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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8311–8319
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Selective reflection of Airy beam at an interface between dielectric and homogeneous atomic medium

Yuan-yuan Li, Li Li, Yi-Xin Lu, Xiao-xia Zhao, Ke-wei Xu, Yi-qi Zhang, and Yan-peng Zhang  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8311-8319 (2013)
http://dx.doi.org/10.1364/OE.21.008311


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Abstract

We examine selective reflection (SR) spectrum of an Airy beam at an interface between a dielectric and a homogeneous atomic medium. It is shown that both the general reflection (GR) and the SR of Airy beams exhibit accelerating dynamics with a parabolic trajectory, however, the accelerating rate for the SR is slightly greater than that for the GR. Due to interaction of atoms and the Airy beams at the interface between dielectric and resonant atoms, the SR beams can create far-field interference patterns. We also show that the amplitude of the SR can be dramatically modified by the detuning of the incident fields, the reduced x-coordinate and the distance from the interface. The SR at the resonant medium interface of Airy beams can probably be a powerful tool in the use of optical power delivering, resonant particle manipulation and spatial spectrum detection of a resonant medium at an interface.

© 2013 OSA

1. Introduction

An Airy wavepacket was initially predicted within the context of quantum mechanics [1

1. M. Berry and N. Balazs, “Non-spreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). [CrossRef]

]. It has two typical properties: resistance to diffraction and accelerating dynamics along the transverse direction during the propagation [2

2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

,3

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef] [PubMed]

]. These remarkable features of ideal Airy beams can be implemented in practice by finite power Airy beams maintaining their shape over several diffraction lengths before they are significantly distorted [2

2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

,3

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef] [PubMed]

]. Another feature of the Airy beams is their self-healing when perturbations are imposed on them [4

4. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef] [PubMed]

]. This self-healing characteristic of the Airy beam was also observed in the turbulence independence of its centroid position and skewness [5

5. X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36(14), 2701–2703 (2011). [CrossRef] [PubMed]

]. It was also shown that an Airy beam can maintain its shape when propagating in a self-defocusing nonlinear medium [6

6. Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35(23), 3952–3954 (2010). [CrossRef] [PubMed]

]. These exotic features of Airy beams may have many applications, e.g., controlling of beam trajectory [7

7. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35(13), 2260–2262 (2010). [CrossRef] [PubMed]

], particle manipulation [8

8. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011). [CrossRef] [PubMed]

], plasma channel generation [9

9. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009). [CrossRef] [PubMed]

] and near-field imaging of Airy surface plasmons [10

10. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011). [CrossRef] [PubMed]

]. To describe an Airy beam, a virtual source for generating an Airy wave was identified [11

11. S. Yan, B. Yao, M. Lei, D. Dan, Y. Yang, and P. Gao, “Virtual source for an Airy beam,” Opt. Lett. 37(22), 4774–4776 (2012). [CrossRef] [PubMed]

], in which the authors derived a spectral integral expression yielding a freely accelerating, non-diffracting, as well as a finite-energy Airy beam in the paraxial limit.

Self-healing and accelerating dynamics can be observed in reflection and refraction beams from a finite power incident Airy beam at the interface between two dielectric media [12

12. I. D. Chremmos and N. K. Efremidis, “Reflection and refraction of an Airy beam at a dielectric interface,” J. Opt. Soc. Am. A 29(6), 861–868 (2012). [CrossRef] [PubMed]

]. In a four-level electromagnetic induced transparency (EIT) atomic vapor system, it is shown that the deflection position and the intensity of the Airy beam can be modulated by the Rabi frequency of the control light. Such a tunable optical behavior may have some potential applications in medicine science [13

13. F. Zhuang, J. Shen, X. Du, and D. Zhao, “Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor,” Opt. Lett. 37(15), 3054–3056 (2012). [CrossRef] [PubMed]

].

