OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 32–37
« Show journal navigation

Coherent response to optical excitation in a strongly absorbing rare-earth ion-doped crystal

J. Ruggiero, T. Chanelière, and J.-L. Le Gouët  »View Author Affiliations


JOSA B, Vol. 27, Issue 1, pp. 32-37 (2010)
http://dx.doi.org/10.1364/JOSAB.27.000032


View Full Text Article

Acrobat PDF (293 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate coherent propagation through a large optical density Tm 3 + : YAG crystal. Using an ultrastable laser, fiber filtering, and site selection, we investigate the transmitted pulse temporal profile. The plane-wave condition is satisfied by selection of the illuminated-spot central area. We pay special attention to π pulse transmission in the prospect of implementing optical quantum storage protocols.

© 2009 Optical Society of America

1. INTRODUCTION

The connection with solitons has stimulated interest in SIT. It was shown [6

6. S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969). [CrossRef]

] that a 2π area pulse with a hyperbolic secant temporal profile can propagate without alteration through an absorbing medium. The breakdown of large area pulses into 2π area components was also predicted [6

6. S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969). [CrossRef]

] and observed [4

4. R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5, 1634–1659 (1972). [CrossRef]

, 5

5. R. E. Slusher and H. M. Gibbs, “Sharp-line self-induced transparency,” Phys. Rev. A 62326–2334 (1972). [CrossRef] [CrossRef]

]. A couple of decades later, the discovery of electromagnetically induced transparency (EIT) in ensembles of three-level atoms [7

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

] renewed interest in the coherent response of optically thick media. Actually, a variety of induced transparency processes have been investigated in three-level systems [8

8. M. J. Konopnicki and J. E. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Phys. Rev. A 24, 2567–2583 (1981). [CrossRef]

, 9

9. S. E. Harris, “Electromagnetically induced transparency with matched pulses,” Phys. Rev. Lett. 70, 552–555 (1993). [CrossRef] [PubMed]

]. The interplay of EIT with SIT was also considered [10

10. V. V. Kozlov and J. E. Eberly, “Ultrashort pulses in phaseonium: the interplay between SIT and EIT,” Opt. Commun. 179, 85–96 (2000). [CrossRef]

, 11

11. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001). [CrossRef]

]. In recent years, effort has been directed to the ultrashort pulse regime, where the usual assumptions, such as the rotating wave and slowly varying envelope approximations, may not be valid [12

12. F. Schlottau, M. Piket-May, and K. Wagner, “Modelling of femtosecond pulse interaction within homogeneously broadened media using an iterative predictor corrector FDTD method,” Opt. Express 12, 182–194 (2005). [CrossRef]

].

Rare-earth ion-doped crystals (REIC) represent an excellent test bed for coherent optical response investigation. Most of the limitations pointed out by Slusher in his review paper on SIT [13

13. R. E. Slusher“Self-induced transparency,” in Progress in Optics, E. Wolf, ed. (North Holland, 1974), p. 55.

] are relaxed in these materials. The superposition state lifetime may reach hundreds of microseconds and is not limited by a transit time across the light beams. No diffusive motion can affect the spatial phase of the atomic states. The inhomogeneous broadening can be considered as infinite. Generally, the level degeneracy is completely lifted by the crystal field so that the ions behave as true two-level atoms on the propagation time scale. Other features depend on the specific host matrix. In yttrium aluminium garnet (YAG, Y3Al5O12) for instance, the D2 symmetry of substitution sites forbids the existence of permanent dipole moments. As a consequence, relaxation processes such as optical excitation-induced instantaneous spectral diffusion (ISD) are strongly reduced. In this matrix, appropriate crystal cutting and adequate polarization orientation make ions in different sites interact with the same dipole moment projection on the incoming field [14

14. Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000). [CrossRef]

].

