- Email: [email protected]
Generation of a dark hollow beam by a small hollow fiber
1 June 1997
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications
138 (1997) 287-292
Generation of a dark hollow beam by a small hollow fiber Jianping Yin a,‘, Heung-Ryoul Noh a, Kwan-11 Lee a, Ki-Hyun Kim a, Yu-Zhu Wang b, Wonho Jhe a** ”
Physics Department
and Condensed Matter
b Lrrboratop,for
Quantum
Received
Research Institute,
Optics, Shanghai
12 December
Institute
Seoul National
University.
of Optics and Fine Mechanics,
1996; revised 29 January
Seoul 151-742, Shanghai
1997; accepted 3 February
201800.
South Korea China
1997
Abstract A new and simple method to generate a dark hollow beam is proposed and demonstrated. This method is based on a micro-collimation technique for the output beam of a hollow optical fiber. In this experiment, the dark spot size of about 50 Km to 100 Frn at the propagation distance Z of 100 mm to 500 mm is obtained. The relative divergent angle at the near field is about 6.5 X 10p5. The potential applications of the hollow beam in atom optics are also discussed.
1. Introduction
Generation [l-5] and application [6] of dark hollow beams (DHB) are one of the very interesting subjects in optics. It has attracted a great deal of attention and has been developed fast in recent years [l-6]. Since 1990, several groups have used different techniques, such as geometrical optical method [l], transverse-mode selected method [2], optical holographic method [3], computer-generated-hologram (CGH) method [4] and optical nonlinear effect [5], to generate dark hollow beams and obtained good results. In particular, Lee et al. (1994) obtained the smallest geometrical dark-spot size (i.e., first-zero ring diameter; geometrical DSS) which is about 70-80 pm [3]. But the diffraction efficiency of the first bright ring of J,-like hollow beam (J, denotes the first-order Bessel beam) and its propagation invariance were not good [3]. Paterson et al. (1996) obtained the best propagation invariance of a J, beam, but its geometrical DSS was greater than or equal to 175 pm (theoretically estimated value) [4]. It should be noted that if we use the full-width half-maximum (FWHM) of the radial intensity distribution of the DHB as the definition of a dark spot size (DSS), the geometric DDS will be far smaller than the DSS. So the actual DSS in Refs. [3] and [4] would be far greater than 100 and 200 pm, respectively. Moreover. the experimental setups and techniques were rather complicated in those experiments mentioned above [l-5]. In this paper, we report a new and simple experimental scheme to produce a dark hollow beam by using the micro-collimation technique for the output beam of a micron-sized hollow optical fiber. The results are DSS = 50-100 pm at Z = 100-500 mm, o = 6.5 X 10p5, and the relative coupling efficiency of the core mode of the hollow fiber is about 35%. A brief discussion of the applications of the DHB in atom optics is also included in the last section.
* Corresponding
author.
’ Permanent address: Department of Physics, Suzhou University, Suzhou, Jiangsu 215006, China. 0030-4018/97/$17.00 Copyright PII s0030-4018(97)00079-5
0 1997 Elsevier Science B.V. All rights reserved.
288
J. Yin et al. /Optics
Communications 138 (1997) 287-292
2. Experiment The principle of this method is very simple. cylindrical hollow-core and a cylindrical cladding, size of the hollow region and the thickness of the the weakly-guiding approximation, the transverse hollow fiber is given by [7,13] Im(ur) E,(r,f3)
[C,J,(ur)
_
i
sin( nt0)
+C?N,(ur)]sin(m0) K,(wr)sin(m@)
where the relative transverse propagation
The relative transverse
First, let us consider a fiber waveguide consisting of a hollow region, a and assume that the thickness of the cladding is far greater than both the core, and use the cylindrical coordinate system (I, 0,~). Then according to component E,(r,#) of the electric field propagating along the Z-axis in a
(hollow region) (coreregion)
(1)
(cladding region)
constant is defined as
attenuation constants are
where /3 and k are the propagation constant and the wave number, respectively. Here J, and N,,, in Eq. (1) are the Bessel functions of the first and the second kind of order m, and I, and Km are the modified Bessel functions of the first and the second kind of order m. Note that, starting from Eq. (1). Ito et al. [7] studied the propagation properties of a light beam in a hollow fiber and the mode structure of the core, both theoretically and experimentally, and obtained some low-order modes for the core of a hollow fiber, such as the LP,,,, LP, , , LP2,, LP,, and LP4, mode. Obviously, the central beam spot of these core modes are dark, like a doughnut beam. When the hollow diameter of the optical fiber is very small (about a few micrometers), an output doughnut beam with a small dark spot at the near field can be observed. So if we