• 검색 결과가 없습니다.

Volume 61, Number 3, 2011¸ 3 Z 4, pp. 268∼271

N/A
N/A
Info
다운로드
Protected

Academic year: 2021

Share "Volume 61, Number 3, 2011¸ 3 Z 4, pp. 268∼271"

Copied!
4
0
0

로드 중.... (전체 텍스트 보기)

전체 글

(1)

Volume 61, Number 3, 2011¸   3 Z 4, pp. 268∼271

New Physics: Sae Mulli (The Korean Physical Society), DOI: 10.3938/NPSM.61.268

° 

 Æ W ¥  Ö כ Ž; c 8 ýA 0 ù m É ’ Ò ×c Ü R 7 _T $ [° Ë Ñ8 ý M 2 ß Ã Å 

† ç

¡ ¬ £

ô

 Çz Œ ™@ /† < Ɠ § F g„   Ó ü t o † < Æõ , @ /„   306-791 (2011¸   1 Z 4 18{ 9  ~ à Î6 £ §, 2011¸   3 Z 4 8{ 9  > F  S X ‰& ñ )

· û

ª“ É r E $ ™Ý ¼_  à º  Y Us $  F g _  M

2

“   \  p u   H % ò † ¾ Ó`  ¦ ì  r$ 3 ô  Ç . €  $ , · û ª“ É r E $ ™Ý ¼\  _ K  | 9 5 Å q

 )

a Y Us $  F g _  4  ˜ Ð& ñ  ) a 1 l x † < Êà º\  ¦ ½ ¨ô  Ç . 4  ˜ Ð& ñ  ) a 1 l x † < Êà º\    H  K " f Y Us $  F g _  M

2

“   

\ 

¦ à ºu  > í ß –ô  Ç . { 9   F g _  ì ø Í â s  ß ¼  , E $ ™Ý ¼_  œ í& h  o   ú ª | 9 à º2 Ÿ ¤ M

2

“    / å L  y  7 £ x 

†

< Ê`  ¦ ˜ Ð# Œï  r  . ‘ : rë  H \  Å Ò# Q”   4  ˜ Ð& ñ  ) a 1 l x † < Êà º  H · û ª“ É r E $ ™Ý ¼\  _ K " f | 9 5 Å q ) a Y Us $  F g _  M

x2

“  



\  ¦   & ñ   H X <  6   x| ¨ c à º e ”  .

Ù þ

˜d ” # Q: 4 Ÿ ¤ ™ è& h , Ä ºÛ ¼ F g , ½ ¨€  à º , M

2

“   

M 2 Factor of a Laser Beam Focused by a Thin Lens

Soo Chang ∗

Department of Physics, Hannam University, Taejon 306-791 (Received 18 January 2011 : accepted 8 March 2011)

We analyze the degradation in the M

2

factor of a laser beam caused by the aberration of a thin lens. First, we formulate the fourth-order correction to a paraxial Gaussian beam focused by a thin lens. Then, we numerically evaluate the M

2

factor of the fourth-order corrected beam propagating through a thin lens. We show that the M

x2

factor increases rapidly either by increasing the incident beam radius or by decreasing the focal length of the lens. The fourth-order corrected wave function given here can be useful in determining the M

2

factor of a laser beam focused by a thin lens.

PACS numbers: 42.30.Va

Keywords: Complex source point, Gaussian beam, Spherical aberration, M

2

factor

I. " e  ] Ø

‚

 ' Ÿ  ƒ  ½ ¨ [1]\ " f Ä ºo   H Ä ºÛ ¼+ þ A Y Us $  F g s    H» ¡ ¤

% ò

% i \ " f 4 Ÿ ¤ ™ èà º & h F g " é ¶ \ " f  “ : r ½ ¨€   ü < 1 p x s  9 [2], “ ¦  ˜ Ð& ñ † ½ Ó`  ¦ — ¸¿ º Ÿ í† < Êr v €   4 Ÿ ¤ ™ è& h  ½ ¨€   ü <

