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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a method for the frequency stabilization of a
laser oscillated from an internal mirror type helium-neon laser device,
which has a structure with a laser capillary disposed in a laser tube, and
having an oscillation wavelength of 543 nm.
2. Description of the Related Art:
As an oscillation wavelength of an internal mirror type helium-neon laser,
a wavelength of 633 nm (red) has been known to date.
As means for stabilizing the oscillation frequency of the internal mirror
type helium-neon laser having an oscillation wavelength of 633 nm
(hereinafter called "633 nm He-Ne laser"), have already been established
many controlling techniques, for example, two-mode method, Lamb dip
method, iodine-absorption cell method, longitudinal Zeeman method,
transverse Zeeman method, magnetic modulation method, etc.
On the contrary, an internal mirror type helium-neon laser having an
oscillation wavelength of 543 nm (green) (hereinafter may called "543 nm
He-Ne laser") is a relatively new laser the first oscillation of which was
reported by Perry in 1970 [D. L. Perry, IEEE J. Quantum Electron, QE-7,
102 (1971)].
Since the oscillation wavelength of this 543 nm He-Ne laser is shorter than
that of the 633 nm He-NE laser, it can be expected that its application to
precision instrumentation will results in improved accuracy of the
instrumentation. On the contrary, the 543 nm He-Ne laser however is
extremely small as about 1/15-1/17 in gain of transition (3s.sub.2
.fwdarw.2p.sub.10) compared to the 633 nm He-NE laser. Its practical use
has hence been difficult for a long time.
Recently, it has however been possible to enhance the oscillation output of
the 543 nm He-Ne laser to the practical extent with a cavity length of 40
cm or so owing to the improved performance of the laser mirrors used
therein.
In 1987, experimental results on frequency stabilization conducted by
making use of a commercial 543 nm He-Ne laser were reported by T. Fellman
et al. [Applied Optics, 126 (14), 2705 (1987)].
The existence of so-called polarization flipping, in which the polarization
directions of axial modes polarizing orthogonally and linearly in the
vicinity of the region where the axial modes become symmetrical
configuration for the center of gain suddenly interchange by 90.degree.,
has been definitely shown by this report.
Accordingly, if the frequency stabilization of the 543 nm He-Ne laser is
performed, for example, by using the two-mode method, it is necessary to
avoid the region at which the above-mentioned polarization flipping occurs
(hereinafter called "polarization flipping region").
The two-mode method mentioned above is a method making use of properties
that polarizations in adjacent axial modes always become orthogonal and
linear, and attempting the frequency stabilization of a laser by
separating the polarizations in the adjacent axial modes by means such as
a polarized beam splitter (PBS) or the like and then using their intensity
difference or intensity ratio as an error signal for controlling the
oscillation frequency of the laser.
The cavity lengths of laser devices commercially available at present are
however adjusted to the extent of about 40 cm in order to enhance their
output to practical levels. Therefore, the 543 nm He-Ne laser usually is
found to oscillate in a range of 3-4 axial modes as illustrated in FIG. 1.
Because a laser tube expands with heat and its cavity length is hence
elongated when electrical input power is turned on to the laser tube, the
axial modes change repeatedly like
(a).fwdarw.(b).fwdarw.(c).fwdarw.(d).fwdarw.(a) . . . in FIGS. 1(a)-1(d).
In FIGS. 1(a)-1(d) C.sub.1 and C.sub.2 are characteristicc polarization
directions of the laser tube. C.sub.1 is the weak direction while C.sub.2
is the strong direction, both, in light intensity.
However, the 543 nm He-Ne laser is greatly different from the 633 nm He-Ne
laser, which has already been forward in putting it to practical use, in
that:
(1) adjacent axial modes do not necessarily polarize orthogonally, but the
group of parallel polarizations is always present; and
(2) in the case of an axial mode configuration such that the gain
competition between the modes becomes strong, namely, in the case of FIG.
1(b) or FIG. 1(d), the polarization flipping, wherein the polarization
directions of each mode suddenly interchanges by 90.degree., occurs.
Accordingly, when the frequency stabilization of the 543 nm He-Ne laser is
performed, for example, by using the two-mode method as is, there are
encountered the following problems:
(1) the region capable of stabilizing frequency is limited; and
(2) since the frequency stabilization can be effected only in the mode
configuration and polarization state illustrated in FIG. 1(a) or FIG.
