Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy

Yi Xue; Cuifang Kuang; Shuai Li; Zhaotai Gu; Xu Liu

doi:10.1364/OE.20.017653

1. Introduction

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 [1], STED microscopy was experimentally demonstrated in 1999 [2]. Since its first implementation, the attainable resolution has been improved in several steps [3–6] to reach the current record of 5.8nm [7]. Following these steps, it is found that resolution improvement depends mostly on the increasing of STED beam intensity, say $I_{S T E D}^{\max}$ from 450MW/cm² [4] to 8.6GW/cm² [7]. According to the relationship between resolution $Δ x$ and the maximum intensity of STED beam $I_{S T E D}^{\max}$ that $Δ x \propto λ_{S T E D} / \sqrt{I_{S T E D}^{\max} / I_{s}}$ [7], 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 [6] or 3D super-resolution spots [8]. 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 [10]. 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 [13], 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 [12].

By only using azimuthally polarized Gaussian beam, a sharper fluorescent super-resolution spot with FWHM of ~19nm ( $λ / 28$ ) 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 $0 / π$ 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 $02 π$ 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 $0 / π$ 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.

Fig. 1 (a) The system constructed to create the STED spot. PC: azimuthally polarization converter; BS: beam splitter; PP1: five-zone binary $0 / π$ phase plate; PP2: quadrant $0 / π$ phase plate; AL: apochromatic lens. Laser: linear polarized Gaussian beam. (b) 3D view of the two phase plates

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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]

\vec{E} (r_{2}, φ_{2}, z_{2}) = i C \iint_{Ω} \begin{array}{l} \sin (θ) \cdot A_{1} (θ, φ) \cdot A_{2} (θ, φ) \cdot [\begin{array}{l} p_{x} \\ p_{y} \\ p_{z} \end{array}] \cdot \exp [i k n (z_{2} \cos θ + r_{2} \sin θ \cos (φ - φ_{2}))] \\ \cdot \exp [i Δ α (θ, φ)] d θ d φ \end{array} .

A_{1} (θ, ϕ)

is the amplitude function of the input light, and

A_{2} (θ, ϕ)

is related to the structure of the imaging lens,

{[\begin{matrix} p_{x} & p_{y} & p_{z} \end{matrix}]}^{T}

is a matrix unit vector of the incident beam polarization, and

Δ α (θ, ϕ)

is the phase delay of phase plate (PP1 and PP2 are different in phase delay). The incident beam is Gaussian beam, focusing by the widely-used aplanatic microscope objectives. For the binary phase plate, it modifies the beam by the transmission function

T (θ)

, where

T (θ) = \exp [i φ (θ)]

.We used a five-belt optical element with [18]

T (θ) = {\begin{matrix} 1, for 0 \leq θ < θ_{1}, θ_{2} \leq θ < θ_{3}, θ_{4} \leq θ < α, \\ - 1, for θ_{1} \leq θ < θ_{2}, θ_{3} \leq θ < θ_{4} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} \end{matrix} .

The four angles

θ_{i} (E_{Z})

, corresponding to four radial positions

r_{i} = \sin θ_{i} / N A

(normalized to the optical aperture), are optimized to deplete the intensity in the center of focal spot. Different

r_{i}

determines different focal field, especially the radii

r_{4}

which is the most sensitive one. Even a tiny change will lead to an obvious difference in the focal field. Consequently, we obtained optimal radius values from reasonable optimization of all parameters in the simulated experiments:

r_{1} = 0.10, r_{2} = 0.40, r_{3} = 0.62, r_{4} = 0.77.

The cross section of five-zone binary phase plate is shown in Fig. 2 . And

r_{1} - r_{4}

are marked in the figure.

Fig. 2 Amplitude transmission function $T (θ)$ for the binary phase plate. 3D figure is shown in Fig. 1(b). The second ring and fourth ring have a phase delay of π

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For a quadrant $0 / π$ phase plate, the phase plate is divided into four quadrants. The phase delay is

Δ α = π (0 \leq ϕ < \frac{π}{2} & π \leq ϕ < \frac{3 π}{2}), Δ α = 0 (\frac{π}{2} \leq ϕ < π & \frac{3 π}{2} \leq ϕ < 2 π) .

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 [18]. 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 E_x component is mainly distributed along Y axis. In Fig. 3(c), the energy of E_y is mostly distributed in X direction. The azimuthally polarized beam has no E_z component in the focal field.

Fig. 3 The intensity of azimuthally polarized beam with the binary phase plate (Fig. 2) (beam (1)), as well as the squares of the local electric field components |E_x|², |E_y|², and |E_z|² in XY plane at the focal point for an aplanatic system with NA = 1.4.

