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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 22 — Nov. 3, 2003
  • pp: 2807–2812
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All-silicon optical temperature sensor based on Multi-Mode Interference

Andrea Irace and Giovanni Breglio  »View Author Affiliations


Optics Express, Vol. 11, Issue 22, pp. 2807-2812 (2003)
http://dx.doi.org/10.1364/OE.11.002807


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Abstract

In this paper we present a novel approach to temperature sensing with optoelectronic devices which relies on the usage of bare silicon as the transducing material. The device is composed by a single mode input waveguide, a MMI region where a number of higher order modes is also allowed to propagate and two output waveguides. The refractive index variation in the MMI section due to temperature shifts induces different phase velocities of the various propagating modes. The position of the input and output waveguides together with the length and width of the MMI section are chosen in order to maximize the sensitivity of the device. Analytical calculations are presented together with BPM simulations aimed to the maximization of the sensitivity of the sensor as a function of its geometries.

© 2003 Optical Society of America

1. Introduction

2. Theoretical approach and description of the device

Fig. 1. Top view of the MMI device with input and output waveguides and the active region

The first part of the design concerns the choice of the dimensions for the input/output waveguide and for the active region. Effective Index Method can be exploited [8

8. S.P. Pogossian, L. Vescan, and A. Vonsovici, “The single-mode condition for semiconductor rib waveguides with large cross section,” IEEE J. Lightwave Technol. 16, 1851–1853 (1998) [CrossRef]

] to study the performances of such kind of waveguides and, if particular care in the definition of the geometry of the input waveguide is taken, a single mode operation can be assured. In particular, if the dimensions of the waveguide fulfill the following relationship: tr1r2 where t=weff/Heff, r=heff/Heff, heff=h+q, Heff=H+q, weff=w+2γc{knf2nc2} , q=γc{knf2nc2}+γs{knf2ns2} , nf, ns and nc are refractive indices of the guiding region, the substrate and the air respectively, H and W are the height and width of the optical waveguide and γc,s can be chosen according to the polarization of the propagating light [8

8. S.P. Pogossian, L. Vescan, and A. Vonsovici, “The single-mode condition for semiconductor rib waveguides with large cross section,” IEEE J. Lightwave Technol. 16, 1851–1853 (1998) [CrossRef]

].

Moreover, in order to guarantee an optimal coupling with an input optical fiber, a square optical channel has to be designed. This choice will be good also for both the output waveguides since light has to be coupled again into optical fibers for readout. Regarding the active region, the rib height will be the same of the output and input waveguides while the length and the width of the MMI zone will be parameter to be optimized for our purposes.

3. Analytical model and calculations

Selt-imaging is the working principle of MMI devices and it has been proposed more than 150 years ago [9

9. H.F. Talbot, “Facts relating to optical science No. IV” London Edimburgh Philosophical Mag., J. Sci. 9, 401–407, (1836)

] and its application to slab waveguides can be found in Ref. [10

10. D. Marcuse, Light Transmission Optics, (New York, Van Nostrand Reinhold, 1972).

12

12. R. Ulrich, “Image formation by phase coincidences in optical waveguides,” Optics Commun. 13, 259–264 (1975) [CrossRef]

] and it can be expressed as follows: “Self-imaging is the property of multi-mode waveguides when the input filed profile is reproduced in single or multiple images which appear periodically along the propagation direction”. In this paragraph we recall the basic principles of MMI theory while we refer to Ref. [9

9. H.F. Talbot, “Facts relating to optical science No. IV” London Edimburgh Philosophical Mag., J. Sci. 9, 401–407, (1836)

] for all the explanations and subtleties.

Fig. 2. Principle of self-imaging

An arbitrary input field (see Fig. 2) Ψ(y,0) totally confined in Wm, can be seen as the superposition of the guided modes inside the waveguides:

ψ(y,0)=νcνψν(y)
(1)

where ψν(y) are the waveguide eigenfunctions and, bearing in mind the ortogonality of the eigenmodes, the coefficients cν can be expressed by the overlap integral:

cν=Ψ(y,0)ψν(y)dyψν2(y)dy
(2)

If the input field Ψ(y,0) does not excite radiative modes it can be decomposed in terms of the m guided modes only:

Ψ(y,0)=ν=0m1cνψν(y)
(3)

and after a distance z it becomes:

Ψ(y,z)=ν=0m1cνψν(y)exp[jν(ν+2)π3LπL]
(4)

So, in some conditions, the field at the abscissa z will be equal to the input field. Now the relationship between the propagating modes depends on the refractive index of the waveguide. This, on its turn, if an appropriate guiding material is chosen, can be strongly dependent on the temperature, therefore, by carefully optimizing the geometries of the device, a very accurate sensor can be designed. In our case, thermo-optical effect in silicon causes a positive temperature induced refractive index variation according to:

Δn=1.84·104ΔT
(5)

and this variation can be recorded at the output of the device. In what follows some details on the simulations strategy will be given and the results presented.