Coherent interactions in strongly absorbing REIC currently receive considerable attention due to prospects of these materials as a base for quantum memories. However, very few SIT coherent propagation data have been collected in REIC [15

15. G. Zumofen, F. R. Graf, A. Renn, and U. P. Wild, “Pulse propagation in rare-earth ion doped crystals,” J. Lumin. 83–84, 379–384 (1999). [CrossRef]

, 16

16. C. Greiner, B. Boggs, and T. W. Mossberg, “Superradiant emission dynamics of an optically thin material sample in a short-decay-time optical cavity,” Phys. Rev. Lett. 85, 3793–3796 (2000). [CrossRef] [PubMed]

]. Reference [16

16. C. Greiner, B. Boggs, and T. W. Mossberg, “Superradiant emission dynamics of an optically thin material sample in a short-decay-time optical cavity,” Phys. Rev. Lett. 85, 3793–3796 (2000). [CrossRef] [PubMed]

] reports on experimental work in Tm3+:YAG. However, inserting the sample in a cavity makes the quantitative analysis more difficult. In addition, coherent excitation conditions are not clearly satisfied since the laser is not stabilized. The same flaw affects the results in [11

11. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001). [CrossRef]

], where the interplay of EIT and SIT is evoked in the context of quantum storage of light. In [15

15. G. Zumofen, F. R. Graf, A. Renn, and U. P. Wild, “Pulse propagation in rare-earth ion doped crystals,” J. Lumin. 83–84, 379–384 (1999). [CrossRef]

], propagation is investigated in Pr3+:YSO. The laser is properly stabilized, but an unexpected low-transmission factor is observed.

In the present paper our aim is twofold. First, we reexamine the MB equation and propose a solution that analytically accounts for the instantaneous part of the atomic response. This fast component spreads over a broad spectral interval and complicates the numerical solution when the absorption line is strongly inhomogeneously broadened. Second, we present a detailed experimental investigation of coherent pulse propagation in a large optical density Tm3+:YAG crystal at liquid helium temperature.

The paper is organized as follows. In Section 2 we present the original aspects of our MB equation solution. In Section 3 we review the main features of pulse propagation through a strongly absorbing medium as predicted by the MB equation. The experimental setup is described in Section 4. We present and discuss the experimental data in Section 5.

2. THE INSTANTANEOUS RESPONSE

The MB equation has been the object of intense theoretical and numerical investigation for many decades by both physicists and mathematicians. We do not intend to bring any new result in this extremely well-documented field. Instead, we rely on physical arguments in order to simplify the computation procedure. Specifically, we show that one can simply account for the contribution from atoms far from resonance. This way, the sum over the inhomogeneous width can be limited to a narrower spectral interval. To the best of our knowledge, this approach was not adopted before.

Let us consider a spatially and spectrally uniform distribution of two-level atoms. Spectral uniformity means that the inhomogeneous width of the optical transition is infinite. Let a monochromatic plane wave be directed to the sample. At the input side z=0, the electric field E(z, t) reads as
E(0,t)=A(0,t)cos(ωLt+φ),
(1)
where φ is time independent. Within the frame of the slowly varying amplitude (SVA) and rotating wave (RWA) approximations, the MB equations read as follows:
zΩ(z,t)=α2πdωabv(ωab;z,t),
tu(ωab;z,t)=Δv(ωab;z,t),
tv(ωab;z,t)=Ω(z,t)w(ωab;z,t)+Δu(ωab;z,t),
tw(ωab;z,t)=Ω(z,t)v(ωab;z,t),
(2)
where Δ=ωabωL, and where Ω(z,t), u(ωab;z,t), v(ωab;z,t), and w(ωab;z,t)represent the Rabi frequency and the components of the Bloch vector B(ωab;z,t), respectively. Let L represent the sample thickness. To further simplify the problem, we assume that the incoming pulse evolution characteristic time, i.e., the inverse spectral width 1Δp, is much longer than Lc. Therefore we can neglect the time derivative tΩ(z,t)c in the wave equation.

