Abstract

An electro-optic (EO) sensing system for measuring free-space electric fields in the microwave range has been developed. The system is based on a phase modulation heterodyning technique using a Mach–Zehnder interferometer. In one of the arms of the interferometer, an acousto-optic frequency shifter is used to downconvert the frequency of the detected signal in order to discriminate it from parasites emitted at the external electric field frequency. The sensing part is a LiTaO3 crystal placed in a Fabry–Perot cavity. The cavity aims at enhancing the sensitivity of the measurements. Cavity-based EO setups already used in the literature propose this sensitivity enhancement at the expense of the frequency bandwidth, whereas our setup allows this without a major impact on the frequency bandwidth. Electric fields are measured at both 15 kHz and 2.4 GHz with cavities of two different finesses; the best EO phase retardation gains obtained with the cavity are 34 and 60, respectively. The minimum detectable electric field is 0.003Vm1Hz1/2.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
    [CrossRef]
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    [CrossRef]

2011

D. J. Lee, N. W. Kang, J. H. Choi, J. Kim, and J. F. Whitaker, “Recent advances in the design of electro-optic sensors for minimally destructive microwave field probing,” Sensors 11, 806–824 (2011).
[CrossRef]

2010

2009

2008

2007

2006

K. Sasagawa and M. Tsuchiya, “Modulation depth enhancement for highly sensitive electro-optic RF near-field measurement,” Electron. Lett. 42, 1357–1358 (2006).
[CrossRef]

2003

2002

L. Duvillaret, S. Rialland, and J.-L. Coutaz, “Electro-optic sensors for electric field measurements. I. Theoretical comparison among different modulation techniques,” J. Opt. Soc. Am. B 19, 2692–2703 (2002).
[CrossRef]

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

1986

B. H. Kolner and D. M. Bloom, “Electrooptic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79–93 (1986).
[CrossRef]

1985

K. E. Meyer and G. A. Mourou, “Two-dimensional E-field mapping with subpicosecond temporal resolution,” Electron. Lett. 21, 568–569 (1985).
[CrossRef]

1984

B. H. Kolner and D. M. Bloom, “Direct electrooptic sampling of transmission-line signals propagating on a GaAs substrate,” Electron. Lett. 20, 818–819 (1984).
[CrossRef]

1983

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

B. H. Kolner, D. M. Bloom, and P. S. Cross, “Electro-optic sampling with picosecond resolution,” Electron. Lett. 19, 574–575 (1983).
[CrossRef]

1982

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[CrossRef]

Bloom, D. M.

B. H. Kolner and D. M. Bloom, “Electrooptic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79–93 (1986).
[CrossRef]

B. H. Kolner and D. M. Bloom, “Direct electrooptic sampling of transmission-line signals propagating on a GaAs substrate,” Electron. Lett. 20, 818–819 (1984).
[CrossRef]

B. H. Kolner, D. M. Bloom, and P. S. Cross, “Electro-optic sampling with picosecond resolution,” Electron. Lett. 19, 574–575 (1983).
[CrossRef]

Chen, K.

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

Choi, J. H.

D. J. Lee, N. W. Kang, J. H. Choi, J. Kim, and J. F. Whitaker, “Recent advances in the design of electro-optic sensors for minimally destructive microwave field probing,” Sensors 11, 806–824 (2011).
[CrossRef]

Coutaz, J.-L.

Cross, P. S.

B. H. Kolner, D. M. Bloom, and P. S. Cross, “Electro-optic sampling with picosecond resolution,” Electron. Lett. 19, 574–575 (1983).
[CrossRef]

Duvillaret, L.

Gabel, C. W.

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[CrossRef]

Gaborit, G.

Huang, C. Y.

Kang, N. W.

D. J. Lee, N. W. Kang, J. H. Choi, J. Kim, and J. F. Whitaker, “Recent advances in the design of electro-optic sensors for minimally destructive microwave field probing,” Sensors 11, 806–824 (2011).
[CrossRef]

Kassi, S.

Kim, J.

D. J. Lee, N. W. Kang, J. H. Choi, J. Kim, and J. F. Whitaker, “Recent advances in the design of electro-optic sensors for minimally destructive microwave field probing,” Sensors 11, 806–824 (2011).
[CrossRef]

Kolner, B. H.