1(c), one polarized component comes to contain 2 frequency components in
which their frequency difference is a axial mode spacing, whereby the
laser becomes disadvantageous when it is used as a light source for a
polarization interfero-water.
SUMMARY OF THE INVENTION
The present invention has been completed with the above circumstances in
view. An object of this invention is to provide a method which effectively
avoids the polarization flipping of a 543 nm He-Ne laser, whereby the
frequency stabilization of the laser can be achieved.
Another object of this invention is to a specific method capable of well
stabilizing the frequency of the laser.
In one aspect of this invention, there is thus provided a method for the
frequency stabilization of a laser oscillated from an internal mirror type
helium-neon laser device, which has a structure with a laser capillary
disposed in a laser tube, and having an oscillation wavelength of 543 nm,
which comprises:
applying into the laser capillary a static magnetic field satisfying the
following conditions (1)-(3):
(1) the direction of the static magnetic field is perpendicular to the axis
of the capillary tube and the angle between the direction of the static
magnetic field and the direction of a characteristic polarization of the
laser tube is equal to 30.degree.-42 .degree.;
(2) the magnitude of the static magnetic field is such that each Zeeman
frequency in .pi. and .+-..sigma. transitions equals an axial mode spacing
when the static magnetic field is applied into the laser capillary; and
(3) the magnitude of the static magnetic field is almost even along the
longitudinal direction of the laser capillary,
so as to interchange the polarization directions of adjacent axial modes of
the laser oscillating at the wavelength of 543 nm into orthogonal and
linear polarizations, thereby preventing polarization flipping.
As described above, when the characteristic static magnetic field
satisfying the above-mentioned conditions (1)-(3) is applied into the
laser capillary, as understood from experimental results which will be
described in detail subsequently, the polarization directions of axial
modes fail to change suddenly by 90.degree. even when the axial modes
polarize orthogonally and linearly in the vicinity of the region where the
axial modes become symmetrical configuration for the center of the gain
profile.
It can be expected that the frequency of the 543 nm He-Ne laser is
stabilized with the same performance as that in the 633 He-Ne laser by
effectively avoiding the polarization flipping of the 543 nm He-Ne laser
in the above-described manner.
The above and other objects, features and advantages of the present
invention will become apparent from the following description and the
appended claims, taken in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
In the accompanying drawings:
FIGS. 1(a)-1(d) diagrammatically illustrates axial modes of a conventional
typical 543 nm He-Ne laser;
FIG. 2(a) is an explanatory illustration showing an example of means for
applying a static magnetic field into a laser capillary;
FIG. 2(b) is an illustration showing the direction of the static magnetic
field applied;
FIGS. 3(a)-3(f) diagrammatically illustrates an example of changes in axial
modes when a static magnetic field has been applied into the laser
capillary;
FIGS. 4(a)-4(d) diagrammatically illustrates axial modes observed by a
Fabry-Perot interferometer in the condition that no static magnetic field
is applied;
FIG. 5 diagrammatically shows a result obtained by following up the moving
of the axial mode in the characteristic polarization direction C.sub.1
from the occurrence of one polarization flipping up to the moment next
polarization flipping occurs by means of a storage oscilloscope;
FIG. 6(a) diagrammatically shows observation results of beat in the mode
configurations corresponding to FIGS. 4(a) and 4(c);
FIG. 6(b) diagrammatically shows observation results of beat in the mode
configuration corresponding to FIG. 4(b);
FIG. 7 is an explanatory illustration showing Ne 543 nm transitions in a
transverse magnetic field;
FIG. 8 is an explanatory illustration showing schematically an experimental
device of a laser;
FIGS. 9(a)-9(d) diagrammatically show axial mode configurations, beat
spectra and beat waveforms, respectively, when set to .theta.=0.degree. in
a characteristic transverse magnetic field;
FIGS. 10(a)-10(c) diagrammatically show axial mode configurations observed
by setting to .theta.=33.degree. in a characteristic transverse magnetic
field without use of a linear polarizer;
FIGS. 11(a) and FIG. 11(b) diagrammatically shows axial mode configurations
when observed in the condition that a linear polarizer has been inserted
so as to square the direction of the insertion with the characteristic
