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Observation of the four wave mixing photonic
band gap signal in electromagnetically induced
grating
Zakir Ullah,1 Zhiguo Wang,1,2,* Mengqin Gao,1 Dan Zhang,1 Yiqi Zhang,1 Hong Gao,2
and Yanpeng Zhang1,3
1
Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information
Photonic Technique, Xi’an Jiaotong University, Xi’an 710049, China
2
School of Science, Xi’an Jiaotong University, Xi’an 710049, China
3
[email protected]
*[email protected]
Abstract: For the first time, we experimentally and theoretically research
about the probe transmission signal (PTS), the reflected four wave mixing
band gap signal(FWM BGS) and fluorescence signal (FLS) under the double
dressing effect in an inverted Y-type four level system. FWM BGS results
from photonic band gap structure. We demonstrate that the characteristics of
PTS, FWM BGS and FLS can be controlled by power, phase and the
frequency detuning of the dressing beams. It is observed in our experiment
that FWM BGS switches from suppression to enhancement, corresponding
to the switch from transmission enhancement to absorption enhancement in
the PTS with changing the relative phase. We also observe the relation
among the three signals, which satisfy the law of conservation of energy.
Such scheme could have potential applications in optical diodes, amplifiers
and quantum information processing.
©2014 Optical Society of America
OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (190.4180) Multiphoton
processes; (300.2570) Four-wave mixing; (270.1670) Coherent optical effects.
References and links
1.
P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. P. Shahriar, and P. Kumar, “Efficient
low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9),
982–984 (1995).
2. Y. Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced
transparency in rubidium atoms,” Opt. Lett. 21(14), 1064–1066 (1996).
3. D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced
transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
4. Y. V. Rostovtsev, Z. E. Sariyanni, and M. O. Scully, “Electromagnetically induced coherent backscattering,”
Phys. Rev. Lett. 97(11), 113001 (2006).
5. C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and
suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
6. H. B. Zheng, X. Zhang, C. B. Li, H. Y. Lan, J. L. Che, Y. Q. Zhang, and Y. P. Zhang, “Suppression and
enhancement of coexisting super-fluorescence and multi-wave mixing processes in sodium vapor,” J. Chem. Phys.
138(20), 204315 (2013).
7. J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in
molecular lithium: Prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291
(1999).
8. J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra,
“Measurement of transition dipole moments in lithium dimers using electromagnetically induced transparency,”
Phys. Rev. Lett. 88(17), 173003 (2002).
9. J. B. Qi and A. M. Lyyra, “Electromagnetically induced transparency and dark fluorescence in a cascade
three-level diatomic lithium system,” Phys. Rev. A 73(4), 043810 (2006).
10. C. Li, H. B. Zheng, Z. Y. Zhang, X. Yao, Y. Z. Zhang, Y. Q. Zhang, and Y. P. Zhang, “Electromagnetically
induced transparency and fluorescence in blockaded Rydberg atomic system,” J. Chem. Phys. 139(16), 164316
(2013).
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29544
11. H. Y. Ling, Y.-Q. Li, and M. Xiao, “Electromagnetically induced grating: Homogeneously broadened medium,”
Phys. Rev. A 57(2), 1338–1344 (1998).
12. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967),
638–641 (2003).
13. Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-Wave Mixing Dipole
Soliton in Laser-Induced Atomic Gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
14. Y. P. Zhang, C. Z. Yuan, Y. Q. Zhang, H. B. Zheng, H. X. Chen, C. B. Li, Z. G. Wang, and M. Xiao, “Surface
solitons of four-wave mixing in anelectromagnetically induced lattice,” Laser Phys. Lett. 10(5), 055406 (2013).
15. A. W. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption
grating,” Opt. Lett. 30(7), 699–701 (2005).
16. M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys.
Rev. Lett. 96(7), 073905 (2006).
17. A. Schilke, C. Zimmermann, P. W. Courteille, and W. Guerin, “Photonic Band Gaps in One-Dimensionally
Ordered Cold Atomic Vapors,” Phys. Rev. Lett. 106(22), 223903 (2011).