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Although beam (1) alone can generate uniform intensity doughnut-like spot (Fig. 3(a)), there is still a deficiency in polarization. In XY plane, E_x is only in Y axis, and E_y is only in X axis. Theoretically, when a pump beam has round shape E_x and E_y focal field, the STED beam should be circular ring so that it can deplete fluorescence uniformly in all three components. As for beam (1), E_x lacks energy distributed in X axis while E_y 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 [12]. Therefore, if beam (1) alone is applied as STED beam, E_x component of excited fluorescent molecules in X axis cannot be depleted by this STED beam. It’s the same with E_y component of excited fluorescent molecules in Y axis. Another beam is indispensible to compensate the polarization drawback of beam (1), which should have strong E_x component in X axis and E_y component in Y axis. Azimuthally polarized beam converted by quadrant $0 / π$ 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 E_z in the focal field.

Fig. 4 The intensity of azimuthally polarized beam with the quadrant $0 / π$ phase plate (beam (2)), as well as the squares of the local electric field components |E_x|², |E_y|², and |E_z|² in XY plane at the focal point for an aplanatic system with NA = 1.4.

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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 [8]. 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 E_x and E_y , 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.

Fig. 5 STED beam is the incoherent superposition result of beam (1) and beam (2) without rescaling. (a) The intensity distribution; (b) |E_x|² component; (c) |E_y|² component; (d) |E_z|² component.

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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 [17]. Azimuthally polarized beam with a vortex $0 - 2 π$ 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 $0 - 2 π$ phase plate as pump beam (Fig. 6 ). After being depleted by STED beam, the effective excitation super-resolution spot is achieved.

Fig. 6 (a) The intensity of azimuthally polarized beam with the vortex $0 - 2 π$ phase plate (pump beam); (b-d) the squares of the local electric field components |E_x|²,|E_y|²,|E_z|² in XY plane at the focal point.

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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 $0 - 2 π$ 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.

Fig. 7 The intensity of right handed circular polarized beam with vortex $0 - 2 π$ phase plate (STED beam), as well as the squares of the local electric field components |E_x|²,|E_y|²,|E_z|² in XY plane at the focal point.

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Fig. 8 The intensity of right handed circular polarized beam (pump beam), as well as the squares of the local electric field components |E_x|²,|E_y|²,|E_z|² in XY plane at the focal point.

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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 E_z 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 E_z 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 E_z 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 E_z 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) ).

Fig. 9 The comparison of azimuthally polarized beam and circular polarized beam. (a) STED beam, cross section of Fig. 5(a) and Fig. 7(a). The peak to peak distance of azimuthally polarized beam is 0.364λ/NA, while that of circular polarized beam is 0.443λ/NA (b) Pump beam, cross section of Fig. 6(a) and Fig. 8(a). The FWHM of azimuthally polarized beam is 0.270λ/NA, while that of circular polarized beam is 0.273λ/NA. (Red dotted curve refers to circular polarized beam, and blue curve refers to azimuthally polarized beam)

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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 [13]. 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]

D = 1 / [1 + C \cdot {(\vec{n} \cdot \vec{E_{S T E D}})}^{2}] .

In Eq. (5), E_STED is the electric field of the STED beam, n is the unit vector along the molecular transition dipole axis, and

C = 3 σ_{d i p} \cdot τ

is a molecular constant that depends on the fluorescence lifetime τ and the dip cross section σ_dip [25], 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 [26], in which

σ_{d i p} \approx 1.1 \times 10^{- 16}

cm², and fluorescence lifetime of

τ \approx 3.75

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 (

λ / 28

). 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 (~

λ / 2

). Even though it excited fluorescence, the light could hardly be collected after filtered by a pinhole.

Fig. 10 (a) The pump beam (i.e., the focal spot without STED beam depletion) and (b) the effective excitation spot, with the incoherent superposition of beam (1) and beam (2) working as the STED beam. (c) The comparison of cross section FWHM between pump beam and effective beam. The FWHM of excitation spot is 201nm, and the FWHM of effective spot is 19nm, that is, 0.026λ/NA.

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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 ( $λ / 18$ ).

Fig. 11 (a) The pump beam (right-handed circular polarized beam) and (b) the effective excitation spot, with right-handed circular polarized beam with vortex $0 - 2 π$ phase plate working as the STED beam. (c) The comparison of cross-section FWHM between pump beam and effective excitation beam. The FWHM of excitation spot is 203nm, and the FWHM of effective spot is 29nm, that is, 0.039λ/NA.