use a microscope objective (MO) with a short focal length to collimate the output beam of a hollow fiber, a dark hollow beam from the core mode can be obtained and its DSS is also very small. In addition, if the output beam of a cladding mode of the hollow fiber is collimated, a dark hollow beam with larger DSS can be also achieved. Of course, the coupling efficiency of the cladding mode is far greater than that of the core mode and up to about 70% can be achieved in our experiment. The experimental setup is shown in Fig. 1. A common He-Ne laser or a laser diode (LD) was used as a laser source (LS). In Fig. 1, two lenses L, and L, consist of a telescope system to play the functions of both expansion and collimation of an incident beam, and the magnification factor is about 20. VA ,, VA, and L, are two variable apertures and a focusing lens, respectively. The inner and outer diameter of the hollow-core of the fiber is 7 pm and 14.6 pm, respectively and the outer diameter of the cladding of the fiber is 123.4 pm. The relative refractive index difference, An = (ni - nz)/(2n:), is about 0.18% and n2 = 1.45, where IZ, and n2 are the refractive index of the core and the cladding, respectively. The numerical
Fig. 1. Experimental setup to generate a dark hollow beam by means of the micro-collimation technique for the output beam of a hollow optical fiber. Here LS, VA, MO and HOF stand for laser source, variable aperture, microscope objective, and hollow optical fiber, respectively.
.I. Yin et al. / Optics Communications
138 (IY97) 287-292
289
aperture, NA = n,sinflNA = n,sin8, = (n: - nil’/‘, is about 0.124 so that the relative optimum incident angle Bi must be smaller than or equal to 7.1”. Because this angle is very small, we used a lens with 100 mm focal length as a final focusing lens in order to get a higher coupling efficiency from the input to the output of the hollow fiber. In our experiment, a microscope objective (MO), such as M-20 X or M-40 X , was used for micro-collimating the output beam from the hollow fiber. A CCD-array was used for the measurement of the DSS of the dark hollow beam and the relative electric signal was fed to a digital storage oscilloscope to display the radial distribution of the intensity of the dark hollow beam. A CCD-camera (Model IVC-841, AMSECO) was used for the observation of the beam spot of the DHB at the far field. At the same time, we used a computer to record the signals from the oscilloscope and the image from the CCD-camera.
3. Results The propagation distance of the DHB, Z, is defined as the distance from the objective lens to a CCD-array or a screen of the CCD-camera. Fig. 2 shows the relative beam-spot image from a CCD-camera, which is an image collimated by a M-20 X objective lens for a LPo, core mode of the hollow fiber for h = 0.78 pm. Because the resolution of the laser printer is only 300 dpi, the form of the beam-spot image in Fig. 2 was slightly changed. In fact, it was a clear circle-ring on the monitor of the computer. The other low-order modes, such as LP, , , LP,, for A = 0.78 pm and LP,, for A = 0.633 pm, were also observed. In Fig. 2. the dark spot in the central region is the image of the hollow region at the output end-facet of the hollow fiber and the average diameter of the dark spot on the screen is about 3.0 mm (Z = 3.8 ml. The bright ring is the image of the hollow-core at the output end-facet of the hollow fiber, and its average thickness is about 2.0 mm at the same screen. Moreover, this method can also be used to study the output modes of a hollow fiber and even to distinguish the core mode, or the cladding mode, or their mixed mode. as well as to measure the geometric sizes of a hollow fiber such as the hollow diameter, the thickness of the core and the outer diameter of the cladding. A detailed description and experimental results will be published elsewhere. The experimental results from a CCD-array are shown in Fig. 3. Figs. 3(a) and 3(b) display the radial distribution of the intensity of the dark hollow beam at Z = 200 mm and 800 mm, respectively. Note that the end-surfaces of the hollow fiber were not well polished and the inner (outer) diameter of the hollow-core of the fiber was 7 pm (14.6 pm>, the weak scattered light from the hollow-core region at the output end-facet of the fiber was mainly concentrated in a very small area around the Z axis due to collimation by an objective lens, and as a result a localized scattering background around the Z axis was formed. In addition, the height and width (25 pm) of each element of a CCD-array is far greater than or is about equal to the geometric dark spot size of the DHB at the near field. So the central intensity of the beam spot cannot be reduced to
Fig. 2. The beam spot images of the DHB from a CCD-camera (Z = 3.8 m), which is an image of the LPa, core mode for A = 0.78 pm, obtained using a M-20X objective lens.