polarization direction C.sub.1 ;
FIGS. 12(a)-12(f) diagrammatically illustrates the moving of modes and the
polarization states depending upon the thermal expansion of a resonator;
FIG. 13 diagrammatically shows a result obtained by recording a period for
which the linear polarization of the characteristic polarization direction
C.sub.1 is oscillated as single axial mode on the storage oscilloscope;
FIG. 14 diagrammatically illustrates results obtained by separating laser
output by a polarized beam splitter into component light of both
characteristic polarization directions C.sub.1 and C.sub.2 and then
recording simultaneously changes of both component light with time;
FIG. 15 diagrammatically shows a state that single beat spectrum is
occurring;
FIG. 16 is an explanatory illustration showing schematically a laser device
of a first embodiment for performing the frequency stabilization of a 543
nm laser in accordance with the present invention;
FIG. 17 diagrammatically illustrates a result of the frequency
stabilization in the first laser device;
FIG. 18 is an explanatory illustration showing schematically a laser device
of a second embodiment;
FIG. 19 is an explanatory illustration showing schematically a laser device
of a third embodiment;
FIG. 20 is an explanatory illustration showing a mode configuration of
laser output light prior to passing through a linear polarizer LP2 in the
device of FIG. 19; and
FIG. 21 is an explanatory illustration showing the frequency of beat
detected through a linear polarizer LP1 in the device of FIG. 19.
DESCRIPTION OF THE INVENTION AND PREFERRED EMBODIMENTS
The present inventors found a particular phenomenon while investigating
polarization properties in a static magnetic field of a laser oscillated
from an internal mirror type helium-neon laser device, which has a
structure with a laser capillary disposed in a laser tube, and having an
oscillation wavelength of 543 nm.
Namely, it was found that by applying a characteristic static magnetic
field into the laser capillary, adjacent axial modes stably maintain their
orthogonal and linear polarization state without polarization flipping
even when the axial modes polarize orthogonally and linearly in the
vicinity of the region where the axial modes become symmetrical
configuration for the center of gain.
The static magnetic field at this time satisfied the following conditions
(1)-(3):
(1) the direction of the static magnetic field is perpendicular to the axis
of the capillary tube and the angle between the direction of the static
magnetic field and the direction of a characteristic polarization of the
laser tube is equal to 30.degree.-42.degree.;
(2) the magnitude of the static magnetic field is such that each Zeeman
frequency in .pi. and .+-..sigma. transitions equals an axial mode spacing
when the static magnetic field is applied into the laser capillary; and
(3) the magnitude of the static magnetic field is almost even along the
longitudinal direction of the laser capillary.
It was also found that in the state of the application of the
above-described static magnetic field, only two axial modes are oscillated
over a wide region of gain curve of the laser.
The present invention has been completed on the basis of such finding.
Namely, this invention makes use of the feature that the characteristic
static magnetic field is applied into a laser capillary of a 543 nm He-Ne
laser, thereby keeping the polarization directions of adjacent axial modes
in the 543 nm He-Ne laser orthogonal and linear to prevent their
polarization flipping.
FIG. 2(a) is an explanatory illustration showing an example of means for
applying a static magnetic field. A magnet 20 is arranged in such a manner
that it surrounds the outer periphery of a laser tube 10. By this magnet
20, a static magnetic field in a direction perependicular to the axis of a
laser capillary 11, i.e., the light axis is applied into the laser
capillary 11.
The magnitude of the static magnetic field is such that each Zeeman
frequency in .pi. and .+-..sigma. transitions equals an axial mode spacing
when the static magnetic field is applied into the laser capillary.
The direction of the static magnetic field is perpendidular to the axis of
the capillary tube 11 and is such that the angle .theta. between the
direction of the static magnetic field and a characteristic polarization
direction C.sub.1 of the laser tube 10 is equal to around
30.degree.-42.degree. as illustrated in FIG. 2(b).
In the terms "characteristic polarization direction C.sub.1 " and
"characteristic polarization direction C.sub.2 " as used herein, are
defined the weak direction and the strong directiopn, both, in light
intensity at each peak as "C.sub.1 " and "C.sub.2 ", respectively, when
monitoring their output through a linear polarizer.