18. D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, and S. Y. Zhu, “Optical Diode Made From a Moving
Photonic Crystal,” Phys. Rev. Lett. 110(9), 093901 (2013).
19. S. A. R. Horsley, J. H. Wu, M. Artoni, and G. C. La Rocca, “Optical Nonreciprocity of Cold Atom Bragg Mirrors
in Motion,” Phys. Rev. Lett. 110(22), 223602 (2013).
20. F. E. Zimmer, A. Andre, M. D. Lukin, and M. Fleischhauer, “Coherent control of stationary light pulses,” Opt.
Commun. 264(2), 441–453 (2006).
21. S. A. Moiseev and B. S. Ham, “Generation of entangled lights with temporally reversed photon wave packets,”
Phys. Rev. A 71(5), 053802 (2005).
22. K. R. Hansen and K. Molmer, “Trapping of light pulses in ensembles of stationary Lambda atoms,” Phys. Rev. A
75(5), 053802 (2007).
23. K. R. Hansen and K. Molmer, “Stationary light pulses in ultracold atomic gases,” Phys. Rev. A 75(6), 065804
(2007).
24. Z. G. Wang, P. Ying, P. Y. Li, D. Zhang, H. Q. Huang, H. Tian, and Y. Zhang, “Switching suppression and
enhancement of fluorescence and six-wave mixing by phase modulation,” Sci Rep 3, 3417 (2013).
1. Introduction
Four-wave mixing (FWM) is a nonlinear optical effect that generates light with different
frequencies and different quantum properties. Experimental and theoretical studies show that
atomic coherence of the electromagnetically induced transparency (EIT) plays a critical role in
the nonlinear wave-mixing process [1–6]. Under EIT conditions FWM signals can be allowed
to transmit through the atomic medium and also the fluorescence induced by spontaneous
emission can be generated [7–10]. Due to the two counter propagating coupling fields, the
EIT-based nonlinear schemes can be driven by traveling wave beams as well as by a standing
wave (SW). The large nonlinearity was obtained in an atomic system driven by two counter
propagating coupling fields which form a SW if the two counter propagating coupling fields
have the same frequency [11, 12]. Interaction of the SW with the atomic coherent medium
results into an electromagnetically induced grating (EIG) [13, 14], which possesses photonic
band gap (PBG) structure as shown in Fig. 1(c). Such EIG has a potential use in all optical
switching [15], manipulation of light propagation to create a tunable photonic band gap [16,
17].This research can also be used to make optical diodes. The idea proposed here for optical
diode implementation is a photonic crystal generated from a periodic modulation of the optical
properties of a medium, which leads to the formation of a band gap. Light is transmitted
through the crystal if its frequency is outside the gap, but it is not transmitted if the frequency is
inside the gap. Due to the Doppler Effect, the counter propagating light are blue shifted and the
co-propagating light is red shifted in the reference frame of the moving photonic crystal [18]. If
only one of the shifted frequencies is inside the gap optical diode is formed. Optical non
reciprocity of cold atom Bragg mirrors in motion may also be used to make optical diode [19].
In this paper, we investigate the optical response of hot rubidium (85Rb) atoms driven by a
stationary SW coupling field and probe field, from which the PBG structure and four wave
mixing band gap signal (FWM BGS) and probe transmission signal (PTS) can be obtained. For
the first time we observe optically controllable PBG structure based on an EIT medium driven
by a SW field. By optically controllable PBG structure not only we experimentally observe
PTS, FWM BGS and Fluorescence signal (FLS), but also observe the enhancement and
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29545
suppression of these signals under the double dressing effect in an inverted Y-type four level
system. Furthermore by measuring the above signals we observed that they satisfy the law of
conservation of energy, this information can be used to enhance any one of the signals at the
cost of suppressing the others. By finding a strong relation among the signals we are able to find
the optimal condition of any one of these signal which can be of interest for particular
applications. One example of this is the optimized enhancement of FWM BGS may be used to
make optical amplifiers. We also demonstrate that the characteristics of PTS, FWM BGS and
FLS can be controlled by frequencies, powers, and relative phase of dressing fields; this
information may be useful for the enhancement and modulation of the signals which highlights
the signification of this research work. Optical response of medium is also examined by
resorting to a set of nonlinear coupled wave equations, which is a powerful tool [20–23] for
describing the nonlinear interaction of light fields in such a dressed medium and are here used
to test the validity of the experiment result.