To solve the equations numerically, one would like to get the spatial distribution Ω(z,t) at time t in terms of Ω(0,t), the boundary value at the sample input and of B(ωab;z,tτ), where τΔp1. Then one would solve the Bloch equation at time t, starting with B(ωab;z,tτ) and Ω(z,tτ). It should be stressed that the material response at time t cannot be simply expressed in terms of the Bloch vector at tτ. Indeed, due to the infinite inhomogeneous bandwidth, the material gives rise to an instantaneous response. Let us formally solve the Bloch equation in the following way:
v(ωab;z,t)=v(ωab;z,tτ)cos(Δτ)+u(ωab;z,tτ)sin(Δτ)0τΩ(z,tτ)w(ωab;z,tτ)cos(Δτ)dτ.
(3)
The first two terms on the right-hand side correspond to the free precession of the Bloch vector from tτ to t. The last term reflects the coupling to the field during this time interval. Initially w(ωab;z,t0)=1, since all the atoms sit in the ground state. As the pulse propagates through the sample, w(ωab;z,t)+1 departs from 0 over a spectral interval given by the pulse width Δp. However, according to Eq. (3), the driving field uniformly excites the atoms all over the inhomogeneous width, since the weight factor w(ωab;z,t0) is initially close to 1 everywhere. Summing over an infinite inhomogeneous width clearly raises a numerical computation issue. An infinite width contribution also reflects an instantaneous response feature that we intend to express analytically, thus relaxing the computation problem. Substituting v(ωab;z,t) into the wave equation one obtains
zΩ(z,t)=α2πdωab0τΩ(z,tτ)cos(Δτ)dτ+α2πdωab0τΩ(z,tτ)[w(ωab;z,t)+1]cos(Δτ)dτα2πdωabvfree(ωab;z,tτ,t),
(4)
where:
vfree(ωab;z,tτ,t)=v(ωab;z,tτ)cos(Δτ)+u(ωab;z,tτ)sin(Δτ).
(5)
The instantaneous response contribution has been isolated in the first term on the right-hand side. This easily reduces to (α2)Ω(z,t). The second term, of order (α2)ΔpτΩ(z,t), can be neglected since Δpτ1. Finally the wave equation solution reads as
Ω(z,t)=Ω(0,t)eαz2α2π0zdzeα(zz)2dωabvfree(ωab;z,tτ,t).
(6)
In the small area limit, the second term on the right-hand side can be neglected. The equation then reduces to the Bouguer law of absorption [17

17. Pierre Bouguer, Essai d’optique sur la gradation de la lumière, print. by Claude Jombert, In-12, 164 pages (1729), Paris.

]. As a starting point for numerical computation, the equation conveniently expresses Ω(z,t) in terms of Ω(0,t) and of B(ωab;z,tτ). In order to get B(ωab;z,t) in terms of B(ωab;z,tτ) and Ω(z,tτ), one complements Eq. (3) with the integral solutions for u(ωab;z,t) and w(ωab;z,t):
u(ωab;z,t)=ufree(ωab;z,tτ,t)+0τΩ(z,tτ)w(ωab;z,tτ)sin(Δτ)dτ,
w(ωab;z,t)=w(ωab;z,tτ)+0τΩ(z,tτ)v(ωab;z,tτ)dτ,
(7)
where
ufree(ωab;z,tτ,t)=u(ωab;z,tτ)cos(Δτ)v(ωab;z,tτ)sin(Δτ).
(8)
According to Eq. (7), the second term on the right-hand side of Eq. (6) still apparently contains far-from-resonance contributions. Indeed, u(ωab;z,t) and v(ωab;z,t) are built from v(ωab;z,t) all over the infinite inhomogeneous width. To show the instantaneous response is actually contained in the first term, let us define the new variables:
U(ωab;z,t)=u(ωab;z,t)+0Ω(z,tτ)sin(Δτ)dτ,
V(ωab;z,t)=v(ωab;z,t)0Ω(z,tτ)cos(Δτ)dτ.
(9)
Those new variables vanish far from resonance with the driving field. Then one easily verifies that Eq. (6) is left unchanged if u(ωab;z,tτ) and v(ωab;z,tτ) are respectively replaced by U(ωab;z,tτ) and V(ωab;z,tτ).

3. PULSE DISTORSION AND AREA THEOREM

According to the McCall and Hahn theorem [3

3. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967). [CrossRef]

], the transmitted pulse area, Aout, can be expressed in terms of the incoming pulse, Ain, as
tan(Aout2)=eαL2tan(Ain2),
(10)
where the pulse area is defined as A=Ω(t)dt. The corresponding variation of the transmission factor AoutAin as a function of Ain is displayed in Fig. 1 .

The rapid growing of the long tails, in both the π and 3π regions, provides us with key features for experimental data analysis.

4. EXPERIMENTAL SETUP

The 0.5% at. Tm3+:YAG crystal is cooled down to 2.2K in a helium bath cryostat. The experiment is performed on the H43H63 transition at 793nm. The sample length is L=5mm. At the operating temperature the opacity is measured to be αL5. The crystal sides are cut perpendicular to direction [1, −1, 0], and the light beam is polarized along direction [1, 1, 1]. This way, three sites out of six interact with the driving field, and they do so with the same Rabi frequency.

