Abstract

We demonstrate a broadband wavemeter by imaging the radiation from multiple interfering modes approaching cutoff in a tapered hollow waveguide (clad by omnidirectional Bragg mirrors). Dispersion of the cutoff point was used to extract a coarse wavelength estimate, and subsequent computational analysis of the complex standing wave radiation pattern leading up to the cutoff point enabled a much finer estimate. This approach leverages the principles of speckle-based spectrometers but with added functionality provided by the spectral-spatial dispersion of the mode cutoff position. In proof-of-principle work, we verified a resolution < 10 pm over an operating range of nearly 100 nm in the near infrared using a tapered waveguide with a length < 1 mm. Significantly enhanced resolution should be possible through feasible refinements of the waveguides and peripheral components.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (1)

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

2016 (1)

2015 (2)

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

J. Bao and M. G. Bawendi, “A colloidal quantum dot spectrometer,” Nature 523(7558), 67–70 (2015).
[Crossref]

2014 (4)

2013 (1)

B. Redding, S. Fatt Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

2009 (2)

2008 (1)

2007 (1)

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

2004 (1)

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Lett. 85(9), 1466–1468 (2004).
[Crossref]

1984 (1)

Allen, T.

Allen, T. W.

Azar, A.

Bao, J.

J. Bao and M. G. Bawendi, “A colloidal quantum dot spectrometer,” Nature 523(7558), 67–70 (2015).
[Crossref]

Bawendi, M. G.

J. Bao and M. G. Bawendi, “A colloidal quantum dot spectrometer,” Nature 523(7558), 67–70 (2015).
[Crossref]

Benech, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Blaize, S.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Bromberg, Y.

Bruce, G. D.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Cao, H.

Ceyssens, F.

Chen, E. H.

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

Choma, M. A.

DeCorby, R. G.

Dennison, C. R.

Dholakia, K.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

M. Mazilu, T. Vettenburg, A. Di Falco, and K. Dholakia, “Random super-prism wavelength meter,” Opt. Lett. 39(1), 96–99 (2014).
[Crossref]

Di Falco, A.

Drobot, B.

Englund, D.

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

Epp, E.

Fatt Liew, S.

B. Redding, S. Fatt Liew, Y. Bromberg, R. Sarma, and H. Cao, “Evanescently coupled multimode spiral spectrometer,” Optica 3(9), 956–962 (2016).
[Crossref]

B. Redding, S. Fatt Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

Fedeli, J. M.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Giaccari, P.

Guldimann, B.

Herzig, H. P.

Ibanescu, M.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Lett. 85(9), 1466–1468 (2004).
[Crossref]

Joannopoulos, J. D.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Lett. 85(9), 1466–1468 (2004).
[Crossref]

Johnson, S. G.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Lett. 85(9), 1466–1468 (2004).
[Crossref]

Kern, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Klaus Metzger, N.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Le Coarer, E.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Leblond, G.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Lerondel, G.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Madi, M.

Maker, G. T.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Malcolm, G.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Mazilu, M.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

M. Mazilu, T. Vettenburg, A. Di Falco, and K. Dholakia, “Random super-prism wavelength meter,” Opt. Lett. 39(1), 96–99 (2014).
[Crossref]

Mcilrath, T. J.

McMullin, J. N.

Meldrum, A.

Meldrum, A. F.

Melnyk, A.

Meng, F.

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

Menon, R.

Miller, B.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Morand, A.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Morris, M. B.

Newman, W.

Olsen, T.

Ponnampalam, N.

Popoff, S. M.

Potts, C.

Povinelli, M. L.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Lett. 85(9), 1466–1468 (2004).
[Crossref]

Redding, B.

Royer, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Sarma, R.

B. Redding, S. Fatt Liew, Y. Bromberg, R. Sarma, and H. Cao, “Evanescently coupled multimode spiral spectrometer,” Optica 3(9), 956–962 (2016).
[Crossref]

B. Redding, S. Fatt Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

Schroder, T.

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

Shiue, R.-J.

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

Shlens, J.

J. Shlens, “A tutorial on principal component analysis,” preprint at https://arxiv.org/abs/1404.1100

Shorubalko, I.

Silverstone, J.

Snyder, J. J.

Spesyvtsev, R.

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Stefanon, I.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Vettenburg, T.

Wan, N. H.

