The Stark anomalous dispersion optical filter is a wide-frequency-tunable ultra-narrow-bandwidth optical filter. The first theoretical investigation of this filter matched to the wavelength of a doubled Nd:YAG laser is reported. The calculations show that such a filter may provide above 80 percent transmission, and a noise equivalent bandwidth of 3 GHz

Shay, T. M.

Yin, B.

English

NASA Technical Reports Server

TDA Progress Rel_d 42-118
pI : /-_ , ,f
N95-14622
August 15, 1994
The Stark Anomalous Dispersion Optical Filter:
The Theory
B. Yin and T. M. Shay
New MexicoState University,Las Cruces, New Mexico
The Stark anomalous dispersion optical filter is a wide-frequency-tunable ultra-
narrow-bandwidth optical filter. The first theoretical investigation of this filter
matched to the wavelength of a doubled Nd:YAG laser is reported. The calculations
show that such a filter may provide above 80 percent transmission, and a noise
equivalent bandwidth of 3 GHz.
I. Introduction
In a deep space laser communication system, a doubled Q-switched Nd:YAG laser is a potential laser
transmitter. At the receiver end, in addition to a very weak signal with a large Doppler frequency shift (up
to -t-77 GHz, typical for the Mars orbital missions), a considerable amount of background noise (sun, sunlit
Earth, etc.) is expected within the field of view of the receiver. A high-sensitivity and high background-
noise-rejection optical filter with wide-frequency tunability around the doubled Nd:YAG laser emission
can simultaneously track Doppler frequency shifts and reject intense background radiation. The Stark
anomalous dispersion optical filter (SADOF) is designed to provide high background noise rejection and
wide frequency tunability and to operate at the wavelength of the doubled Nd lasers [1,2]. The SADOF
is similar to our previously reported nontunable Faraday anomalous dispersion optical filter (FADOF)
[3-5]. It may be considered as simply an addition of an electric field and optical pumping to the FADOF.
In the following sections, the basic design and theoretical calculations are presented, the issues of shifting
the SADOF center frequency using the Stark effect are investigated, and the calculation results for the
SADOF operating at the doubled Nd:YAG laser line are discussed. These results have been used to direct
the thrust of the experimental design.
II. Basic Design
Like the FADOF, the SADOF has a longitudinal magnetic field to induce the polarization rotation
due to the resonant Faraday effect. However, in addition, the SADOF has an external electric field
to shift the energy levels of the atoms. To use the resonant Faraday effect, an atomic transition that
matches the Nd laser lines is required. To have a large energy level shift that results in a filter center
frequency shift, a large scalar polarizability for an energy level in the filter transition is desired. Alkali
atoms have large scalar polarizabilities, and the candidate transitions appropriate for doubled Nd laser
lines are summarized in Table 1. For the transitions in Table 1, the lower states are the first or second
excited states of the atoms, and the upper states are higher lying states. Since the lower-level state of
the filter transition is not the ground state, optical pumping to populate the lower-level state is required
14
https://ntrs.nasa.gov/search.jsp?R=19950008208 2020-06-16T09:06:50+00:00Z
for filter operation at those transitions. The scalar polarizability is determined by examining the Stark
Hamiltonian for the interaction between an atom and an electric field c, which is
H_ = -e(p) (1)
where p is the induced dipole moment. For alkali elements, the perturbation of electrons in the closed
shells may be neglected; then p is given by
p = -er (2)
where r is the position vector of the valence electron, and e is the electron charge. The high-lying states
have much larger < r >, therefore, much stronger Stark interaction, or larger polarizabilities. Because
the upper levels of the SADOF transitions in Table 1 are high-lying levels, their polarizabilities are large.
For example, the scalar polarizability of the Rb(10S) state is about 280 MHz/(kV/cm) 2, while the scalar
polarizability of the Rb(bP) state is only about 0.2 Mttz/(kV/cm) 2.
Table 1. Potential SADOF lines in alkali vapors.
Wavelength Compatible Laser wavelength
Transition
(in air), nm doubled Nd laser (air T = 300 K), nm
Rb 5P1/2-8D3/2 536.26 YALO 536.45
Rb 5Pa/2-9Db/2 526.00 YLF 526.5
Rb 5Pl/_-10Sl/2 532.24 YAG 532.07 _
Rb 5Pal2 -10S1/2 539.06 BEL 539.5
YALO 539 4- 1
Rb 5P3/2 - 11S 1/2 523.39 YLF 523.6
K 4P3/2-6Db/2 535.96 YALO 536.45
K 4P1/2-8Sl12 532.32 YAG 532.07 _
Cs 6P3/2-13Db/2 535.04 BEL 535,05
aNd:YAG laser needs to heated to about 100-150 deg C for the wavelength to
match the filter.
Because the Rb 532-nm transition is the closest transition to the strongest line of doubled Nd:YAG
laser, we discuss the Rb 532-nm SADOF Rb (5P1/2-10S1/2) in this article. The basic structure for an
Rb 532-nm SADOF that operates at the doubled Nd:YAG laser line is shown in Fig. 1. An Rb vapor cell
is placed between two crossed polarizers under the external longitudinal magnetic field and transverse
electric field. The optical pumping is applied from one end of the cell. The colored-glass filter is used to
ensure that the infrared pump radiation does not reach the photodetector.
III. The Energy Hamiltonian in the Presence of Magnetic and Electric Fields
When an electric field is applied to an atom, it shifts the electronic energy levels. This is known as
the Stark effect, and the energy level shift is quadratically dependent on the electric field strength. The
effective Hamiltonian element for the energy shift can be expressed as
(IJFMIH_ IIJF'M ') = --I (aoSFM,F,M, + o_2QFF,,MM,)e 2 (3)
15
SOLENOID 795-nm P2 OUTPUT
PUMP BEAM
_ ELECTRICAL RELD _ --
l_, BEAM
PLATES _ _:::::_ (-'% I \\
_1::_ _ _ l_ _. _" GREEN BANDPASS
_ COLORED-GLASS
,N;UT VAPOROELL
BEAM INPUT GREEN BANDPASS INFRARED
POLARIZER COLORED-GLASS REFLECTOR
FILTER
Fig. 1. The basic structure of an Rb 532-nm SADOF.
where J, I, F = J + I, and M are the quantum numbers for the total orbital angular momentum, the
nuclear spin, the total angular momentum, and the projection of total angular momentum, respectively.
The values of a0 and a2 are the scalar and tensor polarizabilities, respectively. The delta function
_FM, F'M' is unity only if F = F _ and M = MI; otherwise it is zero. The quadrupole matrix element
between hyperfine states is QFF',MM' [6], and its values are dependent on the quantum numbers of the
sublevels. The _FM,F'M' weighting of o_0 in Eq. (3) shows that the change in energy level associated with
the scalar polarizability term is common to all sublevels of a state, whereas the energy change associated
with a tensor polarizability term differs for the various sublevels because of the QFFLMM' factor. Because
of the large scalar polarizability of the high-lying Rb 10S1/2 state, the energy level, i.e., frequency, of the
optical transition can be shifted over a very large range using reasonable electric field strengths. The
tensor polarizability is zero for all J = 1/2 states; hence, c_2 for the 10Sz/2 and 5P1/2 states is zero.
Like the FADOF theory, the theory for the transmission of the Rb 532-nm SADOF begins by con-
structing the energy Hamiltonian. Assuming the Stark splitting is small compared with the fine structure,
the element of the total energy Hamiltonian in the presence of an external electric field and magnetic
field for the Rb 532-nm SADOF is given by
(IJFMIHIIJF'M) = {hyperfine energy} + {Stark energy} + {magnetic energy}
= AEFSr, F,--I_oc_6r, F,+{tLB,(--1)M+J-Z+Zgj
{ ,;;)}x _/J(J+I)(2J+I)(2F+I)(2F'+I) J1 1 F -M 0 (4)
where AEF is the hyperflne energy shift caused by nuclear spin and is not influenced by external fields
[5], p is the Bohr magneton, B_ is the external magnetic field, and gj is the Lande g factor that depends
on J. The 6-j symbol (enclosed by the curly brackets) and the 3-j symbol (enclosed by the parentheses)
are matrix representations of the spherical coordinate components of the electron wave function for the
single atom. The hyperfine energy term and the magnetic energy term are exactly the same as in the
FADOF theory. Since the tensor polarizability is zero for J = 1/2, the only effect of the electric field in
the Rb 532-nm SADOF is to shift the center of gravity of an atomic energy level. Therefore, the atomic
16
transition intensities and polarization rotation calculations are the same as for the FADOF model, except
that the atomic number density of the transition lower energy level will depend on the optical pumping.
An energy level diagram depicting the Rb 532-nm SADOF pumping is shown in Fig. 2.
