We use a SEM to measure the nanofiber profile below a micrometer to verify that our nanofibers truly achieve the desired diameter. Figure, shows a SEM image of a nanofiber, coated with graphite, with an expected diameter of 500 nm, and a measured diameter of 536 ± 12 nm. The error is systematic, coming from the scaling factor associated with the SEM calibration. We attribute this small disagreement to thermal forces that push the fiber away from the nozzle at the end of the pull when the fiber is thin. We could compensate for this in the algorithm by adjusting the effective hot zone as the fiber tapers, but we have not found it necessary to do so.

We validate the accuracy of our simulation of the expected fiber profile using both anoptical microscope and a scanning electron microscope (SEM). Figureshows the measured (blue markers) and simulated profiles (red lines) of a fiber taper imaged optically. The taper profile is designed to have three angles, 5, 2, and 3 mrad, that taper down to radii of 50, 35 and 25 μm, respectively. An exponential profile smoothly links the radius of 25 μm down to the the final radius of 15 μm. The final radius is chosen to be well above the resolution of our optical microscope. The length of the uniform waist is chosen to be 5 mm long. Figureis a compilation of optical microscope images taken of the entirety of the tapered fiber. An edge finding technique then measures the profile of the fiber at different cuts. The error in the measured radius is dominated by a systematic error of ±2.5 μm due to the finite resolution of the imaging system. We first use an image of the unmodified fiber, which has a diameter of 125.1 μm, to determine the pixel to micron conversion. The number of pixels measured for an unmodified fiber has an error of a few pixels as a result of the resolution of the optical microscope. We then binarize the gray levels of the pixels and choose a threshold such that the diameter of the unmodified fiber matches the pixel count from the previous measurement. The edge finding technique itself has an error of about 0.5 pixels for a flat length of fiber resulting from the binarization process. Figuredisplays the relative difference between the measured image radius and the simulated radius normalized to the expected radius. The largest deviation is slightly larger than 2%, while the RMS value is 0.0187. This verifies the accuracy of our algorithm and pulling apparatus for larger radius tapers.

Measuring the length of the waist or fitting the profiles of the taper to an exponential are less accurate methods than the above procedure because Eq. (A1) assumes a uniform hot zone,. In this measurement we keep the flame fixed, which means that our hot zone is not uniform. During the actual pulling procedure we sweep, which creates an effective uniform hot zone. Here, the section of fiber located at the central point of the flame is thinned the most, as a result it is more accurate to measure the profile of the fiber after tapering and find the smallest radius to extract the value of

We characterize the size of the flame by plotting ln ( r 0 / r w ) as a function of v f t h we obtain a fit with a reduced χ 2 of 1.07 that yields L 0 = 0.753 ± 0.014 mm. This parameter should be checked from time to time as the pulling apparatus is used since it can vary by a small amount.

The measurement consists of fixing the pulling velocity at 0.05 mm/s, varying the heating time from 2 to 32 s, and then measuring the final radius of the waist. We limit ourselves to times less than 40 seconds to stay within the 2 μm resolution of our imaging system.

We measureby fixing the flame and letting both motors move apart at a constant velocity. Conservation of volume leads to an exponential profile with a waist of length, and the radius profile is given by :whereis the heating time andthe unmodified radius of the fiber.

Working with reproducible conditions requires that we fix the working distance between the fiber and the nozzle. As a consequence, the fiber is always at the same spot inside the flame and always sees the same distribution of temperature. We check the distance with a microscope before each pull and fix it to 400 ± 50 μm.

One experimental parameter fundamental to the algorithm is the effective size of the flame, L 0 , which corresponds to the zone of the fiber inside the flame that melts and thins during the pulling process. The softening point for the fused silica used by Fibercore for the SM800 fiber occurs at 1585° C. The best way to evaluate this is to measure the impact of the flame on the fiber, since our flame cannot be observed by eye.

Where v b , n is the velocity of the flame in step n and v f , n is the velocity that the fiber motors move apart. The addition of v b , n arises from the transformation to the rest frame of the flame. Typically, v b , n is an order of magnitude greater than v f , n . When transforming to the rest frame of the flame, both motors move in the direction the flame would have swept in that step. The motor whose pull velocity is in the same direction as the flame motion will lead while the other motor will lag. We have verified this sequence using the encoder of the motor that allows us to record the trajectory of the motors and by looking at the output of a Michelson interferometer with one arm spanning the two motorized stages.

Our algorithm,based on the work of the originally Mainz and currently Vienna group,calculates the trajectories of the motors needed to produce a fiber with the desired final radius, length of uniform waist, and taper geometry. The tapers are formed by a series of small sections that are well approximated by lines, allowing us to form a linear taper with a given angle down to a radius of 6 μm, which connects to an exponential that smoothly reduces to a submicron radius, typically 250 nm. The slope of the linear section generally varies between 0.3 and 5 mrad. Our algorithm divides the pull into steps defined by their pulling velocity and the traveling length of the flame. We recursively calculate the parameters, starting from the desired final radius,, until reaching the initial radius,. The full details and code can be found at Ref.

51. We used acetone for the data shown in this paper; however, we do not recommend its use because it can prolong the cleaning process. SM800 fibers have a buffer made of dual acrylate, which dissolves in acetone. This is fine for chemical removal of the buffer when heated or paired with other chemicals, but when cleaning with a wipe, the acetone can spread small buffer particulate along the stripped portion of fiber, which can burn when introduced to the flame.

