Wavelength Shift Determination Using a Common-path
Interferometer
Shyh-Tsong Lin† and Cheng-Chung Chang††
†
Professor and ††graduate student, Department of Electro-optical Engineering,
National Taipei University of Technology, Taipei 10608, Taiwan
E-mail: †[email protected] and ††[email protected]
Abstract
A novel interferometer based on three designs, common-path, unequal optical-path-length, and
rotating analyzer, is proposed for wavelength shift determinations. These designs make the
interferometer with the characteristics of high stability, high sensitivity, and compact optical setup. A
commercial wavelength meter was adopted to determine the interferometer’s sensitivity. And the
interferometer was incorporated into a fibre-optic Bragg grating sensing system to determine the
wavelength shifts of the waves reflected from the Bragg gratings. The experimental results agree the
applicability of the interferometer.
Introduction
The wavelength scanning techniques are widely accepted in the systems adopted for measuring
object parameters [1-6] in the past years and thus become more and more important. In general, the
parameters to be determined are functions of the wavelength shift of the light source incident into the
measurement system, the measurement resolutions thus highly depend on how small the wavelength
shift can be detected. This reminds the researchers of developing the schemes for measuring the
wavelength shift.
The wavelength shift of a beam can be determined by the use of a spectrometer [7], an edge filter
[8], a tunable filter [9-11], a common-path interferometer [12] or an unequal optical-path-length
interferometer [13-14]. In which, the common-path one gives high measurement stability and the unequal
optical-path-length one provides high measurement sensitivity. To enhance an interferometer so it
possesses both the properties of high measurement stability and sensitivity, a feedback control system
[15] or a near common-path design [16] is built into the unequal-path interferometer to eliminate the
environment disturbances.
An interferometer using the designs of common-path, unequal optical-path-length, and rotating
analyzer is thus proposed in this paper. In addition to the inherent performances of a common-path and
unequal optical-path-length interferometer, i.e. high stability and sensitivity, it also possesses the
advantage of using compact optical setup. The theory of the interferometer and a setup constructed to
realize the interferometer are first described. An experiment conducted to determine the constructed
interferometer’s sensitivity is then depicted. And the results of using this constructed setup to examine
the wavelength shifts of the waves reflected from a fibre-optic Bragg grating (FBG) system are finally
presented.
Theory
Figure 1(a) depicts the interferometer proposed in this paper. It is composed of a polarizer (P) with
transmission axis at 45o, a calcite prism with optical axis at 0o, a quarter-wave plate with slow axis at 45o,
a chopper rotated with a frequency f, an analyzer (A) co-axially mounted on the chopper, two
photo-detectors Dm and Dr, and a lock-in amplifier. A laser beam is first separated into a reference beam
and a measurement beam; the reference beam passes through the chopper to generate a TTL signal Ir
on the detector Dr; the measurement beam passes through the polarizer, calcite prism, quarter-wave
plate, and analyzer to generate an interference signal Im on detector Dm; both these two signals are
delivered to a lock-in amplifier where the phase difference
The signal Im and the phase difference
Γ
Γ between these two signals is extracted.
are demonstrated as follows.
Referring to Fig. 1(a) again, as the measurement beam propagates to the detector Dm, its
polarization state can be expressed as:
⎡ Vx ⎤
⎡ V0 ⎤
,
⎢ V ⎥ = AW ⎢
iΓ ⎥
⎣ V0 e ⎦
⎣ y⎦
(1)
where A denotes the Jones matrix of the analyzer whose transmission axis is at angle 2πft, W represents
the Jones matrix of the quarter-wave plate, and V0 is the amplitude of the o-ray and e-ray components of
the beam incident into the wave plate. The intensity signal Im detected by Dm is thus equal
to Vx
⋅ Vx* + Vy ⋅ Vy* , or
I m = V02 [1 + sin( 4πft + Γ )] .
