We present the experimental realization of nanofiber Bragg grating (NFBG) by drilling periodic nano-grooves on a subwavelength-diameter silica fiber using focused ion beam milling technique. Using such NFBG structures we have realized nanofiber cavity systems. The typical finesse of such nanofiber cavity is F ∼ 20 – 120 and the on-resonance transmission is ∼ 30 – 80%. Moreover the structural symmetry of such NFBGs results in polarization-selective modes in the nanofiber cavity. Due to the strong confinement of the field in the guided mode, such a nanofiber cavity can become a promising workbench for cavity QED.
©2011 Optical Society of America
High-Q Fabry Perot resonators have been implemented to manipulate the interaction between light and matter [1–4]. Such experiments have revealed exciting physics of cavity quantum electrodynamics (cavity QED) but are technically challenging for real applications. The rapidly growing field of nano-fabrication techniques has encouraged smarter ideas to control both light and matter. Various designs of high-Q micro/nanostructured resonators have been proposed to control the quantum states of light and matter . Examples will include micropillar/post , microsphere [7,8], microtoroid [9,10], microcoil resonators  and photonic crystal cavities [12–15]. The key point of the designs is to achieve smaller mode volumes and higher Q values to realize strong confinement of the field in these micro/nano photonic structures. Recently subwavelength-diameter silica fibers, known as optical nanofibers, are becoming a promising candidate in this direction. Optical nanofibers are produced by adiabatically tapering commercial single-mode optical fibers. Due to subwavelength-diameter the field in the guided mode is strongly confined in the transverse direction. As a result the spontaneous emission of atoms can be strongly modified around the nanofiber and a significant fraction of atomic emission can be coupled to the guided mode . It has been experimentally demonstrated that using laser cooled Cs-atoms around the nanofiber one can detect few percent of atomic emission at one end of the tapered fiber and using such a technique single atoms can be detected around the optical naonfiber [17, 18]. Moreover due to such coupling between atoms and the nanofiber guided modes one can realize an optically dense system with few atoms around the nanofiber . However, in order to implement such a system for practical applications one has to further improve the coupling efficiency into the guided modes of the nanofiber.
The coupling between the atom and the nanofiber guided modes can be substantially improved by introducing an inline fiber cavity. The inline fiber cavity will provide longitudinal confinement of the field in the nanofiber guided modes. Due to the strong transverse confinement of the nanofiber guided modes even for moderate finesse cavity the coupling between the atom and the guided modes will be significantly enhanced. It is theoretically estimated that when the diameter of the nanofiber is 400 nm and the cavity finesse is 30, for Cs-atom D2-transition (wavelength ∼ 852 nm), almost 94% of the total emission can be channeled into the guided modes . Such high coupling efficiency for such a low finesse condition is in drastic contrast to other known systems and such a nanofiber cavity is quite distinct system to be explored. Theoretical proposal for intra-cavity electromagnetically induced transperency in such nanofiber cavity system has been reported . Also it is predicted that for large cavity lengths (∼ 10 cm) strong coupling can be realized even in such an overdamped-cavity regime . Such a nanofiber cavity system may open up exciting new possibilities in quantum nonlinear optics and quantum information technology.
In order to realize a nanofiber cavity one may splice commercial fiber Bragg gratings (FBGs) to the tapered fiber. However, due to some loss in the tapering region such a technique is not suitable for making a nanofiber cavity. Moreover conventional techniques may not work to make FBGs directly near the nanofiber region. Conventional techniques for making FBGs rely on the photosensitivity of the Ge/GeO2 doped core of single-mode optical fibers and the core refractive index is modified by irradiating UV lasers [22, 23]. Since the diameter of the nanofiber is much smaller than the core-mode cutoff diameter , they are basically vacuum-clad fibers. At such a thin diameter the core of the original single-mode fiber might be almost vanishing and the nanofiber is essentially made of pure silica (cladding material of the original fiber). Assuming that the volume ratio of the core and cladding material of the original fiber is maintained the Ge concentration in the nanofiber region might be only 0.5% of that in the core of the original fiber. Hence such UV irradiation technique might not be efficient enough to make FBGs directly near the nanofiber region.
