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On the optical characteristics of the conical emission
Volume 57, n u m b e r 2
OPTICS COMMUNICATIONS
15 February 1986
ON T H E OPTICAL CHARACTERISTICS OF T H E CONICAL E M I S S I O N I. GOLUB, R. S H U K E R and G. EREZ Physics Department, Ben-Gurion University, Beer-Sheva 84105, lsrael Received 11 September 1985; revised manuscript received 5 November 1985
An intense laser beam blue detuned with respect to an atomic transition produces a forward conical emission. We demonstrate new experimental evidence that in sodium vapor this emission is generated at the surface of self-trapped filaments. This includes comparison of the polarization of the incident and emitted light as well as comparing the output pattern obtained by cylindrical and spherical focusing modes. As a surface phenomenon, the conical emission shares its characteristics with Cherenkov-type processes.
An intense quasiresonant laser radiation profoundly modifies the optical properties of an atomic system. One manifestation of this interaction is the known conical emission [1]. This forward ring emission appears in atomic vapors when the incident laser is blue detuned with respect to a resonant transition. It occurs under conditions of laser intensity, laser detuning and atomic vapor density for which self-trapped filaments are generated [2]. There has been considerable interest in the conical emission [1-7]. However, there is no satisfactory self-consistent explanation for this effect [3,5,6]. In particular, the measured cone angle is larger by a factor of x/2 to 2 than that predicted by previously proposed models [2,6]. The case of recently reported conical emission induced by excitation of a two-photon allowed transition under conditions that avoid self-focussing is in fact due to four-wave mixing, where the two generated photons are actually observed [8]. It is the conical emission involving one photon resonance and accompanying self-focusing which poses difficulties for the four-wave mixing model: in addition to the discrepancy between predicted and measured cone angle, in most experiments the blue counterpart Rabi's sideband is absent [1,3-5,7]. We have recently proposed a model of Cherenkov radiation due to a moving polarization which emits the conical emission from the filament surfaces [7]. In the present letter, we provide new experimental results indicating that the conical emission is formed 0 030-4018/86/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
at the surface of the self-trapped filaments. As a surface phenomenon, the conical emission does not have to conserve the transverse component of the linear momentum [9-11 ] and obeys the condition of the Cherenkov-type process. The tranverse momentum mismatch allows the emission angles to be larger than that in the case of total phase matching [9,12] and renders better angle fit to experimental result. We note that surface radiation, sometimes called class II radiation, was studied in liquids and its properties were found to be different from that of Raman emission [11-13]. In this case, too, there is no model explaining the characteristics of this surface emission and in particular the experimentally measured cone angle. Our experimental setup consists of a sodium containing heat-pipe with 20 cm active length and a H~insch-type 10 kW peak dye laser. The sodium density is 1014-1016 cm -3. The beam of 0.5 cm -1 bandwidth laser is focused by a lens into the sodium cell after spacial filtering. The laser intensity at the focus is 10 MW/cm 2 and is sufficient for the formation of self-trapped Filaments. The forward emission was photographed by an Alphax B216 camera with f/number of 1.9, placed after the sodium cell without any imaging optics. The laser beam was blocked with a small on-axis disk to prevent over-exposure. The spectral and angular properties of the conical emission are well-known [1-7]. The cone angle is 1 - 3 ° and increases as the laser frequency approaches the atomic transition and with increasing sodium den143
Volume 57, number 2
OPTICS COMMUNICATIONS