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

Wang, P.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Lett. 85(9), 1466–1468 (2004).
[Crossref]

Nat. Commun. (2)

N. H. Wan, F. Meng, T. Schroder, R.-J. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun. 6(1), 7762 (2015).
[Crossref]

N. Klaus Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref]

Nat. Photonics (2)

B. Redding, S. Fatt Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[Crossref]

Nature (1)

J. Bao and M. G. Bawendi, “A colloidal quantum dot spectrometer,” Nature 523(7558), 67–70 (2015).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

Optica (1)

Other (1)

J. Shlens, “A tutorial on principal component analysis,” preprint at https://arxiv.org/abs/1404.1100

Supplementary Material (2)

NameDescription
» Visualization 1       Video file showing how a typical radiation stream image varies as the input coupling conditions are varied, for a fixed input wavelength (980 nm).
» Visualization 2       Video file showing how a typical radiation streak image varies as the wavelength is stepped in 5 pm increments over the range from 950 to 952 nm, with fixed input coupling.

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic illustration of the experimental setup. Light is coupled into the wide end of a tapered hollow waveguide, exciting multiple modes. The ray trajectories depict the adiabatic evolution of guided light into a vertical cavity resonance (within the omnidirectional band of the claddings), for one particular mode at two different wavelengths. Radiation loss diverges as the cut-off point is approached. (b) Overhead-view microscope image showing portions of three tapered waveguides (scale bar: 250 μm). (c) (Visualization 1) Typical radiation streak for a monochromatic (980 nm) input signal, captured using a 40x objective lens (NA = 0.65). The streak comprises light radiating near and at cutoff for a family of horizontal (in-plane) modes belonging to one vertical mode order (TE1q for the case shown). The terminal cutoff spot is associated with near-vertical radiation from the fundamental horizontal (i.e. TE10) mode.
Fig. 2.
Fig. 2. (a) (Visualization 2) Radiation streaks captured using a 20x objective lens (NA = 0.40) at 3 different wavelengths (λ = 940, 945, and 950 nm), illustrating the spatial dispersion imparted by the taper. (b) Block diagram illustrating the two-step procedure used to extract the wavelength of a nominally monochromatic input signal. The spectral dependence of the terminal cutoff position is used to extract a coarse wavelength estimate. This estimate is then fed into a PCA-based estimation of the precise wavelength using the ‘speckle’ pattern of the overall radiation streak. (c) Further illustration of the procedure: the operating range B is determined by the waveguides and the image sensor. This range is sub-divided into W ‘coarse’ bins, and a pre-determined calibration set within each of these bins enables the algorithmic determination of a ‘fine’ wavelength estimate.
Fig. 3.
Fig. 3. (a) Plot showing the terminal cutoff position versus wavelength for a typical tapered waveguide, as extracted manually (symbols) and using an automated image processing algorithm (solid line). Inset: typical plot of pixel intensity versus distance for a radiation streak image. The large peak (circled) and subsequent sharp drop-off associated with the terminal cutoff point are characteristic features that occur at a wavelength-dependent position. (b) Inner product covariance plot for images captured at 1 nm intervals across the entire tunable range of the laser.
Fig. 4.
Fig. 4. (a) Series of images captured at 100 pm increments, showing significant variation in the speckle pattern. (b) Spectral correlation function for a set of images captured in 5 pm increments over various ranges as indicated. For the 1 nm range, the HWHM resolution is δλ ∼ 15 pm. (c) Result of SVD matrix inversion on a synthesized image produced by a spectrum comprising lines at 960.30 and 960.31 nm. (d) As in part (c), but for spectral lines spaced by 5 pm.
Fig. 5.
Fig. 5. (a) Plot showing the trajectory of the first 3 principle components extracted from a set of images with 5 pm spacing in the 930–931 nm range. (b) Schematic illustration of wavelength assignment for an unknown input, based on analysis of the nearest calibration point in multi-dimensional PCA space. (c) Plot of extracted wavelength versus input wavelength. (d) Histogram showing the distributions of errors for the extracted wavelength set from part (c). (e),(f) As for parts (c),(d), except in the 950–951 nm range.
Fig. 6.
Fig. 6. Normalized correlations of calibration images at various time intervals with respect to t = 0, for (a) 930–931 nm at 15 minute intervals up to 1 hour and (b) 960–961 nm at 1 hour intervals for 3 hours.

Equations (2)

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C ( x , Δ λ ) = I ( x , λ ) I ( x , λ + Δ λ ) λ I ( x , λ ) λ I ( x , λ + Δ λ ) λ 1.
X j = c 1 j P 1 + c 2 j P 2 + + c N j P N .

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