For STED beam in Fig. 7, the peak-to-peak distance of the doughnut crest is larger than that shown in Fig. 5, especially the distance in Ez component (Fig. 5(d)). Under the same intensity, the tighter STED beam focuses, the stronger depletion ability it has [7, 24]. Fluorescent molecules would be pumped in Z axis (Fig. 8(d)), however, the fluorescence cannot be depleted effectively by Ez of STED beam (Fig. 7(d)). As for the method using azimuthally polarized beam proposed in this paper, neither the pump beam nor the STED beam has Ez component in the focal field (this will be discussed in detail in 3.3 section). The fluorescent molecules in Z direction won’t be excited. The Ez component won’t be residual so that the depleted effect will be more effective. Although the peak intensity of azimuthally polarized STED beam is 3% less than that of the circular polarized STED beam because of the diffraction side lobes, however, the distance between two peaks of STED beam is smaller, so the depletion effect is better (Fig. 9(a) ).
3.2 Analysis and comparison in quantity
In order to make a specific comparison with the method using circular polarized beam, we set the same simulation parameters . We assumed the fluorescent sample consisted of a randomly oriented Rhodamine-6G molecules. The wavelength of the pump beam is 532nm, and the wavelength of the STED beam is 599nm. According to Eq. (5), we calculated the effective super-resolution spot using the vectors for the fluorescent depletion process, assuming a Lorentzian depletion ratio function [25, 26]. The ratio of the fluorescent intensity of the effective excitation beam after the STED beam depletion to that of the pump beam is defined as the depletion ratio, given by [12, 26]Eq. (5), ESTED is the electric field of the STED beam, n is the unit vector along the molecular transition dipole axis, and is a molecular constant that depends on the fluorescence lifetime τ and the dip cross section σdip , where the factor of 3 comes from averaging over random orientations. The value of C was found by fitting the measured value in the experiment , in which cm2, and fluorescence lifetime of ns of Rhodamine-6G. The maximum STED beam photon flux was 1027 photons/cm2s (~370MW/cm2). After the pump beam excited the fluorescent sample, the polarization of this fluorescence would be the same with pump beam, but with lower intensity. The simulated result is shown in Fig. 10 . Noticed that the effective spot is not exactly cylindrical symmetric but cross symmetric, the resolution in diagonal direction and that in cross direction (X or Y axis) are calculated respectively. There is nearly no difference between resolutions in these two orientation. Hence, the effective spot could be regarded as cylindrical symmetric approximately. Thus, it is reasonable to use the resolution in X axis representing the average resolution. According to Fig. 10, the FWHM of pump beam focal spot is ~201nm, and the FWHM of effective excitation focal spot is ~19nm (). Although the light is not depleted to zero around the sharp focal spot, the intensity is lower than 10% of the maximum value. Compared with the radii of the effective spot, this interval distance between side lobes is too large (~). Even though it excited fluorescence, the light could hardly be collected after filtered by a pinhole.
The result by using circular polarized beam is shown in Fig. 11 with the same parameters. The effective excitation focal field is highly concentrated without any side lobe. However, the FWHM of effective excitation spot is larger than the result in Fig. 10(b). The FWHM of pump beam focal spot is ~203nm, and the FWHM of effective excitation focal spot is ~29nm ().
Another more accurate description of STED beam fitting curve was published lately . The doughnut STED intensity pattern was described by a sinusoidal standing wave distributionEq. (5). For azimuthally polarized beam, this equation provides the simulated result Ieff = ~24nm (λ/22). And for circular polarized beam, Ieff = ~30nm (λ/18). These results are very close to FWHM calculated by Eq. (5).
This simulated result of circular beam is confirmed theoretically as following :24]. If the circular polarized beam result achieved FWHM of , ISTED should be as large as 767MW/cm2, which is ~2 times more than ISTED used in the proposed method (ISTED = 370MW/cm2).
Furthermore, the FWHMs of effective spots under different input power of STED beam are calculated. The results are shown in Fig. 12 . When input power is zero, the FWHM of effective spot is equal to that of the pump beam, ~201nm. As the input power increases, the FWHM of the effective spot decreases, and saturation happens.
Compared with the result by circular polarized beam, this novel method using azimuthally polarized beam has a significant improvement in energy saving when achieving the same resolution. In other word, the new method achieves higher resolution costing the same energy. Meanwhile, as a result of Ez absence in both the pump beam and the STED beam focal fields, Ex and Ey share higher energy considering the fact that laser output energy is fixed, which makes higher resolution. Actually, the FWHM of effective excitation spot is influenced mostly by STED beam rather than pump beam (discussed specifically in 3.4 section). Consequently, the new method using azimuthally polarized beam can achieve higher resolution.