The magnitude of the static magnetic field is almost even along the
longitudinal direction of the laser capillary 11.
The magnet 20 for defining the static magnetic field may be either a
permanent magnet made of, for example, ferrite or an electromagnet.
FIGS. 3(a)-3(f) diagrammatically illustrate an example of changes in axial
modes when the static magnetic field has been applied under the conditions
shown in FIGS. 2 (a) and 2(b). The axial modes change repeatedly as
(a).fwdarw.(b).fwdarw.(c).fwdarw.(d).fwdarw.(e).fwdarw.(f).fwdarw.(a) . .
. in FIGS. 3(a)-3(f). Namely, the polarization direction of each axial
mode does not change while moving in such a way.
Therefore, if making use of the case where the axial modes became a mode
configuration of FIG. 3(b), 3(c), or 3(f), the frequency stabilization by
the two-mode method is permitted even in the 543 nm He-Ne laser in the
same manner as in the 633 nm He-Ne laser.
As described above, according to this invention, the occurrence of the
polarization flipping can be avoided. The present invention hence has the
following advantages:
(1) The region capable of stabilizing frequency expands about 6 times
compared to the method by T. Fellman et al.
(2) An automatic locking circuit can be fabricated with extreme ease.
Incidentally, the term "automatic locking circuit" means a circuit by
which the laser frequency is fixed automatically.
Experiments, which have been carried out to support the effectiveness of
this invention, will hereinafter be described.
EXPERIMENT 1
Using a commercial internal mirror type 543 nm He-Ne laser device
("05-LGR-171", trade name; manufactured by Melles Griot) having a
structure with a laser capillary disposed in a laser tube and a cavity
length of 402 mm (axial mode spacing of 373 MHz), polarization properties
of a laser was investigated in the condition that no static magnetic field
is applied, i.e., in zero magnetic field.
In FIGS. 4(a)-4(d), are shown diagrammatically observation results of axial
modes by a Fabry-Perot interferometer. Typical mode configurations and
their polarization states are shown therein. Although the laser always
oscillates with 3-4 axial modes and each mode polarizes linearly, adjacent
longitudinal modes do not necessarily polarize orthogonally, but there are
instances where they polarize parallelly unlike the 633 nm red He-Ne
laser.
When electricity is turned on to the laser device to actuate it, a
resonator expands with heat, whereby the axial modes move to the
low-frequency side within a gain width. Its mode configuration hence
changes repeatedly as (a).fwdarw.(b).fwdarw.(c).fwdarw.(d).fwdarw.(a) . .
. in FIGS. 3(a)-3(d).
When the axial modes becomes a mode configuration that their intensity is
close to a lateral symmetry like FIGS. 4(b) or 4(d), polarization flipping
in which the polarization directions of the axial modes suddenly
interchange by 90.degree. occurs.
When respective experiments were conducted by using to commercial laser
device of the same type as that described above, polarization flipping was
indeed observed on both laser devices.
FIG. 5 diagrammatically shows a result obtained by placing a linear
polarizer in front of the Fabry-Perot interferometer in such a manner that
it is parallel to the characteristic polarization direction C.sub.1 weak
in light intensity at the peak and then following up the moving of the
axial mode in the characteristic polarization direction C.sub.1 from the
occurrence of one polarization flipping up the moment next polarization
flipping occurs by means of a storage oscilloscope. This corresponds to
the change in the mode configuration of FIG. 4(c).fwdarw.FIG. 4(d) and to
the polarization flipping in FIG. 4(d). Two modes on the left in FIG. 5
are those generated by the occurrence of the polarization flipping. At
this point of time, the storage into the storage oscilloscope was stopped.
In this experiment, the stable region in polarization direction from one
polarization flipping to next polarization flipping was found to be about
93 MHz.
The observation of beat caused by the union of axial modes was then
attempted. A linear polarizer which is set to an angle of 45.degree. with
the characteristic polarization direction C.sub.1 weak in light intensity
at the peak and a wide-band amplifier sensitive at 0-20 MHz were used in
the observation.
FIG. 6(a) diagrammatically shows observation results in the mode
configurations corresponding to FIG. 4(a ) and FIG. 4(c). As understood
from FIG. 6(a), a beat was observed near 50 KHz. Incidentally, another
beat was also observed momentarily near 100 KHz, but its intensity was an
extent of one-tenth or lower compared to the beat at 50 KHz.
