We demonstrate an all optical waveguide imprinted by a low power Laguerre Gaussian control laser beam using a coherent Raman process in warm atomic rubidium vapor. We show that the signal beam propagates with a small spot size over several diffraction lengths. We also show that the coupling efficiency of the signal beam into the waveguide varies linearly with the signal power

Howell, John C.

Starling, David J.

Vudyasetu, Praveen K.

English

Chapman University Digital Commons

Chapman University Chapman University Digital Commons Mathematics, Physics, and Computer Science Faculty Articles and Research Science and Technology Faculty Articles and Research 3-26-2009 All Optical Waveguiding in a Coherent Atomic Rubidium Vapor Praveen K. Vudyasetu University of Rochester David J. Starling University of Rochester John C. Howell Chapman University, johhowell@chapman.edu Follow this and additional works at: https://digitalcommons.chapman.edu/scs_articles  Part of the Optics Commons Recommended Citation P. K. Vudyasetu, D. J. Starling, and J. C. Howell, All Optical Waveguiding in a Coherent Atomic Rubidium Vapor, Phys. Rev. Lett. 102(12), 123602. https://doi.org/10.1103/PhysRevLett.102.123602 This Article is brought to you for free and open access by the Science and Technology Faculty Articles and Research at Chapman University Digital Commons. It has been accepted for inclusion in Mathematics, Physics, and Computer Science Faculty Articles and Research by an authorized administrator of Chapman University Digital Commons. For more information, please contact laughtin@chapman.edu. All Optical Waveguiding in a Coherent Atomic Rubidium Vapor Comments This article was originally published in Physical Review Letters, volume 102, issue 12, in 2009. https://doi.org/10.1103/PhysRevLett.102.123602 Copyright American Physical Society This article is available at Chapman University Digital Commons: https://digitalcommons.chapman.edu/scs_articles/854 All Optical Waveguiding in a Coherent Atomic Rubidium VaporPraveen K. Vudyasetu, David J. Starling, and John C. HowellDepartment of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA*(Received 10 December 2008; published 26 March 2009)We demonstrate an all optical waveguide imprinted by a low power Laguerre Gaussian control laserbeam using a coherent Raman process in warm atomic rubidium vapor. We show that the signal beampropagates with a small spot size over several diffraction lengths. We also show that the couplingefficiency of the signal beam into the waveguide varies linearly with the signal power.DOI: 10.1103/PhysRevLett.102.123602 PACS numbers: 42.50.Gy, 42.65.An, 42.65.Jx, 42.65.WiNonlinear optical properties of various gases within anoptical waveguide structure have received considerablerecent attention [1,2]. The use of an optical waveguideenables one to have high intensities at lower optical powersover distances much greater than the diffraction length.The combination of higher intensities, longer interactionlengths, and higher atomic densities within the mode vol-ume results in efficient nonlinear processes [1]. Benabidet al. demonstrated an efficient stimulated Raman scatter-ing process in a hollow-core photonic crystal fiber filledwith hydrogen gas requiring 2 orders of magnitude lesscontrol beam power than any other previously reportedexperiments [1]. Efficient nonlinear processes have beendemonstrated by injecting rubidium vapor in such a wave-guide [2] and also by using the small optical mode area of atapered nanofiber placed in rubidium vapor [3].An all optical waveguide refers to a waveguide whosetransverse refractive index profile is set by the interactionof an optical control beamwith the medium. The propertiesof the waveguide can be altered or modified to fit a par-ticular experimental requirement simply by changing theproperties of the control beam. Several schemes have beenproposed to achieve all optical waveguiding, and therehave been some experimental realizations. Moseley et al.have proposed [4] and realized [5] focusing and defocusingof the signal beam using electromagnetically induced fo-cusing. There are several other papers which addressRaman focusing [6–9]. Truscott et al. have achieved opti-cal waveguiding [10], and their scheme is analyzed indetail by Kapoor et al. [11] and Anderson et al. [12]. Inthis scheme the control beam modifies the refractive indexof the medium by pumping the ground state rubidiumatoms to an excited state. There are several other schemesproposed for waveguiding [13], and more recently imageguiding [14], using electromagnetically induced transpar-ency in lambda and double lambda systems.In this Letter, we present the experimental results dem-onstrating the waveguiding effect in warm rubidium vaporusing an off-resonance Raman transition. The transmissionof the signal beam changes sharply when its frequency isnear Raman resonance with the control beam. This resultsin changes in the refractive index at signal frequenciesaround Raman resonance [15,16]. We use a donut shapedfirst order Laguerre Gaussian (LG01) control beam to im-print a waveguide in the atomic rubidium vapor. Therefractive index at the annulus of the donut control beamis lower than that at the core for signal frequencies tuned tothe blue of Raman resonance.The experimental setup shown in Fig. 1 consists of a795 nm external cavity tunable diode laser followed by atapered amplifier. The beam is split in two at a 50=50 beamΩsΩC|2δ|3∆|1Laser795 nmAOM/2PBS PBSRbSignalControlCamera2f ffSpiralPhase PlateL1L2L3 L4(b)(c)(a)50/50BSFIG. 