B. H. Kolner and D. M. Bloom, “Electrooptic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79–93 (1986).
[CrossRef]

B. H. Kolner and D. M. Bloom, “Direct electrooptic sampling of transmission-line signals propagating on a GaAs substrate,” Electron. Lett. 20, 818–819 (1984).
[CrossRef]

B. H. Kolner, D. M. Bloom, and P. S. Cross, “Electro-optic sampling with picosecond resolution,” Electron. Lett. 19, 574–575 (1983).
[CrossRef]

Kuo, J. Y.

Kuo, W. K.

Kwon, J. Y.

Lee, D. J.

Martin, G.

Meyer, K. E.

K. E. Meyer and G. A. Mourou, “Two-dimensional E-field mapping with subpicosecond temporal resolution,” Electron. Lett. 21, 568–569 (1985).
[CrossRef]

Mitrofanov, O.

Mourou, G.

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[CrossRef]

Mourou, G. A.

K. E. Meyer and G. A. Mourou, “Two-dimensional E-field mapping with subpicosecond temporal resolution,” Electron. Lett. 21, 568–569 (1985).
[CrossRef]

Rialland, S.

Romanini, D.

Ryu, H. Y.

Sasagawa, K.

K. Sasagawa and M. Tsuchiya, “Low-noise and high-frequency resolution electrooptic sensing of RF near-fields using an external optical modulator,” J. Lightwave Technol. 26, 1242–1248 (2008).
[CrossRef]

K. Sasagawa and M. Tsuchiya, “Modulation depth enhancement for highly sensitive electro-optic RF near-field measurement,” Electron. Lett. 42, 1357–1358 (2006).
[CrossRef]

Tsuchiya, M.

K. Sasagawa and M. Tsuchiya, “Low-noise and high-frequency resolution electrooptic sensing of RF near-fields using an external optical modulator,” J. Lightwave Technol. 26, 1242–1248 (2008).
[CrossRef]

K. Sasagawa and M. Tsuchiya, “Modulation depth enhancement for highly sensitive electro-optic RF near-field measurement,” Electron. Lett. 42, 1357–1358 (2006).
[CrossRef]

Valdmanis, J. A.

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[CrossRef]

Whitaker, J. F.

Yang, H.

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

Yi, M.

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

Zhang, D.

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

Zhang, H.

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41, 211–212 (1982).
[CrossRef]

Electron. Lett.

B. H. Kolner, D. M. Bloom, and P. S. Cross, “Electro-optic sampling with picosecond resolution,” Electron. Lett. 19, 574–575 (1983).
[CrossRef]

B. H. Kolner and D. M. Bloom, “Direct electrooptic sampling of transmission-line signals propagating on a GaAs substrate,” Electron. Lett. 20, 818–819 (1984).
[CrossRef]

K. Sasagawa and M. Tsuchiya, “Modulation depth enhancement for highly sensitive electro-optic RF near-field measurement,” Electron. Lett. 42, 1357–1358 (2006).
[CrossRef]

K. E. Meyer and G. A. Mourou, “Two-dimensional E-field mapping with subpicosecond temporal resolution,” Electron. Lett. 21, 568–569 (1985).
[CrossRef]

IEEE J. Quantum Electron.

B. H. Kolner and D. M. Bloom, “Electrooptic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron. 22, 79–93 (1986).
[CrossRef]

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Subpicosecond electrical sampling,” IEEE J. Quantum Electron. 19, 664–667 (1983).
[CrossRef]

J. Lightwave Technol.

J. Opt. Laser Technol.

K. Chen, H. Zhang, D. Zhang, H. Yang, and M. Yi, “External electro-optic sampling utilizing a poled polymer asymmetric Fabry Perot cavity as an electro-optical probe tip,” J. Opt. Laser Technol. 34, 449–452 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Sensors

D. J. Lee, N. W. Kang, J. H. Choi, J. Kim, and J. F. Whitaker, “Recent advances in the design of electro-optic sensors for minimally destructive microwave field probing,” Sensors 11, 806–824 (2011).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Typical heterodyne PM setup.

Fig. 2.
Fig. 2.

FPPMH setup working in reflection mode.

Fig. 3.
Fig. 3.

FPPMH setup working in transmission mode.

Fig. 4.
Fig. 4.

