1. Introduction

Optical micro/nanofibers (MNFs), with sub-wavelength diameter waist regions, have properties of strong light confinement, ultralow loss, enhanced evanescent fields and large waveguide dispersions [1,2]. MNFs with ultrahigh transmission [3] and complex shapes [4,5] could be obtained via flame-brushing or modified flame-brushing technique [6,7], with alternate heating sources as CO₂ laser [8,9] or micro-furnaces [10,11]. They have been widely used in sensors [12,13], nonlinear optics [14–16], optomechanics [17], as well as cavity quantum electrodynamics [18] and quantum optics [19–26]. Particularly in some applications, such as harmonic generation [15], parametric four wave mixing [16], and efficient coupling luminescence from nano-emitters or cold atoms [19–23], precise control of the MNF diameter is essential.

There are many destructive and nondestructive ways to measure a fabricated MNF diameter, such as scanning electron microscopy (SEM) inspection, diffraction pattern analysis [27,28], whispering gallery modes or photonic crystal cavity mode coupling methods [29,30]. On the other hand, to fabricate a fiber taper with the right size demands precise real-time control of the fiber diameter during pulling process. By analyzing the real-time spectrum of transmission signal, one could identify different high-order optical modes based on the mode beating curve. The disappearances of certain high-order modes in the spectrum indicate that the fiber taper reaches corresponding cutoff diameters [31]. But the complementarity between the beating frequency and time window accuracy limits the precision. Diameter estimation based on the uniformly heated hot-zone model [4–7] may reach relatively high control accuracy of 2% for diameters larger than 15um, but decrease to 7% for diameter of 500 nm [3]. By monitoring the harmonic generation during the tapering process, the control accuracy could be better than 2% at the range from 360nm to 500nm [15,32], but high input laser power may cause damage to the MNFs and induce bumps [32].

In this paper, we propose a simple real-time method that could fabricate MNFs with ultrahigh accuracy and precision in diameter control. By accurately measuring the time interval between transmission laser intensity drops during fiber pulling process, we could precisely determine the time to stop the heating and pulling based on a target diameter. Our experimental results showed that both the accuracy and standard deviation of diameters were less than 5 nm for expected taper diameters ranging from 800 nm to 1300 nm.

2. Experimental setup

As showed in Fig. 1(a), the fiber-puller system consists of a hydrogen flame torch, two motorized translation stages, optical measurement components and a computer. To get maximum stability of the flame, the position of torch is fixed, and the hydrogen gas flow is controlled by a digital mass flow controller (MFC, Sevenstar CS200) so that the gas flow can be precisely controlled or shut down by a computer program. Standard communication fiber (Corning SMF-28e) is fixed on fiber clamps and preheated for ~100 seconds before pulled by two computer controlled high-precision translation stages (Newport ESP301) via a Newport XPS controller. Each stage moves with a fixed velocity of 0.1mm/s. A 10X objective lens and a CCD camera are used to monitor fiber position. During fiber pulling, a 785 nm continuous working laser (Pegasus PE.FCL.785.30.SM) with a linewidth of 2 nm is coupled to the fiber, and transmission light is measured by a photo detector (PD, Newport 918D-UV-OD3R). The reading of the detector is recorded and analyzed by computer program via a power meter (Newport 2936-R) with a sampling rate of 1 kHz. All the control and analysis functions are integrated in a single Labview program so that the whole system can stop the stages and shut down the gas flow simultaneously when a setting time meets.

 

Fig. 1 (a) Schematic of the experimental setup. (b)The effective indices of the lowest supported modes as functions of fiber diameter for optical wavelength at 785 nm. For clarity, the high-order HE3n/EH3n/HE4n/EH4n modes are not plotted here. (c) The normalized transmission curve of 785 nm laser as a function of time during the tapering process. Inset shows the transmission curve when a 1550 nm laser was used for comparison, where only fundamental mode was excited. (d) Magnified intensity curve (black solid line) and its derivative (blue dotted line) as functions of time. The red dashed line is the threshold to delimit the cutoff of certain mode.