J. Yin et al./
290
Optics Communications 138 (1997) 287-292
Radial Position (a)
Radial Position W Fig. 3. The radial distribution
of the intensity of the DHB at (a) Z = 200 mm and (b) Z = 800 mm, obtained using a M-20X
0
200
600
400
600
loo0
400
500
objective lens.
Z(mm) (a)
0
100
200
300
J
zmw @I
Fig. 4. The relationship
between the DSS and the propagation
distance
Z of the DHB using (a) M-20X
and (b) M-40X
objective
lens.
J. Yin et al. / Optics Communications
138 (1997) 287-292
291
zero completely. The small peaks at the two sides of the DHB in Fig. 3(a) result from the diffraction effect of a selected-mode aperture VA, at the near field and its imperfect selection of the core-mode. However, when the end-surfaces of the hollow fiber are well polished, and the width and height of each element of a CCD-array are small enough, the central intensity of the beam spot will drop to zero, and the slope of the intensity distribution curve in the central region will become sharper. The relative intensity distribution of the DHB in the central region. like that of the TEM,*, doughnut beam [8], is given by I( r.:)
= [4P,
r’/
TW,‘(Z)]
exp[ -2r’/&(z)],
where P,, is the laser power, u”(z) = ~?a[1 + (:./:$I is the beam waist on the Z-plane, za = (rrwi/A) is the Rayleigh length, and wc is the beam waist on the plane Z = 0. Fig. 4 shows the relationship between the DSS and the propagation distance Z of the DHB. Figs. 4(a) and 4(b) are the results of the DHB collimated by a M-20 X and a M-40 X microscope objective, respectively. It can be seen from Fig. 4 that (i) the DSS of the dark hollow beam collimated by the M-20 X objective is about 50 Km at Z = 100 mm and about 100 pm at Z = 500 mm, (ii) the relative divergent angle at the near field is about 6.5 X 10P5, whereas the divergent angle at the far field is about 4.0 X IO-“. Note that the results on both the DSS and the beam divergence of the DHB collimated by a M-20 X objective lens are better than those collimated by a M-40 X lens, and (iii) we can expect that if we use a hollow fiber with a slightly larger hollow-core than the one used in this experiment, such as lo-15 pm, a dark hollow beam with a smaller dark spot and better propagation invariance may be obtained since a large hollow-core has smaller diffraction effect. Conversely, if we use a hollow fiber with a smaller hollow-core, such as 2 pm, and a microscope objective with a larger magnification (e.g., M-60 X ), a dark hollow beam with a larger divergent angle can be obtained. In addition, the propagation invariance of the DHB between the distance of Z = 0 and Z = 3.8 m in this experiment is not as good as that in Ref. [4], but we believe that it can be further improved by using a more suitable hollow fiber, or a better collimation and transformation beam technique, or optical information processing technology for the beam. On the other hand, the DHB with a certain divergent angle has some interesting applications in atom optics, such as atomic funnel and atomic guiding [ 151 and so on (see next section).
4. Discussion In 1987. Balykin et al. [8] proposed an idea to focus a neutral atomic beam (atomic lens) by using a TEM,, laser beam with blue-detuning. Afterwards. Gallatin [9], McClelland [lo], and Wang [Ill et al. studied theoretically in detail the laser focusing of atomic beams using a TEM;, doughnut beam. Unfortunately, no successful experimental results have been reported so far, partly because it is difficult to produce an ideal TEM,‘, doughnut beam. In recent years, three kinds of atomic waveguiding schemes using hollow optical fibers [ 12-141 and a curved hollow convergent optical waveguide [15] have been proposed [ 12-151, and the former two kinds of atomic waveguiding schemes have been demonstrated experimentally [ 1h- 181. Obviously, it can be seen from Fig. 3 or Eq. (4) that the DHB with blue-detuning has a repulsive potential U(r) which is very similar to that of an evanescent wave in a hollow optical fiber. For two-level atoms, the potential Cl(r) due to the repulsive gradient force is given by [ 171 U(r)
= (/r3/4nk,)ln(
1 + 2[ a( r)]/(
A’ + y’)}.
