Abstract

This study is concerned with the optical response of an electro-optical material consisting of nematic liquid crystal as well as ionic surfactant as a dopant. The dopant is a key component to carry out the working of the resulting device through configuration switching. The operational principle is based on the surface anchoring transition induced by a steady electric field. The dynamic characteristics of the electro-optical cell can be considerably improved when the nematic layer is reoriented from the initially homeoplanar director configuration into the twisted state. Besides, a method to shorten the relaxation time is demonstrated by using a controlling pulse with a bipolar waveform.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. K. Freedericksz, V. Zolina, “Forces causing the orientation of an anisotropic liquid,” Trans. Faraday Soc. 29, 919–930 (1933).
    [CrossRef]
  2. E. Dubois-Violette, P. G. De Gennes, “Local Frederiks transitions near a solid/nematic interface,” J. de Phys. Lett. 36, 255–258 (1975).
  3. G. Ryschenkow, M. Kleman, “Surface defects and structural transitions in very low anchoring energy nematic thin films,” J. Chem. Phys. 64(1), 404–412 (1976).
    [CrossRef]
  4. G. E. Volovik, O. D. Lavrentovich, “Topological dynamics of defects: boojums in nematic drops,” Sov. Phys. JETP 58, 1159–1166 (1983).
  5. J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
    [CrossRef]
  6. J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
    [CrossRef]
  7. L. Komitov, K. Ichimura, A. Strigazzi, “Light-induced anchoring transition in a 4,4’-disubstituted azobenzene nematic liquid crystal,” Liq. Cryst. 27(1), 51–55 (2000).
    [CrossRef]
  8. L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
    [CrossRef]
  9. A. G. Petrov, G. Durand, “Electric field transport of biphilic ions and anchoring transitions in nematic liquid crystals,” Liq. Cryst. 17(4), 543–554 (1994).
    [CrossRef]
  10. V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
    [CrossRef]
  11. V. S. Sutormin, M. N. Krakhalev, V. Ya. Zyryanov, “The dynamics of the response of an electro-optic cell based on a nematic layer with controlled surface anchoring,” Tech. Phys. Lett. 39(7), 583–586 (2013).
    [CrossRef]
  12. J. E. Proust, L. Ter-Minassian-Saraga, E. Guyon, “Orientation of a nematic liquid crystal by suitable boundary surfaces,” Solid State Commun. 11(9), 1227–1230 (1972).
    [CrossRef]
  13. J. Cognard, “Alignment of nematic liquid crystals and their mixtures,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 1(Suppl.), 1–77 (1982).
  14. V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
    [CrossRef]
  15. S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University, 1992).
  16. A. P. Gardymova, V. Ya. Zyryanov, V. A. Loiko, “Multistability in polymer-dispersed cholesteric liquid crystal film doped with ionic surfactant,” Tech. Phys. Lett. 37(9), 805–808 (2011).
    [CrossRef]

2013

V. S. Sutormin, M. N. Krakhalev, V. Ya. Zyryanov, “The dynamics of the response of an electro-optic cell based on a nematic layer with controlled surface anchoring,” Tech. Phys. Lett. 39(7), 583–586 (2013).
[CrossRef]

2012

V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
[CrossRef]

2011

A. P. Gardymova, V. Ya. Zyryanov, V. A. Loiko, “Multistability in polymer-dispersed cholesteric liquid crystal film doped with ionic surfactant,” Tech. Phys. Lett. 37(9), 805–808 (2011).
[CrossRef]

2010

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

2009

V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
[CrossRef]

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

2005

L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
[CrossRef]

2000

L. Komitov, K. Ichimura, A. Strigazzi, “Light-induced anchoring transition in a 4,4’-disubstituted azobenzene nematic liquid crystal,” Liq. Cryst. 27(1), 51–55 (2000).
[CrossRef]

1994

A. G. Petrov, G. Durand, “Electric field transport of biphilic ions and anchoring transitions in nematic liquid crystals,” Liq. Cryst. 17(4), 543–554 (1994).
[CrossRef]

1983

G. E. Volovik, O. D. Lavrentovich, “Topological dynamics of defects: boojums in nematic drops,” Sov. Phys. JETP 58, 1159–1166 (1983).