2. Basic theory and experimental scheme
2.1 Experimental setup
(a)
Δ2
| 2
EF
E2
E2
E3′
| 1
Δ1
E3′
E3
(b)
E3
E1
E1
| 3
| 0
(c)
E3′
PD3
E 2 E3
PD1
L
PD2
EF
E1
y
PBS1
Rb
PBS2
x
z
Fig. 1. (a) Four-level energy system. (b) Schematic of an EIG formed by two coupling beams E3
and E′3. Together with the dressing field E2 and probe field E1, a dressed FWM BGS EF will be
generated according to the phase-matching condition KF = K1−K3 + K′3. (c) The setup of our
experiment.
The experiment was implemented in a cell with rubidium (85Rb) atomic vapors at temperature
of 53 °C with four energy levels consisting of 5S1/2(F = 3)(|0), 5S1/2(F = 2)(|3), 5P3/2(|1) and
5D5/2 ( 2 ) as shown in Fig. 1(a).The laser beams are aligned spatially as shown in Fig. 1(c).
Probe laser beam E1 (frequency ω1 and wave vector k1) probes the transition |0 to |1. The two
coupling laser beams E3 (ω3, k3) and E´3 (ω3, k´3) with wavelength about 780.238 nm and a
vertical polarization are split from an external cavity diode lasers (ECDL) connect the
transition |3 to |1. The dressing laser beam E2 (ω2, k2) with wavelength of 775.978 nm and
vertical polarization is from another ECDL drive an upper transition |1 to |2. The powers of
E1, E3 and E3' are 2.1 mW, 13.2 mW and 8.4 mW, respectively.P2 is set to 21mW in our
detuning and phase experiments. The coupling field E31 = ŷ[E3cos(ω3t−k3x) + E′3cos(ω′3t +
k′3x)], composed by E3 and E´3, which propagates through 85Rb vapor in the opposite direction,
generate a standing wave, which results into an EIG. Furthermore EIG will lead to a PBG
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29546
structure as shown in Fig. 1(b). Rabi frequency of the coupling field is G31 = μ3E31/ħ, that we
have | G31 |2 = μ 2 / h 2 [ E32 + E3′2 + 2 E3 E3′ cos 2k3 x] .The probe field E1 propagates in the same
direction of E´3 through the 85Rb vapors with approximately 0.3° angle between them. The
dressing field E2 propagates in the opposite direction of E´3 with approximately 0.3° angle
between them as shown in Fig. 1(c). Generated FWM BGS and PTS are detected by a
photodiode (PD1) and avalanche photodiode (PD2) detectors respectively. In addition, two
fluorescence signals caused by spontaneous decay are measured. The second order FLS R0 and
fourth order FLS R1 signals are generated due to the spontaneous emission from 1 to 0
and
2
to
1 , respectively. The fluorescence signals are captured by another
photodiode(PD3).
2.2 Basic theory
According to the energy system and Liouville pathways, the first-order and third-order density
matrix elements are given as follows
ρ10(1) = iG1 / (d1 + | G31 |2 / d3 + | G2 |2 / d 2 )
(1)
ρ10(3) = -iG1G3G3′ / [(d1 + | G31 |2 / d3 + | G2 |2 / d 2 ) 2 d3 ]
(2)
where d1 = iΔ1 + Γ10 , d 2 = i (Δ1 + Δ 2 ) + Γ 20 , d3 = i (Δ1 - Δ3 ) + Γ30 and |G31|2 = |G3|2 + |G3′|2 +
2G3G3′cos(2k3x). Gi = μi Ei /  is the Rabi frequency with transition dipole moment μi ,
Δ i = Ωi - ωi ( Ω i is the resonance frequency of the transition driven by Ei ) and Γi j is
transverse relaxation rate between |i and |j. An additional phase factor eiΔϕ can be introduced
into the dressing term | G2 |2 / d 2 by means of altering the incident angle of E2 [24] in which
way the relative phase Δϕ related with the orientations of induced dipole moments μ1 and
μ2 could be manipulated and Eqs. (1)-(2) can be modified as follows:
′(1) = iG1 / ( d1 + | G31 |2 / d 3 + | G2 |2 eiΔϕ / d 2 )
ρ10
ρ10′(3) =
-iG1G3G3′
(d1 + | G31 | / d 3 + | G2 |2 eiΔϕ / d 2 ) 2 (d3 )
2
(3)
(4)
According to the relation ε0χE = Nμρ, in which μ is the transition electric dipole moment and N
is the atoms density, we have formulas for the first and third order susceptibility as follows.