In this paper we present a novel technique for realization of such an optical nanofiber cavity. We drill periodic nano-grooves on the nanofiber using focused ion beam (FIB) milling technique [25, 26]. Such periodic structures on the nanofiber induce strong modulation of refractive index for the field propagating in the guided modes and act as FBGs. Using such FBG structures on the nanofiber we have realized nanofiber cavities. We discuss the characteristics of such nanofiber Bragg gratings (NFBGs) and the nanofiber cavities. Considering our future experiments with laser cooled Cs-atoms (wavelength ∼ 852 nm) and colloidal quantum dots (wavelength ∼ 800 nm) we design the NFBGs for a wavelength region of ∼ 800 – 850 nm.
2. Design of NFBGs and nanofiber cavity
The nanofiber is located at the waist of a tapered optical fiber. The typical length of the taper is ∼ 10 cm to ensure adiabatic tapering condition. The minimum diameter at the waist is ∼ 400 – 600 nm and is uniform for ∼ 2 mm along the length. The typical transmission of such a taper is ∼ 90 – 95%. The nanofiber can support only the fundamental mode HE11. The propagation constant β is determined by the fiber radius (a), the refractive indices of the core (n 0 ∼ 1.45) and clad (n 1 = 1), and the wavelength of the light (λ) [27, 28].
We design two types of NFBGs on the nanofiber, namely single-period and chirped NFBGs. The grooves are drilled in pair on the opposite lateral sides of the nanofiber and a single-period NFBG consists of a set of groove pairs which are equidistant along the fiber axis. The grating period (ΛG) is estimated using the coupled-mode theory . As a first approximation we assume sinusoidal variation of refractive index and the Bragg resonance condition is ΛG = π/β. For a given ΛG value, the Bragg resonance (λR) strictly depends on the diameter (2a) of the nanofiber as the diameter determines the propagation constant β. For a diameter of 2a = 560 nm and Bragg resonance at λR ∼ 852 nm, we estimate a ΛG value of ∼ 360 nm. And for the diameter dependence we numerically estimate a slope value of , in our working region of 2a ∼ 500 – 600 nm. Hence if the diameter of the nanofiber is 20 nm thicker then the resonance (λR) will be 10 nm red-shifted. This suggests that even 10% uncertainty in the diameter measurement can seriously affect the experiments to reach the target Bragg resonance around the atomic resonance. In order to compensate for the uncertainty in the diameter measurement we design chirped NFBGs. The chirped NFBG consists of several consecutive single-period NFBGs having different ΛG values which gives a much broader resonance.
Assuming a groove depth of around 100 nm at a diameter of 560 nm we can easily estimate a refractive index modulation (Δn 0/n 0) of few percent from the volume ratio. Such a high Δn 0/n 0 value suggests that we need only 100 – 200 periods to reach more than 90% reflectivity which is in drastic contrast to conventional UV irradiation techniques where the typical Δn 0/n 0 value is ∼ 10−5 – 10−3 [22, 23]. However these grooves may also induce some scattering loss by coupling light to the radiaiton modes. So the experimental observations will determine more realistic groove depth to realize low loss NFBGs.
Moreover by drilling such grooves the cylindrical symmetry will be broken. Hence in general the reflectance for the polarization perpendicular (x-polarization) to the plane of the grooves and that for the polarization parallel (y-polarization) to it may differ by both phase and amplitude. Such polarization dependence can be theoretically understood from coupled mode analysis using the exact size and shape of the grooves . However a simple qualitative explanation will be as follows. Due to the ellipticity induced by the grooves the y-polarized mode will be of smaller effective index. Such index contrast may also lead to a relative blue shift in the Bragg resonance for the y-polarized mode.
Two NFBGs on the tapered fiber separated by a length L forms a nanofiber cavity. We make two types of nanofiber cavities. One is long nanofiber cavity having L ∼ 5 mm and the other is short nanofiber cavity having L ∼ 50 – 100 μm. As mentioned above due to the diameter uncertainity, matching the resonances of the two NFBGs becomes a crucial issue for making long nanofiber cavities. Hence we use chirped NFBGs for making long nanofiber cavities. Whereas for short nanofiber cavities we use single-period NFBGs since the diameter variation is negligible within such short length of the taper.
