Abstract

We carry out a detailed analysis of angle-sensitive devices based on the critical-angle effect. We consider their use in measuring small angular deflections of a laser beam. We establish the diffraction limit to the sensitivity for optical-angle sensors based on reflection and transmission of a laser beam. We find that this limit is identical to that of the triangulation scheme when using a position-sensitive detector or the autocollimation scheme. We analyze the main proposals to date of optical-angle sensors based on the critical-angle effect, focusing on their maximum sensitivity and their polarization dependence in practical conditions. We propose and analyze theoretically a novel and simple angle-sensitive device for sensing optical-beam deflections with very low polarization dependence and a maximum sensitivity close to the diffraction limit when used with typical laser beams. We discuss the basic principles for designing this type of device, provide numerical results, and point out a convenient fabrication procedure.

© 2004 Optical Society of America

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    [CrossRef]

2003

A. García-Valenzuela, M. Peña-Gomar, J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

2001

A. Zhang, P. S. Huang, “Total internal reflection for precision small-angle measurement,” Appl. Opt. 40, 1617–1622 (2001).
[CrossRef]

B. H. Kim, F. E. Prins, D. P. Kern, S. Raible, U. Weimar, “Multicomponent analysis and prediction with a cantilever array based gas sensor,” Sens. Actuators B 77, 1–7 (2001).

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

R. Raiteri, M. Grattarola, H.-J. Butt, P. Sklàdal, “Micromechanical cantilever-based biosensors,” Sens. Actuators B 79, 115–126 (2001).
[CrossRef]

1999

1998

1997

A. L. Glazov, K. L. Muratikov, “Measurement of thermal parameters of solids by a modified photodeflection method,” Opt. Eng. 36, 358–362 (1997).
[CrossRef]

A. García-Valenzuela, R. Diaz-Uribe, “Detection limits of an internal-reflection sensor for the optical beam deflection method,” Appl. Opt. 36, 4456–4462 (1997).
[CrossRef] [PubMed]

1996

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
[CrossRef] [PubMed]

B. A. Williams, R. J. Dewhurst, “A fiber-optic detection system for laser-ultrasound Lamb-wave examination of defects in thin materials,” Nondestr. Test. Eval. 12, 343–353 (1996).
[CrossRef]

W. Gao, S. Kiyono, T. Nomura, “A new multiprobe method of roundness measurements,” Precis. Eng. 19, 37–45 (1996).
[CrossRef]

B. Zimering, A. C. Boccara, “Compact design for real time in situ atmospheric trace gas detection based on mirage effect (photothermal deflection) spectroscopy,” Rev. Sci. Instrum. 67, 1891–1895 (1996).
[CrossRef]

1994

J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
[CrossRef]

1993

1992

P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
[CrossRef] [PubMed]

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

1990

G. Meyer, N. M. Amer, “Simultaneous measurement of lateral and normal forces with an optical-beam-deflection atomic force microscope,” Appl. Phys. Lett. 57, 2089–2091 (1990).
[CrossRef]

1989

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

A. Salazar, A. Sánchez-Lavega, J. Fernández, “Theory of thermal diffusivity determination by the “mirage” technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

1988

1983

1982

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surfaces by laser autocollimation,” Precis. Eng. 4, 5–8 (1982).
[CrossRef]

1980

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Aamodt, L. C.

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Alexander, S.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Almond, D. P.

D. P. Almond, P. M. Patel, Photothermal Science and Techniques (Chapman Hall, London, 1996).

Amer, N. M.

G. Meyer, N. M. Amer, “Simultaneous measurement of lateral and normal forces with an optical-beam-deflection atomic force microscope,” Appl. Phys. Lett. 57, 2089–2091 (1990).
[CrossRef]

Badoz, J.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Baller, M. K.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

Barnes, J. R.

J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
[CrossRef]

Battiston, F. M.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

Boccara, A. C.

B. Zimering, A. C. Boccara, “Compact design for real time in situ atmospheric trace gas detection based on mirage effect (photothermal deflection) spectroscopy,” Rev. Sci. Instrum. 67, 1891–1895 (1996).
[CrossRef]

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Butt, H.-J.