SR spectroscopy is known as an excellent tool to detect the resonant properties of the medium in the vicinity of the interface [14

14. H. Failache, S. Saltiel, M. Fichet, D. Bloch, and M. Ducloy, “Resonant coupling in the van der Waals interaction between an excited alkali atom and a dielectric surface: an experimental study via stepwise selective reflection spectroscopy,” Eur. Phys. J. D 23(2), 237–255 (2003). [CrossRef]

20

20. Y. Li, X. Hou, J. Bai, J. Yan, C. Gan, and Y. Zhang, “Two-photon Dicke-narrowing selective reflection spectroscopy in thin atomic vapor,” Acta Opt. Sin. 28(8), 1623–1627 (2008) (in Chinese). [CrossRef]

]. It is notably beneficial to get high-resolution spectroscopy in order to study atom-surface interaction [14

14. H. Failache, S. Saltiel, M. Fichet, D. Bloch, and M. Ducloy, “Resonant coupling in the van der Waals interaction between an excited alkali atom and a dielectric surface: an experimental study via stepwise selective reflection spectroscopy,” Eur. Phys. J. D 23(2), 237–255 (2003). [CrossRef]

,15

15. M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II France 2(4), 631–657 (1992). [CrossRef]

,17

17. P. Chaves de Souza Segundo, I. Hamdi, M. Fichet, D. Bloch, and M. Ducloy, “Selective reflection spectroscopy on the UV third-resonance line of Cs: Simultaneous probing of a van der Waals atom-surface interaction sensitive to far IR couplings and interatomic collisions,” Laser Phys. 17(7), 983–992 (2007). [CrossRef]

], and a dense gas atomic medium [16

16. N. Papageorgiou, M. Fichet, V. A. Sautenkov, D. Bloch, and M. Ducloy, “Doppler-free reflection spectroscopy of self-induced and krypton-induced collisional shift and broadening of cesium D2 line components in optically dense vapor,” Laser Phys. 4, 392–395 (1994).

,19

19. Y. Li, G. Zhang, and Y. Zhou, “Selective reflection combined with Fabry-Perot effects from two-level atoms confined between two dielectric walls,” Chin. Phys. 15(5), 985–991 (2006). [CrossRef]

,20

20. Y. Li, X. Hou, J. Bai, J. Yan, C. Gan, and Y. Zhang, “Two-photon Dicke-narrowing selective reflection spectroscopy in thin atomic vapor,” Acta Opt. Sin. 28(8), 1623–1627 (2008) (in Chinese). [CrossRef]

], sensitively. In this paper, our discussion is devoted to the phenomena associated with the SR at an interface between a dielectric and a homogeneous atomic medium. Both the GR and the SR of Airy beams exhibit accelerating dynamics with a parabolic trajectory. However, the accelerating rate of the SR is slightly greater than that of the GR, and the SR beam can create far-field interference patterns. We also show that the amplitude of the SR can be dramatically controlled by the detuning of the incident fields, the reduced x-coordinate and the distance from the interface. The selective reflected Airy beam can probably be a powerful tool in the use of optical power delivering, resonant particle manipulation and spatial spectrum detection of a resonant medium at an interface.

2. Theoretical model

We consider a two-dimensional system with a homogeneous cold atomic medium 2 sandwiched between two dielectric windows 1 and 1' [Fig. 1(a)
Fig. 1 (a) The geometrical configuration of probe and coupling fields impinging on the interface between a transparent dielectric window and a homogeneous sample of cold atoms. The diverse coordinate systems are also shown. (b) Lambda-type three-level system of atoms.
], situated respectively in the regions of z<0 and z>L. We assume that the inner surface of the window 1' is antireflection coated, i.e., the Fabry-Perot effect can be neglected in our discussion. The employed lambda-type three-level atomic system in medium 2 is presented in Fig. 1(b), where the transition frequency of |1|3 is ω31, and that for |2|3 is ω32 . Two laser fields are applied to the system, in which the probe field Ep has frequency ωp (with a detuning Δp=ωpω31, impinging on the interface 1-2 at an angle θ1), and coupling field Ec has frequency ωc (with a detuning Δc=ωcω32, impinging on the interface 1-2 along the normal direction). We denote kp (kp) and kc (kc) the wave vectors (wavenumbers) of the probe and the coupling fields, respectively.