(5)
where f = wL - wg - k~,. is the detuning of the laser frequency off-resonance of an atom, 0(r) = 27r&(r)/h is the atomic Rabi frequency at a given point in space, 2y is the rate of spontaneous radiation, d is the atomic transition dipole moment. and E(r) is the radial field strength of the DHB. In addition, because dark hollow beams have novel and unique physical properties such as small dark spot size (DSS), propagation invariance, heating-free effect, no optical losses during propagation, and no surface-potential effect due to the Van der Waals attraction, one can expect that a dark hollow beam with laser frequency above an atomic resonance can also be widely applied in atom optics such as in manipulation, collimation, cooling and trapping of neutral atoms, atomic lens, atomic funnel, atomic guiding, atomic cavity (including atomic gravito-optical cavity), atomic tweezers and atomic soliton as well as in other fields of modern optics and physics, material science and biological medicine. Moreover, considering the possibility of realizing a novel atom lithography or an atomic microscope (or atom-optical microscope) using the combination of a scanning laser microscope (SLM) and the atomic guiding technique using a dark hollow beam, we propose to demonstrate the laser-induced direct-guiding of an atomic beam or ultracold atoms from an atom trap through a dark hollow beam. In particular, there may be three atomic guiding schemes when the DHB is at blue detuning: (i) laser guiding of atoms in a large hollow fiber using a dark hollow beam, similar to the case of a Gaussian beam
.I. Yin et al./ Optics Communications
292
138 (1997) 287-292
guiding scheme in a large hollow fiber [ 12,161, (ii) laser collimating and guiding of atoms in a dark cylindrical-hollow beam with a small dark spot, which is similar to the case of an evanescent-wave guiding scheme [ 13,14,17,18], and (iii) laser cooling and guiding of atoms in a dark convergent-hollow beam, as proposed in Ref. [15]. It is expected that the final scheme will obtain a better ultracold atomic source with lower temperature and higher phase density as expected in Ref. [ 151. Note that guiding of atoms therein is to be done by using a hollow fiber with a curved convergent optical waveguide. But in our case atomic guiding is proposed using a dark convergent-hollow laser beam.
5. Conclusion In conclusion, we have proposed and demonstrated a new and simple method to generate a dark hollow beam using the micro-collimation technique for the output beam of a small-hollow optical fiber. By using M-20 X and M-40 X microscope objective lenses, we have obtained the DHB with a DSS of about 50-100 pm at Z = 100-500 mm and with a divergent angle of 6.5 X 10P5. In fact, the geometric dark spot size of the DHB in this experiment is far smaller than 50 pm at Z = 100 mm and 100 Frn at Z = 500 mm, respectively. The study also shows that better results on the DHB may be achieved if we use a slightly large-hollow-core fiber with lo-15 pm hollow diameter. In addition, this method can also be used for the study of the output modes of a hollow fiber and the measurement of the geometric sizes of a hollow fiber. Finally, we have briefly discussed the potential applications of the dark hollow beam in atom optics, and proposed three kinds of novel atomic guiding schemes in a dark hollow beam. In addition, if our dark hollow beam with a large dark spot at the far field (about 0.5 mm to 1.O mm) is directly coupled to a conical hollow mirror in single-beam atom trap [ 191, we may obtain a novel slow-velocity intense atomic beam from an atom trap compared with the recent experiment 1201. Obviously, such an atomic beam in free space will have many and important applications in atom optics such as reflection, diffraction and interference as well as holographic manipulation of cold atomic beam.
Acknowledgements This work was supported by the Ministry of Education (BSRI 96-2421) and the Ministry of Science and Technology South Korea.
of
References [I] R.M. Herman. T.A. Wiggins, J. Opt. Sot. Am. A 8 (1991) 932. [2] [3] [4] [5] [6] [7] [8] [9] [lo] 1111 [12] [13] [14] [15] [16] [17] [181 1191
X. Wang, M.G. Littman, Optics Lett. 18 (1993) 767. H.S. Lee, B.W. Atewart, K. Choi, H. Fenichel, Phys. Rev. A 49 (1994) 4922. C. Paterson. R. Smith, Optics Comm. 124 (1996) 121. V. Tikhonenko, N.N. Akhmediev, Optics Comm. 126 (1996) 108. S. Sato, H. Inaba. Opt. Quantum Electron. 28 (1996) 1. H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, Optics Comm. 115 (1995) 57. V.I. Balykin, V.S. Letokhov. Optics Comm. 64 (1987) 151. G.M. Gallatin, P.L. Gould, J. Opt. Sot. Am. B 8 (1991) 502. J.J. McClelland, M.R. Scheinfein, J. Opt. Sot. Am, B 8 (1991) 1974. Y.-Z. Wang, S. W. Fang and X. J. Wang, A proposal of an atomic lens with TEM, laser beam, unpublished. M.A. Ol’Shanii, Yu.B. Ovchinnikov, V.S. Letokhov, Optics Comm. 98 (1993) 77. S. Marksteiner, CM. Savage, P Zoller, S.L. Rolston, Phys. Rev. A 50 (1994) 2680. W. Jhe, M. Ohtsu, H. Hori, S.R. Friberg, Jpn. 3. Appl. Phys. 33 (1994) L1680. V.I. Balykin, D.V. Laryushin, M.V. Subbotin, V.S. Letokhov, JETP Lett. 63 (1996) 802. M.J. Renn, D. Montgomery. 0. Vdovin. D.Z. Anderson, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 75 (1995) 3253. M.J. Renn, E.A. Donley, E.A. Cornell, C.E. Wieman. D.Z. Anderson, Phys. Rev. A 53 (1996) R648. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K.I. Lee, W. Jhe, Phys. Rev. Lett. 76 (1996) 4500. K.I. Lee, J.A. Kim, H.R. Noh and W. Jhe, Optics Lett. 21 (1996) 1177; J.A. Kim, K.I. Lee, H.R. Noh, W. Jhe and H. Ohtsu, Optics Lett. Vol. 22 (19971, to be published.
