Concept for Measuring Laser Beam-Quality Parameters.

Abstract

This paper provides brief descriptions of recent developments in the basic formulas and measurement methods for determining laser beam-quality. The M2 factor concept has been studied in order to describe the laser beam quality of real laser beams, including potentially multimode and arbitrarily distorted laser beams. The study shows that the M2 value can be determined by measuring the beam spot sizes around the beam-waist. In addition, various methods for measuring beam spot sizes are discussed. Finally, the beam quality of fiber-bundled diode lasers is evaluated by the moving-slit method. A good agreement is obtained between the theoretical and experimental beam propagation results. Key Words: Laser beam-quality, M2 factor, ABCD ray matrics , Knife-edge method, Slit method 1.‚Í ‚ ¶‚ß ‚É OEõ-Ê Žq ƒG ƒOE ƒN ƒg ƒ• ƒj ƒN ƒX ‚Ì •i •à ‚É ‚AE ‚à ‚È ‚¢,•ae '[ "I ‚È ƒOE •[ ƒU •[ '• 'u ‚ð Žg ‚¤ ‹@ ‰ï ‚ª '• ‚¦ ‚Ä ‚« ‚½ .ƒOE •[ ƒU •[ ‚ðˆµ‚ðˆµ ‚¤ ‰ß 'ö ‚Å ‚Í,Ží •X ‚Ì •ê-Ê ‚Å,ƒr •[ ƒ€ ‚ð ƒR ƒŠ ƒ• •[ ƒg ‚µ‚½ ‚è,•¬ ‚³ ‚-•W OEõ ‚· ‚é ‚± ‚AE ‚ª-v ‹• ‚³ ‚ê ‚é.‚µ ‚© ‚µ,Žû •· ‚È ‚Ç ‚ð •l-¶ ‚µ ‚Ä ‚à,ŽÀ •Û ‚Ì ƒOE •[ ƒU •[ ‚Å ‚Í OEv ŽZ 'Ê ‚è‚Ì ƒX ƒ| ƒb ƒgƒT ƒC ƒY ‚ª "¾ ‚ç ‚ê ‚È ‚¢ ‚± ‚AE‚ª '½ •X ‚ ‚é.‚» ‚Ì-•-R ‚Í,TEM00Šî-{ ‰¡ ƒ‚ •[ ƒh ƒOE •[ ƒU •[ ‚AE ‚³ ‚ê ‚Ä ‚¢ ‚Ä ‚à,'½ ‚-‚Ì '• 'u ‚Í •‚ ŽŸ ‰¡ ƒ‚ •[ ƒh‚ª •¬ "ü ‚µ,ƒr •[ ƒ€ •i Ž¿ ‚ð-ò ‰» ‚³‚¹ ‚Ä ‚¢ ‚é ‚© ‚ç ‚Å ‚ ‚é.-{ ˜_ • ¶ ‚Å ‚Í,ƒOE •[ ƒU •[ ƒr •[ ƒ€ ‚Ì •i Ž¿ ‚ðŽ¦ ‚·-Ê ‚AE ‚µ‚Ä •W •€ ‰» ‚ª •i ‚ß ‚ç ‚ê ‚Ä ‚¢ ‚éM2ˆö Žq ‚É ‚ ‚¢ ‚Ä ‰ð •à ‚· ‚é.