R. Raiteri, M. Grattarola, H.-J. Butt, P. Sklàdal, “Micromechanical cantilever-based biosensors,” Sens. Actuators B 79, 115–126 (2001).
[CrossRef]

Caron, J. N.

J. N. Caron, Y. Yang, J. B. Mehl, “Gas-coupled laser acoustic detection at ultrasonic and audio frequencies,” Rev. Sci. Instrum. 69, 2912–2917 (1998).
[CrossRef]

Cook, S. R.

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

Cross, J. B.

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

De Grooth, B. G.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Dewhurst, R. J.

B. A. Williams, R. J. Dewhurst, “A fiber-optic detection system for laser-ultrasound Lamb-wave examination of defects in thin materials,” Nondestr. Test. Eval. 12, 343–353 (1996).
[CrossRef]

Diaz-Uribe, R.

Díaz-Uribe, R.

Elings, V.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Ennos, A. E.

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surfaces by laser autocollimation,” Precis. Eng. 4, 5–8 (1982).
[CrossRef]

Fernández, J.

A. Salazar, A. Sánchez-Lavega, J. Fernández, “Theory of thermal diffusivity determination by the “mirage” technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

Fournier, D.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Gao, W.

W. Gao, S. Kiyono, T. Nomura, “A new multiprobe method of roundness measurements,” Precis. Eng. 19, 37–45 (1996).
[CrossRef]

García-Valenzuela, A.

Gerber, C.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
[CrossRef]

Gimzewski, J. K.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
[CrossRef]

Glazov, A. L.

A. L. Glazov, K. L. Muratikov, “Measurement of thermal parameters of solids by a modified photodeflection method,” Opt. Eng. 36, 358–362 (1997).
[CrossRef]

Grattarola, M.

R. Raiteri, M. Grattarola, H.-J. Butt, P. Sklàdal, “Micromechanical cantilever-based biosensors,” Sens. Actuators B 79, 115–126 (2001).
[CrossRef]

Greve, J.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Güntherodt, H.-J.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

Gurley, J.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Hansma, P. K.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Hellemans, L.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Hoffbauer, M. A.

S. R. Cook, M. A. Hoffbauer, J. B. Cross, “A specialized torsion balance designed to measure the absolute flux density of hyperthermal molecular beams containing reactive species,” Rev. Sci. Instrum. 67, 1781–1789 (1996).
[CrossRef]

Huang, P. S.

Kamada, O.

Kern, D. P.

B. H. Kim, F. E. Prins, D. P. Kern, S. Raible, U. Weimar, “Multicomponent analysis and prediction with a cantilever array based gas sensor,” Sens. Actuators B 77, 1–7 (2001).

Kim, B. H.

B. H. Kim, F. E. Prins, D. P. Kern, S. Raible, U. Weimar, “Multicomponent analysis and prediction with a cantilever array based gas sensor,” Sens. Actuators B 77, 1–7 (2001).

Kiyono, S.

Kohno, T.

Lang, H. P.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

Li, Y.

Longmire, M.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Marti, O.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Mehl, J. B.

J. N. Caron, Y. Yang, J. B. Mehl, “Gas-coupled laser acoustic detection at ultrasonic and audio frequencies,” Rev. Sci. Instrum. 69, 2912–2917 (1998).
[CrossRef]

Meyer, E.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

Meyer, G.

G. Meyer, N. M. Amer, “Simultaneous measurement of lateral and normal forces with an optical-beam-deflection atomic force microscope,” Appl. Phys. Lett. 57, 2089–2091 (1990).
[CrossRef]

Miyamoto, K.

Muratikov, K. L.

A. L. Glazov, K. L. Muratikov, “Measurement of thermal parameters of solids by a modified photodeflection method,” Opt. Eng. 36, 358–362 (1997).
[CrossRef]

Murphy, J. C.