The field amplitude of a paraxial probe beam with an incident angle θ1 at the interface can be expressed as
Ep(xi,zi=0)=u0(xi)exp(ik1sinθ1xi),
(1)
where k1=n1kp is the probe wavenumber in medium 1 with dielectric constant ε1 and refractive index n1=ε1. The coordinate system yields (xi,zi)=(x+s,z+h), with s=htanθ1 and z=h being the depth inside widow 1. The transverse input field amplitude for a finite-power Airy beam is [2

2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

,12

12. I. D. Chremmos and N. K. Efremidis, “Reflection and refraction of an Airy beam at a dielectric interface,” J. Opt. Soc. Am. A 29(6), 861–868 (2012). [CrossRef] [PubMed]

]
u0(xi)Ai(±xicosθ1x0)exp(±axicosθ1x0),
(2)
where a is the truncation and x0 an arbitrary transverse scale.

Applying a Fourier transformation in coordinates (x,z) to the probe field Ep, we can decompose it into many plane wave components and the GR, SR and transmission coefficients of each component are denoted as Rgr(k), Rsr(k) and T(k). Here, the SR field represents the radiated waves propagating along the reflective direction from the macroscopic polarization of sandwiched atoms. By applying boundary conditions at the interface, Rgr(k), Rsr(k), and T(k) can be expressed by Eqs. (3a), (3b) and (3c) respectively
Rgr(k)=(q1q2)/(q1+q2),
(3a)
Rsr(k)=i/[Epin(k)(q1+q2][Ep(k)(z)/z]z=0,
(3b)
T(k)2q1/(q1+q2),
(3c)
where we assume that the probe field is s-polarized, q1=k12k2is the z wavenumber of the Fourier component in the medium 1, and q2=kp2k2 the wavenumber in medium 2 as a refractive index n21 of a dilute atomic sample is assumed. The special coefficient Ep(k)(z) of each Fourier component of the probe wave in the medium 2 is given by
Ep(k)(z)=Ep(x,z)exp(ikx)dx,
(3d)
where Ep(x,z) can be written as
Ep(x,z)=12π+[+Ep(x,z=h)exp(ikx)dx]T(k)exp(ikx)exp(iq2z+iq1h)dk.
(3e)
The incident special coefficient Epin(k) at the interface in medium 1 can be obtained in a similar way, and we do not show it here.

We assume that each Fourier component of the probe field through atomic medium satisfies the wave equation
2Ep(k)(z)/z2+2iq2Ep(k)(z)/z=4πq22P(k)(z).
(4)
The second interface 21' in our system is antireflection coated; hence, it is justified to assume that [Ep(k)(z)/z]z=L0, resulting in the expression
[Ep(k)(z)/z]z=0=4πq220LP(k)(z)exp(2iq2z)dz.
(5)
In the above equations, the polarization P(k)(z)=Nμ31σ31(k)(z), with N being the number density of atoms, μ31 the transition dipole moment corresponding to |1|3. The density matrix element σ31 can be obtained by solving the following coupled equations
σ31/t=Λ31σ31+iGp(k)(σ11σ33)+iGcσ21,
(6a)
σ21/t=Λ21σ21iGp(k)σ23+iGcσ31,
(6b)
σ23/t=Λ32*σ23iGp(k)σ21iGc(σ22σ33),
(6c)
whereΛ21=γ21i(ΔpΔc),Λ31=γ31iΔpand Λ32=γ32iΔc, with γ31 and γ32 being the decay rates from level |3 to levels |1 and |2, respectively; Gp(k) and Gc are the Rabi frequencies defined as Gp(k)=μ31Ep(k)(z)/μ31Epin(k)/ and Gc=μ32Ec/, respectively, with μ32 being the dipole moments of the transition |2|3. It is assumed that the transition between levels |1 and |2 is dipole forbidden, as is the case for hyperfine sublevels of an atomic ground sate. The nonradiative decay rate (including transient effects and collisional dephasing) between these two lower levels is denoted by γ21.

