May 22, 2013 A.I. Frank ISINN 21, Alushta 1

Goos – Hänchen effect in neutron

optics

A. Frank FLNP of JINR, Dubna, Russia

frank@nf.jinr.ru

May 22, 2013 A.I. Frank ISINN 21, Alushta 2 2

Goos – Hänchen effect–

Longitudinal shift of the wave beam at total reflection

Total inner reflection

May 22, 2013 A.I. Frank ISINN 21, Alushta 3 3

F. Goos und О. Hänсhen, Ann. der Phys. 1, 333 (1947).

F. Goos und H. Lindberg-Hanchen, Ann. der Phys. 5, 251 (1949)

First observation of the G.-Ch. effect at total

reflection 1947-49 yrs.

May 22, 2013 A.I. Frank ISINN 21, Alushta 4

Goos-Hänchen effect in acoustic

A. Schoch, Acustica 2, 1 (1952)

From: L.M. Brechovskikh, Usp. Fiz. Nauk [Sov.Phys. Uspechy] 50, 539 (1953)

May 22, 2013 A.I. Frank ISINN 21, Alushta 5

Modern optical experiment for the observation G.-H.

effect

May 22, 2013 A.I. Frank ISINN 21, Alushta 6

1. А.А. Seregin. Surface shift of neutron at reflection. Yadernaya Physica

[ Sov. Journ. Nuclear Physics] 33, 1173 (1981). First proposal

2. M. Maaza, B.Pardo. On the possibility to observe the longitudinal Goos-

Hänchen shift with cold neutrons. Opt.Comm. 142, 84 (1997). (Proposal

and calculations based on the Renard’s theory)

3. V.K. Ignatovich. Neutron reflection from condensed matter, the Goos–

Hänchen effect and coherence. Phys. Lett. A, 36, 322 (2004). (Theory)

4. V. -O. de Haan, J.Plomp, Th. M. Rekveldt, W. H. Kraan, and Ad A. van

Well. Observation of the Goos-Hänchen Shift with Neutrons.

Phys.Rev.Lett. 010401 (2010). (Observation of the pseudo Larmor precession)

G.-H. shift and neutron optics

May 22, 2013 A.I. Frank ISINN 21, Alushta 7

x

Y

Geometric reflection

Total reflectiom

G.-Ch shift and the stationary phase principle

К. Artmann, Ann. der Phys. 2, 87 (1948)

L.M. Brechovskikh, Usp. Fiz. Nauk 50, 539 (1953)

H. Hora, Optik 17, 409 (1960)

J. L. Carter and H. Hora. J. Opt. Soc. Am, 61, 1640, (1971)

Maximum of intensity

Geometric reflection

Artmann’s formula

X – component of the reflected wave function

in XZ plane is a superposition

Two waves are falling at angles θ and θ+Δθ at the border of matter Z=0

May 22, 2013 A.I. Frank ISINN 21, Alushta 8

G.-Ch shift the matter wave and its relation with the

group delay time at reflection of particle

Group delay time

(Bohm, Wigner, 1952-55)

May 22, 2013 A.I. Frank ISINN 21, Alushta 9

Delay time and the G.-Ch shift at reflection from the potential barrier

U

E

May 22, 2013 A.I. Frank ISINN 21, Alushta 10

Renard’s theory

d

x

Y

R. H. Renard. Total Reflection: A New Evaluation of the Goos-Hanchen Shift. J. Opt. Soc. Am. 54, 1190 (1964)

May 22, 2013 A.I. Frank ISINN 21, Alushta 11 11

Comparing of the result of Artmann-Hora-Brechovskikh

with Renards’result

Artmann-Hora-Brechovskikh Renard

Group delay time at reflection from barrier

May 22, 2013 A.I. Frank ISINN 21, Alushta 12 12

0 50 100 150 200 250

0

20

40

60

80

100

Re

fle

ctio

n tim

e (

nse

c)

Enorm

(neV)

Group time

Ren

Reflection time from Ni

Group delay time at reflection and effective time , following

from the Renard’s formlula

Contradictions between Artmann’s and Renard”s

results did not discussed during the long time

May 22, 2013 A.I. Frank ISINN 21, Alushta 13 13

The reason of contradiction and correction to the

Renard’s approach

K. Yasimoto, Y.Oishi. J.Apll. Phys. 54, 2170 (1983)

V. G. Fedoseyev J. Opt. Soc. Am. A 3, 826, (1986)

d

x

Y

Artmann-Hora formula

May 22, 2013 A.I. Frank ISINN 21, Alushta 14

Since Atrmann’s and Renard’s approaches (with correction

of Yasimoto-Oishi-Fedoseev) lead to the identical result

We can believe that our conclusion concerning the relation

of Goos-Hänchen shift with group delay time is correct

May 22, 2013 A.I. Frank ISINN 21, Alushta 15 15

Giant G.-Ch. shift

at reflection from multilayred structures

T. Tamir, H.L. Bertoni, J.Opt.Soc.Am. 61, 1397 (1971)

May 22, 2013 A.I. Frank ISINN 21, Alushta 16 16

50 100 150 200 250

0

50

100

150

200

250

300

Quartz film (90nm) at Ni

Energy (E )

Re

fle

cti

on

tim

e (

ns

)

Giant G-Ch. shift of the neutron beam

T. Tamir, H.L. Bertoni, J.Opt.Soc.Am. 61, 1397 (1971)

V.Ignatovich, 2004

10 20 30 40 50 60 70 80 90 100

20

40

60

80

100

120

140

160

180

200

70nm Si at Quartz

Re

fle

cti

on

tim

e (

ns

)

Energy (E

Reflection time at neutron reflection from Si film

(60nm) deposed at the quartz substrate (ns)

Reflection time at neutron reflection from quatz

film (90nm) deposed at Ni substrate

The inset shows the phase of the reflected wave

50 100 150 200 250

0

2

4

6

8

10

12

14

16

18

Ph

as

e

Energy (E )

U E

A films at the wafer (total reflection)

May 22, 2013 A.I. Frank ISINN 21, Alushta 17 17

Fabry-Perrot interferometer (Neutron Interference filter)

E

60 70 80 90 100 110 120

0

50

100

150

200

250

0,0

0,2

0,4

0,6

0,8

1,0

3-layer Ni-Ti-Ni

23-19,5-23nm

Re

fle

cti

vit

y

Re

fle

cti

on

tim

e (

ns

)

Energy (E

Reflection time and reflection coefficient for neutron reflection

from the three layered resonant structure NiMo-Ti-NiMo

Giant longitudinal shift

May 22, 2013 A.I. Frank ISINN 21, Alushta 18 18

Negative longitudinal shift

May 22, 2013 A.I. Frank ISINN 21, Alushta 19 19

Negative longitudinal shift in optics and acoustics

1. T. Tamir, H.L. Bertoni, J. Opt. Soc. Am. 61 1397(1971)

2. M. A. Breazeale and M. A. Torbett. Appl. Phys. Lett. 29 456 (1976)

A. Aniĉin, R. Fazlić and M. Koprić . J. Phys. A: Math. Gen. 11, 1657 (1978).

T. Tamir, H.L. Bertoni, 1971

M. A. Breazeale and M. A. Torbett, 1976

May 22, 2013 A.I. Frank ISINN 21, Alushta 20 20

An example of the negative longitudinal shift detection in optics

May 22, 2013 A.I. Frank ISINN 21, Alushta 21 21

Reflection time for the Ni film (100nm) deposed at

the quartz wafer. The inset shows the phase of the

reflected wave.

Coefficient of reflection for the Ni film (100nm)

deposed at the quartz wafer.