The sample is excited by a monochromatic semiconductor laser (Fig. 3 ). We carefully control the spectro-temporal and spatial properties of the source. The laser linewidth is first reduced to less than 1kHz by Pound–Drever–Hall locking to a high-finesse Fabry–Perot cavity. After a boost up through a tapered semiconductor amplifier, the laser beam is precisely temporally shaped by an acousto-optic modulator (AOM). The AOM is directly driven by a high-frequency arbitrary waveform generator (Tektronix AWG520) operating at 1Gss, which guarantees precise amplitude and phase control. The beam is then spatially filtered by a 2m long single-mode optical fiber.

The experimental conditions must be consistent with the plane-wave assumption of the theory. First we make the laser beam depth of field (DF)L. The DF, defined as twice the Rayleigh range, is given by 2πnw02λ, where n=1.82 stands for the YAG index of refraction and where the waist has been adjusted to w025μm. Therefore DF9mm, which is significantly larger than L. In order to put the beam waist at the crystal center, we position the focusing lens at maximum Rabi frequency, as probed by an optical nutation signal. Then we use a pinhole to select the signal emerging from the center of the illuminated spot. The sample is imaged on the 50μm pinhole through a telescope with 4× magnification. This corresponds to an 8% peak-to-peak excitation intensity variation over the detected area. The signal is detected on an avalanche photodiode.

The input intensity is monitored by photodetector PDcontrol (Fig. 3). We carefully calibrate the detection in Rabi frequency units. This is a critical step of our experiment. Optical nutation offers the best access to Rabi frequency [14

14. Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000). [CrossRef]

]. However this measurement technique is valid only in the low absorption limit. Because of the large sample opacity at resonance, we have to detune the laser about 20GHz from the center of the absorption band to perform the calibration. At this spectral position the opacity is reduced by a factor of about 10. The transmitted intensity is detected on PDcrystal. We calibrate this detector with the raising edge of the rectangular pulse. Indeed, immediately after switch-on, the transmitted intensity simply reads as I0exp(αL), where I0 represents the input pulse intensity that is measured on PDcontrol.

5. RESULTS AND DISCUSSION

We experimentally study the propagation of rectangular-shaped pulses. The pulse duration is adjusted to 7μs, which is significantly smaller than the atomic coherence lifetime of 50μs.

The input area ranges from 0.5π to 3.4π. The observed temporal profiles are displayed in Fig. 4 . They exhibit the features predicted in Fig. 2. As expected, the pulse is strongly stretched around the input π area, since the area has to be conserved in spite of large resonant absorption. Then, as the input area is increased, the pulse shrinks back, which is consistent with reduced absorption. Finally, around 3π, the pulse spreads again as resonant absorption increases, growing a side lobe to simultaneously satisfy area conservation and energy drop.

A possible fault of the setup is the absence of antireflection coating on the crystal. As a consequence, a reflected field counterpropagates through the excited medium with an amplitude reflection coefficient as large as 30%, given the high index of refraction of YAG.

One has also to consider the failure of the plane-wave approximation when the pulse area is close to π. The plane-wave assumption relies on the large size of the depth of field with respect to the sample length and on the selection of the central part of the beam with the pinhole. However, the portions of the Gaussian beam profile corresponding to areas smaller than π are absorbed more efficiently than the central part of the beam [13