4. Simulations’ results

ΔIΔT%=30
(6)

Let us now compare the performance of a MMI device. If we define I1 and I2 as the light intensity coming out of the two output waveguides, we can define the sensitivity S over a temperature range ΔT as follows:

S=I2I1I2+I1T=T0I2I1I2+I1T=T0+ΔT=1f(W,L,y0,y1,y2)
(7)

Therefore the goal of our analysis is to maximize the function S by using a suitable minimization strategy of the function f. This can be achieved by a number of different algorithms (Nelder-Mead, Levemberg-Marquardt), which are of common use in numerical analysis. MATLAB code has been written in order to simulate the behavior or the sensor taking into account the variation of all the aforementioned parameters. In order to avoid some of the problems arising (i.e., local minima) in the minimization of multi-variable functions it has been found convenient to narrow the intervals where the variable could move. In Table 1 the constraints used in all the simulations are resumed.

Table 1. Summary of the optimization parameters and their investigated range

table-icon
View This Table

Fig. 3. Example of multiple images on an optimized 4-mode MMI sensor

Finally the minimization of the function f in terms of all the other parameter has been performed and the overall transfer function of the sensor is reported in Fig. 4 where the output of the sensor is reported as a function of temperature and it is compared to a sensor designed to sustain only the first two propagating modes. In both cases it can be noted the good linearity over a broad temperature range while, for the MMI sensor a better sensitivity to temperature variation is obtained.

Fig. 4. Transfer function of the sensor. Comparison between the MMI and the bi-modal solution

5. Conclusions and future trends

References

1.

A. Alvarez-Herrero, H. Guerrero, T. Belenguer, and D. Levy, “High-sensitivity temperature sensor based on overlay on side-polished fibers,” IEEE Photon. Technol. Lett. 12, 1043–1045 (2000) [CrossRef]

2.

Y.J Rao, K. Kalli, G. Brady, D.J Webb, D.A Jackson, L. Zhang, and I. Bennion, “Spatially-multiplexed fibre-optic Bragg grating strain and temperature sensor system based on interferometric wavelength-shift detection,” Electron. Lett. 31, 1009–1010 (1995) [CrossRef]

3.

A.D Kersey and T.A. Berkoff, “Fiber-optic Bragg-grating differential-temperature sensor,” IEEE Photon, Technol, Lett. 4, 1183–1185, (1992) [CrossRef]

4.

A. Cusano, G. Breglio, M. Giordano, A. Calabrò, L. Nicolais, and A. Cutolo, “Fiber optic sensing system for smart materials and structures,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics 1, 401–409, (2001)

5.

A. Cusano, G. Breglio, M. Giordano, M. Russo, and J. Nasser, “Optoelectronic refractive index measurements: application for smart polymer processing,” Proceedings of IEEE Sensors 2, 1171–1175 (2002) [CrossRef]

6.

G. Breglio, G. Coppola, A. Cutolo, A. Irace, M. Bellucci, and M. Iodice “Temperature Optical Sensor Based on a Silicon Bi-Modal Y Branch,” Proc. SPIE. 4293, 155–161 (2001) [CrossRef]

7.

G. Cocorullo, F.G. Della Corte, M. Iodice, I. Rendina, and P.M. Sarro, “Silicon-on-silicon rib waveguides with a high-confining ion-implanted lower cladding,” IEEE J. Sel. Top. Quantum Electron. 4, 983–989 (1998) [CrossRef]

8.

S.P. Pogossian, L. Vescan, and A. Vonsovici, “The single-mode condition for semiconductor rib waveguides with large cross section,” IEEE J. Lightwave Technol. 16, 1851–1853 (1998) [CrossRef]

9.

H.F. Talbot, “Facts relating to optical science No. IV” London Edimburgh Philosophical Mag., J. Sci. 9, 401–407, (1836)

10.

D. Marcuse, Light Transmission Optics, (New York, Van Nostrand Reinhold, 1972).

11.