sity. The cone spectrum is broad ( 5 - 1 0 cm M ) and is to the red of the transition. For small laser detunings ( 2 - 6 cm - 1 ) the peak of the conical emission is detuning. For large laser detunings ( 6 - 2 0 cm - 1 ) the peak detuning exhibits saturation behavior;the limiting value is at the dispersionless point - 5894 A. Two kinds of experiments were performed to establish the surface character o f the conical emission. Firstly, we used right circular polarized (R) laser light. The polarization is imperfect and contains about 0.1% left circularly polarized (L) light. It was shown by Close et at. [14], that in such a case, due to the difference in nonlinear refractive indices for the two polarizations, the weaker one is self-trapped before the stronger component. As a result, the light changes its polarization into a linear one, with a direction determined by the L - R phase relation in the input beam. Self-trapping of laser light close to the transition is due to saturation effects [ 15 ], and this change in polarization is expected to occur inside the filaments, where the saturation degree is maximum. Experimentally, such phenomenon was observed [14] and was accompanied by similar change in polarization of Raman Stokes emission, originating in the self-trapped ilia-
(a)
15 February 1986
ments. In comparison, the linear polarization is a stable self-trapped component [14]. Experimentally we have found that the conical emission had the same circular or linear polarization as that of the input laser, similar to the result obtained by Skinner and Kleiber [1] and Meyer [3]. Thus, we may conclude that the conical emission is generated at a nonsaturated region such as the self-trapped filament surface. We have also examined the spatial coherence of the conical emission. This, too, enables us to distinguish between volume or surface radiation. We focused the laser light into the sodium cell either by a spherical or a cylindrical lens (fig. 1). In both cases there is a smooth continuous ring which is a trace of the conical emission. At the center, the black area is the blocking disk. In fig. la, produced whith spherical lens, one sees a circular halo around the disk. Fig. lb is produced with a cylindrical lens. The elliptical feature has its major axis perpendicular to the focal line, persists even at wavelength far from the D transitions and represents the image pattern o f the excitation region in the focal plane. We have also found that the angular and spectral distribution o f the conical emis-
(b)
Fig. 1. The pattern of the conical emission at sodium density of 1.8 X 1015 cm-3 and laser detuning of 2 A to the blue of the D2 transition. The laser radiation is focused into the sodium cell by a spherical lens (a) and by a cylindrical lens (b). The laser beam is blocked with a small on-axis disk. The focal line of the cylindrical lens (b) is along the horizontal line. 144
Volume 57, number 2
OPTICS COMMUNICATIONS
sion is independent o f the lens type. As the intense laser beam propagates in the medium it forms saturated filaments in the sodium. The interior saturated part o f the filaments has no dispersion and no shifts as n = 1 and preserves spatial coherence relationships between the radiation from the interior o f the filaments. Emission from surfaces o f different filaments, however, have no phase relationships and do not bear such coherence because o f the different local optical conditions adjacent to each filament surface. This happens because the refractive index at the various filament surfaces may vary locally due to spatial inhomogeneities in sodium density and in laser intensity causing fluctuation in the degree o f saturation at the surfaces. The interior contributions thus interfere to form a pattern representing the spatial distribution o f the filaments - an ellipse for cylindrical focusing. The contributions from the surfaces, however, form a sum o f uncorrelated radiation patterns around the laser beam. In the latter case, the angular distribution is given b y emission from each filament resulting in a ring halo independently o f the focusing mode. Since the conical emission displays no shape dependence on excitation region pattern, i.e. on focusing mode, be it spherical or cylindrical, it can only be formed on the surface o f the filaments and not in their bulk. Similar observation was reported b y E. Garmire in the study o f the emission shape dependence [11 ] : for a cylindrical focusing mode the Raman emission originnating in the filaments gave a hollow ellipse in the far field, while class II radiation was generated in a circularly symmetric cone. In summary, we have shown that the conical emission which occurs for a laser blue detuned with respect to sodium D 2 line is an emission originating at the sur* This is in accordance with observation of Chauchard and Meyer [3], that an individual ring is formed around each filament.
15 February 1986
face o f the self-trapped filaments. The origin o f the conical emission at the surface o f the self-trapped filaments appears to be a necessary condition to explain the experimentally observed cone angles. The conical emission from various filaments add up incoherently and display no interference pattern.