EO gain of the setup in reflection mode (continuous plot) and transmission mode (dashed plot) as a function of r1 and r2 while keeping r1r2 and the finesse of the cavity constant.

Fig. 5.
Fig. 5.

Transfer function of our FPPMH technique (full line), and of an AM technique using the same EO crystal filling the entire cavity (dashed line), as visible in the inset at the lower right. Also shown is the transfer function in the vicinity of the high frequency operating point.

Fig. 6.
Fig. 6.

Experimental calibration of the phase retardation gain relative to the actual finesse.

Fig. 7.
Fig. 7.

Amplified signal I(ωS±ωm) as a function of the voltage at the radiating high-impedance terminal (antenna).

Fig. 8.
Fig. 8.

Phase retardation gain measured as a function of the frequency of the electric field generated by the high-impedance terminal (antenna) for a fixed cavity length of about 64 mm. Also shown are numerically calculated phase retardation gains taking into account different roundtrips in the cavity.

Equations (33)

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EL1=A1exp(i(ωLt+φEO(t)+φ0)),
EL2=A2exp(i(ωL+ωS)t),
I=12A12+12A22+A1A2cos(ωStφ0)+12A1A2φm{sin[(ωS+ωm)tφ0]+sin[(ωSωm)tφ0]}.
φm=2I(ωS±ωm)I(ωS),
I(ωS±ωm)=12A1A2φm.
I(ωS)=A1A2.
φm=2πLλ(ne32r33EZ),
ELR=A1(r1r2(1r12)eiδn=0(r1r2eiδ)n).
δm=22πLλ(ne32r33EZ).
EL1=A1(r1r2eiδ1r1r2eiδ)eiωLt,
EL2=A2exp(i(ωL+ωS)t+ϕ0).
IR=A12r122r1r2cos(δ)+r2212r1r2cos(δ)+r12r22+A22+A1A2r1[2cos(ωSt+ϕ0)+(r121)2cos(ωSt+ϕ0)2r1r2cos(ωSt+ϕ0+δ)12r1r2cos(δ)+r12r22].
IR=A12(r1r2)2(1r1r2)2+A22+A1A2r1{cos(ωSt+ϕ0)+r121(1r1r2)2[2cos(ωSt+ϕ0)2r1r2{cos(ωSt+ϕ0)δm2[cos((ωmωS)tϕ0)cos((ωm+ωS)t+ϕ0)]}]}.
ELT=EL0((1r12)(1r22)eiδ/21r1r2eiδ).
EL2=A2exp(i(ωL+ωS)t+ϕ0).
IT=A12(1r12)(1r22)(1r1r2)2+A22+2A1A2(1r12)(1r22)(1r1r2)2{cos(ωSt+ϕ0)+r1r2cos(ωSt+ϕ0)+r1r2δm4[cos((ωmωS)tϕ0)cos((ωm+ωS)t+ϕ0)]+δm4[cos((ωmωS)tϕ0)cos((ωm+ωS)t+ϕ0)]}.
f=π22(1+r12r22)(1r1r2).
IR(ωm±ωS)=A1A2r121(1r1r2)2r2δm
IT(ωm±ωS)=12A1A2(1r12)(1r22)(1r1r2)2(1+r1r2)δm
I(ωS±ωm)=12A1A2φm,
φm=22πLλ(ne32r33EZ).
GEO(T)=IT(ωm±ωS)I(ωm±ωS)
GEO(R)=IR(ωm±ωS)I(ωm±ωS)
IR=A12+A22+A1A2r1{2cos(ωSt+ϕ0)1+r11r1[2cos(ωSt+ϕ0)2r1{cos(ωSt+ϕ0)δm2[cos((ωmωS)tϕ0)cos((ωm+ωS)t+ϕ0)]}]}.
δm*=2IR(ωS±ωm)IR(ωS)=1+r11r1δm.
Gδ=δm*δm=1+r11r1.
fc=f3dB=12πτ,
I0=Ii1r12(1r1r2)2.
IT=I0(1R2)R1int[tτcav+12]R2int[tτcav],
τcav=[2L+2LEO(nEO1)]/c,
τEO=2nl/c,
IT=I01R2R2exp(t/τ),
H(f)=E(f)[11τ+2πjfI01R2R2][sinc(fτEO)1τcavn=δ(fnτcav)].

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