J. C. Murphy, L. C. Aamodt, “Photothermal spectroscopy using optical beam probing: mirage effect,” J. Appl. Phys. 51, 4580–4588 (1980).
[CrossRef]

Musha, T.

Ni, J.

Nomura, T.

W. Gao, S. Kiyono, T. Nomura, “A new multiprobe method of roundness measurements,” Precis. Eng. 19, 37–45 (1996).
[CrossRef]

O’Shea, S. J.

J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
[CrossRef]

Opsal, J.

Ozawa, N.

Patel, P. M.

D. P. Almond, P. M. Patel, Photothermal Science and Techniques (Chapman Hall, London, 1996).

Peña-Gomar, M.

A. García-Valenzuela, M. Peña-Gomar, J. Villatoro, “Sensitivity analysis of angle sensitive detectors based on a film resonator,” Opt. Eng. 42, 1084–1092 (2003).
[CrossRef]

Prins, F. E.

B. H. Kim, F. E. Prins, D. P. Kern, S. Raible, U. Weimar, “Multicomponent analysis and prediction with a cantilever array based gas sensor,” Sens. Actuators B 77, 1–7 (2001).

Putman, C. A. J.

C. A. J. Putman, B. G. De Grooth, N. F. van de Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[CrossRef]

Raible, S.

B. H. Kim, F. E. Prins, D. P. Kern, S. Raible, U. Weimar, “Multicomponent analysis and prediction with a cantilever array based gas sensor,” Sens. Actuators B 77, 1–7 (2001).

Raiteri, R.

R. Raiteri, M. Grattarola, H.-J. Butt, P. Sklàdal, “Micromechanical cantilever-based biosensors,” Sens. Actuators B 79, 115–126 (2001).
[CrossRef]

Ramseyer, J.-P.

F. M. Battiston, J.-P. Ramseyer, H. P. Lang, M. K. Baller, C. Gerber, J. K. Gimzewski, E. Meyer, H.-J. Güntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sens. Actuators B 77, 122–131 (2001).
[CrossRef]

Rayment, T.

J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
[CrossRef]

Rosencwaig, A.

Rosete-Aguilar, M.

Salazar, A.

A. Salazar, A. Sánchez-Lavega, J. Fernández, “Theory of thermal diffusivity determination by the “mirage” technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

Sánchez-Lavega, A.

A. Salazar, A. Sánchez-Lavega, J. Fernández, “Theory of thermal diffusivity determination by the “mirage” technique in solids,” J. Appl. Phys. 65, 4150–4156 (1989).
[CrossRef]

Schneir, J.

S. Alexander, L. Hellemans, O. Marti, J. Schneir, V. Elings, P. K. Hansma, M. Longmire, J. Gurley, “An atomic-resolution atomic-force microscope implemented using an optical lever,” J. Appl. Phys. 65, 164–167 (1989).
[CrossRef]

Sklàdal, P.

R. Raiteri, M. Grattarola, H.-J. Butt, P. Sklàdal, “Micromechanical cantilever-based biosensors,” Sens. Actuators B 79, 115–126 (2001).
[CrossRef]

Stephenson, R. J.

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J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, C. Gerber, “A femtojoule calorimeter using michromechanical sensors,” Rev. Sci. Instrum. 65, 3793–3798 (1994).
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W. Gao, S. Kiyono, T. Nomura, “A new multiprobe method of roundness measurements,” Precis. Eng. 19, 37–45 (1996).
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[CrossRef]

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[CrossRef]

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B. H. Kim, F. E. Prins, D. P. Kern, S. Raible, U. Weimar, “Multicomponent analysis and prediction with a cantilever array based gas sensor,” Sens. Actuators B 77, 1–7 (2001).

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Figures (9)

Fig. 1
Fig. 1

Plane-wave reflectance and phase difference between the plane-wave reflection coefficients in TE and TM polarization in an internal reflection assuming glass (n i = 1.5151) and air (n e = 1.00).