References [1] C.H. Skinner and P.D. Kleiber, Phys. Rev. A21 (1979) 151. [2] D.J. Harter, T. Narum, M.G. Raymer and R.W. Boyd, Phys. Rev. Lett 46 (1981) 1192; D.J. Hatter and R.W. Boyd, Optics Lett 7 (1982) 491; D.J. Hatter and R.W. Boyd, Phys. Rev. A29 (1984) 739. [3] Y.H. Meyer, Optics Comm. 34 (1980) 434; E.A. Chauchard and Y.H. Meyer, Optics Comm. 52 (1984) 141. [4] G. Brechignac, Ph. Cahuzac and A. Debarre, Optics Comm. 34 (1980) 87. [5] G.L. Burdge and C.H. Lee, AppL Phys. B28 (1982) 197. [6] C.H. Skinner, Optics Comm. 41 (1982) 407. [7] I. Golub, G. Erez and R. Shuker, J. Phys. B: Atomic and molecular physics, to be published. [8] J. Krasinski, D.J. Gauthier, M.S. Malcuit and R.W. Boyd, Optics Comm. 54 (1985) 241. [9] R.W. Terhune, Bull. Am. Phys. Soc. 8 (1963) 359; A. Sz6ke, Bull. Am. Phys. Soc. 9 (1964) 490. [10] C.A. Sacchi, C.M. Townes and J.R. Lifsitz, Phys. Rev. 174 (1968) 439. [ 11 ] E. Garrnke, in: Physics of quantum electronics, eds. P.L. Kelley, B. Lax and P.E. Tannenwald (McGraw-Hill, New York, 1966) pp. 167-179. [12] K. Shimoda, Jap. J. AppL Phys. 5 (1966) 86. [13] Y.R. Shen and N. Bloembergen, Phys. Rev. A137 (1965) 1787; H.A. Hans, P.L. Kelley and H.J. Zeiger, Phys. Rev. A138 (1965) 960; V.N. Lugovoi and A.M. Proldaorov, Soy. Phys. JETP 42 (1976) 42. [14] D.H. Close, C.R. Giullano, R.W. Hellwarth, L.D. Hess, F.J. McClung, and W.G. Wagner, IEEE J. Quantum Electron. QE-2 (1966) 553. [15] A. Javan and P.L. Kelley, IEEE J. Quantum Electron. QE-2 (1966) 470.
145
OPTICS COMMUNICATIONS
15 February 1986
ON T H E OPTICAL CHARACTERISTICS OF T H E CONICAL E M I S S I O N I. GOLUB, R. S H U K E R and G. EREZ Physics Department, Ben-Gurion University, Beer-Sheva 84105, lsrael Received 11 September 1985; revised manuscript received 5 November 1985
An intense laser beam blue detuned with respect to an atomic transition produces a forward conical emission. We demonstrate new experimental evidence that in sodium vapor this emission is generated at the surface of self-trapped filaments. This includes comparison of the polarization of the incident and emitted light as well as comparing the output pattern obtained by cylindrical and spherical focusing modes. As a surface phenomenon, the conical emission shares its characteristics with Cherenkov-type processes.
An intense quasiresonant laser radiation profoundly modifies the optical properties of an atomic system. One manifestation of this interaction is the known conical emission [1]. This forward ring emission appears in atomic vapors when the incident laser is blue detuned with respect to a resonant transition. It occurs under conditions of laser intensity, laser detuning and atomic vapor density for which self-trapped filaments are generated [2]. There has been considerable interest in the conical emission [1-7]. However, there is no satisfactory self-consistent explanation for this effect [3,5,6]. In particular, the measured cone angle is larger by a factor of x/2 to 2 than that predicted by previously proposed models [2,6]. The case of recently reported conical emission induced by excitation of a two-photon allowed transition under conditions that avoid self-focussing is in fact due to four-wave mixing, where the two generated photons are actually observed [8]. It is the conical emission involving one photon resonance and accompanying self-focusing which poses difficulties for the four-wave mixing model: in addition to the discrepancy between predicted and measured cone angle, in most experiments the blue counterpart Rabi's sideband is absent [1,3-5,7]. We have recently proposed a model of Cherenkov radiation due to a moving polarization which emits the conical emission from the filament surfaces [7]. In the present letter, we provide new experimental results indicating that the conical emission is formed 0 030-4018/86/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