13. R. E. Slusher“Self-induced transparency,” in Progress in Optics, E. Wolf, ed. (North Holland, 1974), p. 55.

]. Such a peeling of the outer portions of the beam tends to reduce the spot size and to move the waist to the output of the sample. The effective depth of field, varying as the square of the waist, gets rapidly smaller than the sample length, and since the waist migrates to the output of the sample, the imaging conditions are no longer satisfied at the pinhole position. To be more specific, let us assume that the waist moves to the end of the sample and that its size is changed from w0 to w0. Let the intensity at the center of the beam profile remain unchanged. Then, provided the beam remains Gaussian, the detected intensity is reduced by the factor
1+(Lλ2πnw02)2.
Changing the waist size from w0=25μm to w0=14μm would entail a reduction of the detected area by a factor of 2. The waist position not only moves to the output of the crystal but also undergoes strong temporal variations. This is illustrated in Fig. 6 where we simulate the time evolution of the field radial distribution. The rectangular pulse area is set equal to 1.1π along the beam axis. We neglect the effect of diffraction. Each ray propagates at fixed distance r from the beam axis, with a well defined initial area 1.1πer2w2. According to this model, the output spatial distribution of intensity quite faithfully replicates the input distribution, within the incoming pulse duration, even in the π area region. The transmitted beam distortion occurs during the delayed response of the crystal and grows dramatically as time elapses. We agree this model gives nothing but a rough picture of the beam distortion. Only the 3D MB solution would correctly account for the resulting focusing and diffraction effects, but this by far exceeds the scope of the paper.

The discrepancy with theory probably results from both a coherence decay rate underestimation and violation of the large depth-of-field approximation. Finally the excess of absorption reminds us of previously reported data [15

15. G. Zumofen, F. R. Graf, A. Renn, and U. P. Wild, “Pulse propagation in rare-earth ion doped crystals,” J. Lumin. 83–84, 379–384 (1999). [CrossRef]

], although agreement with theory has been improved in our experiment.

6. CONCLUSION

The propagation of rectangular pulses has been investigated in monochromatic plane-wave conditions. In order to consistently account for the very broad inhomogeneous bandwidth of the absorption line, the standard MB theory has been adjusted so that the instantaneous radiative response has been described analytically. Experimental data qualitatively agree with theory. However a significant quantitative discrepancy subsists, especially in the most interesting π pulse region, where the resonantly excited Bloch vector should undergo a π rotation at any depth inside the sample [19

19. J. Ruggiero, J.-L. Le Gouët, C. Simon, and T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009). [CrossRef]

].

In the context of quantum optical storage, the need for efficient preparation of a large optical density sample has been stressed recently [20

20. Hugues de Riedmatten, Mikael Afzelius, Matthias U. Staudt, Christoph Simon, and Nicolas Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456, 773–777 (2008). [CrossRef] [PubMed]

, 21

21. Mikael Afzelius, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, “Multimode quantum memory based on atomic frequency combs”Phys. Rev. A 79, 052329 (2009). [CrossRef]

]. The preparation step can require sophisticated excitation procedures [22

22. G. J. Pryde, M. J. Sellars, and N. B. Manson, “Solid state coherent transient measurements using hard optical pulses,” Phys. Rev. Lett. 84, 1152–1155 (2000). [CrossRef] [PubMed]

, 23

23. F. de Seze, V. Lavielle, I. Lorgeré, and J.-L. Le Gouët, “Chirped pulse generation of a narrow absorption line in a Tm3+:YAG crystal,” Opt. Commun. 223, 321–330 (2003). [CrossRef]

, 24

24. F. de Seze, F. Dahes, V. Crozatier, F. Bretenaker, and J. -L. Le Gouët, “Coherent driving of Tm:YAG ions using a complex hyperbolic secant optical field,” Eur. Phys. J. D 33, 343–355 (2005). [CrossRef]

]. In the present paper we have concentrated on single rectangular pulse propagation as a preliminary step to the investigation of more complex pulse sequences [22

22. G. J. Pryde, M. J. Sellars, and N. B. Manson, “Solid state coherent transient measurements using hard optical pulses,” Phys. Rev. Lett. 84, 1152–1155 (2000). [CrossRef] [PubMed]

]. The π pulse case deserves special attention, since all the resonantly excited ions should undergo π pulse excitation, wherever they sit in the sample depth. The unsatisfactory agreement with theory in the π pulse case should stimulate further coherent propagation investigation.