iN μ 2
1
hε 0 d1 + | G31 |2 / d3 + | G2 |2 / d 2
(5)
iN μ 2
1
2
hε 0 (d1 + | G31 | / d3 + | G2 |2 / d 2 ) 2 d3
(6)
χ (1) =
χ (3) = -
In order to estimate the reflection efficiency, we start from the nonlinear coupled wave
equations,
∂E1 ( x) / ∂x = −α E1 ( x) + ke − iΔk x x EF ( x)
(7)
−∂EF ( x) / ∂x = −α EF ( x) + keiΔk x x E1 ( x)
(8)
Where E1(x) and EF(x) represents the probe and FWM BGS fields, respectively, α =
(ω1/c)Imχ´(1) /2 is the attenuation of the field due to the absorption of the medium and k =
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29547
i(ω1/c)χ´(3)/2 is the gain due to the nonlinear susceptibility. χ´(1) and χ´(3) are the zero order
coefficients
from
Fourier
expansion
of
χ(1)
and
χ(3),
respectively.
(1)
′
Δk x = {2(ω1 cos θ - ω3 ) + Re[ χ ]ω1 cos θ } / c is the phase mismatch magnitude, in which θ
is the angle between probe E1 and E3′ . If length of the sample in x direction is dx, then by
solving above equations, the reflected FWM BGS (R) and PTS (T) are given as
−λ+d
−λ − d
1
e 2 x −e 2 x
R=
−
+
k e − λ2 d x (λ + + α ) −1 − e − λ2 d x (λ − + α ) −1
1
1
T=
−
+
e( λ1 + λ1 ) d x (λ1− − λ1+ )
−
2
(9)
2
(10)
+
(λ1− + α )eλ1 d x − (λ1+ + α )eλ1 d x
Where λ1± = −iΔk x / 2 ± [(α − iΔk x / 2) 2 − k 2 ]1/ 2 and λ2 ± = λ1± + iΔk x .Generally ρ11(2) related to
(4)
related to fourth order FLS R1 can be obtained by solving the
second order FLS R0 and ρ 22
density-matrix
equations.
The
fluorescence
signal
R0
is
described
by
E
( E )*
1
1
ρ00(0) ⎯⎯
→ ρ10(1) ⎯⎯→
ρ11(2) solving the coupled density-matrix equations, the expression of the
singly dressed density-matrix element ρ11(2)SD (where SD stand for singly dressed) can be obtain
as
2
2
(2)
ρ11
SD = − G1 / [( d1 + G31 / d 3 ) Γ11 ]
(11)
the amplitude squared of which is proportional to the intensity of R0. When the beams E2 is
turned on, the fluorescence process R0 doubly dressed, described by the Liouville pathway
E
( E )*
(2)
(2)
1
1
ρ00(0) ⎯⎯
→ ρ ±(1)0 ⎯⎯→
ρ ±±
. Therefore the expression of ρ11SD
can be modified as
2
2
2
(2)
ρ11
/ d2 )
DD = − G1 / Γ11 (d1 + G31 / d 3 + G2
(where
DD
pathway ρ
(0)
00
stand
E1
⎯⎯
→ρ
(1)
10
for
E2
⎯⎯
→ρ
density-matrix element ρ
(4)
22
doubly
(2)
20
dressed)
( E1 )*
⎯⎯→ ρ
(3)
21
( E2 )*
.For
⎯⎯⎯
→ρ
(4)
22
signal
(12)
R1,
via
Liouville
, Same way we can obtain the
as follows
2
2
ρ 22(4) = G1 G2 / (Γ 22 d1d 2 d 4 )
(13)
(4)
where d 4 = Γ 21 + iΔ 2 , the amplitude squared of ρ 22
is proportional to the intensity of R1. By
considering the dressing effect of E2, the dressed fluorescence process R1 is given as
2
2
2
(4)
ρ 22
G2 / [Γ 22 d1d 4 ( d 2 + G2 / d1 ]
DD = G1
(14)
By changing angle of E2, an additional phase factor eiΔϕ can be introduced into the dressing
2
term G2 / d 2 , it is obvious that the dressing effect can be modulated by manipulating the
relative phase Δϕ , and so the switch between bright and dark states could be achieved. By
means of altering the incident angle of E2, Eqs. (12), (14) can be modified as follows.