1201 Z.T. Lu, K.L. Corwin. M.J. Renn, M.H. Anderson,
E.A. Cornell, C.E. Wieman, Phys. Rev. Lett. 77 (1996) 3331.
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications
138 (1997) 287-292
Generation of a dark hollow beam by a small hollow fiber Jianping Yin a,‘, Heung-Ryoul Noh a, Kwan-11 Lee a, Ki-Hyun Kim a, Yu-Zhu Wang b, Wonho Jhe a** ”
Physics Department
and Condensed Matter
b Lrrboratop,for
Quantum
Received
Research Institute,
Optics, Shanghai
12 December
Institute
Seoul National
University.
of Optics and Fine Mechanics,
1996; revised 29 January
Seoul 151-742, Shanghai
1997; accepted 3 February
201800.
South Korea China
1997
Abstract A new and simple method to generate a dark hollow beam is proposed and demonstrated. This method is based on a micro-collimation technique for the output beam of a hollow optical fiber. In this experiment, the dark spot size of about 50 Km to 100 Frn at the propagation distance Z of 100 mm to 500 mm is obtained. The relative divergent angle at the near field is about 6.5 X 10p5. The potential applications of the hollow beam in atom optics are also discussed.
1. Introduction
Generation [l-5] and application [6] of dark hollow beams (DHB) are one of the very interesting subjects in optics. It has attracted a great deal of attention and has been developed fast in recent years [l-6]. Since 1990, several groups have used different techniques, such as geometrical optical method [l], transverse-mode selected method [2], optical holographic method [3], computer-generated-hologram (CGH) method [4] and optical nonlinear effect [5], to generate dark hollow beams and obtained good results. In particular, Lee et al. (1994) obtained the smallest geometrical dark-spot size (i.e., first-zero ring diameter; geometrical DSS) which is about 70-80 pm [3]. But the diffraction efficiency of the first bright ring of J,-like hollow beam (J, denotes the first-order Bessel beam) and its propagation invariance were not good [3]. Paterson et al. (1996) obtained the best propagation invariance of a J, beam, but its geometrical DSS was greater than or equal to 175 pm (theoretically estimated value) [4]. It should be noted that if we use the full-width half-maximum (FWHM) of the radial intensity distribution of the DHB as the definition of a dark spot size (DSS), the geometric DDS will be far smaller than the DSS. So the actual DSS in Refs. [3] and [4] would be far greater than 100 and 200 pm, respectively. Moreover. the experimental setups and techniques were rather complicated in those experiments mentioned above [l-5]. In this paper, we report a new and simple experimental scheme to produce a dark hollow beam by using the micro-collimation technique for the output beam of a micron-sized hollow optical fiber. The results are DSS = 50-100 pm at Z = 100-500 mm, o = 6.5 X 10p5, and the relative coupling efficiency of the core mode of the hollow fiber is about 35%. A brief discussion of the applications of the DHB in atom optics is also included in the last section.
* Corresponding
author.
’ Permanent address: Department of Physics, Suzhou University, Suzhou, Jiangsu 215006, China. 0030-4018/97/$17.00 Copyright PII s0030-4018(97)00079-5
0 1997 Elsevier Science B.V. All rights reserved.
