This study presents a new three-mode He-Ne laser frequency stabilizer.
A precision stabilized laser is necessary in many optical instruments,
e.g., nano-metrology systems (Yokoyama et al., 2005; Olyaee and
Mohammad Nejad, 2007a). The accuracy of nano-metrology measurements is
essentially depended on the frequency stability of the laser cavity. The
stabilized multimode lasers as reference sources are widely used in various
applications such as laser interferometers.
Many efforts are still being developed for two-mode laser frequency stabilization
systems. First, Balhorn et al. (1972) presented two-mode He-Ne
laser stabilizer. The stability was increased by utilizing the improved
circuits and cavity length controllers (Eom et al., 2002; Kim and
Kim, 2002; Huang et al., 2000). But, three-mode He-Ne lasers should
be stabilized by more complex instruments. Stabilization of the frequency
and power of three-mode He-Ne laser was first introduced by Suh et
al. (1993). Also in development of two-mode He-Ne laser frequency
stabilization, a three-mode oscillation in the gain curve was observed
(Yokoyama et al., 1994). This stabilization was based on the frequency
pulling effect. And finally an effective method with high frequency stability
was reported by Yeom and Yoon (2005). The square-root Allan variance between
their stabilized laser and iodine stabilized He-Ne laser and the frequency
fluctuation were reported as 5x10-11 at average time of 1sec
(short time) and ±1 MHz, respectively.
In the present study, we design a laser frequency stabilization system
for three-mode He-Ne lasers. The designed stabilizer is based on the combination
of frequency locking and power balance methods. We improve the frequency
stability of three-mode laser software based by combination of two mentioned
methods. The simulation results indicate that the laser frequency fluctuation
reaches about 148 kHz.
MATERIALS AND METHODS
The free spectral range or mode spacing in the laser cavities is determined
||The cavity length
||The refractive index of medium
||The velocity of light in free space
Therefore, by increasing the cavity length of a laser, such as a He-Ne
laser, the mode spacing decreases. According to the dimension and structure
of the cavity, the frequency difference range is 3 MHz to 1 GHz in commercial
Zeeman He-Ne lasers, He-Ne lasers with an Acousto-Optical-Modulator (AOM)
and stabilized two-longitudinal-mode laser cavities (Yan et al.,
2003). Inhomogeneous line broadening or Doppler broadening of the laser
is described as:
||The Doppler line width
||The central optical frequency
The curve for the neon in a He-Ne laser will have a half-width in the
order of 1.5 GHz at 633 nm wavelength. As a result, the number of modes
in the gain curve can be determined by the cavity length. Considering
the 35 cm cavity length, the gain profile of the laser source can contain
three longitudinal modes. The polarization of the side modes (λ2
and λ3) is orthogonal to the polarization of the central
mode (λ2) due to the polarization anisotropy of the laser
mirrors (Yeom and Yoon, 2005). Assuming the linearly polarized modes,
the side modes can be separated from central mode by a polarizing beam
splitter. The electrical fields of three modes are obtained as:
|Eoj (j = 1, 2, 3)
||The electrical fields amplitudes
||The unit vectors
||The initial phases
The intermode beat frequency decreased resulting from the cavity thermal
expansion. By differentiation of Eq. 1, it can be given
||The drift of intermode beat frequency
||The cavity length thermal expansion
Interference of the reference and measurement beams produces three intermode
angular beat frequencies, ΩH = 2π(v3-v2),
ΩL = 2π(v2-v1) and ΩH+ΩL=
2π(v3-v1). By using a proper signal conditioner,
as shown in Fig. 1, the secondary angular beat frequency,
ΩS = |ΩH-ΩL|, is extracted
(Olyaee and Mohammad Nejad, 2007b). The photocurrent is converted to voltage
signal and after amplification, ΩH+ΩL
is eliminated by the Band Pass Filter (BPF.1). Then by using a Double-Balanced
Mixer (DBM) and another Band Pass Filter (BPF. 2), the secondary beat
frequency is extracted.
If the intermode beat frequencies are kept constant, the standing position
of modes can be fixed in the gain curve (Yokoyama et al., 1994).
Therefore, cavity length and standing position of modes are fixed by measuring
the secondary beat frequency and feedback to the heater (Fig.
Owing to the square-law behavior of the photo-detector, the photocurrent
is calculated as:
Substitution of Eq. 3 into 5 and elimination of dc
and high order frequency components because of using a Extracting the
secondary beat frequency by signal conditioner circuit band pass filter,
as shown in Fig. 2, the output signal of the BPF. 1
can be written as:
||Extracting the secondary beat frequency by signal conditioner
||The schematic diagram of the designed frequency stabilization
system based on the frequency locking method
Where, vH = v3-v2 and vL
= v2-v1 are the higher and lower intermode beat
frequencies, respectively. This signal is self-multiplied by a double-balanced
mixer and then BPF. 2 eliminates dc and high frequency components. Therefore:
As shown in Fig. 2, the output signal of the frequency
to voltage converter (F/V) is sent to driver and heater controller stage
to adjust the laser cavity length.
In addition, if amplitudes of modes are kept constant, as a result, the
laser frequency can be stabilized (Eom et al., 2002). Figure
3 represents the designed power balance stabilization system for three-mode
He-Ne laser. Two beams are separated by a polarizing beam splitter in
accordance with polarization properties of them and are incident on the
avalanche photodiodes. Photocurrents of APD.2 and APD.3 are converted
to voltage. Because there are high order frequency components in the output
of the current-to-voltage converter (IVC.1), a low pass filter is used.