Download Full Size | PDF

3. Results and analysis

Figure 1(b) shows the numerical calculation results of effective refractive indies of supported optical modes depending on the fiber diameter in an air cladded cylindrical waveguide structure, for optical wavelength at 785 nm [2]. When laser at 785 nm is coupled into the SMF-28e fiber, high-order modes LP11, LP21 and LP02 can be excited other than the fundamental LP01 mode. During the tapering process, LP11 mode may be coupled to LP12 and LP13 modes due to non- adiabatic transition [33]. Eventually, these modes split and evolved to constituent TE, TM and HE modes in MNFs [33,34], and vanish successively when the fiber diameter decreases, as shown in Fig. 1(b).

In our experiments, we observed clearly two abrupt drops of transmission intensity after tapering time > 100 s, as indicated by ellipses in Fig. 1(c). To get accurate timing, we calculated the derivative (or slope) of intensity change and plotted as blue dotted curve in Fig. 1(d). This curve shows double-peaks for the first two drops, indicating cutoffs of multiple optical modes. To identify these modes, we tried to measure the fiber diameters when the drops happened. We set a threshold (−5x10⁻⁵ in our case, indicated as red dashed line in Fig. 1(d)) for the slope of intensity change. Once the slop reached this threshold for the first time in an intensity drop, we stopped the stages and the gas flow immediately. The MNF was then unmounted from stages and checked under SEM. We would like to emphasize that, to get clear peaks in the derivative curve, we intentionally chose short wavelength (785 nm) laser so that high-order modes were excited. When a laser at 1550 nm was used, transmittance of 97% was typically got as the fundamental mode experienced adiabatic transition (shown in the inset of Fig. 1(c)).

Figure 2(a) shows a typical SEM image of a section of fabricated MNF stopped at the second intensity drop. Diameters at different section of the fiber taper were measured every 100 mm along the fiber using magnified images shown as Fig. 2(b). The results reveal that the fiber has a waist with a typical uniform diameter length about 300 mm. The method to determine diameter by the slope threshold turns out to be with very high precision. We repeated the fiber pulling process for six times, and the diameters were measured and plotted as red solid diamonds in Fig. 2(c). The average waist diameter is calculated to be 1293.8 nm with a standard deviation as 3.8 nm (0.29%), which is limited by the SEM image pixel size (5 nm). While for the waist diameters of MNFs stopped at the first intensity drop, we got amazingly the same readings as 2006 nm for all six samples (plotted as black open circles in Fig. 2(c)). Comparing the cut off diameters from Fig. 1(a) (2079 nm for HE23 mode, 2056 nm for TE03 and TM03 modes, 1351nm for HE22 mode, and 1312 nm for TE02 and TM02 modes), we identified that the first peak of first intensity drop indicated the cutoff of HE23 mode, while the first peak of second intensity drop corresponded to the cutoff of HE22 mode. Note that the SEM has a 3% systematic deviation in measuring length, which can be corrected by calibration.

 

Fig. 2 (a)The SEM image of a section of MNF stopped at the second intensity drop. The labeled numbers are the diameters measured at those particular positions. (b) Magnified SEM image used to measure diameter. (c) Diameters measured from six different samples stopped at the first intensity drop (black open circles) and at the second intensity drop (red solid diamonds). The error bars were estimated based on experimental data as well as SEM resolution.

Download Full Size | PDF

Having such high precision of diameters determined by the slop threshold, we were able to calculate the MNF waist diameter at certain time during the pulling process based on the constant hot-zone model [7]:

To check the precision of MNF waist diameters that we could control based on this method, we fabricated MNFs with expected diameters as 1200 nm, 1005 nm, 792 nm and 412 nm, respectively. The measured diameters from different samples are plotted in Figs. 3(a)-3(d) as red squares.