We assume that the probe field is much weaker than the coupling field, so Gp(k) in Eq. (6b) can be neglected, and the initial conditions are σ111, σ220. Solving Eqs. (6a) and (6b), we get σ31=iGp(k)Λ21/(Λ21Λ31+Gc2), and the polarization reads
P(k)(z)=iNμ31Gp(k)Λ21/(Λ21Λ31+Gc2).
(7)
For simplicity the superscript (k) in each density matrix element is omitted, since it does not change the main result in our discussion.

Substituting (7) into (5) and then into (3b), we finally obtain

Rsr(k)=4πq22Epin(k)(q1+q2)0LNμ31Gp(k)Λ21/(Λ21Λ31+Gc2)exp(2iq2z)dz.
(8)

The envelope function for the SR beam is given by the Fourier integral [12

12. I. D. Chremmos and N. K. Efremidis, “Reflection and refraction of an Airy beam at a dielectric interface,” J. Opt. Soc. Am. A 29(6), 861–868 (2012). [CrossRef] [PubMed]

]
u(χr,zr)=12πcosθ1dκF0(κcosθ1)Rsr(k1sinθ1+κ)exp[iκχriκ2(zr+h)2k1cos3θ1].
(9)
Here χr=xrzrtanθ1 is the reduced x coordinate at the propagation direction of the reflected beam along xr=zrtanθ1 predicted by Snell’s law. The Fourier transformation F0(k') is given by F0(k')=x0exp[i(±k'x0+ia)3/3]. For the GR beam, the Eq. (9) holds simply with Rsr(k)replaced by Rgr(k).

It is apparent that the spatial profile of the selective reflected beam can be modulated by the SR coefficient Rsr, i.e., the atomic level structure, the thickness of atomic sample, as well as the detuning and the strengths of the probe and coupling fields. Here we restrict our discussion to the modulation to the SR beam induced by the probe detuning Δp, the reduced x-coordinate χr=xrzrtanθ1 and the distance zr from the interface, while keeping a fixed value of the sample thickness, the detuning and strength of the coupling field.

3. Numerical results and discussion

In numerical calculation, atomic parameters are chosen to be corresponding to the D1 line of 87Rb, the coupling field Ec couples level |2 (F=2,5S21/2) to level |3 (F=2,5P21/2), and probe beam Ep couples level |1 (F=1,5S21/2) to level |3 (F=2,5P21/2). Other selected values are γ31=2π×4.79MHz, γ32=2π×2.87MHz, γ21=2π×10kHz, ω32ω31=2π×377.11THz and Gc=γ31. For a cold atomic sample, we assume that L=2mm and N=6×1015cm−3. In all cases, the refractive index of the medium 1 is assumed to be n1 = 1.5; the coupling field is accurately tuned to the transition |2|3, i.e., Δc=0. For an s-polarized incident probe Airy beam with incident angle θ1=10°, x0=20μm, a = 0.1, and lobes developing toward negative x, i.e., F0(k')=x0exp[i(k'x0+ia)3/3], the diffraction length in medium 1 is Ld1=k1x024.7mm. We let h=Ld1cosθ14.1mm, and therefore the beam can propagate for one diffraction length before it hits the interface.

First, the SR contribution with symmetrically varying Δp is shown in Fig. 2
Fig. 2 The real part contribution of the SR versus the probe detuning Δp/γ31 for Gc=0.3γ31 and Gc=γ31.
. It is obvious that a sharp dispersive change emerges in the interval [γ31,γ31], at the edges of which the SR is significantly enhanced and a maximum value can be achieved. However, since the transmission is largely enhanced in this interval, the SR is weakened. When the probe beam is far detuned from the resonant frequency, the SR shows a decreasing contribution.