3.1. FIB milling on nanofiber
The FIB milling was done with an XVision 200 (SII Nanotechnology Corporation) system. A good point of the system is that the FIB chamber is rather large and can accomodate a sample holder of 8 inch diameter. After production the tapered fiber is collected on to the FIB sample holder and is introduced into the FIB chamber. The length of the fiber on either side of the taper is ∼ 30 cm which is kept to be used for later measurements. During the experiments we have maintained clean conditions which is extremely essential to maintain the nanofiber transmission. A 30 keV beam of Ga+-ions was focused on to the nanofiber with a beam spot size of ∼ 14 nm. The beam current was ∼ 10 pA and the exposure time for milling each groove was 1 s. The diameter measurements are done using scanning ion microscope (SIM). Figure 1(b) shows the SIM image of the NFBG structures on the nanofiber at a diameter of ∼ 560 nm. Each groove has a depth of ∼ 100 nm and width of ∼ 150 nm. The grating period is ΛG ∼ 360 nm.
3.2. Measurement of transmission spectrum of NFBGs and nanofiber cavities
The transmission spectra of the NFBGs and the nanofiber cavities are measured using the following three methods.
Method 1: For meauring the transmission spectrum in a broad wavelength region of λ ∼ 700 – 900 nm we use an optical multi-channel analyzer (OMA). A white light source from a conventional lamp is launched into the tapered fiber and the spectrum of the output light is measured using the OMA. The resolution of the OMA is ∼ 0.5 nm (∼ 6.75 cm−1). Due to the high sensitivity of the OMA, no special setup is necessary to couple light into the fiber and such a method is preferred for quick measurements. The transmission spectra of the single-period and chirped NFBGs are measured using this method.
Method 2: For measuring the transmission spectra of short nanofiber cavities we need much better resolution to observe the cavity modes. Hence we use a Fourier transform spectrometer (FT-spectrometer, Thermo Fisher Scientific, Nicolet 8700) for measuring the cavity spectrum with higher resolution in a broad wavelength region. The resolution of the FT-spectrometer is ∼ 0.125 cm−1. Fiber-coupled superluminescence light emitting diodes, SLEDs (Exalos Inc.) are used as the source. The SLED emission is broadband having a FWHM of ∼ 40 nm and is partially polarized. In order to explore the polarization dependence we introduce a linearly polarized component of the SLED output into the tapered fiber containing the short nanofiber cavity. An inline fiber polarizer is used to control the polarization inside the fiber.
Method 3: For measuring the transmission spectra of the long nanofiber cavities we need to futher improve the the resolution to an order of few MHz. Hence the spectra of the long nanofiber cavities are measured using a tunable, single frequency diode laser (emission wavelength ∼ 852 nm). A linearly polarized input light from the diode laser is introduced into the tapered optical fiber containing the long nanofiber cavity and the transmission is measured while scanning the diode laser frequency. In this method one can easily achieve few MHz resolution but the spectrum can be measured only within a range of ∼ 100 GHz that is limited by the scanning range of the diode laser.
We must mention that the reflectivities of the individual NFBGs used in the nanofiber cavity are not measured, since the pair of NFBGs are fabricated in one fabrication process in order to maintain the conditions constant.
4.1. Characteristics of NFBGs
First we discuss the characteristics of NFBGs. The transmission spectra of the single-period and chirped NFBGs are measured using Method 1. The normalized transmission spectra are shown in Fig. 2. The green solid curve shows the transmission spectrum of a single-period NFBG. The single-period NFBG is made at 560 nm diameter region of the tapered fiber with ΛG = 360 nm and having 60 periods. One can clearly see a dip in the transmission spectrum at around λR = 856 nm. Almost 60% of the input light is reflected at Bragg resonance and the width of the spectrum is ∼ 13 nm (∼ 175 cm−1). We have investigated the spectrum of several single-period NFBGs with the same fabrication parameters. Using coupled-mode theory  and assuming an effective sinusoidal modulation of the core refractive index, we have estimated Δn 0/n 0 value of (1 ± 0.2)%. The blue dashed curve shows the calculated spectrum for Δn 0/n 0 = 1%.