288
J. Yin et al. /Optics
Communications 138 (1997) 287-292
2. Experiment The principle of this method is very simple. cylindrical hollow-core and a cylindrical cladding, size of the hollow region and the thickness of the the weakly-guiding approximation, the transverse hollow fiber is given by [7,13] Im(ur) E,(r,f3)
[C,J,(ur)
_
i
sin( nt0)
+C?N,(ur)]sin(m0) K,(wr)sin(m@)
where the relative transverse propagation
The relative transverse
First, let us consider a fiber waveguide consisting of a hollow region, a and assume that the thickness of the cladding is far greater than both the core, and use the cylindrical coordinate system (I, 0,~). Then according to component E,(r,#) of the electric field propagating along the Z-axis in a
(hollow region) (coreregion)
(1)
(cladding region)
constant is defined as
attenuation constants are
where /3 and k are the propagation constant and the wave number, respectively. Here J, and N,,, in Eq. (1) are the Bessel functions of the first and the second kind of order m, and I, and Km are the modified Bessel functions of the first and the second kind of order m. Note that, starting from Eq. (1). Ito et al. [7] studied the propagation properties of a light beam in a hollow fiber and the mode structure of the core, both theoretically and experimentally, and obtained some low-order modes for the core of a hollow fiber, such as the LP,,,, LP, , , LP2,, LP,, and LP4, mode. Obviously, the central beam spot of these core modes are dark, like a doughnut beam. When the hollow diameter of the optical fiber is very small (about a few micrometers), an output doughnut beam with a small dark spot at the near field can be observed. So if we use a microscope objective (MO) with a short focal length to collimate the output beam of a hollow fiber, a dark hollow beam from the core mode can be obtained and its DSS is also very small. In addition, if the output beam of a cladding mode of the hollow fiber is collimated, a dark hollow beam with larger DSS can be also achieved. Of course, the coupling efficiency of the cladding mode is far greater than that of the core mode and up to about 70% can be achieved in our experiment. The experimental setup is shown in Fig. 1. A common He-Ne laser or a laser diode (LD) was used as a laser source (LS). In Fig. 1, two lenses L, and L, consist of a telescope system to play the functions of both expansion and collimation of an incident beam, and the magnification factor is about 20. VA ,, VA, and L, are two variable apertures and a focusing lens, respectively. The inner and outer diameter of the hollow-core of the fiber is 7 pm and 14.6 pm, respectively and the outer diameter of the cladding of the fiber is 123.4 pm. The relative refractive index difference, An = (ni - nz)/(2n:), is about 0.18% and n2 = 1.45, where IZ, and n2 are the refractive index of the core and the cladding, respectively. The numerical
Fig. 1. Experimental setup to generate a dark hollow beam by means of the micro-collimation technique for the output beam of a hollow optical fiber. Here LS, VA, MO and HOF stand for laser source, variable aperture, microscope objective, and hollow optical fiber, respectively.
.I. Yin et al. / Optics Communications
138 (IY97) 287-292
289
aperture, NA = n,sinflNA = n,sin8, = (n: - nil’/‘, is about 0.124 so that the relative optimum incident angle Bi must be smaller than or equal to 7.1”. Because this angle is very small, we used a lens with 100 mm focal length as a final focusing lens in order to get a higher coupling efficiency from the input to the output of the hollow fiber. In our experiment, a microscope objective (MO), such as M-20 X or M-40 X , was used for micro-collimating the output beam from the hollow fiber. A CCD-array was used for the measurement of the DSS of the dark hollow beam and the relative electric signal was fed to a digital storage oscilloscope to display the radial distribution of the intensity of the dark hollow beam. A CCD-camera (Model IVC-841, AMSECO) was used for the observation of the beam spot of the DHB at the far field. At the same time, we used a computer to record the signals from the oscilloscope and the image from the CCD-camera.