{ 9

u ô  Ç  [3]  H  z  ´\    H  K " f é ß –{ 9  F g † < ƀ  `  ¦ t    H 4

Ÿ

¤ ™ è& h  ½ ¨€   _  „    õ & ñ `  ¦ á ÔY U3 A q-v Ø Ô  ñá Ô  r] X  & h  ì

 r [4] Ü ¼– Ð l Õ ü t ô  Ç Ê ê, F g‚   F g † < Æ& h    H  \  ¦ : Ÿ x K " f 4  ˜ Ð

&

ñ † ½ Ós  Ÿ í† < ʝ ) a Ä ºÛ ¼ F g _  1 l x † < Êà º`  ¦ Ä »• ¸ “ ¦, M 2 “  

∗

E-mail: [email protected]



\  ¦ ì  r$ 3 ô  Ç   e ”  . Õ ª   õ   H ¿ º > h_  Ï ã J] X €  Ü ¼– Ð s  À

Ò# Q”   E $ ™Ý ¼_   â Ä º– Ð / B I  – Ð S X ‰  © œ | ¨ c à º e ”  .

‘

: r  7 Hë  H“ É r · û ª“ É r E $ ™Ý ¼_  ½ ¨€  à º  | 9 5 Å q ) a Ä ºÛ ¼+ þ A Y

Us $  F g _  + þ AI \  # Q‹ "  % ò † ¾ Ó`  ¦ p u   H \  @ /K " f  7 H _  ô

 Ç . s \  ¦ 0 AK " f €  $ , á ÔY U3 A q-v Ø Ôy   ñá Ô  r] X  & h ì  r`  ¦



6   x K " f ¿ º > h_  F g † < ƀ  `  ¦ t    H 4  ˜ Ð& ñ † ½ Ós  Ÿ í† < ʝ ) a 4

Ÿ

¤ ™ è& h  ½ ¨€   _  F g‚   F g † < Æ& h    H  K \  ¦ ½ ¨ô  Ç . ½ ¨€  à º

 Ÿ í† < ʝ ) a F g‚   F g † < Æ& h    H  K \  ¦  „ ½ ÓÜ ¼– Ð Siegmans  ]

jî ß –ô  Ç Y Us $  F g _  M 2 “   \  ¦ à ºu  > í ß –ô  Ç . { 9   F g _  ì

ø Í â s  ß ¼  , E $ ™Ý ¼_  œ í& h  o   ú ª | 9 à º2 Ÿ ¤ M 2 “   

 / å L  y  7 £ x † < Ê`  ¦ ˜ Ð# Œï  r  . ‘ : rë  H \  Å Ò# Q”   4  ˜ Ð& ñ

-268-

(2)

· û

ª“ É r E $ ™Ý ¼\  _ K  | 9 5 Å q ) a Y Us $  F g _  M

2

“    –  © œ à º · Soo Chang -269-

Fig. 1. Propagation of a Gaussian beam through a thin lens with the radii of curvature R 1 and R 2 . The parax- ial waists of the incident, first refracted, and second re- fracted beams are located at distances z 1 , z 1 0 and z 2 0 from the lens surface, respectively. The waist radii of the in- cident, first refracted, and second refracted beams are denoted by w 1 , w 1 0 and w 0 2 , respectively. n 1 (or n 0 2 ) is the refractive index of the incident (or transmitted) medium, and n 0 1 (= n 2 ) is the refractive index of lens material.

 )

a 1 l x † < Êà º  H · û ª“ É r E $ ™Ý ¼\  _ K " f | 9 5 Å q ) a Y Us $  F g _  M x 2 “   \  ¦   & ñ   H X <  6   x| ¨ c à º e ”  .

II. °   Æ W ¥  Ö כ Ž; c 8 ýA 0 ù m É ’ Ò ×c Ü R 7 _T $ [° Ë Ñ8 ý 4 

| ºX N Ë]  §

Õ

ªa Ë > 1“ É r   H» ¡ ¤ œ í& h _  ì ø Í â s  w 1 s “ ¦ ”  / B N ×  æ _   © œ s

 λ“   Y Us $  F g s  / B GÒ  ¦ ì ø Í â R 1 õ  R 2 “   ¿ º > h_  ½ ¨€  Ü ¼

–

Ð s À Ò# Q”   · û ª“ É r E $ ™Ý ¼\  _ K " f D h– Ðî  r œ í& h \  | 9 5 Å q ÷ &



 H õ & ñ `  ¦ ˜ Ð# Œï  r  . F g † < Æ>   H z» ¡ ¤ \  › ' a K " f  r„   @ /g A s

 “ ¦ & ñ “ ¦, 2 " é ¶ ý a³ ð> _  " é ¶& h `  ¦ z» ¡ ¤ õ  E $ ™Ý ¼ €   s

 ë ß –   H & h \  ¿ º% 3  . R 1 õ  R 2   H / B GÒ  ¦×  æd ” s  ½ ¨€  _ 

š

¸ É rA á ¤ \  e ” `  ¦ M : € ª œ(+)_   Ҡ ñ\  ¦ ° ú   H  . n 1 õ  n 0 2 “ É r y Œ • y

Œ

• { 9   x 9 Ø  ¦   B | 9 _  Ï ã J] X Ò  ¦`  ¦ _ p  “ ¦, n 0 1 (= n 2 )“ É r E $

™Ý ¼ F | 9 _  Ï ã J] X Ò  ¦`  ¦    · p .

‚ Ã

Г ¦ë  H‰  ³ [1] \   Ø Ô€  , Y U{ 9 o  % ò % i s  b 1 = n 1 πw 2 1 /λ“   Y Us $  F g s  ' Í   P : F g † < ƀ  `  ¦ : Ÿ x õ ô  Ç Ê ê D h

–

Ðî  r œ í¨ î €   0 A_  & h  (x 0 1 , z 0 1 ) \  • ¸² ú ˜Ù þ ¡`  ¦ M :, 4  ˜ Ð& ñ  ) a

1 l x † < Êà º  H U 1 0 (x 0 1 , z 1 0 ) w A 0 1 exp

"

− x 0 1 2

w 1 0 2 − x 0 1 4

4w 0 1 2 b 0 1 2 − iπ x 0 1 4 4

(z 1 0 + ib 0 1 ) 4 (ib 0 1 ) 4 S 1

# (1) s

  ) a  . 0 Ad ” \ " f A 0 1 “ É r  © œÃ ºs “ ¦, w 0 1 “ É r ' Í   P : Ï ã J] X F g _

 œ í& h  ì ø Í â s  9, Y U{ 9 o  % ò % i “ É r b 0 1 = n 0 1 πw 0 1 2 /λ s  .

¢

¸ô  Ç ' Í   P : €  \  @ /ô  Ç   H» ¡ ¤ Ô  ¦  | ¾ Ó Q 1 = n 0 1

z 0 1 + ib 0 1 − n 0 1 R 1

= n 1 z 1 + ib 1

− n 1 R 1

(2) _

 6   x # Q– Ð ³ ð‰ & ³ ) a à º > à º S 1 = Q 3 1 1

n 0 1 3 − 1 n 3 1

!

+ Q 2 1 1 R 1

 1 n 0 1 − 1

n 1

 (3)

  6   x ÷ &% 3  .



6 £ § Ü ¼– Ð d ” (1)_  1 l x † < Êà º ¿ º   P : F g † < ƀ  \  _ K 

"

f | 9 5 Å q ÷ &  H õ & ñ • ¸ ‚ à Г ¦ë  H‰  ³ [1]\ " f ƒ  / å L ) a á ÔY U3 A q-v  Ø

Ôy   ñá Ô  r] X  & h ì  r _  F g‚   F g † < Æ& h    H  \  ¦ : Ÿ x K " f > í ß –

| ¨

c à º e ”   [5]. Õ ª   õ \  ¦ & ñ o  €   ¿ º   P : F g † < ƀ  `  ¦ t  è ß

– Ê ê D h– Ðî  r œ í¨ î €   0 A_  & h  (x 0 2 , z 2 0 ) \  • ¸² ú ˜ô  Ç 4  ˜ Ð& ñ

 )

a F g _  1 l x † < Êà º  H U 2 0 (x 0 2 , z 2 0 )

w A 0 2 exp

"

− x 0 2 2

w 2 0 2 − x 0 2 4

4w 0 2 2 b 0 2 2 − iπ x 0 2 4 4

(z 2 0 + ib 0 2 ) 4

(ib 0 2 ) 4 (S 1 + S 2 )