Fig. 1 Area theorem: pulse area transmission factor AoutAin as a function of the incoming pulse area Ain. Labels (a) to (l) refer to the different input-area conditions considered in Fig. 2.
Fig. 2 Numerical solution of the MB equation. The incoming rectangular pulse (dotted line) propagates through an αL=5 sample. The temporal profile of the pulse at the output (solid line) is displayed for different values of the input area. Time and outgoing pulse amplitude are normalized to the duration and the amplitude of the incoming pulse, respectively. The box labels refer to the corresponding area values, as predicted by the McCall and Hahn theory in Fig. 1.
Fig. 3 Experimental setup.
Fig. 4 Experimental profile of the transmitted pulse amplitude (solid line). Input area (Ain) ranges from 0.5π to 3.4π. Input pulses (dotted line) are rectangular with 7μs duration.
Fig. 5 Pulse area transmission factor AoutAin as a function of the incoming pulse area Ain. Input pulses are rectangular with 7μs duration. Theory accounts for a finite coherence lifetime of 50μs (solid line) or 10μs (dashed line).
Fig. 6 Time evolution of the radial field distribution at the crystal output. The incoming rectangular pulse with unit time duration exhibits a radial Gaussian profile with waist w1. The field area is set equal to 1.1π on the beam axis. The pulse reaches the crystal at time 0. Within the duration of the incoming pulse, the radial profile of the field is not strongly distorted by propagation. On the contrary, the beam radius shrinks dramatically during the delayed response of the atoms.
1.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954). [CrossRef]

2.

N. E. Rehler and J. E. Eberly, “Superradiance,” Phys. Rev. A 3, 1735–1751 (1971). [CrossRef]

3.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967). [CrossRef]

4.

R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5, 1634–1659 (1972). [CrossRef]

5.

R. E. Slusher and H. M. Gibbs, “Sharp-line self-induced transparency,” Phys. Rev. A 62326–2334 (1972). [CrossRef] [CrossRef]

6.

S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969). [CrossRef]

7.

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

8.

M. J. Konopnicki and J. E. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Phys. Rev. A 24, 2567–2583 (1981). [CrossRef]

9.

S. E. Harris, “Electromagnetically induced transparency with matched pulses,” Phys. Rev. Lett. 70, 552–555 (1993). [CrossRef] [PubMed]

10.

V. V. Kozlov and J. E. Eberly, “Ultrashort pulses in phaseonium: the interplay between SIT and EIT,” Opt. Commun. 179, 85–96 (2000). [CrossRef]

11.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001). [CrossRef]

12.

F. Schlottau, M. Piket-May, and K. Wagner, “Modelling of femtosecond pulse interaction within homogeneously broadened media using an iterative predictor corrector FDTD method,” Opt. Express 12, 182–194 (2005). [CrossRef]

13.

R. E. Slusher“Self-induced transparency,” in Progress in Optics, E. Wolf, ed. (North Holland, 1974), p. 55.

14.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000). [CrossRef]

15.

G. Zumofen, F. R. Graf, A. Renn, and U. P. Wild, “Pulse propagation in rare-earth ion doped crystals,” J. Lumin. 83–84, 379–384 (1999). [CrossRef]

16.

C. Greiner, B. Boggs, and T. W. Mossberg, “Superradiant emission dynamics of an optically thin material sample in a short-decay-time optical cavity,” Phys. Rev. Lett. 85, 3793–3796 (2000). [CrossRef] [PubMed]

17.

Pierre Bouguer, Essai d’optique sur la gradation de la lumière, print. by Claude Jombert, In-12, 164 pages (1729), Paris.

18.

W. Miklaszewski and J. Fiutak, “The effect of the homogeneous broadening on the propagation of the light pulses,” Z. Phys. B 93, 491–499 (1994). [CrossRef]

19.

J. Ruggiero, J.-L. Le Gouët, C. Simon, and T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009). [CrossRef]

20.

Hugues de Riedmatten, Mikael Afzelius, Matthias U. Staudt, Christoph Simon, and Nicolas Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456, 773–777 (2008). [CrossRef] [PubMed]

21.

Mikael Afzelius, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, “Multimode quantum memory based on atomic frequency combs”Phys. Rev. A 79, 052329 (2009). [CrossRef]

22.

G. J. Pryde, M. J. Sellars, and N. B. Manson, “Solid state coherent transient measurements using hard optical pulses,” Phys. Rev. Lett. 84, 1152–1155 (2000). [CrossRef] [PubMed]

23.

F. de Seze, V. Lavielle, I. Lorgeré, and J.-L. Le Gouët, “Chirped pulse generation of a narrow absorption line in a Tm3+:YAG crystal,” Opt. Commun. 223, 321–330 (2003). [CrossRef]

24.