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Another more accurate description of STED beam fitting curve was published lately [27]. The doughnut STED intensity pattern was described by a sinusoidal standing wave distribution

I_{S T E D} (r) = \sin^{2} (r π / p_{d}) .

where p_d is the peak-to-peak distance of the doughnut crests. And the effective spot after depletion is

I_{e f f} (r) = I_{p u m p} (r) \times \exp [I_{S T E D} (r) τ σ_{d i p}] .

τ is the fluorescence lifetime and σ_dip is the dip cross section, which are the same with which in Eq. (5). For azimuthally polarized beam, this equation provides the simulated result I_eff = ~24nm (λ/22). And for circular polarized beam, I_eff = ~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 [28]:

Δ r \approx \frac{λ}{2 n \sin α \sqrt{1 + ς}}

where Δr means the FWHM of the effective spot,

n \sin α

is NA = 1.4, and

ς

is the depletion factor which is defined as

ς = I_{S T E D} / I_{S}

. I_STED is the maximum intensity of the inhibition light and I_s is the maximum of effective depletion intensity which can be defined as the intensity at which the probability of fluorescent emission is reduced by half. I_STED is chosen to be 370MW/cm², and I_S = ~11MW/cm², which are the same with the parameters used in the simulation of azimuthally polarized beam. Thus, the FWHM of the effective excitation spot of the method with circular polarized beam is approximately 32nm (~

λ / 17

). As for intensity, for the same STED beam, increasing I_STED can improve resolution (under the threshold of fluorescent bleaching) [24]. If the circular polarized beam result achieved FWHM of

λ / 28

, I_STED should be as large as 767MW/cm², which is ~2 times more than I_STED used in the proposed method (I_STED = 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.

Fig. 12 The FWHM of effective spot versus the input energy. For the same STED beam, increasing I_STED can improve resolution. And fluorescent molecules are gradually bleached, for the depletion efficiency become lower and lower.

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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 E_z absence in both the pump beam and the STED beam focal fields, E_x and E_y 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 E_z absence in azimuthally polarized beam focal field

Although azimuthally polarized beam lacks E_z 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 E_z 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 E_z component in the focal spot.

Fig. 13 The major axis of the fluorescent molecules is in Z axis. When it is excited, the fluorescence propagates in the XY plane. The fluorescence cannot be collected by the detector in Z direction.

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This conclusion has been confirmed by experiment [11]. This experiment applied azimuthally polarized beam as well, and the experiment result illustrated that the absence of E_z 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 (R_opaque = 0.85R_total) [29] 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.

Fig. 14 Comparison of FWHM of pump beams cross-section. The FWHM of Gaussian beam is 201nm (0.270λ/NA), and the FWHM of Bessel Gaussian beam is 165nm (0.222λ/NA). (Red dotted curve refers to Bessel Gaussian beam, and blue curve refers to Gaussian beam) (NA = 1.4, λ = 532nm)

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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.

Fig. 15 The comparison of effective excitation beam focused by Gaussian beam and Bessel Gaussian beam respectively. (a) Cross-section of Gaussian pump beam and effective beam. The FWHM of Gaussian pump beam spot is ~201nm, and that of the effective spot is ~19nm (0.026λ/NA). (b) Cross-section of Bessel Gaussian pump beam and effective beam. The FWHM of Bessel Gaussian beam spot is much smaller to ~165nm while the FWHM of effective spot is ~17nm (0.023λ/NA). (NA = 1.4, λ = 532nm)

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4. Conclusion

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 $0 / π$ phase plate and the same beam with quadrant $0 / π$ phase plate is tighter focused doughnut spot surrounded completely and uniformly in every electric field component. The same polarized beam with a vortex $0 - 2 π$ phase plate works as pump beam. The FWHM of effective excitation fluorescent spot is ~19nm ( $λ / 28$ ). 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 E_z component in the focal field has no observable negative influence on this experiment. Second, multi-zone binary $0 / π$ 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.

Acknowledgments

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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Sharper fluorescent super-resolution spot generated by azimuthally polarized beam in STED microscopy

Abstract

1. Introduction

2. Basic setup and theory analysis

3. Result and discussion

3.1 Analysis of pump beam and STED beam focal fields

3.2 Analysis and comparison in quantity

3.3 Analysis of the E_z absence in azimuthally polarized beam focal field

3.4 Analysis of the FWHM of pump beam

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (15)

Equations (8)

Optics Express

Abstract

1. Introduction

2. Basic setup and theory analysis

3. Result and discussion

3.1 Analysis of pump beam and STED beam focal fields

3.2 Analysis and comparison in quantity

3.3 Analysis of the Ez absence in azimuthally polarized beam focal field

3.4 Analysis of the FWHM of pump beam

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (15)

Equations (8)

Optics Express

3.3 Analysis of the E_z absence in azimuthally polarized beam focal field