#

(4) s

  ) a  . 0 Ad ” \ " f A 0 2 “ É r  © œÃ ºs “ ¦, w 2 0 “ É r ¿ º   P : Ï ã J] X F g _

 œ í& h  ì ø Í â s  9, Y U{ 9 o  % ò % i “ É r b 0 2 = n 0 2 πw 2 0 2 /λ s  .

d ”

(1)õ   ð ø Ít – Ð ¿ º   P : €  \  @ /ô  Ç   H» ¡ ¤ Ô  ¦  | ¾ Ó Q 2 = n 0 2

z 0 2 + ib 0 2 − n 0 2 R 2

= n 0 1

z 1 0 + ib 0 1 − n 0 1 R 2

, (5) _

 6   x # Q– Ð ³ ð‰ & ³ ) a à º > à º S 2 = Q 3 2 1

n 0 2 3 − 1 n 0 1 3

!

+ Q 2 2 1 R 2

 1 n 0 2 − 1

n 0 1



, (6)

  6   x ÷ &% 3  .

ô

 Ǽ # , Y U{ 9 o  % ò % i  b 1 ü < b 0 1 Õ ªo “ ¦ b 0 2 s  0\    H] X ½ + É  â Ä

º, S j õ  Q j   H y Œ •y Œ • j€  \  @ /ô  Ç 4  ½ ¨€  à º  > à ºü <   Z

… ] j– Ð Ô  ¦  | ¾ Óõ  ° ú   ”    [6].

III. 4  | ºX N Ë]  §T  M 2 ß Ã Å ; c Q V À W ¥ „ ÇÊ Ý

d ”

(4)\  Å Ò# Q”   4  ˜ Ð& ñ  ) a Y Us $  F g _  ”  ; Ÿ ¤ † < Êà º s 



© œ& h “   Ä ºÛ ¼ † < Êà º– РÒ'  # Á # Qè ß – & ñ • ¸\  ¦ ¶ ú ˜( R˜ Ðl  0 A K

" f M 2 “   \  ¦ > í ß –K ˜ Ð . d ” (4)_  1 l x \  @ /ô  Ç / B N ç ß – Å

Ò à º ì  r Ÿ í  H É Òo \  & h ì  r V 2 0 (f x , z 0 2 ) =

Z

dx 0 2 U 2 0 (x 0 2 , z 2 0 ) exp(−i2πf x x 0 2 ) (7) Ü

¼– Ð   è ­ q à º e ”   H X <, f x   H x ~ ½ ӆ ¾ Ó / B N ç ß – Å Ò à º\  ¦ _ p  ô

 Ç . s ] j 0 Au  x 9 / B N ç ß –Å Ò à º\  @ /ô  Ç 2  — ¸F ' pà Ô\  ¦ y Œ • y

Œ

•

< x 0 2 2 > = R dx 0 2 x 0 2 2 |U 2 0 (x 0 2 , z 0 2 )| 2 R dx 0 2 |U 2 0 (x 0 2 , z 0 2 )| 2 ,

< f x 2 > = R df x f x 2 |V 2 0 (f x , z 2 0 )| 2

R df x |V 2 0 (f x , z 2 0 )| 2 (8)

(3)

-270- ô  Dz D GÓ ü t o † < Æ rt  “D hÓ ü t o ”, Volume 61, Number 3, 2011¸   3 Z 4

Fig. 2. The M x 2 factor of an aberrated laser beam that is plotted as a function of the Coddington shape factor q, where we let z 1 = 0, w 1 = 5.0 mm, λ = 632.8 nm, n 1 = n 0 2

= 1.0, n 0 1 = 1.5, and f 0 = 100 mm. The degradation in the M x 2 factor depends upon the shape factor of the lens, The M x 2 factor has a minimum at q w 0.7.