51. We used acetone for the data shown in this paper; however, we do not recommend its use because it can prolong the cleaning process. SM800 fibers have a buffer made of dual acrylate, which dissolves in acetone. This is fine for chemical removal of the buffer when heated or paired with other chemicals, but when cleaning with a wipe, the acetone can spread small buffer particulate along the stripped portion of fiber, which can burn when introduced to the flame.

APPENDIX B

24 19, 8596 (2011). 24. M. Fujiwara, K. Toubaru, and S. Takeuchi, Opt. Express, 8596 (2011). https://doi.org/10.1364/OE.19.008596 Any particulate accumulation on the optical fiber before the pull begins will compromise the quality of the optical nanofiber: it will degrade the transmission, excite higher order modes, change the modal evolution, and scatter light. If any particulate accumulates on the fiber before the pull, the maximum possible transmission for a given taper geometry will not be achieved. Using FIMMPROP, as described in IV A , we have a sense of what this ideal transmission is for a given geometry, and if our transmission deviates, it can generally be attributed to a lack of proper cleaning. If the nanofiber environment is not clean or has a high humidity the transmission will decrease after a pull is finished.Furthermore, if any dust accumulates on the nanofiber surface, it will not withstand high powers under vacuum.

9 r w = 250 nm, leading to more than a 19% loss in transmission when compared to a properly cleaned fiber. The spectrogram in Fig. 9(b) TE 01 , TM 01 , and HE 21 , identified by arrows, that were not present when the fiber was properly cleaned. It is further interesting that there is more energy transferred to these asymmetric modes than any other modes. If the fiber is not properly cleaned before pulling, the final transmission can vary by a few percent. Figuredisplays the extreme case of mechanically stripping the buffer and not cleaning the fiber at all before pulling. Here, the transmission is only 80.5% for a 2 mrad taper down to= 250 nm, leading to more than a 19% loss in transmission when compared to a properly cleaned fiber. The spectrogram in Fig.shows excitation to excited asymmetric mode:, and, identified by arrows, that were not present when the fiber was properly cleaned. It is further interesting that there is more energy transferred to these asymmetric modes than any other modes.

Before every pull, we follow the cleaning procedure described in Sec. III A . After imaging the fiber, we decide whether or not we should start the pull or restart the cleaning process. We restart if anything is obstructing the light traveling through the fiber reaching the CCD. When there is particulate attached on top of or below the fiber, we use a wipe with methanol and remove it. If there is nothing observable within the resolution of the optical microscope we proceed with the pull. When we do not follow these criteria the reproducibility in the transmission will change by a few percent. When we apply this cleaning method, the variability between runs is better than 1%.

The origin of the particulate can come in various forms: remnants of plastic buffer, solvent evaporate, or any small particulate floating in the air. We believe the most common source to be the buffer. Since we use a mechanical fiber stripper to remove the buffer, micro or macroscopic pieces of buffer remain on the fiber after stripping. We apply wipes to remove the buffer remnants. This removal process can be imperfect because mechanical strippers are not designed to make contact with the actual glass of the fiber. Buffer remnants are a particularly insidious form of particulate. The plastic is generally designed with a higher index of refraction than the cladding to help remove cladding modes. If the buffer remains, we believe it may burn into the fiber. This higher index irregularity can lead to an excitation of higher order modes.

9(a) During the pull there may be signatures that the fiber was not properly cleaned. These take the form of large losses in transmission and the excitation of higher order modes. If there is initially loss or beating in the transmission this is a sign that the fiber was not properly cleaned; this is displayed in Fig.. The fiber starts single mode in the core and therefore there should be no beating between modes and negligible losses in the initial pulling process, before the fundamental mode becomes a cladding mode, in which the tapering process reduces the effective index of refraction to and then below the index of refraction of the cladding.

10 EH 11 , HE 12 , and HE 13 . 25 30, 2361 (2013). 25. S. Ravets, J. E. Hoffman, P. Kordell, J. D. Wong-Campos, S. L. Rolston, and L. A. Orozco, J. Opt. Soc. Am. A, 2361 (2013). https://doi.org/10.1364/JOSAA.30.002361 9(b) As the fiber continues to taper and the effective index of refraction of the fundamental mode approaches the index of refraction of the cladding, the mode begins to leak from the core. This is when higher order mode excitation can occur. For the SM800 fiber used in this study, the transition occurs at a radius of 19.4 μm. This transition is captured by Media 1 in Fig.. Here, we see that as the radius reduces, the effective index of refraction approaches the index of refraction of the cladding and the mode begins to leak from the core. If the beating between higher order modes occurs before this point, this is evidence that the fiber was damaged. A nanofiber with a 2 mrad geometry, if handled properly, typically excites only three higher order modes:, andIn Fig., each curve corresponds to beating between different modes and we can identify more than twenty excited modes as a result of the buffer remnants.

Furthermore, any dust on the nanofiber will cause it to break under high power in vacuum. The cleanroom environment and the cleanliness of our pulling and transfer procedures allow us to achieve nanofibers that transmit more than 400 ± 12 mW in an HV environment.

We believe that chemically removing the buffer could be beneficial to the fiber transmission. Chemical removal can lead to less mechanical damage to the fiber and properly remove all of the buffer. This is not a critical issue, since our transmission is in good agreement with simulations from FIMMPROP, but it could improve reproducibility and ease the cleaning process.