Next, we show the propagation of the GR and the SR beam in Figs. 3
Fig. 3 GR amplitude (a1) and SR amplitude (b1) for the Airy beam with an incident angle θ1=10°. (a2), (b2): Beam amplitudes versus the position χr from the Snell’s reflection axis in (a1) and (b1) respectively at different depths inside the medium 1. (i), (ii), (iii), (iv) and (v) are for zr=0, 1cm, 2cm, 3cm and 4cm respectively. Other parameters areGc=γ31,Δp=γ31.
(a1) and 3(b1), respectively, up to a distance of 4cm from the interface. The intensity profiles corresponding to Figs. 3(a1) and 3(b1) are respectively plotted in Figs. 3(a2) and 3(b2) at various distances in medium 1 from the interface. Here, the probe detuning is Δp=γ31 and the amplitude is normalized by the maximum value of the first lobe at zr=0.

It is obvious that both the GR and the SR are quasi-diffraction-free Airy-like beams, which exhibit accelerating dynamics toward the same direction with the incident beam along the Snell’s law axis. The FWHM of the first lobe for the GR and the SR are ~34μm. This feature for the former case can remain almost invariant up to ~2.8cm, and for the latter case up to ~1.6cm. This evidently indicates that the quasi-diffraction-free character of the Airy beam can be maintained in the GR and the SR, but the disturbance-resisting distance for the SR beam is smaller than that for the GR beam due to the contribution from resonant atoms. Although the parabolic trajectories of the SR beams are similar to the case of the GR beams, the accelerating rate in the former case is slightly greater than that in the latter case. Due to the spatial periodical modulation of the radiated waves from the resonant atoms along the reflection direction, a quasi-diffraction-free character periodically remains, and a periodic far field interference pattern also emerges in the resonant case.

The evolution of the SR amplitudes versus the position χr from the Snell’s reflection axis for the Airy beam is plotted in Figs. 4(a)
Fig. 4 SR amplitudes versus the position χr of the Airy beam for various probe detuning and propagating depth in medium 1. (a), (b), (c), (d), (e) and (f) are for zr=0, 1cm, 2cm, 3cm, 4cm and 5cm respectively. Red, blue and green lines are for Δp=0, γ31 and 3γ31 respectively. Other parameters are Gc=γ31,Δc=0.
-4(f) for zr=0, 1cm, 2cm, 3cm, 4cm and 5cm respectively. The red, blue and green lines correspond to Δp=0, γ31 and 3γ31, respectively.

Figure 4 shows that the amplitude of the SR can be dramatically modified by the detuning of the incident fields, the reduced x-coordinate and the distance from the interface. As the probe field is exactly tuned to the transition |1|3, the EIT effects are manifest due to the ac-Stark splitting and the interference between dressed states created by the coupling laser [21

21. K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef] [PubMed]

25

25. M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

]. The absorption of the probe field is largely suppressed, thus the SR from the resonant atoms is very weak (red lines). As the probe detuning is detuned to γ31 and the dressed state resonance occurs, the absorption or resonant radiation approaches a maximum value. In this case, the SR approaches maximum value, and the most significant variation of spatial profile also emerges in the propagation (blue lines). When probe field is further detuned to 3γ31, the SR turns weak because the dressed state resonance is significantly lost (green lines). It can also be observed that the SR beams can create far-field interference patterns. This is due to the periodic spatial radiation behavior from the resonant atoms resulting from the similar modulation behavior of the incident Airy beam. This type spectrum of the beam can have potential application in the detection of resonant properties of particles, as well as the manipulation of the resonant particles.

4. Conclusion

We have investigated the GR and the SR properties of an Airy beam at an interface between a dielectric and a homogeneous atomic medium. Both the GR and the SR of Airy beams are Airy-like and exhibit accelerating dynamics toward the same direction with the incident beam. Although the parabolic trajectories of the SR beams are similar to the case of the GR beams, the accelerating rate of the former is slightly greater than that of the latter. Due to the contribution of resonant atoms, the SR beams can create far-field interference patterns. It is also observed that the amplitude of the SR can be dramatically modified by the detuning of the incident fields, the reduced x-coordinate and the distance from the interface. The SR of Airy beams can probably be a powerful tool in the use of optical power delivering, resonant particle manipulation and spatial spectrum detection of resonant medium at an interface.