“ ¦ ¿ º€  , x~ ½ ӆ ¾ Ó M 2 “     H M x 2 = 4π

q

< x 0 2 2 >< f x 2 > (9) ü

< ° ú  s  & ñ _   ) a   [7]. d ” (4)\ " f 4  ˜ Ð& ñ † ½ Ós  Á ºr  | ¨ c  â Ä

º, M x 2 “     H 1 s   ) a    H  z  ´`  ¦ Å Ò3 l q K  ô  Ç . 7 £ ¤,  1

l

x † < Êà º s  © œ& h “   Ä ºÛ ¼† < Êà º{ 9  M : M x 2 “     H 1 s   ) a



.

Figure 2  H · û ª“ É r E $ ™Ý ¼\  _ K " f | 9 5 Å q ) a Y Us $  F g _  M x 2 “   \  ¦  ï` ç — : r + þ AI “   

q = R 2 + R 1

R 2 − R 1 (10) _

 † < Êà º– Ð    · p / B G‚  s  . # Œl " f E $ ™Ý ¼_  Ê ê~ ½ Ó œ í& h   o

 f 0 `  ¦

n 0 2

f 0 = n 0 1 − n 1 R 1

+ n 0 2 − n 0 1 R 2

(11) ü

< ° ú  s  & ñ _  “ ¦, f 0 = 100 mm – Ð ¿ º% 3  .   É r   à º[ þ t

“

É r z 1 = 0, w 1 = 5.0 mm, λ = 632.8 nm, n 1 = n 0 2 = 1.0, Õ

ªo “ ¦ n 0 1 = 1.5 ü < ° ú  s  ‚  × þ ˜÷ &% 3  . Fig.2  H M x 2 “   

 q w 0.7\ " f þ j™ èe ” `  ¦ ˜ Ð# Œï  r  . à º > à º_  ½ + Ë`  ¦ ¶ ú ˜ (

R˜ Ѐ   Õ ª s Ä »\  ¦ · ú ˜ à º e ”  . { 9   F g _  Y U{ 9 o  % ò % i s  b 1 = n 1 πw 2 1 /λ w 124 m– Ð" f z 1 x 9 f 0 \  q K " f B Ä º ß ¼ l

 M :ë  H \  n 1 = n 0 2 = 1.0{ 9   â Ä º d ” (3)õ  d ” (6)_  à º >  Ã

º ½ + ˓ É r

S 1 +S 2 w (q + 1) 3 + (2n 0 1 − q − 1) 2 (2n 0 1 2 − q − 1) 8f 03 (n 0 1 − 1) 2 n 0 1 2 (12)

Fig. 3. The M x 2 factor of an aberrated laser beam plot- ted as a function of the incident beam radius w 1 . The Coddington shape factor of a thin lens is given by q

= 0.0(solid line), 0.7(dashed line), 1.0(dotted line), and 2.0(dash-dotted line), while the focal length of the lens is fixed at f 0 = 100 mm. Other parameters are the same as in Fig. 2.

ü

< ° ú  s    H   | ¨ c à º e ”  .   " f ∂(S 1 + S 2 )/∂q = 0 “  

›

¸| `  ¦ ¹ 1 ÔÜ ¼€  

q w 2(n 0 1 2 − 1)

n 0 1 + 2 (13)

`

 ¦ % 3   H  . n 0 1 = 1.5 s €   q w 0.7\ " f à º  þ j™ ès “ ¦, s

M : M x 2 “   • ¸ þ j™ è  ) a  .

Figure 3“ É r œ í& h  o  f 0 = 100 mm s “ ¦ + þ AI “   

"

f– Ð   É r · û ª“ É r E $ ™Ý ¼\  _ K " f Ï ã J] X  ) a Y Us $  F g _  M x 2 “  



\  ¦ { 9   F g _  ì ø Í â w 1 _  † < Êà º– Ð Ã ºu  > í ß –ô  Ç   õ s  .

#

Œl " f  ï` ç — : r + þ AI “   \  ¦ y Œ •y Œ • q = 0.0(z  ´‚  ), 0.7( W

‚

 ), 1.0(& h ‚  ), 2.0(1& h   W‚  ) “ ¦ ¿ º% 3 Ü ¼ 9,   É r   à º [

þ

t“ É r Fig.2 _   â Ä ºü < 1 l x{ 9   . M x 2 “     H { 9   F g _  ì ø Í

 â

s   Œ •Ü ¼€   1\    H] X  t ë ß –, { 9   F g _  ì ø Í â s  & t €   /

å L  y  7 £ x    H  ⠆ ¾ Ó`  ¦ ˜ Г   . : £ ¤ y , à º  þ j™ è“   q

= 0.7(  W‚  ){ 9  M :,  © œ …  ;…  ;y  7 £ x ô  Ç .