F. de Seze, F. Dahes, V. Crozatier, F. Bretenaker, and J. -L. Le Gouët, “Coherent driving of Tm:YAG ions using a complex hyperbolic secant optical field,” Eur. Phys. J. D 33, 343–355 (2005). [CrossRef]

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(160.5690) Materials : Rare-earth-doped materials
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(270.6630) Quantum optics : Superradiance, superfluorescence

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: September 14, 2009
Manuscript Accepted: October 27, 2009
Published: December 11, 2009

Virtual Issues
March 5, 2010 Spotlight on Optics

Citation
J. Ruggiero, T. Chanelière, and J.-L. Le Gouët, "Coherent response to optical excitation in a strongly absorbing rare-earth ion-doped crystal," J. Opt. Soc. Am. B 27, 32-37 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-1-32


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954). [CrossRef]
  2. N. E. Rehler and J. E. Eberly, “Superradiance,” Phys. Rev. A 3, 1735-1751 (1971). [CrossRef]
  3. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908-911 (1967). [CrossRef]
  4. R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5, 1634-1659 (1972). [CrossRef]
  5. R. E. Slusher, H. M. Gibbs, “Sharp-line self-induced transparency,” Phys. Rev. A 62326-2334 (1972). [CrossRef]
  6. S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457-485 (1969). [CrossRef]
  7. K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991). [CrossRef] [PubMed]
  8. M. J. Konopnicki and J. E. Eberly, “Simultaneous propagation of short different-wavelength optical pulses,” Phys. Rev. A 24, 2567-2583 (1981). [CrossRef]
  9. S. E. Harris, “Electromagnetically induced transparency with matched pulses,” Phys. Rev. Lett. 70, 552-555 (1993). [CrossRef] [PubMed]
  10. V. V. Kozlov and J. E. Eberly, “Ultrashort pulses in phaseonium: the interplay between SIT and EIT,” Opt. Commun. 179, 85-96 (2000). [CrossRef]
  11. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602 (2001). [CrossRef]
  12. F. Schlottau, M. Piket-May, and K. Wagner, “Modelling of femtosecond pulse interaction within homogeneously broadened media using an iterative predictor corrector FDTD method,” Opt. Express 12, 182-194 (2005). [CrossRef]
  13. R. E. Slusher,“Self-induced transparency,” in Progress in Optics, E. Wolf, ed. (North Holland, 1974), p. 55.
  14. Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443-15451 (2000). [CrossRef]
  15. G. Zumofen, F. R. Graf, A. Renn, and U. P. Wild, “Pulse propagation in rare-earth ion doped crystals,” J. Lumin. 83-84, 379-384 (1999). [CrossRef]
  16. C. Greiner, B. Boggs, and T. W. Mossberg, “Superradiant emission dynamics of an optically thin material sample in a short-decay-time optical cavity,” Phys. Rev. Lett. 85, 3793-3796 (2000). [CrossRef] [PubMed]
  17. Pierre Bouguer, Essai d'optique sur la gradation de la lumière, print. by Claude Jombert, In-12, 164 pages (1729), Paris.
  18. W. Miklaszewski and J. Fiutak, “The effect of the homogeneous broadening on the propagation of the light pulses,” Z. Phys. B 93, 491-499 (1994). [CrossRef]
  19. J. Ruggiero, J.-L. Le Gouët, C. Simon, and T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009). [CrossRef]
  20. Hugues de Riedmatten, Mikael Afzelius, Matthias U. Staudt, Christoph Simon, and Nicolas Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456, 773-777 (2008). [CrossRef] [PubMed]
  21. Mikael Afzelius, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, “Multimode quantum memory based on atomic frequency combs”Phys. Rev. A 79, 052329 (2009). [CrossRef]
  22. G. J. Pryde, M. J. Sellars, and N. B. Manson, “Solid state coherent transient measurements using hard optical pulses,” Phys. Rev. Lett. 84, 1152-1155 (2000). [CrossRef] [PubMed]
  23. F. de Seze, V. Lavielle, I. Lorgeré, and J.-L. Le Gouët, “Chirped pulse generation of a narrow absorption line in a Tm3+:YAG crystal,” Opt. Commun. 223, 321-330 (2003). [CrossRef]
  24. F. de Seze, F. Dahes, V. Crozatier, F. Bretenaker, and J. -L. Le Gouët, “Coherent driving of Tm:YAG ions using a complex hyperbolic secant optical field,” Eur. Phys. J. D 33, 343-355 (2005). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited