Solid-state laser with self-stabilized or linearly chirped output frequency
The specific regimes of the linear tuning and the frequency self-stabilization were proposed and analyzed theoretically in a diode pumped solid-state laser with a thin-film metallic selector.
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2002
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Lopiitchouk, M. Peshko, I. 2017-06-13T16:43:20Z 2017-06-13T16:43:20Z 2002 Solid-state laser with self-stabilized or linearly chirped output frequency / M. Lopiitchouk, I. Peshko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 2. — С. 197-200. — Бібліогр.: 5 назв. — англ. 1560-8034 PACS: 42.62.Eh https://nasplib.isofts.kiev.ua/handle/123456789/121190 The specific regimes of the linear tuning and the frequency self-stabilization were proposed and analyzed theoretically in a diode pumped solid-state laser with a thin-film metallic selector. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Solid-state laser with self-stabilized or linearly chirped output frequency Article published earlier |
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Solid-state laser with self-stabilized or linearly chirped output frequency |
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Solid-state laser with self-stabilized or linearly chirped output frequency Lopiitchouk, M. Peshko, I. |
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Solid-state laser with self-stabilized or linearly chirped output frequency |
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Solid-state laser with self-stabilized or linearly chirped output frequency |
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Solid-state laser with self-stabilized or linearly chirped output frequency |
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Solid-state laser with self-stabilized or linearly chirped output frequency |
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solid-state laser with self-stabilized or linearly chirped output frequency |
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Lopiitchouk, M. Peshko, I. |
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Lopiitchouk, M. Peshko, I. |
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2002 |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The specific regimes of the linear tuning and the frequency self-stabilization were proposed and analyzed theoretically in a diode pumped solid-state laser with a thin-film metallic selector.
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1560-8034 |
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Solid-state laser with self-stabilized or linearly chirped output frequency / M. Lopiitchouk, I. Peshko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 2. — С. 197-200. — Бібліогр.: 5 назв. — англ. |
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197© 2002, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2002. V. 5, N 2. P. 197-200.
PACS: 42.62.Eh
Solid-state laser with self-stabilized
or linearly chirped output frequency
M. Lopiitchouk1), I. Peshko2)
1)Institute of Physics, NAS of Ukraine, 03650 Kyiv, 46 prospect Nauky, Ukraine
Phone: +380 (44) 265-0862; fax: +380 (44) 265�1589; e-mail : lopii@i.com.ua
2) Now I.P. is with Photonics Research Ontario, 60 St.George Str., Suite 331, Toronto, Ontario, M5S 1A7, Canada.
Phone: 1(416)978 -1804; fax: 1(416)978-3936; e-mail: ipeshko@pro.on.ca (office), ipeshko@sympatico.ca (home).
Abstract. The specific regimes of the linear tuning and the frequency self-stabilization were proposed
and analyzed theoretically in a diode pumped solid-state laser with a thin-film metallic selector.
Keywords: diode pumped solid-state laser, single-frequency laser, frequency self-stabilization,
thin-film selector.
Paper received 10.12.01; revised manuscript received 18.04.02; accepted for publication 25.06.02.
1. Introduction
Today, construction of highly stable optical standards
of the fundamental laser parameters, such as energy,
power or frequency is a problem. During the last decade
diode-pumped solid-state lasers achieved fantastically
high frequency stability. The electronically stabilized
system demonstrated relative stability about several hun-
dred mHz [1]. However, such system is quite complex
and non-transportable. For operation in the hospital, in
the plant, or in the airport one needs the standard of mi-
nor stability but simple, small and relatively cheap. To
our mind, the best candidate for this role is the solid-state
diode-pumped laser with the thin-film absorbing selector
[2, 3].
In the single-frequency regime laser line width is
about six orders of magnitude less than that at a free
running mode. This laser has extremely narrow spec-
tral width (~104 Hz). It is very sensitive to thermal dis-
turbances (~109 Hz/K) [4]. A solid-state laser with a thin-
film absorbing selector may be designed to be quite in-
sensitive to mechanical noise. At the same time it has to
provide both the stable single-frequency mode and a wide
range of tunable frequency. Unfortunately, simultane-
ous satisfaction of such requirements is opposite in their
nature.
The principle idea of the absorbing thin-film opera-
tion is the following [5]. The metallic film with a thick-
ness significantly smaller than the standing wave period
is placed into the linear cavity. If the thin film is adjusted
to the node phase surface area of a mode, the losses for
this mode become very low and the single longitudinal
mode starts to operate. It is well known, that phase char-
acteristics of interferometers with an absorbing mirror
depend strongly on layer thickness and its composition
[5]. Due to the high value of the absorption coefficient
the thin film introduces strong distortion into the phase
of the laser radiation. This phase shift depends on the
position of the film relative to the standing wave struc-
ture inside the laser cavity and on the film properties. In
this communication we demonstrate how to make this
dependency predictable and controllable.
2. Basic principles
The phase of a wave that interacts with a metal mirror
interferometer is given by expression [5]:
]
)1()(
)(2
[)(
222 ϕϕ
ϕϕϕ
tgGtgBH
tgtgBH
arctg
⋅−+⋅−
⋅−−=Ψ
(1)
198 SQO, 5(2), 2002
M. Lopiitchouk et al.: Solid-state laser with self-stabilized...
where ϕ = 2πl/λ = λω/c is the interferometer phase, ω is
the radiation frequency, c is the velocity of light, l is the
interferometer base length, l is the wavelength of radia-
tion, B = ξ′′/n1 ; G = ξ′/n1; H = n2/n1, n1 is the index of
refraction of the substrate, n2 is the index of refraction of
the material inside the interferometer, ξ = ξ′+iξ′′ is the
surface conductivity with real and imaginary parts connected
with the mass material parameters as:
ξ′ = 2nχ 2πδd/λ, ξ′′ = (n2 - χ 2)2πδd/λ , (2)
where χ and n are the absorption coefficient and the in-
dex of refraction of the film mass material, respectively,
δd is the film thickness.
The frequency of an electromagnetic wave can be
calculated as a time derivative of the phase:
in
out
F
F
dt
d
dt
d
d
dt
dt
d
d
d === ΨΨΨ ϕ
ϕϕ
ϕ
/
)(
(3)
For an interferometer located in a laser cavity the
parameter Fin is a frequency, which corresponds to the
number of half-wave lengths along the interferometer base,
and Fout is the real frequency of oscillation. Thus, the
derivative dΨ(ϕ)/δϕ demonstrates the output radiation
frequency normalized to �geometrical� frequency
(connected with an integer of the half-waves in the cavity).
Combination of the different parameters B, G, H results in
specific behavior of dΨ(ϕ)/δϕ function. Gathering up
the appropriate B, G, H values (among experimentally
achieved), one can predict the laser output frequency
behavior. Let us consider two examples of such analyses.
3. Linear chirp of frequency
The laser with frequency chirping can be used as a range
finder on middle (some km) distances. In such systems the
radiated frequency has to vary linearly versus the time,
although in laser with a thin-film selector the frequency
changes non-linearly and, sometimes, even by a non-
monotone mode, depending on the position of the selector.
The interferometers, which were considered before [2, 3]
were intended for a single mode selection. Therefore,
principal attention was paid to achieve a maximum sharp
reflection peak with this interferometer. It is evident, that
the presence of a narrow peak of reflection indicates the
presence of a strong phase shift of the reflected signal. It
means that even at minor variations of the position of the
selector in a resonator, owing to the thermal, mechanical, or
piezodriver feeding voltage perturbations, the frequency
changes of the radiation can rather noticeably differ from
linear, though the oscillation remains permanently a single-
frequency one. In elaboration of the laser for the Doppler
range finding purposes an actual problem is control of the
frequency changes rate.
Any profile of a reflection coefficient of an interferometer
takes place at changes of an interferometer base (l)
(scanning an interferometer), or with a constant base,
but variable frequency of a radiation (classical interfer-
ometer Fabry-Perot). The phase of the radiation, which
has interacted with the interferometer has both frequency
and spatial components. If the phase of a reflected signal
by a non-linear mode reacts to the linear selector shift it
means that the additional phase modifications are con-
nected with frequency shift. If the space modifications of
a position of a mirror linearly correspond to the phase
changes of an echo, the resonance frequency of a mode is
shifted proportionally to shifts of a mirror position. Such
case has to be realised in the laser with linear frequency
tuning. In case of film absence B = G = 0, H = 1. The
expression (1) is transformed to that one, which demon-
strates a linear phase change at double pass by the field
of the distance to a mirror and back.
ϕϕ
ϕ
ϕϕ 2)2(
1
2
)(
2
−=−=
−
−=Ψ tgarctg
tg
tg
arctg
(5)
In the case when ξ′ ≠ 0, ξ′′ ≠ 0, but Ψ(ϕ) = -2ϕ, there
are no phase variations connected with a frequency
change. In other words, it is possible to ask: whether there
is an actual set of parameters H, G, B, R, that in the defi-
nite range of the parameter variations the following equal-
ity is valid:
ϕ
ϕϕ
ϕϕ
ϕϕ
2222 1
2
2
)1()(
)(2
tg
tg
tg
tgtg
tgtg
GBH
BH
−
==
⋅−+⋅
⋅−
−
(6)
Under these circumstances dΨ/dϕ = -2, that is the
ratio of oscillation frequency to frequency of set-up is a
constant. From expression (6) one can obtain the follow-
ing equations:
=−⋅−= )1)((0 2ϕϕ tgtgBHY
1)1()( 222 YtgGtgBH =−+⋅−= ϕϕ (7)
If there is a solution of the equation above, the graphs
of the left and right parts should coincide. It correlates with
the experimental conditions, when the changes of the output
frequency are proportional to frequency variations
connected with the selector relocation. And, as it will be
shown below, the velocity tuning can be controlled due to
the definite selection both of the film and the substrate
parameters. So, the frequency velocity chirp can be
controlled in the definite limits but remains a linear one.
For testing we substitute values of the film parameters
close to those that were observed in the experiment [2, 3],
namely ξ′ = 0.6, ξ′′ = 0.01, R = 0.95, n1=1.46, n2=1. In
Fig. 1à the graphs of functions Y(ϕ) and Y1(ϕ), and in
Fig. 1b, accordingly, distribution of reflection coefficient
r(ϕ), linear (spatial) phase change Ψ1(ϕ) = -2ϕ and the
actual phases of an reflected signal are depicted. It is
evident that the functions Y(ϕ) and Y1(ϕ) have no com-
mon points, so the equation (7) has no solution. In such
case the frequency of output reacts on the selector set-up
of. In Fig. 1b and 2b the function Ψ(ϕ) =-2ϕ is marked
as Ψ1.
M. Lopiitchouk et al.: Solid-state laser with self-stabilized...
199SQO, 5(2), 2002
The following graphs (Fig. 2) demonstrate the above-
mentioned functions at ξ′= 0.4 and n1 = n2 = 1.46. That
corresponds to the metallic thin film (6-7 nm thick) lo-
cated between two quartz plates. Thus, Y(ϕ) and Y1(ϕ)
as well as, accordingly, Ψ1(ϕ) and Ψ(ϕ) coincide within
a rather broad interval of values. Practically, to realize
conditions n1 = n2, it is possible when using a deposition
of a SiO2-film on a metal film, or the dielectric layers
deposited on a metal film, which match the necessary
values n1 and n2. Such a multilayer selector may provide
the single-frequency operation and linear tuning inside
the range of several GHz.