3. Results The propagation distance of the DHB, Z, is defined as the distance from the objective lens to a CCD-array or a screen of the CCD-camera. Fig. 2 shows the relative beam-spot image from a CCD-camera, which is an image collimated by a M-20 X objective lens for a LPo, core mode of the hollow fiber for h = 0.78 pm. Because the resolution of the laser printer is only 300 dpi, the form of the beam-spot image in Fig. 2 was slightly changed. In fact, it was a clear circle-ring on the monitor of the computer. The other low-order modes, such as LP, , , LP,, for A = 0.78 pm and LP,, for A = 0.633 pm, were also observed. In Fig. 2. the dark spot in the central region is the image of the hollow region at the output end-facet of the hollow fiber and the average diameter of the dark spot on the screen is about 3.0 mm (Z = 3.8 ml. The bright ring is the image of the hollow-core at the output end-facet of the hollow fiber, and its average thickness is about 2.0 mm at the same screen. Moreover, this method can also be used to study the output modes of a hollow fiber and even to distinguish the core mode, or the cladding mode, or their mixed mode. as well as to measure the geometric sizes of a hollow fiber such as the hollow diameter, the thickness of the core and the outer diameter of the cladding. A detailed description and experimental results will be published elsewhere. The experimental results from a CCD-array are shown in Fig. 3. Figs. 3(a) and 3(b) display the radial distribution of the intensity of the dark hollow beam at Z = 200 mm and 800 mm, respectively. Note that the end-surfaces of the hollow fiber were not well polished and the inner (outer) diameter of the hollow-core of the fiber was 7 pm (14.6 pm>, the weak scattered light from the hollow-core region at the output end-facet of the fiber was mainly concentrated in a very small area around the Z axis due to collimation by an objective lens, and as a result a localized scattering background around the Z axis was formed. In addition, the height and width (25 pm) of each element of a CCD-array is far greater than or is about equal to the geometric dark spot size of the DHB at the near field. So the central intensity of the beam spot cannot be reduced to
Fig. 2. The beam spot images of the DHB from a CCD-camera (Z = 3.8 m), which is an image of the LPa, core mode for A = 0.78 pm, obtained using a M-20X objective lens.
J. Yin et al./
290
Optics Communications 138 (1997) 287-292
Radial Position (a)
Radial Position W Fig. 3. The radial distribution
of the intensity of the DHB at (a) Z = 200 mm and (b) Z = 800 mm, obtained using a M-20X
0
200
600
400
600
loo0
400
500
objective lens.
Z(mm) (a)
0
100
200
300
J
zmw @I
Fig. 4. The relationship
between the DSS and the propagation
distance
Z of the DHB using (a) M-20X
and (b) M-40X
objective
lens.
J. Yin et al. / Optics Communications
138 (1997) 287-292
291
zero completely. The small peaks at the two sides of the DHB in Fig. 3(a) result from the diffraction effect of a selected-mode aperture VA, at the near field and its imperfect selection of the core-mode. However, when the end-surfaces of the hollow fiber are well polished, and the width and height of each element of a CCD-array are small enough, the central intensity of the beam spot will drop to zero, and the slope of the intensity distribution curve in the central region will become sharper. The relative intensity distribution of the DHB in the central region. like that of the TEM,*, doughnut beam [8], is given by I( r.:)
= [4P,
r’/
TW,‘(Z)]
exp[ -2r’/&(z)],
where P,, is the laser power, u”(z) = ~?a[1 + (:./:$I is the beam waist on the Z-plane, za = (rrwi/A) is the Rayleigh length, and wc is the beam waist on the plane Z = 0. Fig. 4 shows the relationship between the DSS and the propagation distance Z of the DHB. Figs. 4(a) and 4(b) are the results of the DHB collimated by a M-20 X and a M-40 X microscope objective, respectively. It can be seen from Fig. 4 that (i) the DSS of the dark hollow beam collimated by the M-20 X objective is about 50 Km at Z = 100 mm and about 100 pm at Z = 500 mm, (ii) the relative divergent angle at the near field is about 6.5 X 10P5, whereas the divergent angle at the far field is about 4.0 X IO-“. Note that the results on both the DSS and the beam divergence of the DHB collimated by a M-20 X objective lens are better than those collimated by a M-40 X lens, and (iii) we can expect that if we use a hollow fiber with a slightly larger hollow-core than the one used in this experiment, such as lo-15 pm, a dark hollow beam with a smaller dark spot and better propagation invariance may be obtained since a large hollow-core has smaller diffraction effect. Conversely, if we use a hollow fiber with a smaller hollow-core, such as 2 pm, and a microscope objective with a larger magnification (e.g., M-60 X ), a dark hollow beam with a larger divergent angle can be obtained. In addition, the propagation invariance of the DHB between the distance of Z = 0 and Z = 3.8 m in this experiment is not as good as that in Ref. [4], but we believe that it can be further improved by using a more suitable hollow fiber, or a better collimation and transformation beam technique, or optical information processing technology for the beam. On the other hand, the DHB with a certain divergent angle has some interesting applications in atom optics, such as atomic funnel and atomic guiding [ 151 and so on (see next section).