FIG. 6(b) diagrammatically shows observation result in the mode
configuration corresponding to FIG. 4(b). As apparent from FIG. 6(b),
complicated changes in two or more spectra were seen near 50 KHz.
As described above, the 543 nm laser device oscillates with 3-4 axial modes
and its characteristic polarization directions and beat also exhibit
complicated changes depending upon cavity detuning. It was hence
impossible to find properties expected to be usable in frequency
stabilization.
Accordingly, in order to conduct the frequency stabilization in this laser
device, it is necessary to avoid the polarization flipping. The region
capable of stabilizing the frequency is so much narrow.
Two frequency components in which their frequency difference is an axial
mode spacing, always come to be contained in the axial mode of one
characteristic polarization direction, whereby the laser device is
disadvantageous when it is used as a light source for a polarization
interferometer.
EXPERIMENT 2
Using the same laser as in Experiment 1, an experiment was conducted to
investigate polarization properties upon application of a static magnetic
field in a direction perpendicular to the axis of a laser capillary, i.e.,
a transverse magnetic field into the laser capillary.
As means for frequency stabilization in Ne 633 nm transition, two-mode
method, Lamb dip method, longitudial Zeeman method, transverse Zeeman
method, etc. have already been put to practical use.
Particularly, the transverse Zeeman method is applicable to laser devices
relatively long (about 26-28 cm) in their cavity length. The lasers
stabilized by this method can also be used as a light source for optical
heterodyne detection and have hence been known to be effective.
Accordingly, an experiment for studying polarization properties in the
transverse magnetic field was carried out in order to confirm whether the
transverse Zeeman method can also be applied to Ne 543 nm transition.
FIG. 7 is an illustration diagrammatically showing the Ne 543 nm transition
in a transverse magnetic field.
Since .DELTA.J equals 0, .pi. transition from m.sub.a =0 to m.sub.b =0 is
forbiden. In the case of the 633 nm transition on the other hand, Lande's
g factors of both low and high levels are g.sub.a =1.295 and g.sub.b
=1.301, respectively, and are almost equal. Therefore, its Zeeman
splitting frequency F.sub.z may be assumed to be represented by the
following equation:
F.sub.z =.mu..sub.B g.sub.a B/h (1)
wherein .mu..sub.B means a Bohr magneton and B denotes a magnetic flux
density. In the case of the 543 nm transition on the contrary, g.sub.b
equals 1.984 and is nonnegligibly different from g.sub.a.
In the transverse Zeeman method, a magnetic field in which F.sub.z is equal
to an axial mode spacing, i.e., a characteristic transverse magnetic field
is applied to enhance the mode coupling between 3 axial modes (gain
competition), thereby attaining the formation of single axial mode.
This has a direct relationship with the coupling between .pi. and .sigma.
transitions, said coupling comprising a high or low level as a common
level. In the 543 nm transition, .pi. and .sigma. transition holding a low
level in common are two types of transition from m.sub.a =1, 0 to m.sub.b
=1 and from m.sub.a =0, -1 to m.sub.b =-1. Their differences in frequency
between .sigma. and .pi. transitions are given by the above-described
equation (1).
On the other hand, .pi. and .sigma. transitions holding a high level in
common are also two types of transitions from m.sub.a =1 to m.sub.b =1, 0
and from m.sub.a =-1 to m.sub.b =0, -1. The Zeeman splitting frequency
F'.sub.z of their .sigma. and .pi. transitions are represented by the
following equation:
F'.sub.z =.mu..sub.B g.sub.b B/h (2)
Namely, the 543 nm transition has 2 values in the characteristic transverse
magnetic field unlike the 633 nm transition. In this experiment, the
former was chosen. In this case, the magnetic flux density giving the
characteristic transverse magnetic field was 206 gausses.
FIG. 8 is an explanatory illustration showing schematically an experimental
device. A laser head is remodeled. Namely, both ends of the laser head are
removed by cutting work so that the output-side (anodeside) end of a laser
capillary can be visually observed and laser light is also derived from
the high-reflection mirror side at the rear of a laser tube.