1982

J. Cognard, “Alignment of nematic liquid crystals and their mixtures,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 1(Suppl.), 1–77 (1982).

1976

G. Ryschenkow, M. Kleman, “Surface defects and structural transitions in very low anchoring energy nematic thin films,” J. Chem. Phys. 64(1), 404–412 (1976).
[CrossRef]

1975

E. Dubois-Violette, P. G. De Gennes, “Local Frederiks transitions near a solid/nematic interface,” J. de Phys. Lett. 36, 255–258 (1975).

1972

J. E. Proust, L. Ter-Minassian-Saraga, E. Guyon, “Orientation of a nematic liquid crystal by suitable boundary surfaces,” Solid State Commun. 11(9), 1227–1230 (1972).
[CrossRef]

1933

V. K. Freedericksz, V. Zolina, “Forces causing the orientation of an anisotropic liquid,” Trans. Faraday Soc. 29, 919–930 (1933).
[CrossRef]

Araoka, F.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

Cognard, J.

J. Cognard, “Alignment of nematic liquid crystals and their mixtures,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 1(Suppl.), 1–77 (1982).

De Gennes, P. G.

E. Dubois-Violette, P. G. De Gennes, “Local Frederiks transitions near a solid/nematic interface,” J. de Phys. Lett. 36, 255–258 (1975).

Dhara, S.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

Dubois-Violette, E.

E. Dubois-Violette, P. G. De Gennes, “Local Frederiks transitions near a solid/nematic interface,” J. de Phys. Lett. 36, 255–258 (1975).

Durand, G.

A. G. Petrov, G. Durand, “Electric field transport of biphilic ions and anchoring transitions in nematic liquid crystals,” Liq. Cryst. 17(4), 543–554 (1994).
[CrossRef]

Felix, J.

L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
[CrossRef]

Freedericksz, V. K.

V. K. Freedericksz, V. Zolina, “Forces causing the orientation of an anisotropic liquid,” Trans. Faraday Soc. 29, 919–930 (1933).
[CrossRef]

Gardymova, A. P.

A. P. Gardymova, V. Ya. Zyryanov, V. A. Loiko, “Multistability in polymer-dispersed cholesteric liquid crystal film doped with ionic surfactant,” Tech. Phys. Lett. 37(9), 805–808 (2011).
[CrossRef]

Guyon, E.

J. E. Proust, L. Ter-Minassian-Saraga, E. Guyon, “Orientation of a nematic liquid crystal by suitable boundary surfaces,” Solid State Commun. 11(9), 1227–1230 (1972).
[CrossRef]

Helgee, B.

L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
[CrossRef]

Ichimura, K.

L. Komitov, K. Ichimura, A. Strigazzi, “Light-induced anchoring transition in a 4,4’-disubstituted azobenzene nematic liquid crystal,” Liq. Cryst. 27(1), 51–55 (2000).
[CrossRef]

Ishikawa, K.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

Jeong, S. M.

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

Kim, J. K.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

Kleman, M.

G. Ryschenkow, M. Kleman, “Surface defects and structural transitions in very low anchoring energy nematic thin films,” J. Chem. Phys. 64(1), 404–412 (1976).
[CrossRef]

Komitov, L.

L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
[CrossRef]

L. Komitov, K. Ichimura, A. Strigazzi, “Light-induced anchoring transition in a 4,4’-disubstituted azobenzene nematic liquid crystal,” Liq. Cryst. 27(1), 51–55 (2000).
[CrossRef]

Krakhalev, M. N.

V. S. Sutormin, M. N. Krakhalev, V. Ya. Zyryanov, “The dynamics of the response of an electro-optic cell based on a nematic layer with controlled surface anchoring,” Tech. Phys. Lett. 39(7), 583–586 (2013).
[CrossRef]

V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
[CrossRef]

V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
[CrossRef]

Lavrentovich, O. D.

G. E. Volovik, O. D. Lavrentovich, “Topological dynamics of defects: boojums in nematic drops,” Sov. Phys. JETP 58, 1159–1166 (1983).

Le, K. V.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

Loiko, V. A.