10S1/2
_\ 532-nmFILTER TRANSITION
\
\
W
5Pl/2
795-nm PUMPING
5S1/2
GROUND STATE
Fig. 2. A simplified Rb 532-nm SADOFenergy-level diagram.
Optical pumping is key to SADOF operation. Significant transmission of the signal radiation is
achieved only if the lower level atomic state 5P1/2 of the filter transition is sufficiently populated. We
have developed a simple model to predict the required optical pumping. In this, our first SADOF design,
we have tailored the filter parameters to achieve operation at reasonable optical pumping powers and
operating temperatures. Our analysis predicts that a 10-cm-long cell operating at a temperature of 190
deg C and pumped by 200 mW of optical power can demonstrate filter performance.
IV. SADOF Transmission
To predict the SADOF performance, the energy Hamiltonian, the hyperfine transition frequencies and
line strengths, and the complex refractive indices need to be determined. The complex refractive indices
are used to calculate the optical polarization rotation and absorption, and hence the filter transmission.
This has been shown in our previous Rb FADOF articles [3-5]. The following is a brief summary of the
equations necessary to predict the filter performance. The polarization rotation angles can be determined
from complex refractive indices,
wL ) ne[fi+(w) - fi_(w)]%-c (5)
where fi+ is the complex refractive index for the two circular polarizations, L is the cell length, and c is
the speed of light. The absorption coefficient is given by
(6)
The transmission of the SADOF filter is
T(w)= l(exp [-k+(w)L]+exp [-k_(w)L]-2 cos [2¢(w)] exp [_k+(w)+k_(w)2 L]} (7)
17
The equivalent noise bandwidth (ENBW) is expressed as
oo
ENBW = _ [ T(w)&o
Tma_J
o
(8)
where T(w) represents the filter transmission spectrum, and Tma= represents the maximum transmission
for the filter. The equivalent noise bandwidth corresponds to the bandwidth of a rectangular notch
filter with transmission Tm_, that transmits the same amount of noise as our filter. The equivalent noise
bandwidth provides a ready comparison of different filter designs and even different kinds of optical filters.
V. Results and Discussion
A. Rotation and Transmission Spectrum
The SADOF transmission spectrum was calculated using the equations presented in the previous
sections. Figures 3 and 4 show the SADOF rotation and transmission spectrum for a filter operating at
a temperature of 190 deg C with 200 mW optical pumping, and in a magnetic field of 700 G.
(5 1.0
UJ
._1
0.5
z
0 0.0
F-
o
rr -0.5
2.0 _ , i , _ , i
n/2
1.5 ................
B = 700 G
E=0
-1.0
-1.5
-10-7.5 -5 -2.5 0 2.5 5 7.5 10
FREQUENCY, GHz
Fig. 3. Rb 532-nm SADOF rotation angles versus
frequency at T= 190 deg C and B = 700 G, where the
horizontal axis is normalized to the frequency shift from
the Rb 532-nm transition.
1.0
0.8
0.6
_0.4
0.2
0.0
-- -- -I- - -1- - "_1 I # - - T -- - -_ -- -- -
J |
i i
ip ,iw
;ADOF II I | It B=700G
TRANSMISSION_ | I I I | S = 0
-10 -7.5 -5 -2.5 0 2.5 5 7.5 10
"FREQUENCY, GHz
Fig, 4. Rb 523-nm SADOF transmission spectrum
at T= 190 deg C, B = 700 G, and E =0 kV/cm,
where the horizontal axis is normalized to the
frequency shift from the 532-nm transition.
As in the FADOF, the peak transmission occurs just outside tSe resonance absorption band where the
rotation angle is nearly -r/2. Under these operating conditions, the SADOF has a peak transmission of
about 0.86, a 1.7-GHz bandwidth across the principal transmission peak, and equivalent noise bandwidth
of 3.0 GHz.
The SADOF center frequency is tuned by varying the electric field. Figure 5 shows tile predicted
E-field frequency shift of the SADOF transmission spectrum. The filter is in a 20-kV electric field, and
the transmission spectrum is red-shifted about 55 GHz without any degradation in filter performance.
18
1.00
0.75
Z
o
G)
0.50
O3
Z
I-
0.25
0.00
t
B = 700 G
E= 20 kV/cm
ENBW= 3 GHz
-,o
FREQUENCY, GHz
Fig. 5. Rb 532-nm SADOF transmission spectrum at
T= 190 deg C, B = 700 G, and E = 20 kV/cm.
B. Frequency Tunability
Because the scalar polarizability in the upper energy level is much larger than the scalar polarizability
in the lower level, the upper energy level shifts determine to a good approximation the Rb 532-nm
transition center frequency shift. Therefore, the filter center frequency shift depends quadratically on the
electric field,