The transverse magnetic field H was formed by fixedly arranging ferrite
magnets (30.times.40.times.10 mm; "FB4B"; product of TDK Corp.) on an iron
plate of 6 mm thick at suitable intervals. An even transverse magnetic
field (uniformity: .+-.4%) having a magnetic flux density of 202.+-.8
gausses was applied into the laser capillary so as to strike on an about
78%-portion of its length (330 mm).
Incidentally, an angle between the direction of the transverse magnetic
field H and the characteristic polarization direction C.sub.1 weak in
light intensity at the peak is defined as ".theta.". In the case of the
transverse Zeeman method, .theta. is 0.degree. or 90.degree..
In FIG. 8, LP, PD, VA, OS, SA, PH, FPI and ST mean a linear polarizer, PIN
photodiode, video amplifier, oscilloscope, spectrum analyzer, pinhole,
Fabry-Perot interferometer and storage oscilloscope, respectively.
(1) Case of .theta.=0.degree.:
FIGS. 9(a)-9(d) diagrammatically show experimental results when set to
.theta.=0.degree..
Typical axial mode configurations, and beat spectra and beat waveforms in
their corresponding mode positions are shown respectively in the upper,
middle and lower rows in FIGS. 9(a)-9(d). By the way, the linear polarizer
LP is set in such a manner that its angle with the characteristic
polarization direction C.sub.1 is 45.degree..
As understood from FIGS. 9(a)-9(d) , when the transverse magnetic field is
applied to the laser capillary, the number of axial modes decreases by 1
mode compared to the case of the zero magnetic field, and the laser hence
oscillates with 2-3 modes.
On the other hand, the best spectra corresponding to the number of the
axial modes appeared near 50 KHz. In the case of the 3-mode oscillation,
the beat spectra however look like one spectrum, as it were, because the
intensity of the axial modes on both sides in FIG. 9(c) is weak, whereby
the beat spectrum corresponding to the axial mode of the center is
predominant. When the linear polarizer LP was turned round to square its
direction with the characteristic polarization direction C.sub.1 or
C.sub.2, the beat spectra vanished.
When the axial modes were observed by means of the Fabry-Perot
interferometer FPI through the linear polarizer LP set in such a manner
that its angle with the characteristic polarization direction C.sub.1 was
45.degree., amplitude modulation was found on each axial mode. When the
liner polarizer LP was set parallel to the characteristic polarization
direction C.sub.1 or C.sub.2, its modulation waveform vanished. In this
case, however, axial modes themselve did not vanish.
From the above experimental results, each of these beat spectra can be
considered to be a Zeeman beat within the same axial mode, which is caused
by the .sigma. and .pi. transitions.
As understood from FIGS. 9(a)-9(d), the axial mode moved Within the gain
width, changes in beat frequency were found to be several KHz or lower. By
the way, the beat waveforms shown in the lower row of FIGS. 9(a)-9(d) can
be explained as the synthesis of the beat spectra shown in the middlle
row.
As described above, when .theta. is 0.degree., the Zeeman beat within the
same axial mode is observed, and the number of the axial modes is less by
one than the case of the zero magnetic field. It could however not be
attained to form single axial mode operation.
As its cause, it is considered that differences in coupling coefficient
between the .sigma. and .pi. transitions by the difference in J number of
the low level, in g value, in mirror quality (or in internal anisotropy),
in cavity length, etc. compared with the 633 nm transition have close
relationship with one another.
As illustrated in FIG. 9(c), in the case of 3-mode oscillation, the
oscillation appears to have a tendency to concentrate on axial mode of the
center. Accordingly, there is a possibility that the formation of signal
axial mode can be realized by reducing the excitation intensity of the
laser.
However, although the reduction of the excitation intensity of the laser
permits the formation of the single axial mode, the laser output becomes
very low, thereby involving a disadvantage upon its practical use. (2)
Case of .theta..noteq.0.degree.:
In the characteristic transverse magnetic field, polarization properties at
general angels in which the characteristic polarization direction C.sub.1
was not parallel to the direction of the transverse magnetic field were
then investigated.
As a result, the present inventors was found that when .theta. is within
the range of about 36.degree..+-.6.degree., the laser oscillates with 2-3
axial modes, the polarizations of adjacent axial modes are always
orthogonal and linear, and no polarization flipping occurs while the axial
modes move within the gain width. At this time, any Zeeman beat within the
same axial mode was not observed even when the linear polarizer LP was set
at any values of .theta..
