Radio-frequency ring resonators for self-referencing fiber-optic intensity sensors

Carmen Vázquez García; Julio Montalvo; Pedro Contreras Lallana

doi:10.1117/1.1883566

1 April 2005 Radio-frequency ring resonators for self-referencing fiber-optic intensity sensors

Carmen Vázquez García, Julio Montalvo, Pedro Contreras Lallana

Author Affiliations +

Optical Engineering, Vol. 44, Issue 4, 040502 (April 2005). https://doi.org/10.1117/1.1883566

Abstract

A theoretical and experimental study of radio-frequency ring resonators (RR) for referencing and improving the sensitivity of fiber-optic intensity sensors (FOS) is reported. The separation between lead and transducer losses in the FOS is solved by converting the light intensity fluctuations to be measured into RR losses that produce high amplitude variations in the proximity of the RR resonance frequencies. Two different self-referencing techniques are developed. Via the definition of the measurement parameter R_M, sensor linearity and sensitivity are analyzed. A calibration using an optical attenuator is reported to validate the model.

1. Introduction

Fiber-optic intensity sensors (FOS) based on multimode¹ (MM) and single mode² (SM) fibers need a self-referencing method to minimize the influences of long-term aging of source characteristics, as well as short-term fluctuations in optical power loss in the leads to and from the transducer. Time division, wavelength normalization,¹ ³ and frequency-based self-referencing methods⁴ ⁵ based on MM fibers, and a Michelson topology with SM fibers⁶ have been reported.

In this letter, we propose a novel frequency-based approach using a ring resonator (RR), with an improved sensitivity. Its principle and properties are discussed and tested.

2. Theoretical Analysis

The new sensing scheme is a RR and a FOS (see Fig. 1). The RR operates under an incoherent regime, so τ≫Tc, where Tc is the source coherence time and τ is the loop transit time. The RR relative output power, P₃/P₁ , is given by:

Eq. (1)

g \sqrt{\frac{K^{2} + {[(1 - 2 \cdot K) \cdot H]}^{2} + 2 \cdot K \cdot (1 - 2 \cdot K) \cdot H \cdot \cos (ω \cdot τ)}{1 + {(K \cdot H)}^{2} - 2 \cdot K \cdot H \cdot \cos (ω \cdot τ)},}

Eq. (2)

H = 10^{- α L / 10} \cdot A \cdot g \cdot F (m),

where g=(1−γ), m is the measurand, F(m) is the FOS calibration curve, γ and K are the coupler excess loss and coupling coefficient ω is the modulating signal, pulsation α is the fiber attenuation coefficient in dB/km, A is an attenuation, and L is the loop length. The FOS modulates the RR loss, H, and the output power frequency P₃/P₁ , see inset of Fig. 1 for K∈(0−0.5); there is a constant maximum if cos(ωτ)=+l , and a dependent on H minimum if cos(ωτ)=−l . The frequency normalization method is based on the sinusoidal modulation of the optical power source at two frequencies f₁ and f₂, as seen in Figs. 1 and 2. In this method, the measurement parameter is R_M1 :

Eq. (3)

R_{M 1} = \frac{| \frac{P_{3}}{P_{1}} | (ω, τ)}{| \frac{P_{3}}{P_{1}} |_{| \cos (ω τ) = 1}} = \frac{| P_{3} | (ω, τ)}{| P_{3} |_{| \cos (ω τ) = 1}} .

The two ports normalization method uses a single frequency (f₁), a coupler inside the RR for measuring P₄, and two down leads under identical external conditions; and the measurement parameter is R_M2 :

Eq. (4)

R_{M 2} = \frac{| P_{3} | (ω, τ)}{| P_{4} |_{| \cos (ω τ) = - 1}} .

The normalized sensitivity of the whole system is:

Eq. (5)

\frac{1}{R_{M i}} (\frac{\partial R_{M i}}{\partial m}) = \frac{\partial R_{M i}}{R_{M i} \partial H} (\frac{\partial H}{\partial m}) = S_{M i} k_{1} S_{F}

being S_F=δF/δm the FOS sensitivity, k₁ is a constant and i=1, 2 for the frequency and two ports normalization method, respectively. This system sensibility is enhanced by S_Mi . If f₁ is the resonance frequency, S_M1 is given by:

Eq. (6)

\frac{- {(1 - K)}^{2}}{(1 + K \cdot H) \cdot [K - (1 - 2 \cdot K) \cdot H]}

So S_M1 tends to ∞ if H→H₀=K/(1–2K), The presence of noise limits the real value of the sensitivity. S_M1 is plotted at Fig. 2, for a f₁ frequency of 1,302 MHz, in a RR with a loop length of 1067 m. There is an inflection point for every K at the H₀ value. For every quiescent point, a certain K can be selected for achieving high sensitivities. S_M2 behaves quite similar to S_M1.

Fig. 1

General scheme of a RR for self-referencing FOS. Inset shows RR relative output powers versus frequency for different H values to illustrate operation.

Fig. 2

Normalized sensitivity, S_M1 , versus H, in the frequency normalization method. f₁=1,302 MHz , L=1067 m, γ=0.05, and (_): K=0.11, (––): K=0.17, (…): K=0.22.

3. Measurements

The experimental setup is made of a LD of 1.5 μm, with 5 MHz linewidth, internally modulated with a signal coming from the tracking generator of a RF spectrum analyzer. The sensing scheme (see Fig. 1) is made of a polarization maintaining 2×2 variable ratio fiber coupler with pigtails of 1 m, 1067 m of standard SM fiber, and an attenuator simulating the FOS. f₁ is 1.302 MHz, f₂ is 1.207 MHz, and K=0.22. The calibration curves, for both self-referencing methods, are reported in Fig. 3. There is a great agreement between theory and measurements, and the system reveals good sensitivity compared to other topologies;⁵ even though f₁ is not in the resonance frequency. Measurements variations, around 4, could be improved using a low coherence source in order to decrease the source induced noise.

Fig. 3

Calibration curves for K=0.22: measurements R_M1 (○) and R_M2 (+) and simulations (dashed line).

4. Conclusions

Two different self-referencing methods for intensity fiber-optic sensors are described and their sensitivities are theoretically analyzed. The proposed scheme, using RR operating under incoherent regime, is flexible because the operation point and sensitivity is controlled by a coupling coefficient. Experimental calibration curves are reported validating the utility of the model developed. This configuration has a better sensitivity to other topologies.

Acknowledgments

We wish to thank J. M. Sa´nchez-Pena and S. Vargas. This work was supported by Comision Interministerial de Ciencia y Tecnologı´a (TIC2003-03783).

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Carmen Vázquez García, Julio Montalvo, and Pedro Contreras Lallana "Radio-frequency ring resonators for self-referencing fiber-optic intensity sensors," Optical Engineering 44(4), 040502 (1 April 2005). https://doi.org/10.1117/1.1883566

Published: 1 April 2005

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KEYWORDS

Fiber optics sensors

Sensors

Resonators

Fiber optics

Calibration

Signal attenuation

Modulation

1.

Introduction

2.

Theoretical Analysis

Eq. (1)

Eq. (2)

Eq. (3)

Eq. (4)

Eq. (5)

Eq. (6)

Fig. 1

Fig. 2

3.

Measurements

Fig. 3

4.

Conclusions

Acknowledgments

REFERENCES

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