Film at the substrate (above barrier reflection)

Negative group time and negative longitudinal shift

200 250 300 350 400

-500

-400

-300

-200

-100

0

100 Thin film of Ni (100nm) at Quartz wafer

Re

fle

ctio

n tim

e

Energy (E )

200 250 300 350 400

0,01

0,1

1

Energy (E )

Re

fle

ctivity

200 250 300 350 400 450

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

Energy (E )

Pha

se o

f th

r re

flection

wave

May 22, 2013 A.I. Frank ISINN 21, Alushta 22 22

Asymmetric interference filter

E

0 50 100 150 200 250

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

2,6

Ni-Ti-Ni

23-13-33 nm

Ph

as

e o

f th

e r

efl

ec

ted

wa

ve

Energy (E

0 50 100 150 200 250

-100

-80

-60

-40

-20

0

20

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

Ni-Ti-Ni

23-13-33 nm

Re

fle

cti

vit

y

Re

fle

cti

on

tim

e (

ns

)

Energy (E

Group reflection time and reflection coefficient for the

asymmetric three-layered resonant structures NiMo-Ti-NiMo

Phase of the reflection wave

Negative group time and negative lateral shift

May 22, 2013 A.I. Frank ISINN 21, Alushta 23

On the measurement of the group reflection

time: Larmor clock

May 22, 2013 A.I. Frank ISINN 21, Alushta 24

Reflection of sate with precessing spin (in magnetic field B).

Group reflection time

Baz’, 1966

In the limit

Baz’ 1967

A.I. Frank et al.. 2001

May 22, 2013 A.I. Frank ISINN 21, Alushta 25

Delay time or precession angle was measured

a) for the case of refraction

d

1dd d

nv

n

vvt

n

0 2 4 6 8 10 12 14 16 18

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

16

18Quartz sample

De

lay t

ime

(n

se

c)

Thickness of the sample (mm)

Ph

ase

sh

ift

(de

gre

e)

810t

t

A.I. Frank, I.V. Bondarenko, A.V. Kozlov, et al.. Physica B 297, (2001) 307

May 22, 2013 A.I. Frank ISINN 21, Alushta 26 26

-10 0 10 20 30 40 50 60

0

1000

2000

3000

4000

5000 Direct transmission

(refraction in Si)

Bragg peak

= 3.1x10-7sec

= 6.8x10-8sec

Ciu

nts

/ 2

00

se

c

Rotation angle (mrad)

A.I. Frank, I.Anderson, I.V. Bondarenko, et al. Phys.of At. Nuclei, 65, 2009 ( 2002)A.I.Frank,

I.V.Bondarenko, A.V.Kozlov, G.Ehlers and P. Høghøj. In: Neutron Spin Echo Spectroscopy,

Eds. F.Mezei, C.Pappas and T.Gutbertlet. Springer, pp164-175.

Si wafer (two-side polished)

MultilayersNiV(7) (130A+Ti 70A)x30

Gd absorber 700-100A

b) for the case of Bragg reflection

Delay time or precession angle was measured

May 22, 2013 A.I. Frank ISINN 21, Alushta 27

To the measurement of the giant G.-Ch. shift.

Time of flight reflectometry

May 22, 2013 A.I. Frank ISINN 21, Alushta 28

d

Detector

Neutron time of flight reflectometer

v

x

v

y

v

0

200 250 300 350 400

-500

-400

-300

-200

-100

0

100 Thin film of Ni (100nm) at Quartz wafer

Re

fle

ctio

n tim

e

Energy (E )

Vy 7 m/s 400ns d 2.8 mkm

Resonant character of the effect makes

possible to extract signal in

reflectometric time of flight experiment

May 22, 2013 A.I. Frank ISINN 21, Alushta 29 29

Conclusion

1. Longitudinal Goose – Chänchen shift always

proportional to the reflection group delay time

2. Group delay time of the neutron wave from the

multilayered structures may exceed the total

reflection time by two order of magnitude and (or)

may be negative

3. The method of the measurement of group delay time,

Larmor clock is exist.

4. Giant and negative G. – Ch. shift are essentially

resonant phenomena and probably may be detected

in time of flight reflectometric experiment

May 22, 2013 A.I. Frank ISINN 21, Alushta 30

Thank you for your attention