at the surface of the self-trapped filaments. As a surface phenomenon, the conical emission does not have to conserve the transverse component of the linear momentum [9-11 ] and obeys the condition of the Cherenkov-type process. The tranverse momentum mismatch allows the emission angles to be larger than that in the case of total phase matching [9,12] and renders better angle fit to experimental result. We note that surface radiation, sometimes called class II radiation, was studied in liquids and its properties were found to be different from that of Raman emission [11-13]. In this case, too, there is no model explaining the characteristics of this surface emission and in particular the experimentally measured cone angle. Our experimental setup consists of a sodium containing heat-pipe with 20 cm active length and a H~insch-type 10 kW peak dye laser. The sodium density is 1014-1016 cm -3. The beam of 0.5 cm -1 bandwidth laser is focused by a lens into the sodium cell after spacial filtering. The laser intensity at the focus is 10 MW/cm 2 and is sufficient for the formation of self-trapped Filaments. The forward emission was photographed by an Alphax B216 camera with f/number of 1.9, placed after the sodium cell without any imaging optics. The laser beam was blocked with a small on-axis disk to prevent over-exposure. The spectral and angular properties of the conical emission are well-known [1-7]. The cone angle is 1 - 3 ° and increases as the laser frequency approaches the atomic transition and with increasing sodium den143
Volume 57, number 2
OPTICS COMMUNICATIONS
sity. The cone spectrum is broad ( 5 - 1 0 cm M ) and is to the red of the transition. For small laser detunings ( 2 - 6 cm - 1 ) the peak of the conical emission is detuning. For large laser detunings ( 6 - 2 0 cm - 1 ) the peak detuning exhibits saturation behavior;the limiting value is at the dispersionless point - 5894 A. Two kinds of experiments were performed to establish the surface character o f the conical emission. Firstly, we used right circular polarized (R) laser light. The polarization is imperfect and contains about 0.1% left circularly polarized (L) light. It was shown by Close et at. [14], that in such a case, due to the difference in nonlinear refractive indices for the two polarizations, the weaker one is self-trapped before the stronger component. As a result, the light changes its polarization into a linear one, with a direction determined by the L - R phase relation in the input beam. Self-trapping of laser light close to the transition is due to saturation effects [ 15 ], and this change in polarization is expected to occur inside the filaments, where the saturation degree is maximum. Experimentally, such phenomenon was observed [14] and was accompanied by similar change in polarization of Raman Stokes emission, originating in the self-trapped ilia-
(a)
15 February 1986
ments. In comparison, the linear polarization is a stable self-trapped component [14]. Experimentally we have found that the conical emission had the same circular or linear polarization as that of the input laser, similar to the result obtained by Skinner and Kleiber [1] and Meyer [3]. Thus, we may conclude that the conical emission is generated at a nonsaturated region such as the self-trapped filament surface. We have also examined the spatial coherence of the conical emission. This, too, enables us to distinguish between volume or surface radiation. We focused the laser light into the sodium cell either by a spherical or a cylindrical lens (fig. 1). In both cases there is a smooth continuous ring which is a trace of the conical emission. At the center, the black area is the blocking disk. In fig. la, produced whith spherical lens, one sees a circular halo around the disk. Fig. lb is produced with a cylindrical lens. The elliptical feature has its major axis perpendicular to the focal line, persists even at wavelength far from the D transitions and represents the image pattern o f the excitation region in the focal plane. We have also found that the angular and spectral distribution o f the conical emis-
(b)