Figure 4  H + þ AI “    q w 0.7s “ ¦ œ í& h  o  " f– Ð



 É r · û ª“ É r E $ ™Ý ¼\  _ K " f Ï ã J] X  ) a Y Us $  F g _  M x 2 “   \  ¦ { 9

  F g _  ì ø Í â w 1 _  † < Êà º– Ð Ã ºu  > í ß –ô  Ç   õ s  . # Œ l

" f E $ ™Ý ¼_  œ í& h  o \  ¦ f 0 = 50 mm(z  ´‚  ), 100 mm( W

‚

 ), 200 mm(& h ‚  ), 300(1& h   W‚  ) “ ¦ ¿ º% 3 Ü ¼ 9,   É r



 à º[ þ t“ É r Fig.2 _   â Ä ºü < 1 l x{ 9   . + þ AI “    ° ú  `  ¦  â Ä

º, œ í& h  o  |   E $ ™Ý ¼{ 9 à º2 Ÿ ¤ { 9   F g _  ì ø Í â s  & 4 R• ¸ M x 2 “    …  ;…  ;y  7 £ x    H  ⠆ ¾ Ó`  ¦ ˜ Ð# Œï  r  . Õ ª s Ä »



 H d ” (12)\ " f ¹ 1 Ô`  ¦ à º e ”  . à º > à º_  ½ + ˓ É r œ í& h  o  _

 [ j] jY  L \  ì ø Íq Y V l  M :ë  H \  œ í& h  o  U  ´€  , E $ ™Ý ¼ _

 à º  / å L  y  y Œ ™™ è l  M :ë  H s  .

(4)

· û

ª“ É r E $ ™Ý ¼\  _ K  | 9 5 Å q ) a Y Us $  F g _  M

2

“    –  © œ à º · Soo Chang -271-

Fig. 4. The M x 2 factor of an aberrated laser beam plotted as a function of the incident beam radius w 1 , where we let q w 0.7 and f = 50 mm(solid line), 100 mm(dashed line), 200 mm(dotted line), and 300 mm(dash-dotted line). Other parameters are the same as in Fig. 2.

{ 9

ì ø Í& h Ü ¼– Ð d ” (4)\  Å Ò# Q”   4  ˜ Ð& ñ  ) a Y Us $  F g _   1

l

x † < Êà º  H · û ª“ É r E $ ™Ý ¼\  _ K " f | 9 5 Å q ) a Y Us $  F g _  M x 2 “  



\  ¦   & ñ   H X <  6   x| ¨ c à º e ”  .

IV. + s Ç Â ] Ø

· û

ª“ É r E $ ™Ý ¼_  ½ ¨€  à º  Y Us $  F g _  M 2 “   \  p u 



 H % ò † ¾ Ó`  ¦ ì  r$ 3  % i  . €  $ , á ÔY U3 A q-v Ø Ôy   ñá Ô  r] X  & h  ì

 r _  F g‚   F g † < Æ& h    H  \  ¦ : Ÿ x K " f · û ª“ É r E $ ™Ý ¼\  _ K  | 9 5 Å q

 )

a 4  ˜ Ð& ñ  ) a Y Us $  F g _  1 l x † < Êà º\  ¦ % 3 % 3  . ½ ¨€  à º 

 Ÿ í† < ʝ ) a   H  K \  ¦  „ ½ ÓÜ ¼– Ð Y Us $  F g _  M 2 “   \  ¦ à º u

 > í ß – % i  . { 9   F g _  ì ø Í â s  ß ¼“ ¦, E $ ™Ý ¼_  œ í& h  o 

  ú ªÜ ¼€  , ½ ¨€  à º  7 £ x  l  M :ë  H \  M 2 “   • ¸ / å L   y

 7 £ x † < Ê`  ¦ ˜ Ð# ŒÅ Ò% 3  . ‘ : rë  H \  Å Ò# Q”   4  ˜ Ð& ñ  ) a Y U s

$  F g _  œ í¨ î €   † < Êà º  H · û ª“ É r E $ ™Ý ¼\  _ K " f | 9 5 Å q ) a F g _

 M 2 “   \  ¦   & ñ   H X <  6   x| ¨ c à º e ”  .