The red solid curve in Fig. 2 shows the transmission spectrum of a chirped NFBG. The chirped NFBG is made at 560 nm diameter region and consists of 4 consecutive single-period NFBG each having 60 periods. The ΛG values for the single-period NFBGs are 358, 360, 363 and 365 nm respectively. As one can clearly see the width of the resonance increases to ∼ 40 nm and peak reflectivity increases to 90%. The calculated spectrum is shown by the black dashed curve. The non-resonant transmission of such tapered fiber samples containing NFBGs are measured using a diode laser at a wavelength of 910 nm. The measured non-resonant transmission is ∼ 90% which is almost equal to the original transmission of the unperturbed tapered fiber. This suggests that the NFBGs do not induce any major scattering loss.
4.2. Characteristics of short nanofiber cavity
Using two single-period NFBGs on the nanofiber we have realized short nanofiber cavities. The transmission spectra of the short nanofiber cavities are measured using Method 2. The transmission spectrum of a 100-μm-long nanofiber cavity is shown in Fig. 3(a). The cavity is made at 560 nm diameter region of the tapered fiber and consists of two single-period NFBGs each having 120 periods and the ΛG value is 360 nm. The region between the two single-period NFBGs having no grooves is 100 μm in length. The spectrum (i) (green curve) and (ii) (blue curve) in Fig. 3(a) show the normalized cavity transmission spectrum for two orthogonal polarizations respectively. The polarization axes are selected using the following procedure. The transmission spectrum is measured for various input linear polarizations. The observations suggest that two types of cavity modes appear depending on the input polarization. The input polarization is adjusted for optimizing each of the cavity modes. It appears that optimization of one of the cavity modes results in suppression of the other cavity mode. The input polarizations for which the cavity modes are optimized are orthogonal to each other. As one can clearly see the spectrum for two orthogonal polarizations are quite different form each other. The central broad dip in the spectrum corresponds to the reflection band of the single-period NFBGs and the equispaced peaks appearing within the reflection band corresponds to the cavity modes. For the spectrum (i) the reflection band is centered around 11850 cm−1 (corresponding to wavelength ∼ 843.88 nm) which is denoted as detuning = 0 cm−1 and the FWHM is ∼ 170 cm−1. Whereas for the spectrum (ii) the reflection band is centered around detuning = 60 cm−1 and the FWHM is ∼ 160 cm−1. The observed relative blue shift in the spectrum (ii) suggests that the spectrum (ii) corresponds to polarization parallel (y-polarization) to the plane of the grooves and the spectrum (i) corresponds to the polarization perpendicular (x-polarization) to the plane of the grooves. Also there are some reflection side bands appearing around detunings of 130 cm−1 and −196 cm−1 for x-polarization and detunings of 192 cm−1 and −112 cm−1 for y-polarization respectively. The observed free spectral range (FSR) for x-polarization is ∼ 27 cm−1 (810 GHz) and that for y-polarization is ∼ 25 cm−1 (750 GHz).
Since the grating length (∼ 65 μm) is comparable to the cavity length, estimation of FSR from the cavity length is not straightforward. Considering the exact shape and dimensions of the grooves we have theoretically calculated  the spectra using coupled-mode theory as shown by the spectrum (iii) and (iv) (brown curves) in Fig. 3(a). For the calculations we have neglected coupling to the radiation modes. The observed spectral shape is almost perfectly reproduced from the theoretical calculations except for the transmission values. The polarization dependence is also revealed from the calculations. From the calculation it is clear that the spectrum (i) corresponds to polarization perpendicular (x-polarization) to the plane containing the grooves. Also the reflection side bands may correspond to additional Fourier components resulting from non-sinusoidal modulation of the refractive index.
A part of the cavity spectrum for the x-polarization is expanded and shown in Fig. 3(b). The cavity modes are marked as A, B and C. As one can see the linewidth becomes narrower towards the center of the reflection band. The Lorentzian fit for the narrowest cavity mode C is shown in the inset. The cavity modes A, B and C have linewidths (Δν) ∼ 0.64 cm−1(19.2 GHz), 0.28 cm−1(8.4 GHz) and 0.23 cm−1(6.9 GHz) corresponding to finesse values (F = FSR/Δν) ∼ 42, 96 and 117, respectively. The peak transmissions for the cavity modes A, B and C are ∼ 55, 41 and 25% respectively. The increase in finesse towards the center of the reflection band may be understood as the increase in the reflectivity of the NFBGs. It is meaningful to estimate the highest reflectivity of the NFBGs. Assuming equal reflectivity for both the NFBGs we estimate a reflectivity of ∼ 97% for the highest finesse value of F = 117 at around the center of the reflection band.