4. Discussion In 1987. Balykin et al. [8] proposed an idea to focus a neutral atomic beam (atomic lens) by using a TEM,, laser beam with blue-detuning. Afterwards. Gallatin [9], McClelland [lo], and Wang [Ill et al. studied theoretically in detail the laser focusing of atomic beams using a TEM;, doughnut beam. Unfortunately, no successful experimental results have been reported so far, partly because it is difficult to produce an ideal TEM,‘, doughnut beam. In recent years, three kinds of atomic waveguiding schemes using hollow optical fibers [ 12-141 and a curved hollow convergent optical waveguide [15] have been proposed [ 12-151, and the former two kinds of atomic waveguiding schemes have been demonstrated experimentally [ 1h- 181. Obviously, it can be seen from Fig. 3 or Eq. (4) that the DHB with blue-detuning has a repulsive potential U(r) which is very similar to that of an evanescent wave in a hollow optical fiber. For two-level atoms, the potential Cl(r) due to the repulsive gradient force is given by [ 171 U(r)
= (/r3/4nk,)ln(
1 + 2[ a( r)]/(
A’ + y’)}.
(5)
where f = wL - wg - k~,. is the detuning of the laser frequency off-resonance of an atom, 0(r) = 27r&(r)/h is the atomic Rabi frequency at a given point in space, 2y is the rate of spontaneous radiation, d is the atomic transition dipole moment. and E(r) is the radial field strength of the DHB. In addition, because dark hollow beams have novel and unique physical properties such as small dark spot size (DSS), propagation invariance, heating-free effect, no optical losses during propagation, and no surface-potential effect due to the Van der Waals attraction, one can expect that a dark hollow beam with laser frequency above an atomic resonance can also be widely applied in atom optics such as in manipulation, collimation, cooling and trapping of neutral atoms, atomic lens, atomic funnel, atomic guiding, atomic cavity (including atomic gravito-optical cavity), atomic tweezers and atomic soliton as well as in other fields of modern optics and physics, material science and biological medicine. Moreover, considering the possibility of realizing a novel atom lithography or an atomic microscope (or atom-optical microscope) using the combination of a scanning laser microscope (SLM) and the atomic guiding technique using a dark hollow beam, we propose to demonstrate the laser-induced direct-guiding of an atomic beam or ultracold atoms from an atom trap through a dark hollow beam. In particular, there may be three atomic guiding schemes when the DHB is at blue detuning: (i) laser guiding of atoms in a large hollow fiber using a dark hollow beam, similar to the case of a Gaussian beam
.I. Yin et al./ Optics Communications
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guiding scheme in a large hollow fiber [ 12,161, (ii) laser collimating and guiding of atoms in a dark cylindrical-hollow beam with a small dark spot, which is similar to the case of an evanescent-wave guiding scheme [ 13,14,17,18], and (iii) laser cooling and guiding of atoms in a dark convergent-hollow beam, as proposed in Ref. [15]. It is expected that the final scheme will obtain a better ultracold atomic source with lower temperature and higher phase density as expected in Ref. [ 151. Note that guiding of atoms therein is to be done by using a hollow fiber with a curved convergent optical waveguide. But in our case atomic guiding is proposed using a dark convergent-hollow laser beam.
5. Conclusion In conclusion, we have proposed and demonstrated a new and simple method to generate a dark hollow beam using the micro-collimation technique for the output beam of a small-hollow optical fiber. By using M-20 X and M-40 X microscope objective lenses, we have obtained the DHB with a DSS of about 50-100 pm at Z = 100-500 mm and with a divergent angle of 6.5 X 10P5. In fact, the geometric dark spot size of the DHB in this experiment is far smaller than 50 pm at Z = 100 mm and 100 Frn at Z = 500 mm, respectively. The study also shows that better results on the DHB may be achieved if we use a slightly large-hollow-core fiber with lo-15 pm hollow diameter. In addition, this method can also be used for the study of the output modes of a hollow fiber and the measurement of the geometric sizes of a hollow fiber. Finally, we have briefly discussed the potential applications of the dark hollow beam in atom optics, and proposed three kinds of novel atomic guiding schemes in a dark hollow beam. In addition, if our dark hollow beam with a large dark spot at the far field (about 0.5 mm to 1.O mm) is directly coupled to a conical hollow mirror in single-beam atom trap [ 191, we may obtain a novel slow-velocity intense atomic beam from an atom trap compared with the recent experiment 1201. Obviously, such an atomic beam in free space will have many and important applications in atom optics such as reflection, diffraction and interference as well as holographic manipulation of cold atomic beam.
Acknowledgements This work was supported by the Ministry of Education (BSRI 96-2421) and the Ministry of Science and Technology South Korea.
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