A. P. Gardymova, V. Ya. Zyryanov, V. A. Loiko, “Multistability in polymer-dispersed cholesteric liquid crystal film doped with ionic surfactant,” Tech. Phys. Lett. 37(9), 805–808 (2011).
[CrossRef]

Matharu, A.

L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
[CrossRef]

Petrov, A. G.

A. G. Petrov, G. Durand, “Electric field transport of biphilic ions and anchoring transitions in nematic liquid crystals,” Liq. Cryst. 17(4), 543–554 (1994).
[CrossRef]

Prishchepa, O. O.

V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
[CrossRef]

V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
[CrossRef]

Proust, J. E.

J. E. Proust, L. Ter-Minassian-Saraga, E. Guyon, “Orientation of a nematic liquid crystal by suitable boundary surfaces,” Solid State Commun. 11(9), 1227–1230 (1972).
[CrossRef]

Ryschenkow, G.

G. Ryschenkow, M. Kleman, “Surface defects and structural transitions in very low anchoring energy nematic thin films,” J. Chem. Phys. 64(1), 404–412 (1976).
[CrossRef]

Shabanov, A. V.

V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
[CrossRef]

Strigazzi, A.

L. Komitov, K. Ichimura, A. Strigazzi, “Light-induced anchoring transition in a 4,4’-disubstituted azobenzene nematic liquid crystal,” Liq. Cryst. 27(1), 51–55 (2000).
[CrossRef]

Sutormin, V. S.

V. S. Sutormin, M. N. Krakhalev, V. Ya. Zyryanov, “The dynamics of the response of an electro-optic cell based on a nematic layer with controlled surface anchoring,” Tech. Phys. Lett. 39(7), 583–586 (2013).
[CrossRef]

V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
[CrossRef]

Takezoe, H.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

Ter-Minassian-Saraga, L.

J. E. Proust, L. Ter-Minassian-Saraga, E. Guyon, “Orientation of a nematic liquid crystal by suitable boundary surfaces,” Solid State Commun. 11(9), 1227–1230 (1972).
[CrossRef]

Volovik, G. E.

G. E. Volovik, O. D. Lavrentovich, “Topological dynamics of defects: boojums in nematic drops,” Sov. Phys. JETP 58, 1159–1166 (1983).

Zolina, V.

V. K. Freedericksz, V. Zolina, “Forces causing the orientation of an anisotropic liquid,” Trans. Faraday Soc. 29, 919–930 (1933).
[CrossRef]

Zyryanov, V. Ya.

V. S. Sutormin, M. N. Krakhalev, V. Ya. Zyryanov, “The dynamics of the response of an electro-optic cell based on a nematic layer with controlled surface anchoring,” Tech. Phys. Lett. 39(7), 583–586 (2013).
[CrossRef]

V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
[CrossRef]

A. P. Gardymova, V. Ya. Zyryanov, V. A. Loiko, “Multistability in polymer-dispersed cholesteric liquid crystal film doped with ionic surfactant,” Tech. Phys. Lett. 37(9), 805–808 (2011).
[CrossRef]

V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
[CrossRef]

Appl. Phys. Lett.

J. K. Kim, F. Araoka, S. M. Jeong, S. Dhara, K. Ishikawa, H. Takezoe, “Bistable device using anchoring transition of nematic liquid crystals,” Appl. Phys. Lett. 95(6), 063505 (2009).
[CrossRef]

L. Komitov, B. Helgee, J. Felix, A. Matharu, “Electrically commanded surfaces for nematic liquid crystal displays,” Appl. Phys. Lett. 86(2), 023502 (2005).
[CrossRef]

J. Appl. Phys.

J. K. Kim, K. V. Le, S. Dhara, F. Araoka, K. Ishikawa, H. Takezoe, “Heat-driven and electric-field-driven bistable devices using dye-doped nematic liquid crystals,” J. Appl. Phys. 107(12), 123108 (2010).
[CrossRef]

J. Chem. Phys.

G. Ryschenkow, M. Kleman, “Surface defects and structural transitions in very low anchoring energy nematic thin films,” J. Chem. Phys. 64(1), 404–412 (1976).
[CrossRef]

J. de Phys. Lett.

E. Dubois-Violette, P. G. De Gennes, “Local Frederiks transitions near a solid/nematic interface,” J. de Phys. Lett. 36, 255–258 (1975).