O. Bryngdahl, “Image formation using self-imaginq techniques,” J. Opt. Soc. Am. 63, 416–419 (1973) [CrossRef]

12.

R. Ulrich, “Image formation by phase coincidences in optical waveguides,” Optics Commun. 13, 259–264 (1975) [CrossRef]

13.

L.B. Soldano and E.C.M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” IEEE J. Lightwave Technol. 13, 615–627 (1995) [CrossRef]

14.

G. Coppola, C. R. de Boer, G. Breglio, M. Iodice, A. Irace, and P. M. Sarro “Temperature Optical Sensor based on all-silicon Bimodal waveguide,” Proc. SESENS (2001).

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(130.5990) Integrated optics : Semiconductors
(130.6010) Integrated optics : Sensors

ToC Category:
Research Papers

History
Original Manuscript: September 12, 2003
Revised Manuscript: October 17, 2003
Published: November 3, 2003

Citation
Andrea Irace and Giovanni Breglio, "All-silicon optical temperature sensor based on Multi-Mode Interference," Opt. Express 11, 2807-2812 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2807


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References

  1. A. Alvarez-Herrero, H. Guerrero, T. Belenguer and D. Levy, D, �??High-sensitivity temperature sensor based on overlay on side-polished fibers,�?? IEEE Photon. Technol. Lett. 12, 1043-1045 (2000) [CrossRef]
  2. Y.J Rao, K. Kalli, G. Brady, D.J Webb, D.A Jackson, L. Zhang and I. Bennion, �??Spatially-multiplexed fibre-optic Bragg grating strain and temperature sensor system based on interferometric wavelength-shift detection,�?? Electron. Lett. 31, 1009-1010 (1995) [CrossRef]
  3. A.D Kersey and T.A. Berkoff, �??Fiber-optic Bragg-grating differential-temperature sensor,�?? IEEE Photon, Technol, Lett. 4, 1183 -1185, (1992) [CrossRef]
  4. A. Cusano, G. Breglio, M. Giordano, A. Calabrò, L. Nicolais, A. Cutolo, �??Fiber optic sensing system for smart materials and structures,�?? IEEE/ASME International Conference on Advanced Intelligent Mechatronics 1, 401 -409, (2001)
  5. A. Cusano, G. Breglio, M. Giordano, M. Russo, J. Nasser, �??Optoelectronic refractive index measurements: application for smart polymer processing,�?? Proceedings of IEEE Sensors 2, 1171 -1175 (2002) [CrossRef]
  6. G. Breglio, G. Coppola, A. Cutolo, A. Irace, M. Bellucci and M. Iodice �??Temperature Optical Sensor Based on a Silicon Bi-Modal Y Branch,�?? Proc. SPIE. 4293, 155-161 (2001) [CrossRef]
  7. G. Cocorullo, F.G. Della Corte, M. Iodice, I. Rendina and P.M. Sarro, �??Silicon-on-silicon rib waveguides with a high-confining ion-implanted lower cladding,�?? IEEE J. Sel. Top. Quantum Electron. 4, 983 �??989 (1998) [CrossRef]
  8. S.P. Pogossian, L. Vescan and A. Vonsovici, �??The single-mode condition for semiconductor rib waveguides with large cross section,�?? IEEE J. Lightwave Technol. 16, 1851 -1853 (1998) [CrossRef]
  9. H.F. Talbot, �??Facts relating to optical science No. IV�?? London Edimburgh Philosophical Mag., J. Sci. 9, 401-407, (1836)
  10. D. Marcuse, Light Transmission Optics, (New York, Van Nostrand Reinhold, 1972).
  11. O. Bryngdahl, �??Image formation using self-imaginq techniques,�?? J. Opt. Soc. Am. 63, 416-419 (1973) [CrossRef]
  12. R. Ulrich, �??Image formation by phase coincidences in optical waveguides,�?? Optics Commun. 13, 259-264 (1975) [CrossRef]
  13. Soldano, L.B.; Pennings, E.C.M., �??Optical multi-mode interference devices based on self-imaging: principles and applications,�?? IEEE J. Lightwave Technol. 13, 615-627 (1995) [CrossRef]
  14. G. Coppola, C. R. de Boer, G. Breglio, M. Iodice, A. Irace, P. M. Sarro "Temperature Optical Sensor based on all-silicon Bimodal waveguide," Proc. SESENS (2001).

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