‚± ‚̈ö‚̈ö Žq ‚Í,ƒOE •[ ƒU •[ ‚Ì ‰¡ ƒ‚ •[ ƒh•i Ž¿ ‚ð 'è-Ê ‰» ‚Å ‚« ‚é ‚¾ ‚¯ ‚Å ‚È ‚-,OE` Ž® "I ‚É •‚ ŽŸ ƒ‚ •[ ƒh ‚ð ŠÜ ‚ñ ‚¾ ƒr •[ ƒ€ "` "À ‚É ‚à"K-p ‚Å ‚« ‚é ‚½ ‚ß,ƒr •[ ƒ€ •Ý OEv ‚É OE ‡ ‚© ‚¹ ‚È ‚¢ "¹ ‹ï ‚É ‚È ‚è‚ ‚ ‚ ‚é .OEã "¼ ‚Å ‚Í,ƒr •[ ƒ€ ƒp ƒ‰ ƒ• •[ ƒ^ ‚Ì 'ª 'è ‚É •K-v ‚È ƒX ƒ| ƒb ƒgƒT ƒC ƒY 'ª 'è-@ ‚É ‚ ‚¢ ‚Ä-á ‚ð OE𠂦 ‚Ä ŠÈ 'P ‚É •Ð ‰î ‚· ‚é. 2•A ƒr •[ ƒ€ ƒp ƒ‰ ƒ• •[ ƒ^ ‚Ì 'è ‹` 2.1ƒr •[ ƒ€ ƒp ƒ‰ ƒ• •[ ƒ^ •‚ ŽŸ ƒ‚ •[ ƒh‚ª •¬ "ü ‚· ‚é ƒOE •[ ƒU •[ ‚Å ‚Í,‹ß Ž‹-ì(ƒOE •[ ƒU •[ •o ŽË OEû•t ‹ß)‚É ‚¨‚¯‚¨‚¯ ‚é ƒr •[ ƒ€OEa ‚AE‰" Ž‹-ì ‚Å ‚Ì Šg ‚ª ‚èŠp ‚¾ ‚¯ ‚Å ‚Í,ƒr •[ ƒ€ "` "À ‚𕳠Šm ‚É‹L •q ‚Å ‚« ‚È ‚¢.ISO/DIS‚Å ‚Í ,zŽ² •û OEü ‚É"` "À ‚· ‚é ƒr •[ ƒ€ ‚Ì "Á •« ‹L •q ‚É,(i)‰~ OE`OE`‚Ì Ž² 'Î •Û ‚È ƒOE•[ ƒU •[ ƒr •[ ƒ€ ‚É 'Î ‚µ‚Ä ‚Í, 1)ƒr •[ ƒ€ ƒE ƒF ƒC ƒX ƒgˆÊ 'uZ0; 2)ƒE ƒF ƒC ƒX ƒg'¼ OEad0; 3)‰" Ž‹-ì Šg ‚ª ‚èŠp ƒAE; ‚Ì3‚ ‚Ì ƒp ƒ‰ ƒ• •[ ƒ^ ‚ª •K-v ‚AE 'ñ ˆÄ ‚µ‚Ä ‚¢ ‚é5,8).‚³ ‚ç ‚É, (ii)Ž² 'Î •Û ‚Å ‚È ‚¢ •ê • ‡ ‚É ‚Í,Z0,d0,ƒAE ‚ðƒÈ‚¨‚ae‚ðƒÈ‚¨‚ae ‚ÑyŽ² •¬ •ª ‚É •ª-£ ‚µ,ƒr •[ ƒ€ ‚Ì •À •W OEn ‚AE ŽÀ OE± Žº •À •W OEn ‚Ì ‚È ‚· Šp ƒÓ‚AE•¹ ‚¹ ‚Ä7 ‚ ‚Ì ƒp ƒ‰ ƒ• •[ ƒ^ ‚ª •K-v ‚AE ‚µ ‚Ä ‚¢ ‚é1).(i)‚Ì •ê • ‡ ,"` "À Ž² •ã ‚Ì "C ˆÓ ‚ÌˆÊ‚ÌˆÊ 'u ‚É ‚¨‚¯‚¨‚¯ ‚é ƒr •[ ƒ€ '¼ OEa ‚Í, (1) ‚AE ‚µ ‚Ä ‹• ‚ß ‚ç‚ê ‚é.‚AE ‚± ‚ë ‚Å,Šô ‰½ OEõ Šw ‚É ‚¨‚¯‚¨‚¯ ‚é ƒN ƒ‰ ƒW ƒE ƒX(Clausius)‚Ì ŠÖ OEW ‚ae ‚è,-³ Žû •· ‚Å ŠJ OEû ‚Ì •R ‚ç‚ê ‚Ì ‚È ‚¢-• 'z OEõ Šw OEn ‚ð-p ‚¢ ‚½ 'oe •Ï Š· ‚Å ‚Í,ƒG ƒ^ ƒ" ƒf ƒ…(etendu)‚ª •Û ' ¶ ‚³ ‚ê ‚é.ƒr •[ ƒ€"` "À ‚Å ‚à "¯-l ‚É,ƒr •[ ƒ€ ƒE ƒF ƒC ƒX ƒg‚É ‚¨‚¯‚¨‚¯ ‚é '¼ OEad0‚AE ‰" Ž‹-ì ‚Å ‚Ì Šg ‚ª ‚èŠp ƒAE‚Ì •Ï ‚Í,'oe •Ï Š· ‚Ì •Û ‚É •s •Ï ‚Å ‚ ‚é.•Å ‹ß ‚Å ‚Í,‰ñ •Ü OEÀ ŠE ‚ÌTEM00ƒK ƒE ƒV ƒƒ ƒ" ƒr •[ ƒ€ ‚ð Šî •€ ‚AE ‚µ ‚Ä,ˆÈ ‰º ‚É Ž¦ ‚·ˆö‚·ˆö Žq ‚ª ƒr •[ ƒ€ ‚Ì ‰¡ ƒ‚ •[ ƒh•i Ž¿ ‚ðŽ¦ ‚·-Ê ‚AE ‚µ ‚Ä "± "ü ‚³ ‚ê ‚Â ‚ ‚ ‚é2-4). (2) ‚± ‚± ‚Å,ƒÉ0‚Í •^ ‹ó ' † ‚Ì"g '·,ƒÉ‚Í‹ü •Ü-¦ ƒÅ‚Ì"} Ž¿ ' † ‚É‚¨‚¯‚É‚¨‚¯ ‚é 'ae26Šª 'ae10• † ƒOE•[ ƒU •[ ƒr•[ ƒ€ •iŽ¿ 'ª 'è ‚ÌŠî 'b 723