 

Fig. 3 (a)-(d):The measured waist diameters (red squares) for MNFs fabricated based on Eq. (2) with expected diameters (solid black lines) as (a) 1200 ± 3.1 nm, (b) 1005 ± 4.1 nm, (c) 792 ± 4.8 nm, and (d) 412 ± 4.8 nm, respectively. The dashed blue lines indicate the extrapolated diameters based on Eq. (3) as (a) 1199 ± 4.9 nm, (b) 997 ± 5 nm, (c) 779 ± 5.4 nm, and (d) 395 ± 4.4 nm, respectively. (e)-(f): The measured waist diameters (red squares) for MNFs fabricated based on Eq. (3) with expected diameters as (e) 1107 ± 4.6 nm, (f) 910 ± 5.2 nm. The errors for expected diameters were inherited from the error of D₀ measurement.

Download Full Size | PDF

Though $\Delta T$ varied slightly from time to time, the stopping time $\Delta t$ calculated based on the updated $\Delta T$ turned out to be very accurate. We calculated the average diameters and standard deviation based on the statistics of experimentally measured data points. For MNFs with expected diameter as 1200 nm, the measured average diameter was 1198.9 nm, which was only 1.1 nm away from the target size. The standard deviation of diameter from 8 samples was calculated as 4.2 nm (0.35%), which was limited by SEM image pixel size (5 nm). The results for 1005 nm were also excellent with average diameter of 997.3 nm and standard deviation of 3.5 nm (0.35%), considering the SEM image pixel size as 3.6 nm. The average diameter was measured as 779.3 nm for MNFs with expected diameter as 792nm, which showed relatively large deviation. However, the precision was still very high as the standard deviation was calculated as 4.4 nm (0.56%). Both the accuracy and precision decreased remarkably when the MNF diameter was targeted at 412 nm. The average diameter was measured as 354.1 nm, and the standard deviation was 15.2 nm (4.2%). We attributed such large deviation to the elevation of MNF by flame gas flow as we observed that the fiber was no longer straight when the fiber was too thin. This could be improved if the flame torch is replaced by electric micro-heater [10.11].

Though the experimental results show that the diameter control of MNFs in the range between 1300 nm and 800 nm has very high precision (< 5 nm), the diameter control accuracy is not satisfying. We tried to improve it by calibrating the parameters in Eq. (2) based on the results shown in Figs. 3(a)-3(c) as:

Based on this equation, the deviations between the measured average diameters and the target diameters are < 0.5 nm for the diameters shown in Figs. 3(a)-3(c). To verify that we have improved accuracy of diameter control, we targeted the diameters at 1107 nm and 910 nm, and fabricated MNFs based on Eq. (3). The SEM measurement results shown in Figs. 3(e) and 3(f) indicated that the average diameters were 1108.7 nm and 914.9 nm, with standard deviations as 4.9 nm (0.44%) and 4.0 nm(0.43%), respectively. Thus, for the diameter ranging from 800 nm to 1300 nm, we have realized real-time control of MNF diameter with both accuracy and precision within 5 nm.

We would like to note that 800 nm and 1300 nm are not rigid diameter borders for MNFs to be obtained with ultrahigh accuracy and precision based on our method. As discussed above, once the issue of gas flow is overcame, in principle, the diameter lower limit can be extended to deep sub-wavelength region. In addition, the peak (around 139 seconds in the intensity derivative curve in Fig. 1(d)) due to the cutoff of EH21 mode may also be utilized to increase the diameter control accuracy. And the top limit can also be broken when a laser with longer wavelength is used, where the cutoff diameter of the fiber for HE22 mode increases.

4. Conclusion

In summary, we have realized MNF diameter control with ultrahigh accuracy and precision during fiber pulling process. The results we got from experiments are superior to those got from other real-time control method in term of diameter accuracy. Such a simple and accurate method are especially useful in MNF diameter sensitive applications, such as parametrical nonlinear fiber optics and quantum optics.