FIGS. 10(a)-10(c) diagrammatically show observation results of axial modes,
which have been obtained by setting to .theta.=33.degree. in the
characteristic transverse magnetic field without using the linear
polarizer LP. As understood from FIGS. 10(a)-10(c), the laser oscillates
with 2-3 modes.
Mode observation was then conducted in the condition that the linear
polarizer LP was inserted in front of the Fabry-Perot interferometer FPI
so as to be parallel to the direction of the characteristic polarization
direction C.sub.1. As shown in FIG. 11(a) and FIG. 11(b), the adjacent
modes vanished, but two axial mode appeared apart by two times the axial
mode spacing.
At this time, when the linear polarizer LP was turned round by 90.degree.,
an axial mode, which had extingushed till then, appeared while the axial
mode, which has appeared till then, was extinct. Accordingly, it could be
confirmed that the adjacent modes polarize orthogonally and linearly along
two characteristic polarization directions, respectively, and any Zeeman
beat within the same axial mode does not occur.
FIGS. 12(a)-12(f) diagrammatically illustrates the moving of a series of
axial modes and the polarization states depending upon the thermal
expansion of a resonator. In FIGS. 12(a)-12(f) mode changes are repeated
in an (a).fwdarw.(b).fwdarw.(c).fwdarw.(d).fwdarw.(e).fwdarw.(f) cycle.
FIG. 13 diagrammatically shows a result obtained by recording a period for
which C.sub.1 component is oscillated as single axial mode on the storage
oscilloscope. The region of the single mode was about 591 MHz.
FIG. 14 diagrammatically illustrates light intensities obtained by
separation laser output by a polarized beam splitter into C.sub.1 and
C.sub.1 components and recording simultaneously the changes of both
components with time. At this time, the output from the high-reflector was
detected to monitor simultaneously the moving of the axial modes.
It was confirmed from these results that both components in regions other
than those corresponding to X and Y in FIG. 14 were single axial modes. It
is therefore possible to stabilize the laser frequency by the two-mode
method without polarization flipping even in the 543 nm transition like
the case of the 633 nm transition when using a linear slop portion in FIG.
14.
In this case, there is a disadvantage of requiring a transverse magnetic
field compared to the method of T. Fellman et al., while there are
advantages that the region capable of stabilizing the frequency broadens
and both components of the characteristic polarization directions
oscillate with single axial modes, respectively, because the occurrence of
the polarization flipping can be prevented.
The region shown by A in FIG. 14 is another region capable of using in the
frequency stabilization. In the region A, the component of the
characteristic polarization direction C.sub.2 generates a dip in its
output near almost center of its gain width and oscillates with single
axial mode. Accordingly, it is possible to stabilize the oscillation
frequency of the laser in the center of the dip by modulating the cavity
length in the same manner as in the Lamb dip method, taking out only the
component of the characteristic polarization direction C.sub.2 by the
polarized beam splitter PBS to subject the same to phase-sensitive
detection, and then using the thus-detected component as an error signal.
The observation of beat was then conducted by setting the angle between the
directions of linear polarizer LP and C1 at 45.degree., in the condition
of .theta.=33.degree.. As a result, when the axial mode configurations
corresponded to the points A, B and X, Y in FIG. 14, single beat spectrum
appeared near 100 MHz as shown in FIG. 15. The points A, B and X, Y
correspond to the mode configurations of FIGS., 12(c) and 12(f)
respectively. Namely, the single beat appeared while the axial modes kept
three modes, and its change region was 90-100 MHz.
In view of the fact that the beat occurs only upon the 3-mode oscillation,
the beat is considered to be a difference frequency spectrum between 2
mode spacings generated upon the 3-mode oscillation unlike the Zeeman beat
of the case of .theta.=0.degree..
This beat properties are also effective from the viewpoint of the frequency
stabilization. It is possible to stabilize the frequency, for example, by
detecting this beat from the output from the high-reflection mirror,
converting it to voltage signal by a frequency-voltage converter and then
controlling the cavity length by a heater or the like depending upon the
output obtained by the frequency-to-voltage co | | |