1 (color online). (a) The experimental schematic for alloptical waveguiding using atomic rubidium vapor. (b) The fo-cusing scheme for control beam (black) and signal (gray).(c) The energy level diagram. We have a positive single photondetuning, , of about 500 MHz. Note that according to ourconvention positive Raman detuning is to the red of Ramanresonance frequency. The waveguide is imprinted onto therubidium atoms by a Laguerre Gaussian control beam. Thesignal is focused into the core of the control beam at the frontof the cell. We measure the beam diameters at the back face ofthe cell to demonstrate guiding by imaging the back face of thecell onto the camera using the lenses L3 and L4 in a 4f imagingconfiguration.PRL 102, 123602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending27 MARCH 20090031-9007=09=102(12)=123602(4) 123602-1  2009 The American Physical Societysplitter. One beam acts as the signal after frequency shift-ing it by about 3.035 GHz to the red by double passing itthrough a 1.5 GHz acousto-optic modulator (AOM). Theother beam acts as the control beam which is sent through aspatial filter in order to clean up its mode and is followedby a charge one spiral phase plate, resulting in a first orderLaguerre Gaussian beam. The orthogonally polarized con-trol and signal are then combined at a polarizing beamsplitter (PBS). We use a configuration where the controlfocuses at the back face and the signal focuses into the coreof the donut control beam at the front face of the vapor cell.The control is filtered at another polarizing beam splitterafter the cell. We image the back face of the cell with a 4fimaging system to determine the size of the signal. Theantireflection coated vapor cell is 5 cm long and contains anatural abundance of rubidium isotopes with a 20 torr neonbuffer gas. The vapor cell is placed inside a magneticallyshielded oven and is maintained at a temperature of about80 C, which results in number densities of approximately1012 cm3.The experimental parameters are chosen such that thecore of the LG beam has a higher refractive index than theannulus of the beam. For a lambda system the susceptibil-ity at the signal frequency is given by [16]ðc; ;Þ ¼ N2@0þ iðþ iÞðþ iÞ 2c=4; (1)where  is the excited state decay rate,  is ground statedecoherence rate, and  and  are the single photon andtwo photon detunings, respectively. The real part of thesusceptibility is given by0ðc;;Þ ¼ N2@0 2c4ð2þ2Þð 2c4ð2þ2ÞÞ2 þ ðþ 2c4ð2þ2ÞÞ2:(2)One can observe from Eq. (2) that the variation of0ðc; ;Þ versus control beam Rabi frequency has theform of dispersion near a homogeneously broadened spec-tral line. Figure 2 depicts this behavior for various combi-nations of  and . We note that the refractive index forzero c depends on the magnitude and sign of  and thenumber density. When there is no control beam,0ðc; ;Þ ¼ N2@01: (3)We also see that for all combinations of parameters,0ðc; ;Þ approaches zero for very large c. The realpart of susceptibility for large c can be approximated as0ðc; ;Þ ’ N2@042c: (4)Note that the above approximation is valid as long as  ismuch smaller than 2c4ð2þ2Þ. For the cases where we have afocused signal or focused coupling beams, a large  result-ing from the residual Doppler broadening due to angularmismatch of signal and coupling beams is compensated byhaving higher coupling beam intensities so that the powerbroadening dominates all other decoherence mechanisms.We can design the waveguide by choosing appropriateparameters. A donut shaped control beam with  and having the same sign results in a refractive index profileanalogous to a fiber. One significant difference of thisscheme from [10] is that the latter relies on pumping ofthe population to one of the excited states, which requiresmuch more control beam power (400 mW) than ourscheme (20 mW). Even with very large control beampowers, only 50% of the population can be pumped tothe excited state, limiting the refractive index differencebetween ‘‘core’’ and ‘‘cladding.’’ On the other hand, thescheme in [10] guides the signal over wider bandwidth.The plot showing the transmission of the signal beam asa function of Raman detuning is shown in Fig. 3(a). Thecontrol and the signal are tuned to be about 500 MHz to theblue of Rb85 F ¼ 2 to F0 ¼ ð2; 3Þ and F ¼ 3 to F0 ¼ ð2; 3ÞD1 transitions, respectively. Both control and signal arecollimated and are copropagating. The dispersion of themedium is obtained by using Kramers-Kronig relations.Figure 3(b) shows the plot of the variation of the refractiveindex at a fixed signal frequency with a  ¼ 1:5 MHzversus control beam power. We can see that the refractiveindex decreases with increasing control beam intensity. Wechoose the signal frequency to be close to Raman reso-nance such that there is good contrast in the refractiveindex for higher and lower control beam powers and0 1 2 3 4 5 6 7 8 9 10x 107−6−4−20246 x 10−3Control Beam Rabi Frequency (Hz)'(c) = -500 MHz= -1 MHz = 500 MHz= -1 MHz = 500 MHz= 1 MHz = -500 MHz= 1 MHzFIG. 2 (color online). The theoretical plot of the real part ofthe susceptibility as a function of the control beam Rabi fre-quency. We plot for different signs of two photon detuning andsingle photon detuning to show the qualitative features of thesusceptibility. The parameters  and  are indicated in the figurefor each plot, and N is taken as 1012 cm3.PRL 102, 123602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending27 MARCH 2009123602-2away from the absorption dip shown in Fig. 3(a). We foundthat we have optimum guiding at a  ¼ 2 MHz.Figure 3(c) shows the refractive index profile along thetransverse plane. The intensity profile at the front of thevapor cell is captured with a camera and Eq. (2) is used toobtain the refractive index. Figure 3(d) shows the indexprofile along one of the axes of the beam. We see that wehave a refractive index contrast of about 105 betweenmaximum and minimum refractive indices. Figure 4 showsthe results of the experiment. The control beam is converg-ing along the cell and has a focus at the back face of thecell. The signal is focused into the ‘‘core’’ of the controlbeam at the front face as shown in Fig. 4(c). In the absenceof the control beam, the signal beam diverges along thelength of the cell as shown by the gray curve in Fig. 4(d).The Gaussian width of the signal at the front face of the cellis 56 m, and at the back face it is 102 m without thecontrol beam. When the control is on, the signal is guidedalong its core, and so the signal beam diameter is smaller atthe back face of the cell. For example, the Gaussian widthof the signal at the back face is 35 m with an 18 mWinput control [black curve of Fig. 4(d)]. The integratedintensity of the black curve is approximately 43% of thegray curve, implying that there is a good coupling of thesignal power into the waveguide. Note that the peak inten-sity of the black curve is more than that of the gray curve.The control beam intensity in Figs. 4(c) and 4(d) is nor-malized to fit in the figure, while the signal intensities inFig. 4(d) are relative. The laser beams are slightly ellip-tical, and so the axis mentioned above is along the longeraxis. The snapshots of the signal beamwith and without thecontrol beam at the back face of the vapor cell are shown inFigs. 4(a) and 4(b).The size of the signal at the back of the cell also dependson the control beam power, as shown in the Fig. 5(a),and on the two photon detuning, as shown in Fig. 5(b).Figure 5(b) also shows that we can have waveguiding for arange of frequencies to the blue of Raman resonance. Thismeans that we can potentially guide optical pulses withbandwidths of a few megahertz. Figure 5(c) shows theoutput powers for different frequencies. To verify that thewaveguide is linear in signal power, we measure the outputsignal power for various input signal powers as shown inFig. 5(d). We see that the plot is linear with a slope of about0.43, which means that we couple 43% of input signalFIG. 4. (a) and (b) are snapshots of the signal beam profile atthe back of the vapor cell with the control beam off and on,respectively. The back face of the cell is imaged on to the cameraby a 4f imaging system. (c) shows the beam profiles along thelonger axis of the beams at the front face of the cell. The dashedline is the measured control beam intensity, the dotted line is themeasured signal intensity, and the solid line is the Gaussian fit tothe measured signal intensity. The Gaussian width of the signalis 56 m. The plots in (d) show the beam profiles at the backface of the cell. The black dashed line is the measured controlbeam profile, the gray and black dotted lines are the measuredsignal beam profiles when the control is off and on, respectively,and the solid gray and black lines are Gaussian fits to the dottedlines. The Gaussian widths of gray and black curves are 102 mand 35 m, respectively. Note that the integrated intensity of theblack curve is approximately 43% of the gray curve, indicating agood coupling of power into the waveguide. The control beampower is 18 mW. The control beam intensity in (c) and (d) isnormalized to fit in the figure, while the signal intensities in (d)are relative.0 5 10 15 20 25 30−16−14−12−10−8−6−4−202 x 10   −7Control Beam Power (mW)Refractive Index - 1Raman Detuning (MHz)-3 -2 -1 0 1 2 300.20.40.60.811.21.41.61.8Transmission (AU) (a) (b)-792 -342 108 5589.69.659.79.75x 10−4Position (micrometers)Refractive Index - 1(c)(d)FIG. 3 (color online). (a) shows the experimental plot of thevariation in the transmission of signal versus Raman detuning.