Fig. 2
Fig. 2

(a) Use of a prism to reflect an incoming optical beam near the critical angle in the RT scheme. (b) Two-prism configuration used to improve linearity. The angle of travel of the beam outside the prism θ p is related to the angle of incidence at the base of the prism θ i , by Snell’s law at the entrance interface of the prism. R and T are the reflectance and the transmittance of the optical beam.

Fig. 3
Fig. 3

Sensitivity in the RT scheme for both polarizations (dashed curve, TE polarization; dotted curve, TM polarization) and of the PI scheme (solid curve). The values assumed are λ = 0.6328 μm, n 1 = 1.5151, ω0 = 300 μm.

Fig. 4
Fig. 4

(a) Sensitivity of the multiple-critical-reflection scheme versus angle of incidence for 1, 5, 10, 15, and 20 number of internal reflections: solid curves, TE polarization; dashed curves, TM polarization. The maximum height of the curves are of the order of the number of reflections. (b) Maximum sensitivity divided by the diffraction limit as a function of the number of reflections.

Fig. 5
Fig. 5

(a) Plane-wave-reflectance curves near the critical angle and (b) angle derivative of the reflectance for an increasing number of layers, 0, 1, 2, 3, 4, and 5. The number of layers is indicated for each curve. All curves are for TE polarization.

Fig. 6
Fig. 6

Plane-wave reflectance and Gaussian-beam reflectance for the TR scheme with a single AR layer on a glass substrate near the critical angle for TE polarization and for n 1 = 1.6105, n 3 = 1.51509, δn = 0.005, λ = 0.6328 μm, d 1 = 2λ, and ω0 = 300 μm.

Fig. 7
Fig. 7

Sensitivity for the RT scheme with a single AR layer on a glass substrate [2n 1 -1R/∂θ i ] about the critical angle for n 1 = 1.6105, n 3 = 1.51509, δn = 0.005, λ = 0.6328 μm, d 1 = 2λ, and ω0 = 300 μm. For comparison we also show the curves for a single critical reflection at a glass-air interface (no layer).

Fig. 8
Fig. 8

Maximum sensitivity for the RT scheme with a single antireflection layer on a glass substrate as a function of the waist radius ω0 for n 1 = 1.6105, n 3 = 1.51509, δn = 0.005, λ = 0.6328 μm, and d 1 = 2λ: dotted curve, diffraction limit, 2(2π)1/2 ω0/λ; shaded area, typical range for laboratory lasers.

Fig. 9
Fig. 9

Structure of the proposed device if the internal prism is cemented with the external glass n 3, on which the AR layer is grown.

Tables (2)

Tables Icon

Table 1 Sensitivity in TE (TM) Polarization and for Different Film Thicknesses

Tables Icon

Table 2 Maximum Sensitivity for TE (TM) Polarization as a Fraction of the Diffraction Limit with a Second Layer of Refractive Index nc = n1 + Δn on Top of the Bottom Prism

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

rTE=kzi-kztkzi+kzt, rTM=εikzt-εtkziεikzt+εtkzi,
Rθi=ω0k12π1/2- |rθ|2 exp-ω02k122θi-θ2dθ,
Rθp=Rθiθiθp.
Rθp=1n1Rθi.
S/θp=2 1n1Rθi.
Rθi=-ω03k132π1/2- |rθ|2θi-θ×exp-ω02k122θi-θ2dθ.
θi-θexp-ω02k122θi-θ2
Rθi=ω03k132π1/20 u exp-ω02k122 u2du.
u exp-12 ω02k12u2=ω0-2k1-2u×exp-12 ω02k12u2
Rθi=ω0k12π1/20uexp-12 ω02k12u2du=ω0k12π1/2=2π1/2ω0λ n1.
S/θp=22π1/2ω0λ.
ItPW=I041+cosϕθi+π/2.
SPW=cosϕ1+π/2-cosϕ2+π/22+cosϕ1+π/2+cosϕ2+π/2.
rθi=r12+r23 exp-2jkz2d11+r12r23 exp-2jkz2d1,
rnm=amkzn-ankzmamkzn+ankzm
n2=n3+δn,

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