1 211 ]Av=--_c_0(10S1/2)C- -- cr0(5P1/2)e 2 l 2 (9)
The calculated center frequency shift of the filter passband versus the electric field is plotted in Fig. 6.
It shows that the center frequency is shifted by about 250 GHz, or 0.25 nm by a 40-kV/cm field.
C. Optimized Operating Conditions
Figure 7 gives a series of transmission curves with different operating conditions. These curves are
for different B-fields and temperatures and can be used to tailor the SADOF performance to tile specific
application based on the ENBW and peak transmission requirements.
This figure is calculated for a zero electric field since adding the electric field only tunes the center
frequency. These curves also demonstrate that the bandwidth of the transmission can be varied by
changing the magnetic field and the temperature.
D. Noise Leakage From Adjacent Filter Lines
The nearest green transition for the Rb 532-nm SADOF is the Rb (5Pl/2-8D3/2) 536.3-nm transition.
This transition can contribute a background noise component to the Rb SADOF. However, radiation
from this and other Rb green transitions can be suppressed by using a commercial interference filter
(BW _ 6 nm) as a prefilter. The transition probability of Rb 5P1/2-8D3/2 is seven times larger than the
Rb 5PI/2-10Sa/2; the equivalent noise bandwidth of the 5P1/2-8D3/2 transition is much larger than that
of the 5P1/2-10S1/2. The calculated ENBW for the Rb 5P1/2-SD3/2 transition at a temperature of 190
deg C and a magnetic field of 700 G is 8 GHz. A lower ENBW (--_ 3 GHz) can be achieved by using a
narrower bandpass prefilter.
19
oI-50 --1 O0 -
o -7-
-2001-
,_ -250I_
,,==_ooI-
--,350[-
-400 f i i
0 10 20 30 40
ELECTRIC FIELD, kV/cm
Fig. 6. Rb 532-nm SADOF center frequency versus external
electric field.
50
(3
"10
u_
n"
I-
,<
cc 0.6
W
n
:E _0.4
wI-
" 0.2
,_]
UJ
o 0.0
n-
1.0
1.0 , i i
o8 (a)
0.6
0.4
0.2
0.0 " '
1.0 ' ' '
0.8- (b)
I I I
O.B (c)
0.6
0
GO
"" 0.4
0.0 ' '
-10 -5 5
5OO
I I I
I I !
(h)
I ! I
O)
I I I
(d)
A
I ! I
(0 ' ' ' t
t
,A,1
-10 -5 0 5 10
7OO
MAGNETIC FIELD, G
10 10
0
-10 -5 0 5
900
Fig. 7. Rb 532-nm SADOF transmisslon spectrum at E = 0 and st (e) 500 G, 200 deg C, ENBW=
3.9 GHz; (b) 500 G, 190 deg C, ENBW= 3.2 GHz; (c) 500 G, 180 deg C, ENBW= 2.0 GHz; (d) 700 G,
200 deg C, ENBW= 4.2 GHz; (e) 700 G, 190 deg C, ENBW= 3.0 GHz; (f) 700 G, 180 dec C, ENBW
= 3.2 GHz; (g) 900 G, 200 deg C, ENBW= 4.0 GHz; (h) 900 G, 190 deg C, ENBW= 3.4 GHz; and (|)
900 G, 180 deg C, ENBW= 3.0 GHz.
20
Vl. Concluslons
The first theoretical model for calculating the performance of the SADOF is developed. The operating
conditions for a 532-nm SADOF are determined. The filter is compatible with the strongest line of a
frequency-doubled Nd:YAG laser. The results show that the SADOF can provide very narrow bandwidth,
high transmission, low equivalent noise bandwidth, and, most of all, can be tuned over a very large
frequency range (250 GHz at E = 40 kV/cm). The SADOF is a good candidate for a filter in the deep
space laser communications using a doubled Nd:YAG laser as a source.
Acknowledgments
The authors wish to thank Drs. K. Wilson and :]. R. Lesh in the JPL Optical
Communications Group for reviewing this work.
References
[1] B. Yin and T. M. Shay, "Theoretical Model for a Stark Anomalous Dispersion
Optical Filter," Proc. Laser '92, Houston, Texas, pp. 837-843, December 1992.
[2] B. Yin and T. M. Shay, "A Rb 532 nm Stark Anomalous Dispersion Optical Filter
for Doubled Nd:YAG Lasers," Proc. LEOS '93, San Jose, California, pp. 359-360,
November 1993.
[3] D. J. Dick and T. M. Shay, "Ultra-High Noise Rejection Optical Filter," Opt.
Lett., vol. 16, p. 867, June 1991.
[4] B. Yin and T. M. Shay, "Theoretical Model of Faraday Anomalous Dispersion
Optical Filter," Opt. Lett., vol. 16, pp. 1617-1619, October 1991.
[5] B. Yin, L. S. Alvarez, and T. M. Shay, "The Rb 780-Nanometer Faraday Anoma-
lous Dispersion Optical Filter: Theory and Experiment," The Telecommunica-
lions and Data Acquisition Progress Report 42-116, voI. October-December 1993,
Jet Propulsion Laboratory, Pasadena, California, pp. 71-85, February 15, 1994.
[6] H. L. Zhou and B. W. Norcross, "Improved Calculation of the Quadratic Stark
Effect in the 6P3/2 State of Cs," Phys. Rev. A, vol. 40, no. 9, pp. 5048-5051,
November 1989.
21


The Stark anomalous dispersion optical filter: The theory

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server