4.3. Short nanofiber cavity with reduced groove depth
We have made such short nanofiber cavity even at smaller diameters ∼ 520 nm using groove depth of ∼ 100 nm. However it is observed that the transmission of such nanofiber cavity is drastically reduced to ∼ 1%. Hence we suspect that usual groove depth of ∼ 100 nm is rather lossy at a diameter of ∼ 520 nm. In order to further improve the transmission of such nanofiber cavity we reduce the groove depth. The transmission spectrum of a 50-μm-long nanofiber cavity with reduced groove depth is shown in Fig. 4. The cavity is made at 520 nm diameter region of the tapered fiber and consists of two single-period NFBGs each having 180 periods. Each groove has a depth of ∼ 50 nm and width of ∼ 150 nm. This cavity is designed for resonance at a wavelength of ∼ 800 nm and the ΛG value is 345 nm. The transmission spectrum shown in Fig. 4 is for an input polarization perpendicular to the plane containing the grooves (x-polarization). The reflection band is centered around 12468 cm−1 (corresponding to wavelength ∼ 802.05 nm) which is denoted as detuning = 0 cm−1 and the FWHM is ∼ 140 cm−1. There is only a single dominant cavity mode at detuning = 0 cm−1. The linewidth of this mode is ∼ 1 cm−1 (30 GHz) corresponding to a finesse value of F ∼ 35. The peak transmission of the cavity mode is ∼ 80%.
4.4. Characteristics of long nanofiber cavity
Using chirped NFBGs on either side of the nanofiber we have realized long nanofiber cavities. The chirped NFBGs are made at 560 nm regions of the tapered fiber and the separation between the two chirped NFBGs is ∼ 5 mm. Each chirped NFBG consists of 4 consecutive single-period NFBGs each having 60 periods. The ΛG values for the single-period NFBGs are 358, 360, 363 and 365 nm respectively. The transmission spectra of the long nanofiber cavities are measured using Method 3. The transmission spectrum of a 5-mm-long nanofiber cavity is shown in Fig. 5. The black and red curves show the cavity modes for two orthogonal polarizations respectively. The modes for the orthogonal polarizations are separated by ∼ 2.8 GHz. The FSR of the cavity is ∼ 18.1 GHz. The finesse of the cavity is F ∼ 20. The peak transmissions for black and red curves are ∼ 30 and 20% respectively.
The experiments clearly demonstrate that making such periodic nano-grooves on such a thin subwavelength diameter silica fiber is possible using the FIB milling technique. We have demonstrated drilling grooves of dimension ∼ 50 – 150 nm on a 560 nm diameter fiber. We note that FIB milling on much thicker fibers with diameters ∼ 35 – 100 μm has been reported by few groups [25, 26]. For the thicker fibers some unwanted periodic structures were observed . However for nanofibers we have not observed any such structures up to a resolution of ∼ 4 nm.
A groove depth of 100 nm at a diameter of 560 nm induce an effective sinusoidal index modulation of ∼ 1%. Hence with only 100 – 200 periods one can realize more than 90% reflectivity. It is obvious to expect that these structure may induce huge scattering loss by coupling light to radiation modes. However unlike to common believe these structures do not induce any major scattering loss. We suspect that due to the periodicity of the structures some back-coupling between radiation and guided modes may appear which might be the reason for such low scattering loss in these NFBGs.
The peak transmission and the finesse of the nanofiber cavity may be limited by the loss in the cavity. There are mainly two types of loss mechanisms. One is the scattering loss due to the nano-grooves and the other is the propagation loss in the nanofiber. For the short nanofiber cavity (L ∼ 100 μm) the transmission for some modes is more than ∼ 55% even for finesse F ∼ 42. Moreover by reducing the groove depth to ∼ 50 nm we have realized cavity transmission of ∼ 80% for finesse F ∼ 35, as observed for the 50-μm-long nanofiber cavity. Hence we suspect that such loss is mainly due to the scattering loss in the NFBG region. Assuming negligible propagation loss due to the short length of the cavity, the single pass scattering loss might be ∼ 2%. On the other hand for long cavities the maximum transmission is only ∼ 30% for finesse F ∼ 20 and we suspect that such loss is mainly due to propagation loss in the nanofiber region. Although the samples are handled under clean conditions still there may be some contamination that causes such propagation loss and we have also observed gradual degradation of the samples during the experiments. The transmission of the nanofiber cavities may be further improved by thermal annealing and plasma cleaning treatments.