Fig. 1. The pattern of the conical emission at sodium density of 1.8 X 1015 cm-3 and laser detuning of 2 A to the blue of the D2 transition. The laser radiation is focused into the sodium cell by a spherical lens (a) and by a cylindrical lens (b). The laser beam is blocked with a small on-axis disk. The focal line of the cylindrical lens (b) is along the horizontal line. 144
Volume 57, number 2
OPTICS COMMUNICATIONS
sion is independent o f the lens type. As the intense laser beam propagates in the medium it forms saturated filaments in the sodium. The interior saturated part o f the filaments has no dispersion and no shifts as n = 1 and preserves spatial coherence relationships between the radiation from the interior o f the filaments. Emission from surfaces o f different filaments, however, have no phase relationships and do not bear such coherence because o f the different local optical conditions adjacent to each filament surface. This happens because the refractive index at the various filament surfaces may vary locally due to spatial inhomogeneities in sodium density and in laser intensity causing fluctuation in the degree o f saturation at the surfaces. The interior contributions thus interfere to form a pattern representing the spatial distribution o f the filaments - an ellipse for cylindrical focusing. The contributions from the surfaces, however, form a sum o f uncorrelated radiation patterns around the laser beam. In the latter case, the angular distribution is given b y emission from each filament resulting in a ring halo independently o f the focusing mode. Since the conical emission displays no shape dependence on excitation region pattern, i.e. on focusing mode, be it spherical or cylindrical, it can only be formed on the surface o f the filaments and not in their bulk. Similar observation was reported b y E. Garmire in the study o f the emission shape dependence [11 ] : for a cylindrical focusing mode the Raman emission originnating in the filaments gave a hollow ellipse in the far field, while class II radiation was generated in a circularly symmetric cone. In summary, we have shown that the conical emission which occurs for a laser blue detuned with respect to sodium D 2 line is an emission originating at the sur* This is in accordance with observation of Chauchard and Meyer [3], that an individual ring is formed around each filament.
15 February 1986
face o f the self-trapped filaments. The origin o f the conical emission at the surface o f the self-trapped filaments appears to be a necessary condition to explain the experimentally observed cone angles. The conical emission from various filaments add up incoherently and display no interference pattern.
References [1] C.H. Skinner and P.D. Kleiber, Phys. Rev. A21 (1979) 151. [2] D.J. Harter, T. Narum, M.G. Raymer and R.W. Boyd, Phys. Rev. Lett 46 (1981) 1192; D.J. Hatter and R.W. Boyd, Optics Lett 7 (1982) 491; D.J. Hatter and R.W. Boyd, Phys. Rev. A29 (1984) 739. [3] Y.H. Meyer, Optics Comm. 34 (1980) 434; E.A. Chauchard and Y.H. Meyer, Optics Comm. 52 (1984) 141. [4] G. Brechignac, Ph. Cahuzac and A. Debarre, Optics Comm. 34 (1980) 87. [5] G.L. Burdge and C.H. Lee, AppL Phys. B28 (1982) 197. [6] C.H. Skinner, Optics Comm. 41 (1982) 407. [7] I. Golub, G. Erez and R. Shuker, J. Phys. B: Atomic and molecular physics, to be published. [8] J. Krasinski, D.J. Gauthier, M.S. Malcuit and R.W. Boyd, Optics Comm. 54 (1985) 241. [9] R.W. Terhune, Bull. Am. Phys. Soc. 8 (1963) 359; A. Sz6ke, Bull. Am. Phys. Soc. 9 (1964) 490. [10] C.A. Sacchi, C.M. Townes and J.R. Lifsitz, Phys. Rev. 174 (1968) 439. [ 11 ] E. Garrnke, in: Physics of quantum electronics, eds. P.L. Kelley, B. Lax and P.E. Tannenwald (McGraw-Hill, New York, 1966) pp. 167-179. [12] K. Shimoda, Jap. J. AppL Phys. 5 (1966) 86. [13] Y.R. Shen and N. Bloembergen, Phys. Rev. A137 (1965) 1787; H.A. Hans, P.L. Kelley and H.J. Zeiger, Phys. Rev. A138 (1965) 960; V.N. Lugovoi and A.M. Proldaorov, Soy. Phys. JETP 42 (1976) 42. [14] D.H. Close, C.R. Giullano, R.W. Hellwarth, L.D. Hess, F.J. McClung, and W.G. Wagner, IEEE J. Quantum Electron. QE-2 (1966) 553. [15] A. Javan and P.L. Kelley, IEEE J. Quantum Electron. QE-2 (1966) 470.
145