2
2
2
iΔϕ
′(2)
ρ11
/d 2 )
DD = − G1 / Γ11 (d1 + G31 /d 3 + G2 e
2
2
2
′(4)DD = G1 G2 / [Γ 22 d1 d 4 ( d 2 + G2 eiΔϕ / d1 ]
ρ 22
(15)
(16)
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29548
The system obeys law of conservation of energy, according to which
R + T + I R = I in
(17)
0
where Iin is intensity of the incident probe, IR0 is intensity of fluorescence signal R0, R is
reflected four wave mixing band gap signal and T is the transmission of probe signal.
The condition of generating PBG structure is that the medium should have a periodic
refractive index. According the relation of the refractive index with the susceptibility, i.e.,
n = 1 + Re( χ ) , in order to get the periodic refractive index, the susceptibility should also be
periodic. Further we should generate the periodic energy level structure for getting the periodic
susceptibility. Hence, by introducing periodic standing wave field E31, we can obtain the
periodic energy levels as shown in Fig. 2. In Figs. 2(a1)-2(a3), the level 1 will be split into
two dressed states G31 ± depending on ∆3 and |G31|2. The two dressed states G31 ± have
= −Δ 3 /2 ± Δ 32 / 4 + G 31
the Eigenvalues λ G
31 ±
2
. Since |G31|2 is periodic along x-axis, so λ G
31 ±
values are also periodic along x. Thus we can obtain the periodic energy levels as shown in Fig.
2(b1)-2(b3). When the probe reaches two-photon resonance Δ1-Δ3 = 0, absorption will be
suppressed, i.e. the PTS becomes strong. At the same time, the FWM BGS will be suppressed
correspondingly. Thus, we define Δ1-Δ3 = 0 as the suppression condition.
|G31+>
|G31+>
|1>
|G31-> |1>
|G31+>
|1>
|G31->
|G31->
|3>
|3>
|3>
|0>
Split Level (MHz)
|0>
|0>
|G31+>
|G31->
X (µm)
|2>
X (µm)
|G31+G2+>
|G31+G2+>
|G31+G2->
|1>
X (µm)
|G31->
|G31+>
|G31G2+>
|G31+G2->
|G31+>
|G31-G2+>
|G31-G2+>
|G31G2->
|G31->
|G31-G2->
|3>
|0>
Split Level(MHz)
|G31-G2->
(c1)
(c2)
(c4)
(c3)
(c5)
|G31+G2+>
|G31+G2->
|G31->
X (µm)
(d1)
X (µm)
X (µm)
X (µm)
(d2)
(d3)
(d4)
X (µm)
(d5)
Fig. 2. (a1)-(a3) the single dressed energy level schematic diagrams and (b1)-(b3) the calculated
single dressed periodic energy levels with changing Δ3. (c1)-(c5) the double dressed energy level
schematic diagrams and (d1)-(d5) the calculated double dressed periodic energy levels with
changing Δ2.
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29549
When E2 is turn on, |G31 +  is further split into two dressed states |G31 + G2 ±  due to the
second level dressing effect of E2, moreover G31 +G2 ± move with changing Δ2 as shown in
Fig.