Note, referring to Fig. 1(b),
Γ
(2)
is phase difference between the o-ray and e-ray components as they
pass through the calcite prism. If the principal indices of the calcite prism are no and ne and the thickness
of the prism is t,
Γ=
Γ
can be expressed as:
2π
(n o − n e )t .
λ
(3)
As the wavelength of the laser beam is shifted by ∆λ , the phase difference becomes
Γ − ∆Γ =
2π
(n o − n e )t
λ + ∆λ
(4)
which can also be extracted by the lock-in amplifier. The comparison between the phases detected
before and after the wavelength shifting gives
∆Γ = 2π ⋅ (n o − n e ) ⋅ t
∆λ
.
λ2
(5)
This is the equation governs the relation of the phase increment
∆Γ and the wavelength shift ∆λ .
In addition to the description and derivation of the proposed interferometer, it is to be emphasized
that the interferometer is a common-path and unequal optical-path-length one. Since the interference
components of Im travel through the same path but with an optical-path-length difference (n o
− ne ) ⋅ t .
The interferometer can thus provide high stability and high sensitivity detections of wavelength shift.
Fig. 1 (a) The proposed interferometer; (b)the calcite prism of the interferometer
Experimental setup and results
An interferometer as that shown in Fig.1 was constructed. In which, the calcite prism was with a
thickness of t=10mm and principal indices of
n o =1.634 and n e =1.477, the lock-in amplifier was SR830
from Standford Research Systems, Inc. Base on this interferometer, two experiments were completed
and are described as follows:
Experiment 1: As indicated in Fig.2, a beam radiating from a wavelength tunable laser source
(Santec TSL 210) was guided to the proposed interferometer and a wavelength meter. As the wavelength
of the laser was shifted, the wavelength shift
phase increment
∆Γ
∆λ
was determined by the wavelength meter and the
was detected by the interferometer. Fig. 3 represents the experimental result.
Fig.2 Optical setup for determining the sensitivity of the proposed interferometer
Now Eq. (5) can be rewritten as
∆Γ = K∆λ ,
(6)
where, as indicated in Fig. 3, K=269.88deg./nm was the sensitivity of the proposed interferometer. In the
following experiment, the wavelength shift ∆λ was related to the phase increment ∆Γ by Eq. (6).
Fig. 3 The measured phase increment ∆Γ V.S. the wavelength shift ∆λ
Experiment 2: The interferometer was then conducted to determine the strains of FBGs. As that
shown in Fig. 4, the wave radiating from the wavelength tunable laser source was first delivered to the
FBGs and then reflected to the interferometer. Note FBG1 and FBG3 were bonded on the surfaces of a
four-point bending beam, and FBG2 was a floating one (i.e. it was without strain).
Once the wavelength shifts of the waves reflected from the FBGs were determined by the
interferometer. The strains of the FBGs were obtained by [17-20]
1 ∆λ
.
(7)
1− P λ
Where P ≈ 0.26. Figs. 5 and 6 represent the measured strains of FBG1 and FBG3, respectively.
ε=
Fig.4 (a) Experimental setup for examining the wavelength shifts of the waves reflecting from the
fibre-optic Bragg gratings; (b) the four-point bending beam and the gratings bonded on the beam
surfaces
Discussion and conclusion
In addition to the performance of high stability and sensitivity, the interferometer has the advantage
of compact optical setup since it adopts a simple rotating assembly, i.e. the co-axial chopper and analyzer,
to generate AC reference and measurement signals. This makes the interferometer be a good choice if
the wavelength shift of a light source is to be examined.
In conclusion, an interferometer using the designs of common-path, unequal optical-path-length,
and rotating analyzer is proposed and described. The setup developed to realize the interferometer was
with a sensitivity of 269.88deg./nm. Experimental results from applying the setup confirm the applicability
of the interferometer.
Fig. 5 The measured strain of FBG1
Fig. 6 The measured strain of FBG 3
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