The polarization-dependent modes can be understood from the structural symmetry of the NFBGs. Since the cylindrical symmetry is broken the reflectance for the polarization perpendicular to the plane of the grooves (x-polarization) and that for the polarization parallel to it (y-polarization) may differ by both phase and amplitude. As expected, for short nanofiber cavity we clearly observe a relative blue shift of ∼ 60 cm−1 in the Bragg resonance for y-polarization. Also the polarization dependence is almost perfectly reproduced from theoretical calculations as discussed in Fig. 3(a).
On the other hand for long nanofiber cavity we use chirped NFBGs. For chirped NFBG the FWHM of the reflection band is ∼ 540 cm−1 (see Fig. 2). Also due to the uncertainty in the diameter measurements the reflection bands of the two chirped NFBGs may not coincide which may lead to much broader reflection band for the long nanofiber cavity. Such a blue shift of ∼ 60 cm−1 might be ∼ 10% of the FWHM of the reflection band and is difficult to observe. Hence the polarization assignment based on the blue shift may become difficult. However considering the scattering loss we suspect that the polarization for which the cavity mode has higher transmission may correspond to the x-polarization. Such polarization assignment can be further clarified by observing the angular distribution of scattered light in a plane perpendicular to the fiber axis.
One may notice that in Fig. 3(b) the observed lineshape of the cavity mode B is quite asymmetric. We have also observed such asymmetric lineshapes and sometimes splitting of the cavity modes for several other nanofiber cavity samples. We have not thoroughly understood such observations. We suspect that such effects might be associated with interference between the two orthogonal polarization modes of the fiber. Such orthogonality is defined for a perfectly cylindrical fiber. However by making the nano-grooves some perturbation is included which may lead to some cross coupling between the orthogonal polarization modes. Further investigation is needed to clarify such interference effects.
The nanofiber cavity will be combined with laser cooled Cs-atoms and quantum dot (q-dot) system. Especially long (L ∼ 5 mm) nanofiber cavity will be implemented for atoms since a longer atomic medium can be used to realize higher optical depth. Moreover these long cavities have much narrow linewidth and the cavity modes can be easily tuned to match a specific atomic resonance. The cavity modes can be tuned by controlling the cavity length using thermal expansion technique and for this a longer cavity length is preferred. We note that such FIB milling technique may be extended to fabricate nanofiber cavities for shorter wavelengths around ∼ 600 nm which can be implemented for other alkali atoms like Rb/Na-atoms. On the other hand short nanofiber cavities (L ∼ 50 – 100 μm) will be implemented for q-dot system as the q-dot spectrum is much broader and can be easily matched to the cavity resonance. Especially placing a single q-dot on the nanofiber cavity one can realize an efficient single photon source. Such nanofiber cavities are quite robust and broadband and can be implemented for various sensing applications. Also the polarization-dependent cavity modes may be useful for various applications.
In conclusion we have realized nanofiber Bragg grating (NFBG) by drilling periodic nano-grooves on a subwavelength-diameter silica fiber, using FIB milling technique. Using such NFBG structures we have realized nanofiber cavity systems. The typical finesse of such nanofiber cavity is F ∼ 20 – 120 and the on-resonance transmission is ∼ 30 – 80%. Moreover the structural symmetry of such NFBGs results in polarization-selective modes in the nanofiber cavity. Due to the confinement of the field in the guided mode of the nanofiber, even with such low-finesse nanofiber cavity strong enhancement of the spontaneous emission of atoms can be realized. Such “atom + nanofiber cavity” system can become a promising workbench for cavity QED and quantum nonlinear optics and will find various applications in quantum information technology. Apart from atoms, solid-state quantum emitters like quantum dots or diamond nano-crystals can also be implemented.
We are thankful to Makoto Morinaga for fruitful discussions. This work was supported by the Japan Science and Technology Agency (JST) as one of the Strategic Innovation projects.
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