4. Frequency control
Owing to the voltage instability of the power supply, the
piezodriver moves the selector chaotically. At piezodriver
sensitivity of 18 nm/V and at a voltage of, for example,
100 V and with a typical voltage instability about 1%,
twitching of the selector is possible, within an order of
magnitude, of the typical internode space in the place of
a selector position in a linear cavity. With length of a
resonator of about 10 cm and coefficient of the linear
expansion of a cavity material of about 10�5/K, the vari-
ation of the cavity length is 100 nm per a degree. It means
that at variations of temperature about 1Ê the hopping
between several longitudinal modes is possible. Let�s
consider the problem: whether to fix such parameters of a
film so that the frequency of oscillation would not depend
on a selecting interferometer phase. Mathematically it
means satisfaction of the equality d2Ψ/dϕ2 = 0 or ab-
sence of the frequency shift versus the selector shift. The
second derivative from expression (1) has an extremely
complex view and practically does not yield to the ana-
lytical analysis at variations of the parameters both of
1
0.5
0
-1 0 1
Y ( )φ
Y1 ( )φ
Phase [rad]
a
1
0.5
0
-0.5 0 0.5
r ( )φ
Ψ φ ( )
Ψ1 φ ( )
Phase [rad]
b
Fig. 1 (à) Graphs of left and right parts of an expression (7) at ξ′
= 0.6, ξ′′ = 0.01, R = 0.95, n1 = 1.46, n2 = 1. (b) Reflection coeffi-
cient and an output phase versus the input phase.
Y ( )φ
Y1 ( )φ
1
0.5
0
-1 0 1
a
Phase [rad]
r ( )φ
Ψ φ ( )
Ψ1 φ ( )
b
1
0.5
0
-0.5 0 0.5
Phase [rad]
Fig. 2 (à) Graphs of left and right parts of an expression (7) at ξ′
= 0.4, ξ′′ = 0, R = 0.95, n1 = n2 = 1.46. (b) Reflection coefficient
and an output phase versus input phase.
200 SQO, 5(2), 2002
M. Lopiitchouk et al.: Solid-state laser with self-stabilized...
the film and the substrate. In Fig. 3 the examples of the
computer evaluation of the phase curves that make possible
versions of the construction of a laser with self-stabilization
are demonstrated. At such combinations of the parameters
the output frequency is independent on the phase of the
selecting interferometer within limits of approximately ±0.3
rads. The period of a standing wave for the neodymium
laser is 530 nm. The phase change of about one radian
corresponds to a 100 nm space shift of a selector position
that exceeds many times the typical space between the
nodes of the modes around a location of the selector. It
-1 -0.5 0.5 10
1
-1
Interferometer phase [rad]
O
u
tp
u
t
fr
e
q
u
e
n
c
y
F
re
q
u
e
n
c
y
c
h
a
n
g
e
s
[a
r
b
.u
n
.]
Fig. 3. Oscillation frequency dependences (solid curves) and
frequency changes (dash curves) versus the phase of selecting
interferometer for the sets of the parameters: a) ξ′ = 0.625, ξ″ = 0,
n1 = 1, n2 = 1.46; b) ξ′ = 0.295, ξ″ = 0, n1 = 1.37, n2 = 1.46.
means that in the limits of an intermode space the output
frequency would not depend on the position of the thin-
film selector. It is necessary to note, that these conditions
are possible with the film faced to an active medium (or a
substrate to an output mirror) that is the inverse orienta-
tion as compare with the single-frequency operation de-
sign [2, 3]. In this case, the reflection peak is more wide
and smooth and, probably, for sure mode selection it
would be necessary to keep the length of an active me-
dium shorter than that used in [2, 3].
4. Conclusion
We propose the new specific regimes of the linear tuning
and the frequency self-stabilization provided with the thin-
film metallic selector in the diode pumped solid-state la-
ser.
References
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stabilized laser-diode-pumped Nd:YAG ring lasers // Opt.
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2. J.Jabczyñski, I.Peshko, J.Firak. Single-frequency, thin-film
tuned, 0.6 W diode pumped Nd:YVO4 Laser // Applied Op-
tics, 36 (12), pp. 2484 - 2490 (1997).
3. I.Peshko, J.Jabczyñski, J.Firak. Tunable Single- and Dou-
ble-Frequency Diode-Pumped Nd:YAG Laser // IEEE J
QE, 33, p.1417-1423 (1997).
4. T.J. Kane, R.L. Byer. Monolithic, unidirectional, single-mode
Nd:YAG ring laser // Opt.Lett. 10, p.65-67 (1985).
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Novosibirsk, Nauka, 1985, 205p.
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