λG
2(c1)-2(c2).The
31 + G 2 ±
=
two
-Δ 3 + Δ + 4 G 31
2
3
2
2
dressed states
Δ"2 ± Δ"2
2 +4 G2
+
2
G31 +G2 ±
have
the
Eigenvalues
2
with
Δ"2 =Δ 2 -{-Δ 3 + Δ32 +4 G 31 2 }/2 .The same way G31 - is further dressed into two second level
dressed states G31 -G2 ±
λG
=
as shown in Fig. 2(c4)-2(c5), the Eigenvalues of which are
-Δ3 − Δ 32 + 4 G 31
2
+
Δ '2 ± Δ '22 + 4 G 2
2
, where Δ '2 =Δ 2 -{-Δ 3 − Δ32 +4 G 31 2 }/2 .
2
2
.In Fig. 2(c3), because of three photon resonance with Δ 1 = −Δ 2 = Δ 3 only two dressed states
appear. Thus we also obtain the double dressed periodic energy levels as shown in Fig. 2
(d1)-2(d5).
31 − G 2 ±
3. Results and discussions
(a1)
(b1)
Peak
Peak
(a2)
-100
Dip
FL Signal(a.u.)
0.25
FWM BGS(a.u.)
PTS(a.u.)
0.45
0.05
(c1)
Peak
100 -100
0
Δ1 (MHz)
Dip
(c2)
(b2)
0
Peak
Δ1 (MHz)
100 -100
0
100
Δ1 (MHz)
Fig. 3. Measured (a) PTS, (b) FWM BGS and (c) FLS versus Δ1 from −100 MHz to 100 MHz
when different beams are blocked. (a1)-(c1) E2 blocked with Δ3 = 10 MHz and (a2)-(c2) no
beam blocked with Δ2 = −10 MHz and Δ3 = 10 MHz.
First, we observed the PTS, FWM BGS and FLS when we scan the probe frequency detuning
Δ1. When E2 is blocked in Fig. 3(a1), there is a Doppler absorption background at the
single-photon resonant condition Δ1 = 0 due to the term d1 = Γ10 + iΔ1 in ρ10(1) and small PTS
peak caused by the dressing effect of E3 (E´3) according to the term |G31|2/d3 in Eq. (1). When
E2 beam is on, due to the dressing term | G2 |2 / d 2 in ρ10(1) of Eq. (1), the energy level 1 can
be dressed to influence PBG structure so that the PTS increases as shown in Fig. 3(a2). The
PTS reaches maximum at Δ1 = Δ3 = - Δ2 due to double dressing effect of E2 and E3 (E´3)
according to ρ10(1) . In Fig. 3(b1) the emission peak is FWM BGS give by R in Eq. (9) which is
from the reflection of the PBG structure. With E2 on, the FWM BGS will be suppressed due to
the dressing effect of E2 according to | G2 |2 / d 2 in ρ10(3) as shown in Fig. 3(b2). Suppression
condition is Δ1 + Δ2 = 0. In Fig. 3(c1), the profile curve represents the second order FLS R0
related to ρ11(2) . The small dip in the profile curve is induced by the dressing fields E3 and E´3,
2
(2)
which appear at Δ1 = Δ3 according to G31 / d3 in ρ11SD
. When E2 is turn on, a narrow
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29550
emission peak appears in the profile curve shown in Fig. 3(c2), which is the fourth order FLS R1
(4)
related to ρ 22
.Compared to Fig. 3(c1) the dip becomes deeper because of the double dressing
(2)
effect of E2 and E3 (E´3) according to ρ11DD
. Compared Figs. 3(a1)-3(c1) with Figs.
3(a2)-3(c2), due to the dressing effect of E2, the intensity of PTS increases and the intensities of
FWM BGS and FLS R0 decrease, and the whole energy is conserved according to Eq. (17).