P

c p 8 ý ò k >

‘

: r ƒ  ½ ¨  H 2010¸   Ê êì ø Íl  ƒ  ½ ¨¸   l ç ß –\  à º' Ÿ ÷ &% 3 _ þ v m

 .

Y

c p w Š à U Ø ”  ô

[1] S. Chang, New Physics: Sae Mulli 60, 1216 (2010).

[2] G. A. Deschamps, Electron. Lett. 7, 684 (1971).

[3] M. Couture and P. A. Belanger, Phys. Rev. A 24, 355 (1981).

[4] M. Born and E. Wolf, Principles of Optics (Perga- mon, Oxford, 1980), p. 378.

[5] S. Chang, Optik, to be accepted (2011).

[6] W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), p. 15, 130.

[7] A. E. Siegman, Proc. SPIE 1224, 2 (1990).

수치

Fig. 1. Propagation of a Gaussian beam through a thin lens with the radii of curvature R 1 and R 2
Fig. 2. The M x 2 factor of an aberrated laser beam that is plotted as a function of the Coddington shape factor q, where we let z 1 = 0, w 1 = 5.0 mm, λ = 632.8 nm, n 1 = n 0 2
Fig. 4. The M x 2 factor of an aberrated laser beam plotted as a function of the incident beam radius w 1 , where we let q w 0.7 and f = 50 mm(solid line), 100 mm(dashed line), 200 mm(dotted line), and 300 mm(dash-dotted line)

참조

지금 다운로드하기 ( PDF - 4 페이지 - 405.31 KB )

관련 문서

Volume 62, Number 3, 2012¸ 3 Z 4, pp. 285∼288

We demonstrate that based on complete single Dirac theory at the surface, where disorder is properly taken into account, the thickness of the surface state or the fundamental

Volume 60, Number 8, 2010¸ 8 Z 4, pp. 827∼829

We are developing a dynamical model in which chemical freeze-out occurs at high temperatures and, in the ensuing expansion and cooling of the system, the numbers of each hadron

Volume 60, Number 3, 2010¸ 3 Z 4, pp. 316∼319

The phosphors were synthesized by changing the amounts of Y and Gd, and the crystalline structures and surface morphologies of the phosphors were investigated using X-ray

½ ¨ 7 Hë H À Sae Mulli (The Korean Physical Society), Volume 57, Number 1, 2008¸ 7 Z 4, pp. 32∼35

PACS numbers: 05.50.+q, 05.70.−a, 64.60.Cn, 75.10.Hk Keywords: Square-lattice Ising model, Partition function zeros. ∗

ƒ ½ ¨ 7 Hë H Sae Mulli (The Korean Physical Society), Volume 54, Number 5, 2007¸ 5 Z 4, pp. 409∼412

To control the emitted light from the laser engraved side of the fiber, used for the light-emitting-diode (LED) display, we prepared fiber array and then make grooves in the clad

ƒ ½ ¨ 7 Hë H Sae Mulli (The Korean Physical Society), Volume 52, Number 6, 2006¸ 6 Z 4, pp. 549∼552

The order of the relaxation time of electrons in a quantum dot within the Coulomb blockade region is calculated by applying a square-wave voltage pulse to the gate electrode.

ƒ ½ ¨ 7 Hë H Sae Mulli (The Korean Physical Society), Volume 49, Number 4, 2004 ¸ 10 Z 4, pp. 329∼332

We have produced a plastic aspherical lens by designing the optical system of a mobile phone camera that uses a 1/7inch(diagonal = 2.72 mm) CMOS type image sensor. The peak to

ƒ ½ ¨ 7 Hë H Sae Mulli (The Korean Physical Society), Volume 48, Number 3, 2004¸ 3 Z 4, pp. 213∼215

When a coil with multiple turns is connected to a battery instead of a constant-current source, we discuss and show by experiments how the magnetic field produced by the coil depends