3.3 Analysis of the Ez absence in azimuthally polarized beam focal field
Although azimuthally polarized beam lacks Ez component in the focal field, it has little influence on the super-resolution spot. For these fluorescent molecules in the same orientation of Z axis (Fig. 13 ), even the fluorescence is excited, it may not be effectively collected by the lens. The electric field is perpendicular to the propagation direction. Because the fluorescent molecule orientation is in Z axis, the excited fluorescence would propagate in XY plane. According to Fig. 13, only the fluorescence propagates out of XY plane might be collected by the lens. But the propagation direction of the fluorescent beam now is parallel to the sample’s upper surface, as well as the entrance pupil of the lens. In that way, the light cannot enter the lens, thus the light may be dissipated rather than effectively used. If the Ez component is too strong, it may not only waste energy, but also bleach the fluorescent sample. While the novel method avoids this energy waste problem by applying azimuthally polarized beam, because of the absence of Ez component in the focal spot.
This conclusion has been confirmed by experiment . This experiment applied azimuthally polarized beam as well, and the experiment result illustrated that the absence of Ez component had little effect on the sample images, because most light was collected and the sample’s information was hardly omitted. Hence, the new method can be applied in the STED microscopy system, even taking advantage of this property to save energy.
3.4 Analysis of the FWHM of pump beam
The role of the FWHM of pump beam focal spot will be discussed as following. In the experiment setup, nothing is changed except for the pump beam, compared with simulation configuration. Bessel Gaussian azimuthally polarized beam focused through a sharp opaque pad (Ropaque = 0.85Rtotal)  instead of Gaussian beam (as shown in Fig. 14 ). It’s clear that the FWHM of pump beam doesn’t play a significant role in STED microscopy. Detailed explanations are as follows.
Compared with Gaussian beam, focal field of Bessel Gaussian beam has remarkable side lobes. The side lobes of the pump beam might remain after depletion (e.g. Figure 10 (b)). At the same time, side lobes probably excite fluorescence so it may add extra burden to STED beam.
Figure 14 and Fig. 15 indicates that the Gaussian pump beam focal spot is much larger than Bessel Gaussian pump beam focal spot (201nm vs. 165nm), while Gaussian beam and Bessel Gaussian beam have almost no observable difference in the effective excitation spot (19nm vs. 17nm). This result illustrates that the FWHM of pump beam is a minor factor about the FWHM of effective excitation spot compared with the FWHM of STED beam. In most cases, the dark spot of STED beam is smaller than the pump beam focal spot, and the peak-to-peak distance of the doughnut crest is larger than the FWHM of the pump beam. The side lobe around the pump focal spot is larger than the surrounding light of STED, thus the outer edge of the side lobe will remain after the depletion. As a result, the depletion effect is related tighter to the peak-to-peak distance of the STED beam crest. On the other hand, sharper focal spot accompanies with more serious side-lobes sometimes. However, side lobes can be hardly depleted completely. Although they have little negative influence on the resolution, side lobes squander the total energy so they should be as dim as possible. For example, in Fig. 15(b), the effective excitation spot has more energy in side lobes. For the first side lobe, the intensity is nearly 20% of the maximum part. Consequently, it is not necessary to suffer serious side lobes just in order to achieve tighter focused pump beam in STED microscopy.
A proposed method for generating sharper fluorescent super-resolution spot is discussed in this paper. The STED beam forms by the incoherent superposition of azimuthally polarized beam with five-zone binary phase plate and the same beam with quadrant phase plate is tighter focused doughnut spot surrounded completely and uniformly in every electric field component. The same polarized beam with a vortex phase plate works as pump beam. The FWHM of effective excitation fluorescent spot is ~19nm (). At the same time, the novel method using azimuthally polarized beam is energy-saving, only costing ~50% energy compared with the method using circular polarized beam. The following conclusions are drawn in the simulated experiment. First, azimuthally polarized beam used in the STED microscopy system modified properly by phase plates can generate better effective excitation fluorescent spot. The absence of Ez component in the focal field has no observable negative influence on this experiment. Second, multi-zone binary phase plate is not only used for extending depth of focus but also facilitating the process to generate super-resolution fluorescent spot in the STED microscopy system. Third, the FWHM of pump beam is less important than the peak-to-peak distance of the doughnut crest of STED beam concerning the resolution issue.
We would like to express thanks to Dr. Nandor Bokor for all his help to our work. This work is financially supported by grants from the Doctoral Fund of Ministry of Education of China (20110101120061), the Qianjiang Talent Project (2011R10010) and the Fundamental Research Funds for the Central Universities (2012FZA5004).
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