0.3 (a1)
PTS(a.u)
0.2
0.1
30
0.3 (b1)
0.2
Profile
-60 -30
0.3 (c1)
0
30
60
(b2)
0
30
60 -60 -30
(c2)
0
30
60
0
30
60 -60 -30
0
30
60
0.2
0.1
-60 -30
60 -60 -30
FWM BGS(a.u)
0
FL Signal(a.u)
-60 -30
0.1
(a2)
Baseline
Fig. 4. Measured (a1) PTS, (b1) FWM BGS and (c1) FLS versus Δ2, when we select five
different discrete values of Δ1 as black(−47 MHz), red(−23 MHz), blue(0 MHz), pink(28 MHz)
and green(47 MHz) and Δ3 = 0 MHz. (a2), (b2) and (c2) are the theoretical calculations of (a1),
(b1) and (c1), respectively.
Furthermore, we observe second level dressing effect on PTS, FWM BGS and FLS by
scanning Δ2, at different discrete values of Δ1. Figure 4(a1) represents the second level dressed
PTS. The profile (dashed curve) of these PTS baselines shows Doppler absorption background
with a peak on it. The profile peak is the intensity of single-dressed PTS induced by E3 and E3',
which appear at Δ1 = Δ3 according to | G31 |2 / d3 of ρ10(1) in Eq. (1). In each sub curve, the
peak on the baseline stands for the enhanced PTS induced by the second level dressing effect of
E2, which meets Δ2 = -Δ1 according to the dressing term | G2 |2 / d 2 in Eq. (1). The total PTS
reaches maximum at Δ2 = -Δ1 = -Δ3. In Fig. 4(b1), profile (dashed curve) of the baselines shows
the FWM BGS related to R in Eq. (9) from reflection of the PBG structure. Dip in each sub
curve shows that FWM BGS is suppressed due to the dressing effect of E2 at Δ2 = -Δ1 according
to | G2 |2 / d 2 of ρ10(3) in Eq. (2). The deepest dip appears at Δ2 = -Δ1 = -Δ3 corresponding to the
total strongest PTS. In Fig. 4(c1), the profile(dashed curve) of the baselines is the second order
FLS R0 signal suppressed by E3 and E′3 and it reaches minimum at Δ1-Δ3 = 0 due to the term
(4)
|G31|2/d3 in Eq. (12). In each sub curve, the peak is the fourth order FLS R1 related to ρ 22
, and
it reaches the smallest one at Δ1 = 0 because of the strongest dressing effect of E2 according to
2
(4)
G2 / d1 of ρ 22DD
in Eq. (14) as shown in Fig. 4(c3).
Next, we observe the power dependences of the PTS, FWM BGS and FLS versus Δ2.
Variations in the three types of signals are shown from bottom to top with increasing power of
E2 (P2) as shown in Figs. 5(a)-5(c). In Fig. 5(a), the baselines of the signals represent the
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29551
intensity of the PTS induced by E3 (E´3). Peaks in the baselines at Δ1 = Δ3 shows the
enhancement of the PTS induced by the second level dressing effect of E2.Changing P2 from
small to large values, the peaks becomes higher due to the dressing term | G2 |2 / d 2 in ρ10(1) of
Eq. (1). The FWM BGS signal intensity is shown by the baselines in Fig. 5(b). Dip in the
baseline shows suppression of reflected FWM BGS signal because of the second level dressing
effect of E2 according to the dressing term | G2 |2 / d 2 in ρ10(3) of Eq. (2). The dip is shallow at
small values of power and become deeper with increasing P2 due to the enhanced dressing
effect of E2.In Fig. 5(c), the baselines represent the second order FLS R0 suppressed by E3. By
changing P2 from small to large values the dip change from shallow to a deeper one because of
the enhanced dressing effect of E2. Variation of the dips shows that R0 are further suppressed by
2
(2)
of Eq. (12). R0 signal with the deepest dip
E2 according to the term G2 / d 2 in ρ11DD
correspond to the FWM BGS with deepest dip and PTS with higher peak. Peaks in the baseline
(4)
are R1 related to ρ 22DD
, which become higher with increasing the power of the dressing field
E2. By observing these three signals we conclude, with the PTS increasing, the FWM BGS and
FLS R0 decrease to ensure the conservation of energy according to Eq. (17).