Acknowledgments

This work is supported by the Science and Technology Project of Xi’an in China (No. CXY1134WL02, CX12189WL02).

References and links

1.

M. Berry and N. Balazs, “Non-spreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). [CrossRef]

2.

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

3.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef] [PubMed]

4.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef] [PubMed]

5.

X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36(14), 2701–2703 (2011). [CrossRef] [PubMed]

6.

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35(23), 3952–3954 (2010). [CrossRef] [PubMed]

7.

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35(13), 2260–2262 (2010). [CrossRef] [PubMed]

8.

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011). [CrossRef] [PubMed]

9.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009). [CrossRef] [PubMed]

10.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107(11), 116802 (2011). [CrossRef] [PubMed]

11.

S. Yan, B. Yao, M. Lei, D. Dan, Y. Yang, and P. Gao, “Virtual source for an Airy beam,” Opt. Lett. 37(22), 4774–4776 (2012). [CrossRef] [PubMed]

12.

I. D. Chremmos and N. K. Efremidis, “Reflection and refraction of an Airy beam at a dielectric interface,” J. Opt. Soc. Am. A 29(6), 861–868 (2012). [CrossRef] [PubMed]

13.

F. Zhuang, J. Shen, X. Du, and D. Zhao, “Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor,” Opt. Lett. 37(15), 3054–3056 (2012). [CrossRef] [PubMed]

14.

H. Failache, S. Saltiel, M. Fichet, D. Bloch, and M. Ducloy, “Resonant coupling in the van der Waals interaction between an excited alkali atom and a dielectric surface: an experimental study via stepwise selective reflection spectroscopy,” Eur. Phys. J. D 23(2), 237–255 (2003). [CrossRef]

15.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II France 2(4), 631–657 (1992). [CrossRef]

16.

N. Papageorgiou, M. Fichet, V. A. Sautenkov, D. Bloch, and M. Ducloy, “Doppler-free reflection spectroscopy of self-induced and krypton-induced collisional shift and broadening of cesium D2 line components in optically dense vapor,” Laser Phys. 4, 392–395 (1994).

17.

P. Chaves de Souza Segundo, I. Hamdi, M. Fichet, D. Bloch, and M. Ducloy, “Selective reflection spectroscopy on the UV third-resonance line of Cs: Simultaneous probing of a van der Waals atom-surface interaction sensitive to far IR couplings and interatomic collisions,” Laser Phys. 17(7), 983–992 (2007). [CrossRef]

18.

A. Laliotis, I. Maurin, M. Fichet, D. Bloch, M. Ducloy, N. Balasanyan, A. Sarkisyan, and D. Sarkisyan, “Selective reflection spectroscopy at the interface between a calcium fluoride window and Cs vapor,” Appl. Phys. B 90(3-4), 415–420 (2008). [CrossRef]

19.

Y. Li, G. Zhang, and Y. Zhou, “Selective reflection combined with Fabry-Perot effects from two-level atoms confined between two dielectric walls,” Chin. Phys. 15(5), 985–991 (2006). [CrossRef]

20.

Y. Li, X. Hou, J. Bai, J. Yan, C. Gan, and Y. Zhang, “Two-photon Dicke-narrowing selective reflection spectroscopy in thin atomic vapor,” Acta Opt. Sin. 28(8), 1623–1627 (2008) (in Chinese). [CrossRef]

21.

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef] [PubMed]

22.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995). [CrossRef] [PubMed]

23.

S. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997). [CrossRef]

24.

M. Scully and M. Zubairy, Quantum Optics (Cambridge University, Cambridge, 1997).

25.

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Physical Optics

History
Original Manuscript: January 14, 2013
Revised Manuscript: March 18, 2013
Manuscript Accepted: March 19, 2013
Published: March 28, 2013

Citation
Yuan-yuan Li, Li Li, Yi-Xin Lu, Xiao-xia Zhao, Ke-wei Xu, Yi-qi Zhang, and Yan-peng Zhang, "Selective reflection of Airy beam at an interface between dielectric and homogeneous atomic medium," Opt. Express 21, 8311-8319 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8311


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