JETP Lett.

V. S. Sutormin, M. N. Krakhalev, O. O. Prishchepa, V. Ya. Zyryanov, “Electrically controlled local Fredericksz transition in a layer of a nematic liquid crystal,” JETP Lett. 96(8), 511–516 (2012).
[CrossRef]

V. Ya. Zyryanov, M. N. Krakhalev, O. O. Prishchepa, A. V. Shabanov, “Inverse regime of ionic modification of surface anchoring in nematic droplets,” JETP Lett. 88(9), 597–601 (2009).
[CrossRef]

Liq. Cryst.

L. Komitov, K. Ichimura, A. Strigazzi, “Light-induced anchoring transition in a 4,4’-disubstituted azobenzene nematic liquid crystal,” Liq. Cryst. 27(1), 51–55 (2000).
[CrossRef]

A. G. Petrov, G. Durand, “Electric field transport of biphilic ions and anchoring transitions in nematic liquid crystals,” Liq. Cryst. 17(4), 543–554 (1994).
[CrossRef]

Mol. Cryst. Liq. Cryst.

J. Cognard, “Alignment of nematic liquid crystals and their mixtures,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 1(Suppl.), 1–77 (1982).

Solid State Commun.

J. E. Proust, L. Ter-Minassian-Saraga, E. Guyon, “Orientation of a nematic liquid crystal by suitable boundary surfaces,” Solid State Commun. 11(9), 1227–1230 (1972).
[CrossRef]

Sov. Phys. JETP

G. E. Volovik, O. D. Lavrentovich, “Topological dynamics of defects: boojums in nematic drops,” Sov. Phys. JETP 58, 1159–1166 (1983).

Tech. Phys. Lett.

V. S. Sutormin, M. N. Krakhalev, V. Ya. Zyryanov, “The dynamics of the response of an electro-optic cell based on a nematic layer with controlled surface anchoring,” Tech. Phys. Lett. 39(7), 583–586 (2013).
[CrossRef]

A. P. Gardymova, V. Ya. Zyryanov, V. A. Loiko, “Multistability in polymer-dispersed cholesteric liquid crystal film doped with ionic surfactant,” Tech. Phys. Lett. 37(9), 805–808 (2011).
[CrossRef]

Trans. Faraday Soc.

V. K. Freedericksz, V. Zolina, “Forces causing the orientation of an anisotropic liquid,” Trans. Faraday Soc. 29, 919–930 (1933).
[CrossRef]

Other

S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic of nematic structure transition from the homeoplanar director configuration to the twisted one. (a) Electric field is switched off. The boundary condition at the top substrate is homeotropic whereas the anchoring on the bottom substrate is planar. (b) At an applied steady voltage, the top substrate’s anchoring changes from homeotropic to planar and yet the planar boundary condition remains invariable on the bottom substrate. The rubbing directions at the substrates are mutually perpendicular. CTA+ are the surface-active cations of cethyltrimethyl ammonium; Br are the bromide anions.

Fig. 2
Fig. 2

Microphotographs of optical textures of the nematic 5CB layer doped with CTAB under crossed polarizers (top and middle rows) and in the parallel-polarizer scheme (bottom row) made at different β angles between the rubbing direction of the bottom substrate (R1) and the transmission axis of the polarizer. (а) β = 0°, (b) β = 45°, and (c) β = 90°. The top row corresponds to the initial state; the middle and bottom rows present the textures at the applied voltage of 3.3 V. Polarizer directions are represented by the double arrows. R2 is the rubbing direction of the top substrate.

Fig. 3
Fig. 3

Oscillograms of optical response of LC cells containing nematic 5CB doped with CTAB in the crossed-polarizer scheme. (a) A cell with β = 45° switched by a monopolar voltage pulse, (b) a cell with β = 0° or 90° switched by a monopolar voltage pulse, and (c) a cell with β = 0° or 90° switched by a bipolar voltage pulse. τon is the field-on time and τoff is the field-off time.

Metrics