0.5
0
120 -120
FL Signal(a.u.)
PTS(a.u.)
FWM BGS(a.u.)
1.0
-120
(c)
(b)
1.5 (a)
0
120 -120
0
120
Fig. 5. Measured (a) PTS, (b) FWM BGS and (c) FLS versus Δ2 from −120 MHz to 120 MHz
with Δ3 = Δ1 = 0, when we set the power of E2 (P2) from bottom to top as (1) 9.2 mW, (2) 13.0
mW, (3) 17.1 mW, (4) 21.6 mW, (5) 25.7 mW, respectively.
Finally, we regulate the PTS, FWM BGS and FLS with the relative phase of E2 (Δφ) by
changing its incident angle. The experimental results can be obtained by scanning Δ2 with Δ1 =
0 as shown in Figs. 6(a)-6(c). With the relative phase Δφ changing from - π /3 to 2π /3 , the
PTS in Fig. 6(a) can be switched from a dip to a peak due to the change of dressing effect of E2
according to ρ10′(1) . The peaks stand for the transmission enhancement of probe signal and the
dips stand for the absorption enhancement of the PTS. During this process, the deepest dip and
the highest peak separately appear at Δφ = 2π /3 and Δφ = −π /6 , respectively. In Fig. 6(b)
and Fig. 6(c) where Δφ is altered from - π /3 to 2π /3 , a change from shallow to deep then to
shallow occurs due to the regulating of the relative phase Δφ. With the variation of the dressing
effect of G2 caused by Δφ, the deepest suppression dips in FWM BGS and R0 appear at Δφ =
−π /6 which corresponds to the strongest PTS peak. Compared with the signals at the
reference phase Δφ = 0, the FWM BGS and R0 can be suppressed, i.e. the suppression dip
become deeper, with Δφ changed as −π /6 . And the FWM BGS and R0 can be enhanced, i.e.
the suppression dip become shallower, with Δφ changed as - π /3 and 2π /3 . These
variations are because of the switch of the dressing effect caused by regulating the relative
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29552
phase Δφ according to the term | G2 |2 eiΔϕ / d 2 in Eqs. (3)-(4) and Eqs. (15)-(16). The
controllable enhancement of FWM BGS may be used to make optical amplifiers.
(a)
−π /3
−π /6
−π /6
0
10
π /3
2π /3
5
0
120
240
Δ 2 (MHz)
0
π /3
2π /3
0
120
Δ 2 (MHz)
240
−π /3
Dip
FL Signal(a.u.)
−π /3
FWM BGS(a.u.)
PTS(a.u.)
15
(c)
(b)
−π /6
0
π /3
2π /3
0
120
240
Δ 2 (MHz)
Fig. 6. Measured (a) PTS, (b) FWM BGS and (c) FLS versus Δ2 with Δ1 = Δ3 = −120 MHz, when
we change the relative phase of E2 as 2π /3 , π /3 , 0, −π /6 and −π /3 , respectively.
4. Conclusion
In summary, the single-dressed and double-dressed PTS, FWM BGS and FLS are compared for
the first time to deeply comprehend the double-dressing effect on the PBG. We experimentally
and theoretically demonstrated that, PTS and FWM BGS and FLS can be manipulated by
multiple parameters like, changing power, detuning and relative phase of incident beams. We
also observed, the three types of signals satisfy law of conservation of energy. Such research
could find its applications in optical amplifiers and quantum information processing.
Acknowledgments
This work was supported by the 973 Program (2012CB921804), NSFC (61108017, 11474228,
61308015, 11104214, 11104216, 61205112), KSTIT of Shaanxi Province (2014KCT-10),
NSFC of Shaanxi Province (2014JZ020), KLP of Shaanxi Province (2013SZS04-Z02),
FRFCU (2012jdhz05, xjj2012080), and CPSF (2014M560779).
#223118 - $15.00 USD Received 15 Sep 2014; revised 23 Oct 2014; accepted 23 Oct 2014; published 19 Nov 2014
(C) 2014 OSA
1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029544 | OPTICS EXPRESS 29553