Abstract

A new method is proposed and analyzed for measuring the timing jitter of the transmitted pulse relative to the reference pulse using two type II phase-matched nonlinear crystals for second harmonic generation (SHG). The polarizations of the two pulses are exchanged in two crystals and the difference between two detected second harmonic signals can reflect the transmitted jitter. This new method provides a high sensitivity and timing resolution compared with the conventional RF (radio frequency) method. Since the overlapping levels in the two crystals are the same, the final output is zero when there is no time delay between the two pulses. Thus no offset is necessary to be subtracted from the final output and no time delay adjustment is required between the two pulses, compared with the previous optical method using one crystal and two dichroic beamsplitters. The jitter measuring performance is studied theoretically using non-stationary nonlinear wave-coupled equations for type II SHG of two pulses. The theoretical computation and analysis show that the sensitivity and the dynamic range of this new method depend on pulse width, crystal pulses and group velocity difference between two fundamental pulses.

© 2009 OSA

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References

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  1. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
    [CrossRef] [PubMed]
  2. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
    [CrossRef]
  3. F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
    [CrossRef]
  4. M. Calhoun, S. Huang, and R. L. Tjoelker, “Stable photonic links for frequency and time transfer in the deep-space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
    [CrossRef]
  5. K. W. Holman, D. J. Jones, D. D. Hudson, and J. Ye, “Precise frequency transfer through a fiber network by use of 1.5-microm mode-locked sources,” Opt. Lett. 29(13), 1554–1556 (2004).
    [CrossRef] [PubMed]
  6. K. W. Holman, D. D. Hudson, J. Ye, and D. J. Jones, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett. 30(10), 1225–1227 (2005).
    [CrossRef] [PubMed]
  7. S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
    [CrossRef]
  8. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
    [CrossRef] [PubMed]
  9. S. Qian and R. Zhu, Nonlinear Optics (Fudan University Press, Shanghai, 2005), Chap. 3.
  10. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale, 2nd ed. (Academic Press, Burlington, 2006), Chap. 3.
  11. M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38(11), 4365–4372 (1967).
    [CrossRef]

2007 (3)

M. Calhoun, S. Huang, and R. L. Tjoelker, “Stable photonic links for frequency and time transfer in the deep-space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[CrossRef]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[CrossRef] [PubMed]

2006 (2)

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

2005 (1)

2004 (1)

2002 (1)

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

1967 (1)

M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38(11), 4365–4372 (1967).
[CrossRef]

Amy-Klein, A.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Bagayev, S. N.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Birks, T. A.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Bize, S.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Calhoun, M.

M. Calhoun, S. Huang, and R. L. Tjoelker, “Stable photonic links for frequency and time transfer in the deep-space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[CrossRef]

Chardonnet, C.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Chen, J.

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Chepurov, S. V.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Clairon, A.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Daussy, C.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Denisov, V. I.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Dmitriyev, A. K.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Dychkov, A. S.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Foreman, S. M.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[CrossRef] [PubMed]

Hobden, M. V.

M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38(11), 4365–4372 (1967).
[CrossRef]

Holman, K. W.

Huang, S.

M. Calhoun, S. Huang, and R. L. Tjoelker, “Stable photonic links for frequency and time transfer in the deep-space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[CrossRef]

Hudson, D. D.

Ilday, F. O.

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Jones, D. J.

Kartner, F. X.

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Kärtner, F. X.

Kim, J.

Kim, J. W.

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Klementyev, V. M.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Kolker, D. B.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Korel, I. I.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Kuznetsov, S. A.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Loehl, F.

Lopez, O.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Lours, M.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Matyugin, Y. A.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Narbonneau, F.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Okhapkin, M. V.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Pivtsov, V. S.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Russell, P. S. J.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Santarelli, G.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Schlarb, H.

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Schmuser, P.

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Skvortsov, M. N.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Tjoelker, R. L.

M. Calhoun, S. Huang, and R. L. Tjoelker, “Stable photonic links for frequency and time transfer in the deep-space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[CrossRef]

Wadsworth, W. J.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Winter, A.

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Wong, F. N. C.

Ye, J.

Zakharyash, V. F.

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

Zhang, Z.