Therefore, the output signals of two paths are given, respectively by:
|k2 and k3
||The transfer gains of two paths
The differential value can be applied as an error signal to heater controller
of the laser cavity. The cavity length is adjusted by controlling the
current of thin-film heater.
Figure 4 shows the optical head of a new scheme of
laser frequency stabilizer by combination of designed frequency locking
and power balance stabilization systems. The back beam of three-mode laser
is separated by a non-polarizing Beam Splitter (BS).
||The schematic diagram of the designed frequency stabilization
system based on the power balance method
||The optical head of laser frequency stabilizer
After passing the reflected beam through 45° linear polarizer, it
is focused on a high-speed low-noise SLIK avalanche photodiode (APD.1).
A signal having primary beat frequencies is produced by avalanche photodiode
resulting from interference of the electrical fields of three modes after
passing through the linear polarizer. The passed beam of non-polarizing
beam splitter is directed towards the polarizing beam splitter and two
photo-currents in accordance with amplitude of the electrical fields are
The output signal of APD.1 through the current to voltage converter is
sent to the band pass filter (Fig. 5). Earlier, interference
of modes produces intermode beat frequencies and dc components. Therefore,
it is needed to extract the secondary beat frequency by double-balanced
mixer and another band pass filter. Then, the signal is sent to a frequency
to voltage converter (F/V). The output signal of F/V can be used as a
part of error signal. On the other hand, in parallel path, a differential
amplifier produces another part of the error signal.
According to Fig. 4, the central mode and side modes
are incident on the APD.2 and APD.3, respectively. Therefore, a low pass
filter is needed at the end of IVC.1. Two error signals are added by a
dc level to produce control signal.
If the standing position of modes is not changed, the control signal
will be constant. Changing in the cavity length causes the error signal
to be produced. The control signal is sent to a Voltage Control Oscillator
(VCO) and through a phase/frequency detector and loop filter is sent to
a Pulse-Width Modulation (PWM) controller.
||The laser frequency stabilization system based on the
combination of frequency locking and power balance methods
When laser turn on, as shown in Fig. 5, a pre-heating
cycle is activated. Therefore, the temperature of laser cavity reaches
suitable value. The cavity temperature can be measured by a thermistor.
Then, stabilization loop is closed and cavity length is controlled. The
loop filter is chosen as a PID controller in which can be adjusted the
transient time and steady-state response.
This study that is a joint study between the Optoelectronic and Laser
Laboratory of Iran University of Science and Technology (IUST) and Shahid
Rajaee Teacher Training University (SRTTU), is based on the theoretical
materials which all results are obtained from software simulations.
RESULTS AND DISCUSSION
To have a three-mode laser, the free spectral range and secondary beat
frequency are considered as 435 MHz and 300 kHz, respectively, at 633
nm wavelength (Yokoyama et al., 2005).
From Eq. 4, the intermode beat frequency is decreased
by 387.4 Hz resulting from one period change (λ/2). Consequently
thermal coefficient is given about 1.2 kHz μm-1.
The stabilization of three-longitudinal-mode He-Ne laser based on the
thermal phase locking of the secondary beat frequency was reported by
Yeom and Yoon (2005).
||The block diagram of the laser cavity and its stabilizer
They improved the short-term frequency stability to 5x10-11.
But we suggest a power balance stabilizer in parallel to the phase locking
of the secondary beat frequency to achieve higher stability.
Thermal transfer function of the laser cavity and its enclosure is complex,
but its Laplace (S) transfer function can be modeled in the SIMULINK as
(Chien and Pan, 1991):
||The transfer gain of power driver
||The time constant of laser cavity
The loop filter is defined as a Laplace transfer function, F(S)/G(S),
which is designed for PID controller (Fig. 6).
||The result of stabilization, (a) response to the
step and (b) laser frequency fluctuations
||(a) Simulation result of the beat frequency fluctuations
and (b) estimated fluctuations of the laser frequency in the steady
The simulation results for laser behavior are also shown in Fig.
7. First, preheating cycle is activated to reach suitable temperature. Then
stabilization loop is closed. According to Fig. 5, in stabilization
loop, two error signals (Ve1 and Ve2) are added to a dc
In the experimental setups, the stability is commonly measured by Allan
variance between the stabilized laser and iodine stabilized He-Ne laser
and here we assumed ideal laser for comparing (Fig. 8).
As shown in Fig. 8a, the peak-to-peak range of error
signal corresponded to the beat frequency. When stabilization loop is
closed, this range considerably decreases. The frequency instability can
be estimated from the error signal fluctuations which it is theoretically
confined to about 148 kHz, as shown in Fig. 8b. This
value corresponds to stability of 3 parts in 1010 or 3x10-11
which is better than other stabilizers.
A new system of frequency stabilization based on the frequency locking
and power balance methods has been presented. The stabilization system
was designed for three-mode He-Ne laser with 435 MHz free spectral range
and 300 kHz secondary beat frequency. The simulation results indicated
that frequency fluctuations was successfully reached about 148 kHz or
frequency stability of 3x10-11.
We would like to thank Prof. Tai Hyun Yoon for many interesting and useful