(b) is the plot of the refractive index of the signal, tuned1:5 MHz away from Raman resonance, as a function of controlbeam power. The dotted line in the figure is the experimentaldata, and the solid line is to guide the eye. (c) shows the spatialvariation of refractive index. White indicates higher refractiveindex and black, along the ring of the donut, is lower refractiveindex. (d) shows the plot of refractive index versus positionalong one of the axes. We use a single photon detuning of500 MHz, a Raman detuning of 1 MHz, and 30 mW controlbeam power in Eq. (2) to obtain the refractive index profiles froma camera snapshot of the intensity profile.PRL 102, 123602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending27 MARCH 2009123602-3power into the waveguide. This implies that we can expectto guide light of very low power without significant loss.This all optical waveguide can be used to achieve effi-cient nonlinear processes at very low light levels. Forexample, in the case of naturally abundant rubidium, wecan use one isotope to guide the signal and the otherisotope as a medium for the nonlinear processes such astwo photon absorption, Stark shift, Kerr effect, etc. Lukinand Imamoğlu [17] suggested the use of rubidium isotopesfor two simultaneous, independent nonlinear processes toachieve large Kerr nonlinearities. One can also optimizethe waveguide to increase the bandwidth and allow formultiple frequency waveguiding. Finally, one can use thiswaveguide as a building block for an all optical beamcoupler and beam splitter, similar to solid-state waveguidedevices.In summary, we use the intensity dependent refractiveindex resulting from a Raman transition in a  system tocreate an all optical waveguide. We are able to transmitabout 43% of the power along the waveguide, for lengthsmuch greater than the diffraction length, using a low powercontrol beam. This waveguide can be used to achieveefficient nonlinear processes at very low light levels.We gratefully acknowledge support from DARPA DSOSlow Light, the DODMURI for Quantum Imaging, and theNational Science Foundation.*praveen@pas.rochester.edu[1] F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J.Russell, Science 298, 399 (2002).[2] S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L.Gaeta, and B. J. Kirby, Phys. Rev. Lett. 97, 023603 (2006).[3] S.M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar,R. G. Beausoleil, and M. S. Shahriar, Phys. Rev. Lett. 100,233602 (2008).[4] R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair,and M.H. Dunn, Phys. Rev. A 53, 408 (1996).[5] R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair,and M.H. Dunn, Phys. Rev. Lett. 74, 670 (1995).[6] D. R. Walker, D. D. Yavuz, M.Y. Shverdin, G.Y. Yin,A. V. Sokolov, and S. E. Harris, Opt. Lett. 27, 2094 (2002).[7] D. D. Yavuz, D. R. Walker, and M.Y. Shverdin, Phys.Rev. A 67, 041803(R) (2003).[8] M.Y. Shverdin, D.D. Yavuz, and D. R. Walker, Phys. Rev.A 69, 031801(R) (2004).[9] N. A. Proite, B. E. Unks, J. T. Green, and D.D. Yavuz,Phys. Rev. A 77, 023819 (2008).[10] A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, andH. Rubinsztein-Dunlop, Phys. Rev. Lett. 82, 1438 (1999).[11] R. Kapoor and G. S. Agarwal, Phys. Rev. A 61, 053818(2000).[12] J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek,P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. A 63, 023820 (2001).[13] H. Shpaisman, A.D. Wilson-Gordon, and H. Friedmann,Phys. Rev. A 71, 043812 (2005).[14] O. Firstenberg, M. Shuker, N. Davidson, and A. Ron,Phys. Rev. Lett. 102, 043601 (2009).[15] J. P. Marangos, J. Mod. Opt. 45, 0471 (1998).[16] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev.Mod. Phys. 77, 633 (2005).[17] M.D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419(2000).Signal Gaussian Width (m)Control Beam Power (mW)0 5 10 15 20 250102030405060708090100-6 -4 -2 0 2 4 6020406080100120140Frequency  (MHz)Signal Gaussian Width (m)0 1 2 3 4 5 600.51.01.52.02.5Outputsignalpower(100 W)Input signal power (100 µW)(a)(d)-6 -4 -2 0 2 4 6050100150200250Frequency  (MHz)Output Power (AU) (c)(b)FIG. 5. (a) and (b) are the plots of the signal beam size at theback face of the vapor cell versus the control beam power andRaman detuning, respectively. (c) is the plot of output signalpower versus Raman detuning. (d) is the plot of output signalpower versus input signal power. The plot is nearly linear; theslope of the linear fit to data is 0.43. In (a), (b), and (c) gray is themeasure along longer axis, and black is the measure along theshorter axis of our elliptical beam.PRL 102, 123602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending27 MARCH 2009123602-4

All Optical Waveguiding in a Coherent Atomic Rubidium Vapor

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All Optical Waveguiding in a Coherent Atomic Rubidium Vapor

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