J. Appl. Phys. (1)

M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38(11), 4365–4372 (1967).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

M. Calhoun, S. Huang, and R. L. Tjoelker, “Stable photonic links for frequency and time transfer in the deep-space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[CrossRef]

Proc. SPIE (2)

S. N. Bagayev, S. V. Chepurov, V. I. Denisov, A. K. Dmitriyev, A. S. Dychkov, V. M. Klementyev, D. B. Kolker, I. I. Korel, S. A. Kuznetsov, Y. A. Matyugin, M. V. Okhapkin, V. S. Pivtsov, M. N. Skvortsov, V. F. Zakharyash, T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Femtosecond optical clock with the use of a frequency comb,” Proc. SPIE 4900, 125–131 (2002).
[CrossRef]

F. O. Ilday, A. Winter, J. W. Kim, J. Chen, P. Schmuser, H. Schlarb, and F. X. Kartner, “Ultra-low timing-jitter passively mode-locked fiber lasers for long-distance timing synchronization,” Proc. SPIE 6389, 63890L (2006).
[CrossRef]

Rev. Sci. Instrum. (2)

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[CrossRef] [PubMed]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[CrossRef]

Other (2)

S. Qian and R. Zhu, Nonlinear Optics (Fudan University Press, Shanghai, 2005), Chap. 3.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale, 2nd ed. (Academic Press, Burlington, 2006), Chap. 3.

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Figures (3)

Fig. 1
Fig. 1

(Color online) Schematic diagram for the jitter measurement of the transmitted pulse relative to the reference pulse using type II phase-matched SHG. The blue solid pulse represents the reference pulse and the red dashed pulse represents the transmitted pulse. The green solid pulse represents the second harmonic field. The dark dashed line represents the electric signal detected by PMD.

Fig. 2
Fig. 2

Final output Sdiff as a function of delay time τ between two pulses for the two pulse cases: (a) Gaussian pulse type; (b) hyperbolic secant pulse type.

Fig. 3
Fig. 3

Sensitivity KS and Dynamic range Δτ as a function of ξ/TP .

Equations (31)

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E1s(z,t)={12U1s(z,t)exp[i(k1szω1t)]+c.c.}e1s
E1f(z,t)={12U1f(z,t)exp[i(k1fzω1t)]+c.c.}e1f
E2(z,t)={12U2(z,t)exp[i(k2zω1t)]+c.c.}e2
U1s(z,t)z+1υg1sU1s(z,t)t=iω1deffcn1sU2(z,t)[U1f(z,t)]
U1f(z,t)z+1υg1fU1f(z,t)t=iω1deffcn1fU2(z,t)[U1s(z,t)]
U2(z,t)z+1υg2U2(z,t)t=2iω1deffcn2U1s(z,t)U1f(z,t)
U1s(z,t)=U1s(0,tzυg1s)U1s(tzυg1s)
U1f(z,t)=U1f(0,tzυg1f)U1f(tzυg1f)
U2(z,t)z=2iω1deffcn2U1s(t+zυg2zυg1s)U1f(t+zυg2zυg1f)
U2(L,t)=2iω1deffcn20LU1s(t+βzαsz)U1f(t+βzαfz)dz
U2(L,t)=2iω1deffcn21(βαs)αsLβLU1s(tt1)U1f[tγt1+(γ1)βL]dt1
U2(t)=2iω1deffcn2LU1s[t(β+αs)L2]U1f[tγ(β+αs)L2+(γ1)βL]
Ij(t)=12ε0cnj|Uj(t)|2
I2(t)=8ω12deff2L2ε0c3n1sn1fn2I1s[t(β+αs)L2]I1f[tγ(β+αs)L2+(γ1)βL]
I21(t,τ)=AL2Itrs(ttaτ)Ireff(ttb)
I22(t,τ)=AL2Irefs(tta)Itrf(ttbτ)
SPD1(τ)=ηI21(t,τ)dt=ηAL2Itrs(ttaτ)Ireff(ttb)dt
SPD2(τ)=ηI22(t,τ)dt=ηAL2Irefs(tta)Itrf(ttbτ)dt
Irefs(t)=Ireff(t)=I01e(t/TP)2
Itrs(t)=Itrf(t)=I02e(t/TP)2
Irefs(t)=Ireff(t)=I01sech(2t/Tp)
Itrs(t)=Itrf(t)=I02sech(2t/Tp)
SPD1(τ)=πηAL2I01I02TPe(τ+tatb)2/(2TP2)
SPD2(τ)=πηAL2I01I02TPe(τta+tb)2/(2TP2)
SPD1(τ)=4ηAL2I01I02TP(τ+tatb)/TPe(τ+tatb)/TPe(τ+tatb)/TP
SPD2(τ)=4ηAL2I01I02TP(τta+tb)/TPe(τta+tb)/TPe(τta+tb)/TP
Sdiff(τ)=SPD2(τ)SPD1(τ)=πηAL2I01I02TP[e(τξ/2)2/(2TP2)e(τ+ξ/2)2/(2TP2)]
Sdiff(τ)=4ηAL2I01I02TP[(τξ/2)/TPe(τξ/2)/TPe(τξ/2)/TP(τ+ξ/2)/TPe(τ+ξ/2)/TPe(τ+ξ/2)/TP]
KSπηAL2I01I02ξTPexp[18(ξTP)2]
ΔTrms=f1f2ST(f)df
ST(f)=Sφ(f)(2πfrep)2

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